University Of London
Imperial College Of Science 6 Technology
Behaviour Of Grouted Dowelled Connections
Between Precast Concrete Columns.
A thesis submitted for the degree of
Doctor of Philosophy of the University of London
and for the Diploma of Imperial College.
by
ATALLAH SHAFIC KUTTAB
Concrete Section
Department of Civil Engineering
1986 2 ABSTRACT
The work described deals with the behaviour of grouted dowelled connection between precast columns in compression and compression combined with flexure.
The literature review of precast concrete connections revealed that their efficiency relates directly to their dimensional accuracy, i.e. tolerance, which in turn can only be obtained using correct manufacturing process.
A purpose built rig, providing axial and lateral loads, was used for this study. Prototypes of the specimens were made to test the adequacy of the grouting. Detailing of the connection was based on a concrete confinement model developed in this thesis. The column failed away from the connection when subjected to pure axial load, confirming the adequacy of the detailing. In all other tests, the joint was subjected to more severe loading than the remainder of the column and failure occurred at the joint. Shear seemed to have negligible effect on this behaviour .
When subjected to flexural stresses, precast specimens behaved similar to monolithic ones up to peak load. Beyond this point, the joint behaved as a hinge leading to a local angular discontinuity within the length of the jointed column. A feature of the work was the use of instrumentation to study this localised behaviour and to isolate the behaviour of the joint from the column as a whole.
The sensitivity of the joint performance to errors in construction was examined by varying the joint thickness. This had a number of effects, in addition to reducing confinement, which led to significant reduction in strength with increase in joint thickness . 3
Table of Contents
Page
Acknowledgement 9
Chapter 1- Introduction. 10
1.1- General. 10
1.2- Objective of the research. 14
1.3- Organization ofthis work. 15
Chapter 2- Review of literature dealing with column-to-column joints.
2.1- Introduction. 16
2.2- Types of column-to-column joint. 18
2.3- Previous research. 4-5
2.3.1- General. 4-5
2.3*2- Tests by Somerville. 4-8
2.3.2.1- Behaviour of mortar joints
in compression. 52
2.3.2.2- Influence of percentage reinforcement
on mortar joints. 54
2.3*3- Ad hoc tests at Polytechnic of Central London 58
2.4- - Critique of present practices 62
2.4- • 1 — General. 62
2.4.2- Tolerances in the precast industry. 63
2.4*2.1- Historical background. 63
2 .4*2.2- Theoretical analysis of tolerances. 69
2.5- Summary, evaluation and conclusion. 77 4
Chapter 3- A confinement model for detailing concrete structures. 80
3.1- Introduction. 80
3-2- Concrete confinement. 82
3.2.1- Passive confinement. 82
3.2.2- Active confinement. 86
3.3- Passive confinement by rectilinear ties. 89
3•3•1- Introduction. 89
3.3*2- Comparative study of the confinement models. 89
3*3.3- Sheikh & Uzumeri experimental programme. 98
3.3*3.1- Experimental observations. 98
3.3*3.2- Analytical model. 99
3.3*4- Experimental programme by Park et.al. 103
3.3.4*1- Experimental observations. 103
3.3-4*2- Analytical model. 110
3.4- Analytical model of concrete confined by
rectilinear steel ties. 112
3.4*1 - Critique of existing models. 112
3.4*2- Proposed analytical model. 113
3*4*3- Two models of confinement. 118
3.4.3.1- The K-N model. 118
3.4*3.2- The A-S model. 118
3.4*4- Application to specimens tested
by Sheikh & Uzumeri. 122
3*5- Practical application of the confinement model. 133
3.6- Summary. 136 5
Chapter 4- Description of experiment. 137
4.1- Introduction. 137
4*2- Test rig. 139
4.2.1- Alternatives for the test rig. 139
4.2.2- Description of the test rig. 142
4.2.2.1- Axial load rig. 142
4.2.2.1.1- End blocks. 142
4.2.2.1.2- Accessories. 147
4.2.2.2- Lateral load rig. 148
4.2.3- Eccentricity of the test rig. 156
4»3- Test specimens. 160
4.3.1- Formwork 160
4»3.2- Reinforcement. 160
4-3.3- Concrete mix and casting of specimens. 166
4.3*4- Grouting. 173
4.3.4*1- Introduction. 173
4.3*4*2- Pump. 173
4.3.4*3- Trial mixes of grout. 176
4*3.4*4- Grouting technique. 178
4*3.5- Stacking of grouted specimens. 180
4.4- Instrumentation. 183
4*4*1- Measurements required. 183
4.4*2- Instruments. 183
4«4*3- Calibration. 189
4«5- Test procedure. 190
Acknowledgement. 191 6
Chapter 5- Results of the main test series. 192
5«1- Introduction. 192 5.2- General observations. 196 5.3~ Measurement of angular change across the thickness of the joint. 205
5.3.1- General. 205 5.3.2- Exact Method. 213 5.3-3- Approximate Method. 218 5.3.4- Comparison between both methods. 221 5.4- Other measurements made during testing. 224
5.4*1- Lateral deflections. 224 5.4*2- Deformation of embedded strain gauges. 225
5.5- Effect of shear. 234 5.6- Summary. 235
Chapter 6- Analytical view of behaviour. 236
6.1- Introduction. 236 6.2- Behaviour to peak load. 237 6.2.1- Introduction. 237
6.2.2- Column Theory. 237
6.2.2.1- Assumptions. 237
6.2.2.2- Mathematical formulation. 238
6.2.3- Application to specimens in main test series. 243
6.2.4- Comparison with experimental results. 251
6.2.5- Conclusion. 262 7
6.3- Post peak load behaviour. 271
6.3*1- Introduction. 271 6.3*2- Failure mechanism. 271
6.3*3- Literature review. 272 6.3*4- Analysis of angular change across the joint thickness. 275
6.3*5- Discussion of results and conclusion. 279
6.4- Analysis of the shoe joint. 280
6.4*1- Introduction. 280 6.4*2- Analysis of the various sections. 280 6.4*3- Comparison with experimental results. 284
6.4*4- Discussion of the shoe and grouted joints results. 291
6.5- Summary and conclusions. 295
Chapter 7- Results of tests on the influence of joint thickness. 296
7.1- Introduction. 296 7.2- Tests undertaken. 298
7.3- Presentation and discussion of experimental results. 298
7*4- Summary & conclusions. 315
Chapter 8- Discussion and Conclusions. 319
8.1- Summary and general discussion. 319
8.2- Conclusions. 321 8
List of references. 324 Appendix 1- Chapter 4» 338
(a) Calculation of the amount of ties in the joint region. 338
(b) Calibration of the 200 ton jack. 339
(c) Calibration of the 50 ton jack. 340 Appendix 2- Chapter 5. 341 (a) Estimation of rotation of the precast columns
near the joint. 341 (b) Tables of results of the main test series. 345
Appendix 3- Chapter 6. 381 (a) Listing of computer programme for the Column Theory. 381
(b) Input file for the computer programme. 384 9
ACKNOWLEDGEMENT.
I wish to acknowledge the considerable help and encouragement given to me by Prof. J.W.Dougill who supervised this work. I also want to thank Dr. J.Bobrowski (Jan Bobrowski & Partners), Dr. M.Kotsovos (Imperial College), and Dr. B. Cranston and Dr. G. Somerville (Cement & Concrete Association) for their valuable comments and advice. My thanks are due too to the staff of the Concrete Laboratory at Imperial College, especially Mr. R. Loveday and Mr. W. Bobinski, without whose help this work would have been impossible, and to Mr. A. Chipling of the photographic section for making all the plates. Also, I am very grateful to the Civil Engineering Department (Concrete Section) for supporting this work. My gratitude must be extended to the British
Council and Birzeit University (Israeli- Occupied West Bank) who supported me financially for the duration of this work. Also, I wish to thank all my colleagues at Birzeit University who provided facilities for the writing up of this thesis. Finally, my thanks to many other colleagues and friends who have contributed much, both directly and indirectly, to this thesis. 10
Chapter 1- Introduction.
1.1- General. The technique of precasting parts of a concrete structure in a factory away from the site is one which has evolved slowly. Perhaps this technique, in its crudest form, is represented in masonry structures where bricks are fabricated in a factory and joined on the site.
Since World War II - especially during the last three decades- precast concrete has gained considerable publicity, although not always with the right emphasis. Far too many engineers started thinking of precast concrete frames without giving adequate consideration to problems associated with the joints. In the 194-0's the idea of precasting the entire frame originated because it was realised that prefabrication was a most useful tool in the tool-box of the engineer. Unfortunately, with the type of joints used- cleated, bracketed and bolted joints with connections based on the use of steelwork- it was found more difficult to use concrete than to use steelwork. The degree of tolerance that was needed for constructing units in precast concrete was extremely small and indeed was far more limited than in steelwork. Many engineers had had experience in forcing a structural steel unit into position and in wedging it over so that it could be bolted into place; if, however, this is attempted with precast concrete units, edges splinter off and the result is unsightly or sometimes even dangerous.
Workmanship on site is likely to be inferior to that in the factory, so there are many technical and economical advantages in using precast components which have been made under controlled conditions in a highly automated factory. The advantages depend on the 11
design, production, transportation and erection processes all being satisfactorily undertaken. Up to date, problems related to the production of individual units have been solved to a large extent but the design of the method of jointing these precast units remains a controversial subject. In some cases, the problems associated with jointing have discouraged progress in the precast concrete building industry. In precast concrete construction, the basic problem is that the components must be physically connected on site. Therefore, it is essential to devise ways of achieving the connection which will provide a satisfactory final structure. It is probably true that the design and detailing of joints have a greater effect on the performance and economy of precast concrete structures than any other single factor. In practice, joints are devised by individual designers or precast manufacturers to meet their own particular production and construction techniques. Discussions with various manufacturers and reference to the manual published by the Institution of Structural
Engineers[1.1], have shown that techniques can vary considerably and that conflicting opinions are held as to the feasibility of different jointing methods. Jointing techniques in precast concrete structures vary extensively. At one extreme, precast structures are designed- similar to traditional structural steelwork and timber- as pin jointed, and the stability of the structure is provided by shear walls supporting the floors which act as horizontal plates. Such a concept is sound both structurally and economically. Nevertheless, the absence of bending continuity means that it is necessary in Codes of Practice to specify requirements for tying elements together to ensure stability.
At the other extreme, a fully continuous structure, similar to that 12 obtained with in situ reinforced concrete, is achieved, for example, by using H-frames where jointing in beams and columns is by welding reinforcements or embedded plates providing bending continuity. Sometimes jointing is made at points of contraflexure where bending is minimal.
Occasionally, ad hoc tests are carried out to check the strength of a particular joint detail, but little thought, apparently, is given to whether or not the joint, as constructed on site, will permit the assumptions made in analysing the structure as a whole to be realised. However, the close coordination between the designer and the manufacturer should ensure that a simple, practical, economical and safe method is devised. The manual published by the Institution of Structural
Engineers[1.1] states that the construction of the joint must be such that;- (a) the precast members can be erected safely and speedily,
(b) the accuracy of manufacturing precast members, and the setting out on site, do not materially affect the adequacy of the structural performance of the joint,
(c) the precast member can be manufactured and erected economically, (d) and, the appearance of the joint should be satisfactory.
In addition to the Institution’s criteria, Somerville[1.3] recommended the following extra requirements for the construction of joints 13
(a) the joint should be structurally sound with regard to strength,
stiffness and stability at all stages during the joint life, and, (b) the joint should be proof against deterioration due to exposure and should have an adequate resistance against fire; i.e.
durability of the joint should match and not limit that of the
structure.
The various factors can be conflicting, especially if coordination between design and construction teams is minimal. Hence, good coordination between design and construction planning is essential for satisfactory precast construction. Joints are critical in the design of precast concrete, and often the design of the joint is more difficult than that of the structural member. Precast concrete structures can be divided into two main categories: framed structures and large-panel structures. Within each category, the joints are most easily classified according to their position in the structure; thus, for framed structures, we have;- (a) beam-to-slab joints, (b) beam-to-beam joints,
(c) beam-to-column joints, (d) column-to-column joints,
(e) column-to-base joints,
(f) parapet-to-roof joints, and, (g) staircase flight to landing joints.
This classification is somewhat arbitrary, particularly with subgroups
(c) and (d) where most of the joints are made adjacent to the column irrespective of whether multi-storey or storey-height columns are used. 14
1.2- Objectives of the research.
This research is concerned only with column-to-column joints in framed structures. The column-to-column joint is a key connection on which the overall stability of the framed structure depends.
Somerville[1.3 ] has made an extensive study on single dowel grouted column-to-column joints where there is no moment continuity.
The research presented here is concerned with the behaviour of four dowels grouted column-to-column joint which can provide moment continuity. The objective of this research is to study the behaviour of the dowelled and grouted column-to-column joint. The main parameters to be considered are the following;- (a) behaviour of the joint under combinations of axial load, bending
moment and shear, and, (b) sensitivity of the joint thickness to errors in construction.
The reason for choosing the above parameters lies in the fact that little is known about the behaviour of full size grouted precast
columns. As Somerville was interested in behaviour of grouted columns under mainly axial loading, this research programme extends the previous work in order to explore the whole range of loading; namely, axial load, bending moment and shear. Increasing the joint thickness
is an indirect way of changing the passive confinement in the joint zone and so examining the sensitivity of the joint to construction
tolerances. The grouted and dowelled joint is compared with the shoe
joint used in the H-frame tested at the Polytechnic of Central
London[1.2]. The inclusion of the shoe joint in this study offers a
broader base for recommending factors of safety relevant to precast
structures. 15
Besides looking at the design of the grouted column-to-column connections, in particular, the research has been undertaken with the idea of identifying the need for detailing precast joints, in general. The work is not sufficiently broadly-based to lead to final recommendations for practice but some preliminary guidelines are included in the final conclusions.
1.3- Organization of this work. A review of previous work on column-to-column connections is given in chapter 2. With grouted connection, particular attention must be given to joint spacing and to the provision of local reinforcement.
Because of this, chapter 3 is devoted to an assessment of the effects of confinement provided by rectangular binders on strength. Chapters A and 5 provide details of the experimental arrangements and results obtained. Following this, an analytical view of the behaviour of the grouted joint and a comparison with results from tests on the shoe joint[1.2] are presented in chapter 6. The sensitivity of the grouted joint to joint thickness due to errors in construction is considered in chapter 7. Finally, chapter 8 presents a general discussion and
conclusions together with recommendations for future work. 16
Chapter 2- Review of literature dealing with column-to-column joints.
2.1- Introduction. The column-to-column joint can be considered to be the most fundamental joint in a precast framed structure. The whole stability of the structure depends on it. Also, the manner in which this joint can be constructed significantly affects the progress of the construction, and so the overall cost. As a result, the column-to- column joint has passed through a radical ’'evolution” in the last two decades mainly for economic reasons to achieve more efficiency in
construction. This "evolution" can be categorized into three phases. Phase 1 is exemplified by joints where temporary support of jointed columns has to be provided until the joint gains strength, see for example figures 2.1-2.7. This process is slow and means no work can be done before the joint gains its strength. Also, additional equipment may be necessary for the temporary supports. The need for more sophisticated and quicker jointing techniques led to Phase 2 which is characterized by joints achieving instantaneous partial bearing strength capacity by the use of turnbuckles, welding or bolting as shown in figures 2.8-2.1 J+. This partial bearing strength capacity is normally enough to take the dead load of the concrete
column so allowing no interruption of work continuity on site.
However, with these techniques, construction based imperfections sometimes led to failures since the joint detail depended for its
strength on the precise location of reinforcement bars. Essentially, insufficient allowance was made for tolerance and workmanship on site.
The importance of adequate tolerances will be discussed later in this
chapter. Such difficulties provided the incentive to move to Phase 3
characterized by the elimination of column-to-column joints 17 altogether. This is done by designing long unspliced columns which are prestressed to avoid cracking while handling. This was made possible by the development of adequate lifting facilities and prestressing techniques. However, eliminating column-to-column joints is not always possible and the need remains to study the limitations and adequacy of this type of joint. Past experience indicates that joints should be devised so that they will still behave satisfactorily if workmanship is substandard. Therefore, the aspect of workmanship should be considered carefully in any planned programme of research or design to adopt a particular type of joint. 18
2.2- Types of column-to-column joint.
It is convenient to classify column-to-column joints according to their structural behaviour in a precast concrete structure, i.e.
(a) column-to-column joint carrying axial load only, and,
(b) column-to-column joint providing full or partial moment continuity
as well as carrying axial load.
The above classification is arbitrary in the sense that all joints should be designed to provide some continuity to allow for unforeseen effects and to help control cracking and deflection. In practice, there are two philosophies in designing precast concrete structures. One, beams are assumed to be simply supported and columns to be pin-ended. Lateral forces, such as those due to wind, are carried by bracing walls or in situ concrete cores designed especially for this purpose. The beams and floor slabs transmit the lateral forces to the solid core, which is intended to provide the required stability of the structure as a whole. Second, the framed structure is designed such that all joints are capable of developing full moment continuity and hence the structural behaviour approaches that of a monolithic reinforced concrete framed structure.
The two philosophies of design have led to a variety of joint details that have been developed by designers and manufacturers during the last three decades. A literature review has indicated that the following column-to-column joints are the most commonly used in practice [references 2.11,2.17,2.20,2.21,2.29];- 19
(a) Column-to-column joints using bolts [2.17,2.21,2.29].
This category of joints involves three types namely CC1, CC2 and CC3 shown in figures 2.1,2.2 and 2.3 respectively. The column is cast with four pockets and a base plate e.g. types CC1 and CC2, or two angles e.g. type CC3. The base plate for types CC1 and CC2 is welded to main steel reinforcement whenever possible. Otherwise, it is anchored using the technique shown in figure 2.3• The top column is erected over anchor bolts protruding from the column below. The space between the columns is filled with a dry pack or shrinkage compensated grout.
Temporary support and levelling are accomplished by tightening the nuts with the column resting on a centre stack of shims.
Type GG1 (refer to figure 2.1).
Advantages:
- corner pockets allow easy spanner access,
- holes in the base plate are oversized to reduce tolerance problems,
- connection is concealed and protected from corrosion when patched,
- and, bolting allows quick and easy erection in any weather.
Disadvantage:
- anchor bolts have limited moment capacity; 20
Figure 2«1 - Column-to-Column Joint Type CCj (2.17) 21
Type CC2 (refer to figure 2.2).
Advantages:
- side pockets allow corner bars to be welded to base plate,
- holes in the base plate are oversized to reduce tolerance problems,
- connection is concealed and protected from corrosion when patched,
- and, bolting allows quick and easy erection in any weather.
Disadvantages:
- side pockets restrict spanner movement and provide less effective
placement of anchor bolts for moment resistance, and,
- anchor bolts have limited moment capacity.
Type CC3 (refer to figure 2.3)•
Advantages:
- long pocket allows easy spanner access,
- oversized holes for bolts reduce tolerance problems,
- connection is concealed and protected from corrosion when patched,
- and, bolting allows quick and easy erection in any weather.
Disadvantages:
- axial load and moment capacity are limited by available angle
thickness,
- more patching required than types GC1 and CC2, and,
- anchor bolts have limited moment capacity. ■ mrfriig'-**
22
(2.17) Figure 2.2 - Column-to-Column Joint Type CC2 23
Figure 2.5 - Column-to-Column Joint Type CC5 24
(b) Column-to-column joint using dowels and grouting[2.11,2.17,2.21].
With these joints, dowel bars are slotted into ducts cast in the
top column as in type CC5 (figure 2.5)• Depending on the structural requirements for the joint , all or only some of the main bars of a
column need be accomodated in ducts as types CC4 and CC5. In some i \ cases, all the bars are discontinued near the joint zone and a central dowel projects into a duct as shown in type CC6 (figure 2.6). There are many variations from the simple form of jointing presented by types GC4-, CC5 and CC6. Only one case is discussed here: type CC7
(figure 2.7).
In general, the ducts on one side of the joint accomodate the projecting reinforcement from the other side. The ducts are filled with grout as the column is erected. When set, the grout produces a
lap splice. More details about making this type of joint will be presented in Chapter Temporary support and levelling is normally
accomplished by guys or some other means of bracing until the ducts
are grouted and the joint has gained sufficient strength. 25
Types CC4, CC5 and CC6 (figures 2.4* 2.5 and 2.6 respectively).
Advantages:
- moment resistance is provided by the connection (only CC4 and CC5),
- usually few tolerance problems,
- connection is protected from corrosion and usually acceptable for
exposed columns, and,
- no patching required.
Disadvantages:
- requires additional means of temporary support or bracing,
- type CC6 can take only axial load,
- lap length for larger bars can be quite long (only CC4 and CC5),
- main reinforcement must be bent in the vicinity of the ducts
(only CC4 and CC5),
- for type CC5, precautions must be taken to keep ducts free of water
and debris,
- for type CC5, good weather is necessary for grouting ,
- for type CC5, the dowel bars can be damaged when the top column is
lifted, and,
- the upper column may be lifted out of position if the grouting
pressure is too high: 10 psi. grout pressure would be enough to lift
a 10 ft. high column. 26
(a) (b)
Figure 2»4 - Column-to-Co lumn Joint Type CC4 (2.11,2.17) 27
(2.17) Figure 2,5 - Column-to-Column Joint Type CCj 28
Figure 2,6 - Column-to-Column Joint Type CC6 29
Type CC7 (figure 2.7)
This is a proprietary bar splicing system. The shape of the sleeve provides the structural continuity by producing a lap splice. Special devices are provided by the manufacturer to aid installation.
In the preferred version, bars project from the lower column and sleeves fit over the top. Levelling is accomplished by shims. Grout is pumped into the bottom tube until it comes out the top. In the alternate version shown in the inset, the bars project from the upper column section. Grout may be placed in the sleeves and the shim space in the same operation, prior to placing the top section. Lack of care whilst lifting the top column might result in damage to the dowels.
Care must be taken to keep the sleeves free of water and debris. This type of joint was used successfully in constructing the office tower at 100 Washington Square, U.S. [2.32].
Advantages:
- moment resistance is provided by the connection,
- few tolerance problems,
- no patching required,
- column bars need not be bent, and,
- reduction in lap length for larger bars.
Disadvantages:
- additional means of bracing must be provided, and,
- requires a proprietary mechanical sleeve. fit'll11"111"
30
(2.17) Figure 2.7 - Column-to-Column Joint Tyye CC7 31
(c) Column-to-column joints by welding steel sections[2.17,2.20,2.29]•
This type of joint is commonly used when a moment transfer splice is desired* There are two main types. The first type comprises flat plates welded to the main column reinforcement. The area of the embedded plates is slightly smaller than the column section. The columns are normally match cast together with the top and bottom plates and then welded together when the columns have been erected.
This is shown as type CC8 in figure 2.8. The second type has flat plates located on the side of the column section and welded to the main reinforcement bars. The two columns, to be jointed, are levelled using a pad and dry pack mortar. A set of plates are welded from the outside to the embedded plates forming the joint. This is shown as type CC9 in figure 2.9» A modified version of CC8 and CC9 was used by
Bobrowski[2.1,2.2,2.20] and referred to as a "shoe joint". The shoe joint, as used by Bobrowski, will be discussed in detail later in this chapter. 32
Type CC8 (figure 2.8).
Advantages:
- moment resistance is provided by the connection,
- field fitting problems are minimized if correctly match cast,
- immediate full bearing; hence erection of upper levels can proceed
with no disruption to continuity of work on site, and,
- connection is concealed and protected from corrosion when patched.
Disadvantages:
- match casting requires special procedures during precasting,
- a significant amount of welding is required, especially if column is
heavily reinforced, and,
- correction of minor errors is difficult.
Type CC9 (figure 2.9).
Advantages:
- moment resistance is provided by the connection,
- few tolerance problems, - full bearing is achieved after outside plates are welded, and,
- connection is concealed and protected from corrosion when patched.
Disadvantages: - a significant amount of welding is required, and,
- welding of outside plates cannot be done unless the top column is
levelled; therefore, more erection time than type GC8. 33
(2.17) Figure 2.8 Column-to-Column Joint Type CC8 34
(2.29) Figure 2«9 - Column-to-Column Joint Type CC9 35
(d) Column-to-column joints by welding of rebars[2.11,2.17,2.29].
This type of joints is only used when full moment transfer is desired in large, heavily reinforced columns. Both column sections are cast with reinforcement protruding from the ends which are welded together when erected. One example is shown as type GC10 in figure
2.10 to illustrate the important details involved.
Temporary support and levelling are accomplished by resting the column on a centre stack of shims and welding several of the bars together. The entire connection is later grouted or patched with in situ concrete and dry pack mortar.
Advantages:
- moment resistance is provided by the connection,
- long lap lengths of reinforcement are not required, and,
- connection is concealed and protected from corrosion when patched.
Disadvantages:
- reinforcement must be a weldable grade steel,
- reinforcement must be precisely placed to accomplish welding;
if bars are forced in place the strength of joint will be inhibited.
- and, strength is partly determined by the effectiveness of the dry
packing. ■ I P^I'I trim
Figure 2.10 - Column-to-Column Joint Type CClQ (2.11,2.17,2.29) 37
(e) Column-to-column joints by post-tensioning.[2.11,2.17,2.29]
This system uses vertical post-tensioning for the column reinforcement and for splicing the column sections. Sleeves are cast in the columns at the precasting plant. The tendons (usually bars) are attached to an anchor at foundation level, or a coupler at intermediate levels. The upper column is then "threaded" over the bars. The bars are tensioned and anchored, leaving enough projection to attach a coupler to receive the bars for the next level. This type is classified as type CC11 in figure 2.11. Martin & Korkosz[2.17] consider this method of jointing as complex. But, with modern techniques, post-tensioning, can hardly be considered as more complicated than any of the jointing methods mentioned in this section.
Advantages:
- moment resistance is provided by the connection, and,
- connection is concealed and protected from corrosion when patched.
Disadvantages:
- alignment of sleeves is critical, and,
- requires supplementary reinforcement or pretensioning for handling. 38
Figure 2»il - Column-to-Column Joint Type CC11 (2*17) 39
(f) Miscellaneous column-to-column joint details[2.11,2.17,2.21,2.29]•
Some other techniques that are used in practice are described in this section. They combine features of joints already described and are used where a fully continuous section is required.
Type CC12 (figure 2.12).
This type uses turnbuckles or couplers to join reinforcing bars protruding from both sections of column in the joint zone. The couplers are attached to reinforcement extending from the bottom column. The top column is then "threaded” over the bars. The upper column is levelled by rotating the couplers.
Advantages:
- moment resistance is provided by the joint,
- a levelling system is incorporated,
- column do not need extra propping,
- couplers can be designed to carry the dead load of the column,
- no lap length is required, and,
- connection is concealed and protected from corrosion.
Disadvantages:
- reinforcement must be located to great accuracy,
- when beam reinforcement passes through the joint, precautions must
be taken to avoid honeycombing of the in situ concrete, and,
- making the joint involves many activities; hence, relatively
extensive site work is required. 40
Figure 2.12 - Column-to—Column Joint Type CC12 ^2*11 ^ 41
Type CC13 (figure 2.13)
This joint incorporates a plate welded to the ends of reinforcement of one end of the column with holes to receive threaded bars of the jointed column. So, it is a combined welded and bolted joint. The bolts in this joint are used to level the upper column.
Advavantages:
- moment resistance is provided by the joint,
- a levelling system is incorporated,
- columns do not need extra propping,
- the joint can take the dead load of the column before the in situ
concrete gains strength,
- holes in plates are drilled larger than required to accomodate
fitting discrepancy, and,
- connection is concealed and protected from corrosion.
Disadvantages:
- reinforcement must be a weldable grade steel,
- when beam reinforcement passes the joint, precautions must be taken
to avoid honeycombing of in situ concrete, and,
- making the joint involves many activities; hence, relatively
extensive site work is required. Figure 2.13 - Column-to-Column Joint Tyne C C H (2.11) 43
Type CC14 (figure 2.14)•
Temporary support is provided by sleeve-in-sleeve joint. A structural pipe or tube protruding from the upper section fits into a slightly larger pipe or tube in the lower section. A small weld holds the assembly in place. No weld is required if the fit is tight enough.
Advantages:
- moment resistance is provided by the joint,
- next level can be erected before the in situ concrete gains full
strength,
- a ductile joint, and,
- joint is concealed and protected from corrosion.
Disadvantages:
- sleeves must be accurately positioned when precasting,
- joint zone is congested; so extreme care is necessary to avoid
honeycombing of the in situ concrete, and,
- extensive site work is required. 44
Figure 2.14 ^ Column—to~Column Joint Type CCl4. (2.17) 45
2.3- Previous research.
2.3.1- General.
A lot of research work has been done to study the variables affecting behaviour and strength of column-to-column joints providing different degrees of moment continuity across the joint.
The mechanical types of connection shown in figures 2.1-2.14 are frequently used in situations were no advantage is taken in design of the continuity of reinforcement in transmitting bending moments. This fact is reflected in the available test data on the behaviour of these types of joints obtained by Apcar and loralmaz at the Building
Research Station[2.6].
Various other techniques for achieving continuity of reinforcement bars between columns, generally involving the use of welded or lapped bars, have also been investigated experimentally.
Gurshkii and Fedafycheva[2.7] studied the behaviour under axial load of column joints where the column reinforcement was welded.
Heynisch[2.9] and Kovolev and Korovin[2.15] carried out tests where the column reinforcement was lapped rather indirectly by using a spigot and socket arrangement; in each case, both axial and eccentric loads were applied and simple design rules for detailing the column ends were devised. As part of a general study of lapped splices in insitu columns, Pfister and Mattock[2.19] carried out a test series where the longitudinal column bars were located in a metal sleeve.
This type of connection has also been investigated by Utescher[2.30] as part of a study into the behaviour of different joints used in one particular building. Utescher’s tests are of special interest since the test specimens were made on the site and were therefore representative of normal construction practice. 46
The sleeve method of connecting reinforcing bars has been the subject of a number of general investigations, usually by carrying out simple tension and compression tests on specimens having a single reinforcing bar. The sleeve is normally filled with mortar, grout or epoxy resin. An extensive test programme was completed by Erikson[2.4J under static load conditions; he recommended an overall splice length of eight times the bar diameter. This work was later extended by
Ivey[2.12] to cover fatigue load conditions. Both these investigations were conducted on specimens made using grout or mortar as the binding agent. Work by Igonin[2.10] and by Spyra and Smith[2.28] would indicate that the sleeve length could probably be halved if epoxy resins were used; although Johnston[2.13] emphasized the importance of studying such joints under sustained load because of variations in the creep characteristics of the adhesives and grout or fines. A comprehensive description of the various aspects of mechanical jointing is presented in the CIRIA report 92.
Joints such as those shown in figures 2.9 and 2.18 are very dependent on the maximum compression force that can be transmitted by direct bearing of the concrete. This can vary depending on the degree of confinement that is provided, e.g. in a reinforced concrete hinge, average stresses several times higher than the cube strength can be sustained before failure occurs. Some research was carried out in recent years to study this problem for some of the situations that occurred in precast concrete construction.
A notable contribution was made by Kriz and Raths[2.14J who studied the bearing strength of column heads, when subjected to loads applied through well defined bearing areas. Their extensive experimental programme covered the following variables;- 47
(a) the strength of concrete in the column,
(b) the dimensions of bearing plates and their distance from the edge
of the column,
(c) the quantity and, type of lateral reinforcement in the vicinity of
applied loads, and,
(d) the ratio of horizontal to vertical load applied to the column.
Based on their test results, Kriz and Raths developed an empirical equation for calculating the bearing strength of column heads, which they adopted for use in the design office by means of a design chart. The most significant result of the part of this test series related to the behaviour of corbels is the considerable reduction in bearing strength when horizontal forces act in conjunction with the vertical load. For example, for a horizontal force of one quarter of the vertical load, the bearing capacity is halved. With this type of bearing, especially where the column-to- column joint is at floor level, horizontal forces resulting mainly from creep, shrinkage and temperature changes in the supported elements must be accurately assessed and appropriately incorporated in the design of the joint.
The factors investigated by Kriz and Raths were also studied by
Niyogi[2.18]. His main conclusion was that the bearing strength increased with increasing lateral or confining reinforcement in the vicinity of applied loads.
Somerville[2.25] studied the interaction of the various parameters affecting the behaviour of precast joints. He did extensive testing on single dowel grouted full size column specimens typical of the precast columns used in the Public Building Frame (PB-frame). As mentioned earlier, several ad hoc tests by manufacturers and designers on column-to-column joints have been made. Amongst these tests are 48
those conducted at the Polytechnic of Central London (PCL) on full size shoe joint specimens manufactured by DowMac Concrete and designed by Jan Bobrowski & Partners[2.20]. Details of both tests by Somerville and Bobrowski will be discussed next because of their importance in that the interaction of the various factors affecting the strength of a joint is considered.
2.3.2- Tests by Somerville[2.25]•
Extensive research has been carried out on the PB-frame column joint by Somerville[2.23,2.24,2.25]• The first part of the programme was to study the behaviour of mortar joints in compression. A typical sample of the column-to-column joint tested is shown in figure 2.15.
The second part of the research programme concentrated on the influence of percentage reinforcement on mortar compression joints for framed structures. A typical sample of the column-to-column joint is shown in figure 2.16. The difference in shape of specimens between the two series was due to the fact that the PB-frame was designed initially for flat slab flooring (i.e. no beams); but, was later modified to have slabs spanning between beams with the floor loads being transferred to columns through the beams. Since Somerville was mainly interested in the testing of the PB-frame column joints, it was quite sensible that specimens were changed to meet the modification if the experiments were to have technical importance.
The columns in the PB-frame were not intended to resist any bending or shear. Consequently, Somerville was primarily interested in the behaviour of the column joint when subjected to pure axial loading. Figure 2.17 shows the main testing frame. The axial load was
applied concentrically. Few specimens were tested for flexural
capacity by applying lateral loads in conjunction with the axial load. 49
TOP COLON
Figure 2.15 - Type Of Joint Tested By Somerville. ^2*23') (2.25) Figure 2.16 - Modified Joint Detail Tested By Somerville 51
(2.25) Figure 2.17 General View Of Test Frame 52
2.3.2.1- Behaviour of mortar joints in compression[2.23,2.25]•
Somerville*s programme involved:
(a) pilot tests to study the strength of the basic design,
(b) tests using weak mortar in the joint,
(c) an investigation of the role of binding reinforcement in the
column ends,
(d) the erection procedure and the method of making the joint, and,
(e) the influence of bending and shear on the joint strength.
The tests showed that the influence of mortar strength needed further investigation. Accordingly, the test programme was augmented by supplementary series of tests to study the strength of the mortar and variations in the thickness of the joint.
The pilot tests showed that all specimens behaved satisfactorily since the strength of the joint proved greater than that of the column in each case. The mortar in the joint, whose strength was of the same order as that of the concrete in the column, had been very thoroughly compacted and therefore provided a uniform bearing area of the column.
This was evident since there was no detectable "end block effect" in the horizontal strain readings which had been taken on the upper column. Varying the joint thickness from 12.7mm to 25.4mm and altering the end cover to the longitudinal steel did not have any noticeable effect on the strength of the joint. This adequate behaviour of the joint can be attributed to the confinement provided by the slab rather than to the detailing of the joint.
Somerville concluded that when workmanship is poor, i.e. where the mortar is weak and poorly compacted, failure is initiated at the joint by the cover spalling off the end of the column. This can occur at loads appreciably less than those predicted by the Codes of 53
Practice. Somerville detected similar mode of failure when he studied the effect of the methods of construction. Tests have shown that the method of construction can influence the behaviour of the joint under load. The presence of a steel plate in the joint, the dimensions of the plate and whether or not it has been levelled can all influence the strength of the jointed columns and in some cases induce premature failure of the precast elements.
Therefore, the thickness of the joint and the properties of the material in the joint are primary factors affecting the specimen strength. Consequently, Som*erville made the following recommendations;- (a) the joint should be properly made with well compacted mortar, (b) the strength of the mortar should preferably be equal to that of
the concrete in the column and not less than 7 5 % of that strength,
(c) the joint thickness should not be greater than about 1/8 of the
least lateral dimension of the column, and,
(d) the bearing plates used for erection purposes should not be left permanently in position.
For the type of column and joint made according to Somerville's recommendations, it was established that minimum lateral reinforcement provided in accordance with the requirements of current Codes of Practice will be sufficient to develop full column strength when the amount of longitudinal reinforcement is less than 2%. Research on columns with higher percentage of reinforcement is discussed next. 54
2.3.2.2- Influence of percentage reinforcement on mortar joints.
The columns used for the test specimens discussed in section
2 .3 .2 .1 were relatively lightly reinforced (1 .5% longitudinal steel).
As current Codes of Practice permit a maximum of 8% longitudinal reinforcement in columns, higher percentages of longitudinal reinforcement was considered for the PB-frame. Therefore, the main variables were the percentage of longitudinal reinforcement and the type and quantity of transverse reinforcement. The experimental results showed that there was no reliable
strength increase with increasing steel percentages. Failure generally occurred in the joint zone rather than in the column. No matter how
strong the individual columns were, the strength of the jointed columns was limited by that of the joint zone. The mode of failure was
similar to that observed for those specimens described earlier and which had weak mortar in the joint. It is possible that this is due to a proportion of the force in the longitudinal steel bars being transferred to the concrete by end bearing, resulting in a lateral splitting action in the concrete and mortar under the ends of the
bars. To avoid such premature failure of the present columns,
Somerville added two more recommendations
(a) the longitudinal reinforcement should be stopped at least two bar
diameters from the joint, and, (b) helices rather than stirrups should be used as lateral binding in
the ends of the columns over a length equal to 300mm or the
maximum column dimension whichever is greater.
Somerville supported his experimental work with analysis based on
a plane stress - plane strain finite element model. This was not a
completely satisfactory approach. The problem of bursting effects at 55 the joint can only be realistically solved by taking into consideration the triaxial behaviour of concrete. The approach of providing binding reinforcement in the joint region is a right one since ties can provide passive confinement to the concrete increasing the load capacity, the energy absorption and the ductility of the structural concrete member. Somerville*s conclusion that helices have a better ability to confine concrete than rectilinear ties, although true, was not based on a comprehensive study. Therefore, his experimental programme should be regarded as exploratory. However, the main objectives were achieved in that the work was originally undertaken simply to establish the mode of failure and the magnitude of the failure load. Further consideration of the technique of utilising confined concrete to prevent premature failure of the joint zone will be explored in chapter 3 «
Table 2.1 shows some of the specimens tested by Somerville. 56 (2.25) TABLE 2.1 Reinforcement details for specimens 51 to 66.
SO I mm dia. hot* A B C
______\ end y \\\ ______Specimen 2S-4 mm dia. (rout hole* 25-4 m m cover to tn nn tfH steel Notes: 1. Details el lofl(itudinai reinforcement are jhrrn In th« Table (or rath specimen. 2. Dimensioni of Zones A. 6 and C art also riven In tha Table. tO(nh*r wnh details of b>ndm( steel for Zones A and B; Zone C always contained 12-7 mm dta. stirrups at 25-4 mm centre*. 1. All lon(itud!na! steel Is GK40 (normally stopped 2S-4 mm from end *-) All transverse steel n mild steel.
31 mm cover to main reinforcement 165 mm
+
7-1 mm dla. hell*. S1 mm phch H 7*7 mm dla. stirrups
31 mm cover to main reinforcement 330 mm 228-4 mm 241 mm -i (~
*-i“* 52
I------1------1------1------H I — —' ■ " ■ ( 7-9 mm dla. stirrups
228-4 mm i— ■— f
9-S mm dla. helix. 22-23 mm 50-1 mm pitch I--- 1--- h H12-7 mmdta. stirrups 101-4 mm 101-4 mm 152-4 mm
2S-4 mm cover to 30S mm stirrups r + -
I------1------1------1------h •4 7-9 mm dia. stirrups 203-2 mmA
404-4 mm 221-4 mm
37 e+. t 7-9 mm dla. helix. 2S-4 mm pitch I I I “ H 7-9 mm dia. stirrups 203-2 mm 57 (2.-25) TABLE .2.1 (cont'd)
RJrrup tfp* B uirrup type A 130 mm 356 mm 30$ mm
9-S mm helix. 30$ mm lonj at 50 -8 mm pitch
H-----1-----1---- 1 i-- j i 4 12-7 mm ulrmpt 4 Specimen! 4$ and (4 9-5 mm stirrups . 1014 mm ^ 101-6 mm ^ 151-4 mm Longitudinal Reinforcementt*/m 58
2.3.3- Ad hoc tests at the Polytechnic of Central London (PCL) [2.20].
A series of tests were carried out at the PCL to evaluate the performance of an on-site welded connection between precast concrete structural elements. The connection consists of two different sections of tubular steel anchored to and partially embedded in adjacent reinforced concrete columns. The tube sections locate one with the other to make a positive connection which is subsequently welded to provide additional shear and bending resistance across the joint.
The tests were undertaken in the Civil Engineering Department at the PCL under the direction of Messrs. Bobrowski & Partners using a
1000 tons compression testing machine and a purpose-built frame for the application of loads in two directions as shown in figure 2.18.
Details of the specimen are shown in figure 2.19» All specimens were fabricated by Messrs. DowMac Concrete Ltd..
The tests comprised three series. Test Series 1 consisted of testing three specimens concentrically and three others with an eccentricity of 30mm between machine platens. Test Series 2 consisted of seven specimens which were loaded concentrically with a longitudinal load which was combined with lateral loading as shown in figure 2.18. With this arrangement the joint was subjected to a combination of bending and axial load but no shear. The results of
Test Series 1 suggested that nominally axial loading did, in fact, lead to some bending presumably due to variation in concrete quality through the thickness of the column. This led to the addition of Test
Series 3 where a further six columns were cast using internal vibration for three and external vibration for the remaining three.
These columns did not incorporate a joint. These homogeneous and monolithic columns, were loaded concentrically to failure. The tests 59
served two purposes. One was to study the effect of the vibrating technique and the other was to compare the behaviour of the jointed precast columns to the monolithic ones.
In all specimens the joint showed no distress at failure.
Consistently, failure occurred in the precast member rather than in the joint. Bobrowski exploited the concept of confining the concrete by means of a steel tube welded to the main reinforcement. Although, as noted in figure 2.19> the concrete section at the joint is reduced by more than 50% still no failure occurred in the joint zone. The use of a steel tube or a box section to confine concrete is indeed an ideal solution and a practical one as well, to prevent premature failure in zones of potential distress in a structural element.
Comparing the behaviour of jointed precast columns to the monolithic ones: both types achieved the same maximum load levels so proving the efficiency of the method of confinement. Comparative behaviour of columns cast with internal poker and external vibration were examined but no conclusive results were obtained. A much more comprehensive study would be necessary to establish any positive trends.
The results of the ad hoc tests will be discussed in more detail when they are compared with the results of the present research programme. 60 61
( 2. 20) Figure 2.19 Details Of Units 62
2.4- Critique of present practices.
2.4.1- General.
Geometric imperfections are inevitable in the construction of
cast in situ and prefabricated concrete structures. Variations in dimensions, initial curvature, crookedness, and misplacement of
elements are common types of imperfections which can arise during
manufacture, setting out and assembly. While a structure cannot, in
practice, be absolutely geometrically accurate, imperfections must be
limited to ensure that a safe, functional, and aesthetically pleasing
structure is obtained with a minimum of construction difficulties,
legal entanglements, and costs.
To date, most tests on precast concrete joints have been
undertaken to establish the load capacity of a joint made under ideal
conditions. Very few have been concerned with studying the effect of
construction tolerances on the adequacy of the proposed joint. Special
consideration of the adequacy of joints is of utmost importance
because of the need to balance the conflicting requirements of the
designer, the contractor and the manufacturer. To be able to assess
the performance of the joints presented in figures 2.1-2.14 it is
necessary to present first what is meant by tolerance and how
tolerance can be integrated in the design of a joint. 63
2.4..2- Tolerances in the precast industry.
2.4.2.1- Historical background.
The problems connected with specifications of suitable and
adequate tolerances for the dimensions of precast concrete components have been recognized for some time. Designers and architects have
usually been in the habit of specifying very small dimensional
tolerances, and contractors and manufacturers have in the past only
rarely disputed the specifications in spite of the fact that these
small tolerances were rarely met, for example reference 2.16.
Recently, a number of European countries have made an effort to
establish suitable tolerance classes for concrete components. The main
problem was that, until the early seventies, tolerances were set by
the designer without sufficient understanding of the construction and
manufacturing process. Accordingly, the tolerances tended to be
impractical and so disregarded and subject to dispute.
In 1969 the Association of Danish Manufacturers of Precast
Concrete Components decided to publish some of the manufacturer’s
inspection results [2.16]. As expected a wide discrepancy was found
between the actual dimensional deviations and the tolerances as
specified in system-building projects. The ratio between design
requirements and characteristic deviation was generally found to be of
an order between 1 to 2 and 1 to 3* Once the need has been
established, all relevant Codes of Practice recommended tolerances
dealing exclusively with manufactured concrete components, but not
with erection of these components; although the interaction was always
emphasized. 64
The definition of tolerance [2.22] generally includes;-
1- the permitted variation from a basic dimension or quantity,
2- the range of variation permitted in maintaining arfbasic dimension,
3- and, a permitted variation from location or alignment.
The groups of tolerances, suggested by PCI Committee on
Tolerances[2.22], which should be established as part of precast
concrete design and to which final component details should conform
are;-
1- Product Tolerances.
Deals with the dimensions and dimensional relationships of the
individual precast concrete elements. Table 2.2 shows variations of
tolerances for precast column dimensions advised by various Codes of
Practice. The table also emphasizes the basic principles and concepts
on which the various tolerances are based.
2- Erection Tolerances.
Deals with those tolerances which are required for the acceptable
matching of the precast elements after they are erected. Up to date,
there are no clear cut values specified in any Code of Practice ,
although the need for such tolerance is always noted.
3- Interfacing Tolerances.
Deals with those tolerances which are associated with other materials
in contact with or in close proximity to precast concrete and includes
materials so related either before or after precast erection; for
example, embedded elements, architectural fixtures such as windows,doors,etc.. Table 2.2 - Tolerances For Columns.
V Country HOLLAND^ DENMARK^ GERMANY^2* u .K.(3> Section Dimensions^ 1m* 6mm* 2-5 mm. 6-10 mm. 4-10 mm* 5-10 mm*
Lengthy7*2 m* 13 mm* 4-8 mm. 10-16 mm. '.6-17 mm* 20—30 mm*
Based on references 2*3 • 2*16 t 2*31
1- Based only on "formation method"$ i*e* tolerances depend on nominal dimensions* 2- Based on both "formation method" and "grading method"* The values reported cover grades from the middle range of eleven grades in the case of the Dutch code,
and ten: grades in the case of the German code. 3- Based on. both "formation method" and "grading method"* Both the Danish and British codes include three grades only* The values reported cover the range between the special or first grade and second grade* 66
Tolerances should be established for the above three categories for the following reasons;-
1- Structural- To ensure that the structural design properly accounts for factors sensitive to variations in dimensional control. Examples include eccentric loading conditions, bearing areas, and locations of reinforcing or prestressing steel.
2- Feasibility- To ensure acceptable performance of joints and interfacial materials in the finished structure.
3- Visual- To ensure that the variations will be controllable and result in an acceptable appearance.
4- Economic- To ensure ease and speed of production and erection by having a known degree of accuracy in the dimensions of precast elements.
5- Legal- To avoid encroaching on building lines.
6- Contractual- To establish criteria for acceptability and quality control.
Note that although erection tolerances and interfacing tolerances are mentioned in terms of their importance, no clear recommendation,
similar to that of production tolerances, has yet been published.
Clearly such tolerances would be hard to define in general as they vary from one project to another and from one place to another. The
conceptual design of a precast project is the stage to begin to deal with dimensional control considerations. Architectural and structural
concepts should be developed with the practical limitations of dimensional control in mind.
This implies that the architect and engineer should have the primary responsibility for conceiving the overall dimensional control
concepts for the project and specifying the tolerances required for 67
the various individual elements. Such tolerances must be practicable.
They should be achieved without undue difficulty under normal contract procedures. If the specified tolerances are exceeded the product may be accepted, according to PCI committee[2.22], if;-
1- Exceeding the tolerance does not affect the structural integrity or architectural performance of the project.
2- The product can be brought within tolerance by structurally and architecturally satisfactory means.
3- The total erected assembly can be modified to meet all structural and architectural requirements.
In a unique effort, the Cement and Concrete Research Institute at the Norwegian Institute of Technology[2.$] studied the actual geometric imperfections in a prefabricated structure. Variations in the size, shape and placement of precast columns used in an industrial building were studied. The study included measurements of the cross section dimensions, crookedness i.e. initial curvature, verticality, and placement of 64. concrete columns. The data obtained for the structure are considered representative of normal quality concrete work. The following conclusions were made;-
1- Column cross sectional dimensions which were nominally 350mm by
350mm had a mean of 352.7mm and a standard deviation of 2.3mm. The distribution of the variations could be sensibly represented by a normal distribution curve. Based on the measurements, a tolerance of
10mm was considered practically attainable for the elements, which were cast in wood forms.
2- The verticality of the columns, expressed as the deviation of the top of the column from a vertical line through its base was measured in two directions and showed normal distribution. It is believed that 68
with greater control over the assembly operations it should be feasible to limit the variations to within 15mm.
3- The crookedness of the columns, measured in two perpendicular directions, was defined as the deviation of the centreline of the column from a straight line between the ends of the column. Assuming symmetry and mean value equal to zero, a standard deviation of 2.5mm was obtained for the deviations. Based on the measurements, a tolerance of 8mm was considered practically attainable.
4- - The placement of the columns was determined with respect to least squares lines fitted through the data for each row of columns. The mean value of the relative skewness between consecutive rows of columns was 2.5mm/m. The maximum value was 5«8mm/m.
To be able to appreciate the integration of dimensional control with the design of a precast concrete structure, more work similar to that documented by Fiorato[2.5] and presented above needs to be undertaken. Additionally, a theoretical study of tolerances is needed to help integrate the concept of dimensional control with the design of a precast structure. 69
2.4..2.2- Theoretical analysis of tolerances.
The position of any rigid building component in space is rigorously determined by six parameters- three translations along the
X , Y and Z axes; and three rotations with regard to these axes.
Figure 2.20 defines the axes and rotations used in this section.
Hence, six conditions need to be fulfilled for a building component to fit in place. Until the building elements are finally fixed by welding or in situ jointing they retain their mechanical character i.e. the capacity for a given movement.
The mechanical engineer refers to any two elements to be jointed as a kinematic pair. Knowing the characteristics of the connection within such a pair, one can evidently determine the consequent reduction in the degrees of freedom and use this result for predicting difficulties which are likely to arise during the assembly. Within a pair of elements the restriction of degrees of freedom can vary from one to five and are termed accordingly as kinematic pairs of first to fifth degree. Figure 2.21 shows illustrations of the various degrees of freedom.
Table 2.3[2.1] shows a summary of possible combinations and corresponding classification of kinematic pairs. For example, with restriction of possibility of movement along the x-axis in figure
2.21(e) the kinematic pair transforms into a rigid body.
The above conditions could also be considered with respect to one single plane i.e. each element would only be able to move in a plane parallel to the plane of reference. This condition of parallelism will automatically restrain each element in a connection three times; namely, the possibility of translation perpendicular to the plane of reference and rotations about perpendicular axes in this plane. Table 2*3 - Types of Kinematic Pairs
Restricted Degree 1 2 3 h 5 of Ereedom
Possibilities 1 1 2 1 2 3 1 2 1 2
'd ^ Rotation 0 0 1 0 1 2 1 2 2 3 ■oo $ o> d o •Hh -ti 1 2 1 3 2 1 3 2 3 2 •pahR) oA) Translation n o Jh fig# ? a ball fig. fig. n s * fS ** CM Examples 2.21a seating 2*21c 2*21d 2.21a Degree of Ereedom 5 h 3 2 1 71
Legend:
Axis 1 = translation along the x-axis
Axis 2 =5 translation along the y-axis
Axis 3 = translation along the z-axis
Axis 11= rotation about the x-axis
Axis 22= rotation about the y-axis
Axis 33= rotation about the z-axis
Figure 2*20 - Definition Of Axes Figure 2.21A Figure 2.2IB Figure 2.21C Third Degree Of Restriction. First Degree Of Restriction Second Degree Of Restriction.
to
Z
Figure 2.21D Figure 2.2iE Fourth Degree Of Restriction. Fifth Degree Of Restriction.
Figure 2.21 — Details Of Various Degrees Of Restriction 73
Consider for instance a prefabricated column element in its final form and refer to figure 2.22. To classify a connection by considering solely its degree of freedom does no more than explain the character of the problem. For a real assessment of the actual connection it is necessary to establish a relevant measure of difficulty for making such an assembly. One approach to this is by considering the so called
"points of conflict" as defined by Bobrowski[2.1]. Each of these would be denoted by "PC" with an appropriate number for each kind of movement and respective axis of reference as defined in figure 2.20.
The points of conflict could be defined usually as actual obstructions, and sometimes also as specified restrictions, to translation and/or rotation of an element resulting from the actual detail of a connection. Illustration of the meaning of points of conflict is given in figure 2.22.
In determining the number of points of conflicts it is assumed that all sides, other than the one under consideration, of the element in the joint are free. It should be noted that the degree of the kinematic pair, as defined above, is numerically equal to the number of points of conflict, or the number of restrictions of the degrees of freedom. It is therefore sufficient to determine the degree of kinematic pair in each connection to define the problem facing the designer.
As an illustration of the above, consider figure 2.22. The figure shows the problem related to erection of precast columns. The points of conflict can be summarized as follows;- 4>
Figure 2.2 2 - Assembly of Precast Columns
Points Of Conflict For Columns
(Refer to figure 2.20 for definition of axes.) 75
1- For vertical contact against side slabs or beams for the system shown in figure 2 .2 2 (b) only and as a specified restriction on elevational alignment externally and internally for both cases shown, namely (a)&(b); the points of conflict are,
2PC1+2PC2+2PC11+2PC22+4PC33
2- For horizontal contact at the top and the bottom of the column element the points of conflict are,
2PC11+2PC22+2PC3
Summing up the points of conflict with respect to axis of reference
Rotation. Translation.
about x-axis= 4PC11 along x-axis= 2PC1
about y-axis= 4PC22 along y-axis= 2PC2
about z-axis= 4PC33 along z-axis= 2PC3
Subtotal 1 2PC 6PC
Grand total for the element being
12PC + 6PC = 18 points of conflict. 76
A practical design that incorporates a rigorous analysis of fitting restraints of precast columns in the design of a complete framed structure, has to allow for the various constraints which must be accomodated within the design or eliminated entirely. It is usually most practical to eliminate the points of conflict by appropriate
detailing. The alternative course of action, i.e. to accomodate all
the constraints simultaneously, would result in very small tolerances
approaching perfect fit design. Such a course can be justified only if
the accuracy required can be attained. It is important to bear in mind
that the use of small tolerances does not necessarily mean increase in
the total cost of the project though it would normally imply an
increase in the production costs of the precast components.
Bobrowski[2.2] reported that high accuracy of 0.125mm in the shoe
centre was achieved by means of positioning setting-out stations on
the factory floor using high precision equipment. The shoe joints were
used in the construction of the Queensway Hotel in Gibraltar where the
overall cost analysis justified using a design based on near perfect
fit. 77
2.5- Summary, evaluation and conclusion.
As mentioned earlier, most column-to-column joints used in framed concrete structures are tested for satisfactory structural behaviour.
Although all Codes of Practice express explicitly the importance of dimensional accuracy they fail to quantify tolerances related to erection. Any evaluation of joint details should be based on both strength criterion and the manufacturing and assembly techniques to be adopted during construction.
Referring to figures 2.1-2.14- presented earlier in this chapter the following comments are valid based on the theoretical analysis of dimensional accuracy presented earlier;-
1- Where bolting or grouting techniques are used i.e. typical of figures 2.1-2.7 and 2.13> the holes drilled in the embedded plates or ducts left in concrete need not conform to tight tolerances, if dimensionally possible. There is no justification in any of the above mentioned types of joints to comply to tight tolerances because it is easier and more economical to allow for the elimination of the various restraints or points of conflict rather than accomodate them simultaneously.
2- Inaccurate location of the reinforcement bars or plates, e.g. typical of figures 2.8-2.12 and 2 .14-, would result in "forced” fitting of the joint thereby affecting its structural integrity. Most prominently this effect can be seen in figure 2.12 where bars are coupled by turnbuckles. For the bars to fit the couplings they need to have perfect alignment which is practically impossible. Future research programmes studying the effectiveness of these joints should include some consideration of the sensitivity of the joint to erection and fabrication techniques. 78
3- The shoe joint incorporated in H-frames shown in figure 2.22 has been used in several projects[2.1,2.2,2.20] where high accuracy was achieved to the extent of claiming perfect fit. Although the cost of production of the precast units was higher, the overall cost analysis proved the feasibility of using such techniques.
U- In view of the above, one can conclude that the required efficiency of connections between precast components relates directly to their dimensional accuracy, which in turn can only be obtained by using the correct manufacturing process. As suggested by Bobrowski[2.2], basically there can be but only two practical approaches to this fundamental problem:
(a) connections with near perfect fit, or,
(b) connections with generous tolerances.
The first category, resulting in dry instantaneous connections, can only be achieved by using the advanced manufacturing and assembly techniques that have been developed in the mechanical engineering industries. The production of precast elements with "crude" tolerances is, on the other hand, reasonably simple and economical. Construction however, is correspondingly slower when generous tolerances are employed. Of necessity, the connection is, in most cases labour intensive and always indirect; through an additional medium, like mortar between the bricks, in situ concrete or grout between precast elements, etc..
5- Finally, all Codes of Practice give advice on factors of safety relevant to monolithic concrete structures. For precast concrete structures the factor of safety required is left to the discretion of the designer. Joints with generous dimensional tolerances are subject 79
to variations in site practice and the quality of the finished joint may be extremely variable. A study made by Raths[2.21] on precast concrete connections incorporating embedded steel members concluded that a factor of safety of 1.33 times the load factor appropriate for monolithic construction should be used in designing safe precast concrete connections. Taking into account likely variations, this approach should lead to an actual factor of safety not less than two.
The work done by Raths was based on design experience and was a result of an analytical work rather than an experimental one. J.l
80
Chapter 3- A confinement model for detailing concrete structures.
3-1- Introduction.
In the previous chapter the importance of detailing and lateral confinement on joint behaviour was emphasized. In a structural member,
lateral reinforcement increases shear resistance, keeps longitudinal reinforcement in place during concreting, prevents the compression reinforcement from buckling and provides some confinement to the concrete. Most national codes effectively ignore the effect of lateral
reinforcement upon the behaviour of concrete, even though they contain
clauses limiting the size and spacing of ties. It appears that code recommendations and some of the early investigations[3.5] are based on
the premise that the main function of lateral reinforcement is to prevent the compression reinforcement from buckling, rather than to confine the core concrete.
Numerous investigations have been carried out during the last eighty years into the strength and deformation characteristics of concrete loaded in triaxial compression in a triaxial cell [3.9,3.18,3.21]. The resulting expressions for the strength and
ductility of confined concrete cannot, however, be applied directly to the case of laterally reinforced concrete. There are two important
differences between confinement due to lateral reinforcement and that due to lateral pressure as in a triaxial cell;-
(a) Confinement due to lateral reinforcement depends on transverse
deformation of concrete indicating its "passive" nature. (b) Confining forces are applied by lateral reinforcement along
discrete lines and vary along ties as well as between them. The mechanism of confinement will be discussed in detail later in this
chapter. Some efforts have been made in the past to modify expressions 81 for triaxially loaded concrete for application with concrete specimens confined by spiral steel ties, and results were satisfactory. These good results stem from the fact that hoop stresses in the spirals exert axisymmetric confinement on the concrete when the transverse deformation makes the concrete bear against the lateral reinforcement.
However, the application of results from triaxial tests to concrete specimens confined by rectilinear ties is more complex due to the fact that ties are subjected to bending and direct tension resulting in non-uniform confinement.
The objective of this chapter is to review the literature dealing with concrete confined by rectilinear steel ties, and to develop a model that exploits the constitutive relations for triaxially loaded concrete and concrete confined by spiral steel ties. Success in this would lead to direct method of design for structural details including connections betweeen precast elements. 3-3
82
3*2- Concrete confinement.
Concrete which is restrained in the directions at right angles to
the applied stress will be referred to as confined concrete. Concrete
confinement can be classified, according to the method of confinement
as either
(a) passive confinement, or,
(b) active confinement.
3.2.1- Passive confinement.
In practice, concrete may be confined by transverse reinforcement
commonly in the form of closely spaced steel spirals or ties.
Confinement becomes effective only when the transverse strains are
sufficiently high to develop a significant force in the ties. This
occurs when, as stresses approach the uniaxial strength, the
transverse strains become very high due to progressive internal
cracking causing the concrete to bear against the ties which in turn
provide the restraint to stop further deformation. This restraint is
passive in nature, hence the term passive confinement. The mechanism
of passive confinement is illustrated in figure 3*1 •
Ideally, the concrete will never fail as long as there are
appropriate lateral stresses acting, as suggested by Kotsovos[3»18],
to prevent tension cracks from propagating. Experimental results have
shown that if the spacing of the lateral steel is large and the steel
has a high ultimate strength, the failure of the column specimen will
be due to the complete internal failure of the concrete indicating low
restraint with high capacity. In the case of very closely spaced ties,
the column failure will be due to the yielding of lateral steel and
its not being able to supply an increase of lateral restraint with an
increase of lateral deformation indicating high but limited restraint. 83
Effect of spacing of transverse steel on efficiency of confinement.
Confinement by square hoops and circular spirals, (a) Square hoop, (b) Circular
Figure 3.1 Confinement Mechanism. 84
Tests by many investigators in the past, e.g. references 3.2-
3.4.,3.6-3.8,3.10-3.15,3*19,3.20,3.22-3.33, have shown that such confinement can considerably increase the compressive strength and ductility of a concrete member. However, the tests showed that rectangular or square ties do not confine concrete as effectively as circular spirals, as illustrated in figures 3*2 and 3«3* This is because the spirals are subjected to tension hoop stresses, and concrete confinement is dependent on the pitch of the spirals. If the pitch is small enough, the confinement of the concrete can approach that provided by uniform lateral pressure. In contrast the square or rectangular ties are subjected to both bending and tensile stresses since confinement of the concrete is provided by arching between adjacent transverse and longitudinal bars. Hence, in this latter case, concrete confinement is dependent on both the spacing of the ties and the spacing of the vertical bars.
A review of the literature, dealing with passive confinement, indicates that the following variables are relevant;-
1- cross sectional area of the ties,
2- centre to centre spacing of the ties,
3- ratio of the tie spacing to minimum dimension of section,
4- - ratio of tie diameter to section dimension,
5- tie yield stress,
6- longitudinal reinforcement content,
7- distribution of longitudinal steel and resulting tie configuration,
8- strength of concrete,
9- strain gradient,
10- rate of loading, and,
11- thickness of cover. so
40 (6000) J^Pi ch£o.
a 30 iv n •:7 r9 - j Sw J <5^ ^ — (4000) E K jS' v® V \ C 20 /**/*^lj ’60 Hf^n & ^ \ 0 m °° s0 (2000) V
10 N* * U o Spira pitch >eside each % curve in millimeters (1mm = 0.04 in) ______i______l______l______0.01 0.02 0.03 0.04 0.05 0.06 Average strain over a 200 mm (7.9 in) gauge length F ig . ^2 Stress-strain curves for concrete cylinders 150 mm (5.9 in) diameter by 300 mm (11.8 in) high, confined by circular spirals from 6.5 mm (0.26 in) diameter mild steel bar.
CONFINEMENT INDEX
F i g . 3,3 . Comparison of increase in ultimate strength due to different binders. (3.24) 86
These variables will be discussed later in this chapter when discussing passive confinement analytical models.
3.2.2- Active confinement.
As mentioned earlier, in the case of very closely spaced ties or spirals, the column failure will be due to the yielding of the binders and its not being able to supply an increase of lateral pressure.
Using high tensile steel binders provides a higher confinement capacity. However, to develop the high stress in the binders, the lateral deformation of the concrete must be greatly increased. With such large transverse deformation there could be excessive internal damage to the concrete which can adversely influence the durability, and serviceability of the structural member. This effect can be avoided by prestressing the binders thereby creating a triaxial state of stress independent of the transverse deformation of the concrete at the initial stages of the load application, as suggested for example by Ben-Zvi et.al.[3»3]» In this case, initial level of confinement is independent of the applied load since concrete is in contact with the lateral reinforcement due to precompression.
Figure 3.4- shows qualitative variation of stresses for a triaxially loaded specimen and the two types of confinement. It is worthwhile noting that in the triaxially loaded case all the lateral confining stress (i.e. f2 and f3) is acting before the load is applied. For the passive confinement, the lateral confining stress is noticeably increased only after an appreciable amount of the acting load has been applied. This is so because, as explained earlier, the material has to 87 develop an appreciable amount of internal fracture before confinement is significantly activated. Finally, the active confinement starts with the applied precompression and, upon application of load, more
confinement is provided, depending on the capacity of the binders.
The specimens in this research programme include precast columns reinforced with rectilinear ties; therefore, the rest of this chapter will deal with passive confinement by rectilinear ties. 88
0AB1 Passive confinement. Confinement starts beyond point A. 0CB2 Active confinement. Confining stresses due to, for example, prestressing are applied first, denoted by point C. Passive confinement is activated with application of load. 0DB3 Triaxial loading of plain concrete. Confining stresses are fully applied before application of loading stress FI.
Figure 3.4 Types of Confinement 89
3.3- Passive confinement by rectilinear ties.
3.3.1- Introduction.
Although circular spirals confine concrete much more effectively than rectilinear ties, and the mechanism of confinement is better understood than for ties, the relative ease of detailing makes use of ties more attractive than spirals. Numerous studies have been reported on the behaviour of concrete confined by rectilinear ties (refer to table 3*1). Several analytical models with various degrees of sophistication have been proposed. Some models predict only the ascending part of concrete's stress-strain curve, while others predict the curve up to a certain point on the descending part. A few models predict only concrete strength and corresponding strain, figure 3*5 shows some of the models which describe the stress-strain curve for concrete confined by rectilinear ties.
3.3.2- Comparative study of the confinement models.
The variables considered in the analytical models described in figure 3»5 are listed in table 3.2. The amount of lateral reinforcement received most attention. Some of the other variables which appear in these models are strength of plain concrete, steel strength, distribution of longitudinal steel and the resulting tie configuration, tie spacing and section dimensions.
Most of the early research work on confinement by rectilinear ties was carried out on small specimens with simple tie configurations
(e.g. only four longitudinal bars in a column section). A summary of some representative tests is presented in table 3.1. In most of these tests, the ratio of the area of the core bounded by the centre line of the perimeter tie to the gross area of the specimen was small. 90
M 2 . B a sa a rc h e r No. Size of section * e o re Longitudinal V o lu o e tric H e ig h t o f B eeerk a t i e s p e c ie an Ag ro s s s t e a l r a t i o ( t )
Strength gain . 3.14 King (1946) 200 8 8 .9 x 8 8 .9 0.54-0.61 4 corner bars 0-7.8 297,305,915 Saall speciaana giva 3 .1 5 King (1946) 18 254x254 0.36-0.66 4 corner bars 0 -1 0 .5 6 915 only trendb eof h a v io u r. 3.B Qian (1955) 9 152.4x152.4 0 .6 3 -0 .9 2 4 comer bars 0 .8 4 -4 .1 3 292 7 152.4x92.1 0.92-0.96 4 corner bars 0 .8 5 -4 .5 5 1321 g a in 7 152.4 dlaa. 0 .9 7 4 b a rs 1 .6 4 -3 .2 8 305 3 .S Bresler 4 Gilbert 2 203.2x203.2 0.61 6 b a rs 0.41-0.62 1524 No strength gain. Mein concern was (1961) 2 203.2x203.2 0 .6 1 8 b a r s 0.43-0.69 1524 buckling of rebars. 3.20 Pfister (1964) 4 304.8x304.8 0 .4 2 -0 .5 3 12 b a r s 0 -0 .4 5 1828 No strength gain. 3 203.2x457.2 0.36-0.49 12 bars 0 -0 .6 4 1828 Ties other than the one cn the periphery 4 254.0x304.8 0.49 6 bars 0 -0 .3 9 1828 had no contribution. 3.23 JtoylSozen (1965) 45 127x127 0.86-0.90 4 comer bars 2 .1 - 2 .4 635 No strength gain. 3.4 Bertiro 4 Felippa 2 76.2x76.2 0.89 non* (1965) 2 114.3x114.3 0 .9 1 none 0-2.6 Strength gain. 5 76.2x76.2 0.89 4 comer bars 6 114.3x114.3 0.91 4 comer bars 3 .1 0 Hudson (1966) 32 101.6x101.6 0 .4 6 -0 .4 7 8 bars 0-0.32 813 No strength gain. 28 152.4x152.4 0 .6 3 -0 .6 6 8 b a rs 0 -0 .6 9 1220 3 .3 1 Sol In an 4 Yu 3 152.4x101.6 0.92-1.00 2 bars 0-0.40 1321 Strength gain. (1967) 11 152.4x101.6 0.44-0.92 4 comer bars 0.6-3.43 1321 1 152.4x76.2 0.91 4 comer bars 1 .4 6 1321 1 152.4x127 0 .9 3 4 comer bars 1 .0 5 1321 3.26 Shah 4 Jiang an 4 5 0 .8 x 5 0 .8 0.83 none 0-1.00 254 Strength gain. (1970) 7 5 0 .8 x 5 0 .8 0 .8 3 n one 0 -1 .0 0 152 3.32 Senses (1970) 42 101.6x101.6 0.88-0.92 none 0.67-9.04 305 Strength gain. 3 .13 Kant 4 Park (1970) Data reported In references 3.4,3.23 4 3. 31 were used for analysis No stength gain. 3 .1 1 Iyengar at al (1970! Data reported In re fe re n c e s 3.4 s 3.23 were used for analysis Strength gain. 3 .2 4 Saxgln at al (1971) 41 125x125 0 .5 9 -0 .9 7 none 0.59-5.32 510 Strength gain. 3 .7 Burdetta 4 Hilsdorf 45 127x127 0 .7 2 -1 .0 0 n o ne 0 -3 .7 635 Strength gain. (1971) 12 127 d la a . 1 .0 0 none 1.85-6.68 152 3.6 Bunnl (1975) 4 127x127 - none - 504 to Strength gain. 50 127x127 0.88-0.95 1 comer bars 0 -6 .5 5 2540 3 .1 2 Kaar at al (1977) 11 254x 4 0 6 .4 0 .6 8 -0 .7 2 4 comer bars 0 .9 6 -3 .8 6 6 127x203.2 0 .7 1 comer bars O o r 1 .7 2 3 .3 3 Vail an aa at al 3 254x2 54 0 .7 8 8 b a rs (1977) 3 228.6x228.6 0 .9 6 8 b a rs 0 -1 .4 0 Strength gain. 3 254x254 0 .7 8 none 3 228.6x228.6 0 .9 6 none 3 .2 9 Shaikh 4 Uziaarl 9 304.8x304.8 0 .7 8 8 b a rs O .B O -2.32 1955 Strength gain. (1980) 6 304.8x304.8 0 .7 8 12 bars 1.60-2.40 1955 9 304.8x304.8 0 .7 8 16 bars 0.76-2.30 1955 3 .1 9 Park at al (19B2) 4 550x550 0.70 12 bars 1.50-3.50 3300 Strength gain. 3.25 Scott at al 8 450x450 0 .7 9 -0 .8 0 8 b a rs 1 .3 4 -2 .9 3 1200 Strength gain. (1982) 12 4 5 0(45 0 0 .7 9 -0 .8 0 12 b a rs 1.40-3.09 1200
Table 3.1 S mm ary of available f»t« 91
Table 3.2 List of variables for various models.
Researcher Variables
Bertiro & Felippa(3.4) Volumetric ratio of lateral steel. Bresler & Gilbert(3.5) Spacing and size of lateral steel, but main concern was buckling of longitudinal bars rather than confinement of core. Bunni(3.6) Effect of longitudinal and lateral steel on strength and ductility of concrete; and buckling effect of longitudinal steel between ties. Burdette & Percentage of lateral reinforcement Hilsdorf(3.7) expressed by the ratio of volume of lateral steel to volume of concrete; spacing of lateral steel , and flexural rigidity of the lateral steel. Chan(3.8) Volumetric ratio of lateral steel to concrete core; and ratio of section dimension to tie spacing. Hudson(3.10) Column size, spacing of ties, strength of concrete, size of tie, percentage of longitudinal steel, and position of load. Iyengar(3.11) Strength of concrete, size & shape of test specimen, diameter & type of ties. Park et al (3.13,3.19, Volumetric ratio of lateral steel to core, &3.25) ratio of width of core to tie spacing, strength of plain concrete,rate of loading. King(3.14,3.15) Percentage of longitudinal steel, spacing of lateral steel, diameter of lateral steel, and size of the specimen. Pfister(3.20) Arrangement and spacing of lateral ties. Roy & Sozen(3.23) Volumetric ratio of lateral steel to core, and ratio of section dimension to tie spacing. Sargin et al (3.24) Volumetric ratio of lateral steel to core, ratio of core width to tie spacing,steel strength,and strength of plain concrete. Shah & Rangan(3.26) Volumetric ratio of tie steel to core. Sheikh & Uzumeri(3.29) Volumetric ratio of tie steel to core, distribution of longitudinal steel around core perimeter and resulting configuration of ties, tie spacing and characteristics. Soliman & Yu(3.31) Area of tie steel, tie spacing and section geometry. Somes(3.32) Spacing and cross section of ties. Va lien as et al(3.33) Volumetric ratio of ties to core,main steel content,sizes of steel,ratio of core dimension to tie spacing,steel and plain concrete strength. 92
(b) Roy & Sozen (3.23)
(c) Soliman & Yu (3.31) (d) Sargin (3.24)
F c Modified Confined
(e) Vallenas et al (3.33)
(g) Sheikh & Uzuaeri (3.30) (h) Modified CPllO
F - Compressive Strength Of Confined Concrete. F^C- Compressive Strength Of Plain Ooncrete. F - Concrete Stress. Ec - Concrete Strain, c K - Strength Gain Factor F - cc
Figure 3.5 Various Stress-Strain Curves For Ooncrete Confined By Rectilinear Ties 93
Therefore, despite any possible strength enhancement of the confined concrete, the total capacity of the specimen, after the cover had
spalled off, did not exceed the capacity of the unconfined specimen.
This, perhaps, is one of the main reasons for the disagreement among researchers about the beneficial effects of the rectilinear ties on the strength of the confined concrete.
Another significant factor contributing to disagreement between results from different researchers is the size of the specimens
tested. Here, the height of the specimen and the influence of end
effects can be particularly influential. Results in many cases reflect
the behaviour of the specimen rather than that of confined concrete.
King[3*14->3.15], following his extensive research, concluded that
small specimens give trends of behaviour only. Park et.al.[3-13>3*19] modified the analytical model, intended to describe the behaviour of
concrete confined by ties, which was based on tests using small
specimens, by doing further tests using full size specimens. The
influence of end effects is very notable when comparing results of
tests by Bertiro and Felippa[3*4-] and Roy and Sozen[3»23l. While all
specimens had the same ratio of confined area to gross sectional area
and the same volumetric ratio of lateral reinforcement, the former
reported an increase of concrete strength of about 20% while the
latter found no strength gain.
Sheikh[3»27] conducted a comprehensive comparative study of
several analytical models describing the behaviour of concrete
confined by rectilinear ties. He noted that in all the models he
reviewed the amount of longitudinal steel had no effect on the
properties of confined concrete. He also noted that in specimens with
only four corner bars, the effectively confined concrete area at the
critical section between the ties could be very small compared with 94
the core area bounded by the centre line of the tie. This resulted in poor confinement of the concrete. In addition, small specimen sizes, simple steel arrangements, low volumetric ratios of lateral steel to concrete core, and low ratios of core area to gross area of the section, all resulted in small increases in confined concrete strength and ductility.
In figure 3.6, Sheikh[3 .27] compares some of the results of columns of his test programme with results obtained by applying analytical models of other researchers to his own specimens. Figure
3.7 shows the various tie steel configurations of specimens tested by
Sheikh. His conclusions can be summarized in the following
1- Chan's[3.8] equation overestimates the strength increase of confined concrete in several cases, particularly for all specimens of configuration "A" and those with large tie spacings. As no consideration is given to tie spacing and steel configuration, the equation underestimates concrete strength for columns with tightly knit cages. (Refer to figure 3.7 for configuration "A").
2- The analytical models proposed by Roy and Sozen[3«23] and Kent and
Park[3*13] do not recognize any strength increase in confined concrete. Therefore, a complete lack of agreement is found between results from their models and those obtained by Sheikh. In a recent publication, Park[3-28] admitted that the discrepancy was due to the small-scale specimens, which were reinforced with four corner bars.
Park[3.19] later modified his analytical model by introducing a factor which accounted for passive confinement.
3- The increased concrete strength due to confinement is underestimated for all specimens, tested by Sheikh, by the analytical model proposed by Soliman and Yu[3«31]. The difference between the experimental and analytical values increases with the increase in the 95 number of laterally supported longitudinal bars. This is because no consideration is given to steel configuration in the model.
U- Sargin’s proposed analytical model[3«24] underestimates the strength of confined concrete for most of the specimens. The difference between experimental and calculated values is higher for specimens of configurations ,,Bn,,,Cn, and nD" than for type nAn shown in figure 3»7. The effect of tie spacing, it seems, is not appropriately accounted for in this model. Increase in concrete strength is considered to be directly proportional to the stress in the tie steel. The experimental data does not support this assumption.
5- The analytical model proposed by Vallenas et.al.[3*33] underestimates the strength of confined concrete in all specimens.
Experimental data does not support the assumption that strength of confined concrete is dependent upon longitudinal steel contents.
Effect of tie spacing appears to be more pronounced than predicted by this model. Also, experimental evidence indicates that increase in concrete strength is not directly proportional to the stress in lateral steel, as suggested by this model.
The comparative study by Sheikh brings about the fact that the relevant models of passive confinement are those that are based on testing full-size specimens, with various arrangements and numbers of longitudinal bars and overlapping ties. Considering table 3«2, it is realised that the analytical models developed by Sheikh and
Uzumeri[3»29l and Park et.al.[3*19] both satisfy the above conditions, and hence need special consideration. AVERAGE COLUMN STRAIN AVERAGE COLUMN STRAIN
AVERAGE COLUMN STRAIN p = Volumetric ratio of steel ties, s p = Ratio of longitudinal steel.
(3.27) Figure 3.6 Comparison of experimental and analytical stress-strain curves (3.27) Figure 3.7 Various steel configurations.
Figure 3.8 Effectively confined concrete area as a function of tie spacing (3 29) and core size for various square steel configurations.
(3.29) Figure 3.9 Variation of tie strains with axial load levels. 98
3 .3*3- Sheikh _& Uzumeri Experimental Programmed *29,3 *30] *
3 *3 *3«1 - Experimental 0b3ervations[3»29]«
Sheikh & Uzumeri conducted an experimental programme on twenty- four columns nearly full-size with various arrangements of longitudinal bars as shown in figure 3*7* Based on experimental observations their conclusions can be summarized in the following;
1- Specimens with configuration "A" showed the least enhancement of concrete strength and ductility, while specimens with configuration
"C" showed the maximum gain in strength and ductility, (refer to figure 3*7 for various configurations). It appears that the proper distribution of the longitudinal steel around the core perimeter, and the resulting tie configuration, enhances the strength and ductility of the concrete section (up to 70% gain in the tests reported) . The pattern of longitudinal steel determines the area of effectively confined concrete, since the confined area increases with an increase in the number of longitudinal bars that are effectively supported by a bend of a tie.
2- The effect of the volumetric ratio of lateral steel on the behaviour of confined concrete is well recognized. The gain in strength does not appear to be directly proportional to the amount of lateral reinforcement. Increasing the amount of lateral reinforcement results in less than proportional increase in concrete strength. The ductility of the confined concrete is clearly enhanced with the increase of lateral steel content.
3- Tie spacing appears to be a very important parameter in determining
the behaviour of the confined section. Increased tie spacing, even with the same volumetric ratio of tie steel, results in a reduction in 99 the strength gain of the concrete section. The ductility is also adversely affected. In addition to controlling the area of effectively confined concrete, tie spacing also controls buckling of the longitudinal bars; large tie spacing may result in premature buckling of the longitudinal bars.
4- The stress-strain characteristics of the lateral steel determine the state of the confining pressure at any level of the applied load.
On the otherhand, the yield strength of the lateral steel determines the upper limit of the confining pressure capacity. Heat treatment of the lateral steel, and thus the introduction of flat yield plateau, results in a reduction of the gain in concrete strength, due to the reduction in steel strength, and due to elimination of strain hardening region at lower strains. The change in the gain in concrete strength is less than proportional to the change in steel stress.
3 »3«3«2- Analytical Model.[3 «30]
The curve shown in figure 3»5(g), was used to represent the behaviour of confined concrete. The curve consists of three parts.
Part "OA" is a second degree parabola with point "A" at the peak of the curve. Parts "AB" and "BC" of the curve are straight lines. The zone beyond point "C" was not covered by the experimental programme.
However, it was assumed that beyond point "C", the curve can be expected to continue in the same straight line until stress is dropped to about 30% of the maximum value, therefrom continuing as a horizontal line. Full details of the model can be found in reference
3.30.
In deriving their model, Sheikh and Uzumeri set the following expression to describe the relationship between concrete strength and 100 lateral confinement produced by rectilinear lateral reinforcement;
f = f + f(p ,s,f ,1m,ns)------(3• 1) cc cp rs’ * s f
where;
f = compressive strength of confined concrete in the specimen.
f = compressive strength of concrete in plain specimen.
p = volumetric ratio of lateral reinforcement, s s = the spacing of lateral reinforcement.
f = the stress in lateral reinforcement, s (dependent on transverse strain of concrete),
lm = a factor that takes into account the configuration of the
section and location of the longitudinal bars,
ns = effect of the size of the section.
Equation 3*1 can be expressed as,
f 1 cc K = -- = 1 + -- (gain in strength)------(3.2)
f f cp cp where;
K = strength gain factor.
The increase in the strength of confined concrete is calculated on the basis of the "effectively confined" concrete area. This area is less than the nominal core area bounded by the center line of the perimeter tie and is determined by the tie configuration and tie spacing as shown in figure 3*10. Variation of such area with tie spacing and lateral steel arrangement is shown in figure 3 .8 . 101 w |tnj>o|W
C = centre-to-centre distance of longitudinal bars S — spacing of ties
0 - defined as 45*
If B&U are defined as centre-to-centre distance of perimeter tie of rectangular core, then,
Area of core = A — B x H co and, area of effectively confined core at tie level
Neglecting the reduction of A cq at tie level, the area of effectively confined core at a section midway between ties,
= (B-2y)(B-2y)
therefore, area of effectively confined concrete.
Ae -^(B-2y) (H-2y)
Special case
For a square section B = H also if longitudinal bars are equally spaced then X <$ = ■<* ui therefore, 2 A = U - , > (B-0.5S)2 * 5. SB2
if o C is defined as 5.5 based on experimental data.
Figure 3.10 Definition of area of effectively confined concrete (3.30) 102
A number of researchers[3 • 8, 1 3,3» 22] have reported that the effect of rectilinear reinforcement in terms of confining presure, in enhancing the strength of the concrete is proportional to (p f )m , s s where "m" is a constant less than one but greater than half. Hence,the gain in strength can be expressed as,
m Gain in strength = a(p #f ) (3.3) s s and m (3-4) Padd = V a(V fs} where;
a = constant.
= effective area defined in figure 3*10.
Padd= increase in load capacity.
Hence, the strength gain has been calculated by using the effective area concept and all constants determined empirically.
The application of the model requires the knowledge of the stress in the lateral steel at the time of maximum force in concrete. Since the gain in concrete strength is not very sensitive to the stress in the steel, the yield strength of tie steel can be used for the actual stress in tie steel. This assumption is not unrealistic and supported by many researchers. For example Bunni[3.6] concluded that the strains measured in the ties indicated that the yield strain was reached before or at failure of the columns tested. Park et.al.[3»19] and
Scott et.al.[3*25] used the same assumption in the analysis of tested specimens and achieved satisfactory results. Also,Sheikh and
Uzumeri[3•29] measured strains along lateral reinforcement in the specimens they tested and concluded that in most cases the lateral reinforcement yielded; figure 3*9 shows the typical trend of variation of tie strains with axial load levels. It is worth mentioning that 103
Scott et.al.[3.25], in all the reported specimens, measured yielding stresses in the lateral steel, which in some cases fractured.
Similarly, Park et.al.[3«19] measured strains in the lateral ties amounting to six times the strain required for yield.
3 . 3 . J+- Experimental programme by Park et.al. [3*19>3-25] •
In an effort to resolve the considerable differences in the quantity of rectangular binders required by various seismic design codes in the potential plastic hinge regions of rectangular reinforced concrete columns, a research programme was initiated at University of
Canterbury in New Zealand. This programme included three phases;-
1- to study ductility of spirally-confined concrete columns,
2- to study ductility of concrete columns confined by rectilinear
ties, and,
3- to study behaviour of confined concrete columns at low and high
strain rates.
Only the last two phases will be discussed in this chapter since in this work only confinement by rectilinear ties is considered. The results of Phase 1 were similar to those of Phase 2 except that spirally-confined concrete columns showed more strength gain and ductility than square-confined columns.
3.3-4--1— Experimental observations.
Phase 2 involved the testing of four nearly full size reinforced concrete columns with a 550mm square cross section. Details of a typical specimen and loading arrangement are shown in figure 3-11- The main variables included in the tests were the level of the applied 104
UNITS I t 3 UNITS 3 U SetTION : LONGITUDINAL STFCt M O S E T S o r HOOP STEEL N bH i •- t LonfKKtmol tlttl - C ro a t 310 dttgrm td bort Twtlvt 3i mm dro with SO mm COtte 3. Hoop ttr tt • Groat 375 ptom round bort. th PtottK Hngt Htgon OLttrdt fttsnr Hmgt Hrgion U*f Ha of Bardro Spacmg Nj of Bor do Spacing hoop trtI mm krtJmm hooottntnm krtlmm 1 1 ID BO 5 10 135 3 6 13 75 3 13 310 3 a 10 75 e 10 105 l w 13 73 3 13 300 Hoop tlrtl m btom ttub wot ef tomt tat and opprotimotti/ of dm temt toocmg et m tht pbttK ftngt rtgton 3 I mm m O.OJMm
F i g . 3.11 -Dimanslons, Rainforcing Dataila, and Loading of Column Tast Units ( 3 . 1 9 )
tfOff • d/r 0imtftn9f>t m mm itm m t O.CJPdfAt Fig. ^12 Typical details of test units(3.19) 105
axial load and the corresponding amount of transverse reinforcement.
The steel binders were provided in the two basic arrangements shown in figure 3«11» Electrical resistance strain gauges were attached at various locations on the transverse reinforcement within the plastic hinge regions. More detailed information about the testing details can be found in reference 3 ‘19-
Phase 3 comprised testing twenty-five nearly full size reinforced concrete columns with a 4-50mm square cross section. Details of these specimens are shown in figure The main variables included the effect of eccentricity of load and resulting strain gradient along the column section, strain rate, amount and distribution of longitudinal steel, and amount and distribution of lateral steel. Similar to Phase
2 specimens, electrical resistance strain gauges were attached to the underside of the transverse reinforcement. More detailed information about the testing details can be found in reference 3«25•
The appearance of vertical cracks in the concrete cover was always the first sign of distress in the test units. These cracks spread rapidly as crushing of the concrete cover caused the cover to become ineffective. As expected, this was particularly evident for the specimens with closely spaced transverse steel since they caused a plane of weakness between the core and the cover concrete. It was observed that for concrete confined by closely spaced ties, the cover will separate from the concrete core at compressive strains of 0 .004- or higher, and hence cannot be relied on to carry stress at higher strains.
The results by Park et.al. were confirmed by Sargin et.al.[3-24-], who performed tests on 125 by 125 by 510mm concrete prisms. He noted that the bearing capacity of the cover is less than that of the core and, indeed, less than even that of plain concrete because;- 106
(a) ties interrupt the continuity of concrete,
(b) lateral tensile strains in the core are smaller than those in the
cover, because of the lateral confinement of the core, and this
causes a separation between the core and the cover, and,
(c) when separation starts, the slender cover is more vulnerable to
instability effects than the solid core.
The above points suggest that the closer the spacing and the larger the amount of lateral reinforcement, the more the continuity of concrete is impaired and hence the less should be the effectiveness of the cover. Furthermore, the thicker the cover, the more effective it should be in resisting loads, because a thick cover is less vulnerable to instability effect and the quality of concrete in a thick cover is usually better than that in a thin one.
However, with the cover lost, Park et.al. observed that the load still continued to increase as the core concrete became confined by arching between the ties and between the longitudinal bars.
Eventually, this load decreased. Buckling of the longitudinal bars occurred at higher strains (approximately 0.02). This was invariably associated with fracture of the binders at or near the buckling load.
It should be noted that fracture of the outer binders occurred later, if at all, than fracture of the inner ones. This phenomenon, which was not reported by any of the other research programmes, could be due to the loss of bond at the outer binders, caused by the loss of the concrete cover, allowing an averaging of the strain across the width of the concrete core. Hence, loss of bond prevents stress concentration and allows distribution of stresses within the outer transverse steel thereby preventing its fracture.
The following conclusions summarize the experimental observations of Park et. al., 107
1- The presence of the strain gradient due to lateral forces has significantly reduced the slope of the falling branch of the stress strain curve for the concrete. This is because the compressive stresses resulting from the flexural behaviour of the specimen tend to increase the triaxial effect on the concrete. Kotsovos[3-17] suggested that the concrete surrounding the regions of large tensile strain concentrations restrains significantly the transverse expansion of these regions. This restraint, combined with the longitudinal compressive force and the radial actions due to the deformed shape of the flexural member, causes a complex multiaxial compressive state of stress which would enhance the strength and ductility of concrete.
Similar observations were reported by Sargin et.al..
2- The longitudinal strain rate influenced both the peak stress and the slope of the falling branch of the stress strain curve of the concrete. For the high strain rate in these tests (0.0167/sec.), the peak stress was increased by about 25% compared with that for the low strain rate (0.0000033/sec.). Also, the slope of the falling branch of the stress strain curve from the peak stress to about 0.02 strain was much steeper for the high strain rate than for the low strain rate.
This increase in the peak stress compared favourably with the results of concrete cylinders reported by Watstein[3*34]• The average increase in concrete cylinder strength, for specimens tested by Watstein, for strain rates of 0.01/sec. and 0.1/sec. were 17 and 39 percent, respectively, for concrete with a cylinder strength of 17MPa
(2500psi.), and 16 and 23 percent, respectively, for concrete with a cylinder strength of 45 MPa (6500psi.). Dilger et. al.[3»36] reported also similar trends clarified in figure 3•13•
3- An increase in the volume ratio of transverse reinforcement increased the peak concrete stress level, and decreased the slope of 108 Kll
STRAIN tIO3 )
Fig. 3.13 Stress-strain relationship for plane
concrete under different strain rates.(3.36)
F i g . 3 . 1 4 Failure envelopes of passive & active confinement. 109 the falling branch of the concrete stress strain curve. An increase in the spacing of the binders, while maintaining a constant volumetric ratio of transverse reinforcement by the use of larger diameter bars, tended to reduce the efficiency of the concrete confinement. This conclusion matches the experimental findings of Sheikh and Uzumeri.
A- An increase in the number of longitudinal reinforcing bars resulted in better confinement of the concrete, for a given longitudinal reinforcement area, due to the closer spacing of the longitudinal bars. This observation is also consistent with the observations made by Sheikh and Uzumeri.
5- Flexural strength of the test units exceeded predicted values based on ACI column charts by an unexpectedly high margin. This was due to an increase in concrete compression strength, as a result of the confining action of the lateral reinforcement, to the maximum moment being reached at a high concrete compression strain, and to the strain hardening of the longitudinal reinforcement at large displacements.
6- Ultimate moment capacities based on ACI column charts led to very conservative estimates of the ultimate lateral load. This is because an enhancement of the moment capacities due to confinement would lead to higher capacities of lateral load that can be carried by a column, resulting in a possibility of brittle shear failure, as occurred in one of the specimens.
7- In the eccentrically loaded units the tension cracks were slightly inclined to the horizontal due to the shear induced by the amount of moment gradient resulting from high, but variable P-delta moments. For a pin-ended column, as in this case, the P-delta moments were maximum at mid-height and zero at ends creating a moment gradient with height, and thus a shear force distribution along it. 110
3.3*4-*2- Analytical model.
The curve shown in figure 3.5(f) was proposed to represent the behaviour of confined concrete. The only difference between the modified model suggested in 1982 and the original model suggested in
1971 is the strength gain factor nKn defined as,
P s -f yh U K 1 + (3.5) f ' c
where;
p = ratio of volume of rectangular steel binders to volume of
concrete core measured to outside of peripheral binder,
f , = yield strength of the steel binders, and, yh f' = compressive cylinder strength of concrete.
Details of the analytical model can be found in references 3•13&3-19*
Equation 3.5 considers the steel ties to yield when calculating the strength gain factor. This is justified from results of many research programmes, mentioned earlier in this chapter, which measured strains in the lateral steel larger than the strains required for yield at load levels well below the failure load.
Another point of interest is that the concrete strain corresponding to maximum concrete stress is taken as 0.002K, in which
0.002 is the assumed value of the strain at maximum stress of unconfined concrete. This assumed value of the strain at maximum stress enables the parabola defining the region "AB” on figure 3.5(f) to have the same slope at the origin, i.e. the same tangent modulus of elasticity of concrete at zero stress, as for unconfined concrete, Ill
regardless of the confining steel content. In fact, both curves, of confined and unconfined concrete, are approximately identical up to a I stress of about 0.8f and beyond this the material becomes stiffer c for confined concrete with more pronounced difference, depending on the degree of confinement. This observation highlights the fact, that the model by Park et.al. emphasizes the concept of passive confinement
The only disadvantage of the model by Park et.al. is that while the research showed the importance of the distribution of the longitudinal steel within a section and the spacing of the lateral steel, they were not reflected in the proposed model. For example, the model cannot explain the higher strength and ductility due to smaller spacing of ties and better distribution of the longitudinal steel when the steel contents are kept constants.
If Park et.al.'s model is complemented by limitations on the spacing of ties and distribution of longitudinal steel, it can be as widely used as other sophisticated models while maintaining its simple approach. Alternatively, equation 3*5 can be written as,
K 1 + k (3.5a) f ' c
where, k is a factor to be determined empirically and accounts for the deficiencies of equation 3«5« However, introducing the value of k makes equation 3.5a more difficult to apply in practice. 112
3 »4- Analytical model of concrete confined by rectilinear steel ties,
3,4,1- Critique of existing models.
Two analytical models, describing the behaviour of concrete
confined by rectilinear ties, have been presented earlier in this
chapter. Both models highlighted many aspects concerning the
behaviour of confined concrete and were based on experimental
programmes which avoided most of the drawbacks of previous research
presented in table 3»1» The main approach of all analytical models of
concrete confined by rectilinear ties is to develop empirical
relations defining the compressive strength of confined concrete based
on experimental results. No attempt has been made to assess the
confining pressure at peak load and no limitations have been imposed
on the empirical equations developed. Nearly all researchers concluded
that increasing the volumetric ratio of the rectilinear ties would
increase either ductility or both strength and ductility of reinforced
concrete. However, none have established an upper bound for the
ability of rectilinear ties to confine concrete.
In the case of triaxially loaded concrete the strength increases
with increase in lateral pressure and in fact the failure envelope is
open-ended, i.e. has no upper limit, as suggested by Kotsovos and
Newman[3»18]. On the other hand, an upper limit is expected for the
strength of a concrete member confined by rectilinear ties. This is
because the confining forces vary along ties as well as between them.
The concrete confinement at tie level is controlled primarily by the yield strength of the steel ties. Meanwhile, the concrete confinement
between the tie levels is dependent on the interlock between concrete
particles. Hence, the upper bound of confinement is invariably
controlled by two modes of behaviour. Either low restraint with high 113 capacity as the case with widely spaced ties, or high but limited restraint as the case with closely spaced ties. Therefore, no matter how well a section is confined by rectilinear ties an upper limit is bound to exist. Figure 3*14- describes qualitatively the difference between active and passive confinements in terms of maximum confined compressive stress versus the confining stresses.
3.4-*2- Proposed analytical model.
The analytical model developed in this section is based on the work by Sheikh and Uzumeri. In an attempt to define the stress-strain curve of confined concrete, Sheikh and Uzumeri based their analysis on the idea that not all the concrete in the core, i.e. concrete bound by the lateral reinforcement, is confined. Some concrete zones within this core are not affected by the presence of the ties and remain unconfined, as illustrated in figure 3»10. The area within the core which is confined by the lateral ties is defined as the "effectively confined area".
The proposed analytical model considers the concrete section reinforced by rectilinear ties as equivalent to a circular section of a reduced area reinforced by a fictitious circular tube of the same properties as the rectilinear ties. The area of this modified circular section is the same as the effectively confined area; and, the volumetric ratio of the steel tube of the modified section is lower than that of the original section by a factor defined by the ratio of the effectively confined area to the total area of the core as defined by Sheikh and Uzumeri in figure 3«10.
It is expected that such a model would be most accurate for square sections with symmetric distribution of longitudinal steel bars and steel ties. Any deviation from such symmetry will make the model 114 less accurate, depending on the extent of deviation. Unfortunately, most experiments are performed on square sections with ties symmetric about centroidal axes. Hence, it is not possible to assess the inaccuracy of the model with deviation from symmetry without more experiments being performed. However, this should not affect the validity of the model since all sections in this experimental programme are square and symmetrical, which are typical of precast columns used in the precast industry.
The importance of the proposed analytical model is that it can correlate the lateral confining pressure exerted by the lateral steel to the volumetric ratio of lateral steel in the section under consideration, reducing considerably the complexity of the problem.
The behaviour of a concrete section reinforced with rectilinear ties becomes as easy to analyse as that of a spirally reinforced concrete section. Referring to figure 3-15» which describes the analytical model, and considering a height equal to the spacing of one set of ties then, 115
(a) Section used in this experimental programme.
B - 4 ------f
0 — ----%
a ____ e
p = volumetric ratio of ties _ volume of steel ties
percentage of effective confinement A — x 100% BZ
(b) Modified equivalent section.
Confined concrete core s s
s s
A 0 p rr modified confinement n — — p m 2 B percentage of effective confinement is 100%
Note: For all notations refer to text and figure 3.10
Figure 3.15 Details of analytical model. 116 from equilibrium,
2«'A.f = f . D. s ----■------(3.6) 5 s r giving,
2« A ,f s s
f r = ------(3.7)
D # s but,
volume of fictitious tube 4.A s
p m = ------= ------(3.8)
volume of confined concrete D.s substituting equation 3*8 in equation 3-7 gives,
f r = 0.5-p m -f s ------(3-9)
where;
A g = effectively confined concrete area (fig.3.10).
Ag = longitudinal sectional area of fictitious steel tube
along a height of tube equal to "s".
B = center to center distance of perimeter tie.
D = diameter of confined cylinder defined in fig.3*15* f = lateral confining pressure. f = stress in steel tube, s p = volumetric ratio of lateral steel (fig.3.10). p * modified volumetric ratio of lateral steel ties, m A e = — p
B2 s * spacing of ties. 117
Equation 3»9 evaluates the confining pressure due to rectilinear ties which can be calculated from the geometry of the section and the amount of lateral reinforcement. Concrete cover is assumed not to contribute to confinement of the core. This assumption is justified because designers are normally interested in the maximum strength provided by the confined concrete at which point the concrete cover is no longer effective having separated from the core as observed by
Sargin et.al.[3-24J and Scott et.al.[3*25]• Furthermore, at peak load the lateral steel has been observed by many researchers to be yielding. Therefore, equation 3«9 can be rewritten as,
f = 0.5.p .f u ------(3.10) r yh
where,
f yield stress of the lateral steel.
The new form of confining pressure expressed in equation 3«10 makes the proposed model easier to apply and so avoids lenghty computations. If this modification is not applied to equation 3«9> then iterative procedure must be used to satisfy the compatibility conditions in order to get a solution. 118
3.4.3- Two models of confinement.
The analytical model to assess the confining pressure due to rectilinear ties, presented above, is now combined with constitutive relations defining the behaviour of triaxially stressed concrete, and referred to as the K-N model. However, when combined with constitutive relations defining the behaviour of concrete confined by spiral steel ties, it will be referred to as the A-S model.
3.4«3.1- The K-N model.
Extensive work, at Imperial College, has been made by Kotsovos and Newman[3«l6,3«18] to describe the behaviour of concrete under multiaxial stress. Although the work is valid for active confinement, it is adopted here to make this study as comprehensive as possible. Structural compatibility between steel and concrete must be satisfied at all times in this model; therefore, equation 3«10 is not suitable and equation 3«9 should be used instead because the tie steel cannot be assumed to be yielding or else the failure load might end outside the failure envelope defined by Kotsovos and Newman and shown in figure 3•16. An iterative procedure satisfying equilibrium equations and compatibility conditions is proposed and detailed in figure 3 • 1V.
3.4»3»2- The A-S model.
The K-N model is based on active confinement which is different in nature than passive confinement. To approach a more realistic model, constitutive relations by Ahmad and Shah[3»2], which are based
on an extensive research programme in which concrete specimens were confined by tubes and spirals, are combined with the proposed analytical model. The tubes and spirals used by Ahmad and Shah are similar in nature to the fictitious tube assumed in the proposed 119
^ j /i ^ 'S' CarreJfeU & £ t £ , ^ a “ / £ {so'fcesjes)
(3.16,3.18) Figure 3.16 Kotsovos failure envelope 120
Steps of algorithm; 1- Assume any value of Fl (a good value is that of unconfined strength) 2- Assume F2= F3 — 0 3- From constitutive relations get El,E2,& E3 4- From compatibility, Es=rE2=. E3 5- The stress-strain curve shown above gives stress in tie steel •e.g. Fs, once strain in steel (Es) is known. 6- Using equation 3.9, calculate the value of confining stresses F2*- F3* 7- If F2*-F2 Go To step 3 with new values of F2 & F3 If F2 *-F2 = 0 Go To step 8 8- Are Fl,F2 & F3 on failure envelope of figure 3.16 If yes, solution is reached -----> END If within failure envelope, Go To step 1 with higher value of Fl If outside failure envelope, Go To step 1 with lower value of Fl and repeat procedure.
Note: For notation refer to figure 3.16
Figure 3.17 Algorithm used with *the K-N model. 121 analytical model. Therefore, results of this model should predict experimental results with better accuracy than the K-N model. Ahmad and Shah concluded, from experimental observations, that for the purpose of assessing the strength gain due to confinement by spirals or tubes, the lateral steel could be assumed to have yielded at the peak load. The equation they proposed to assess the strength gain was as follows,
f f1*04 K = — = 6.61 -j------( 3 . / / ) f0 V where,
= confined concrete strength, (ksi)
f = unconfined concrete cylinder strength, (ksi)
f = confining stress as defined by equation 3.10, (ksi)
K = strength gain.
The stress strain relationship of confined concrete can be described either by the curve proposed by Park et.al.[3«13] and illustrated in figure 3-5(f) 1 with the value of K as defined in equation 3*11; or, by using the CP110 curve with minor modifications to account for strength enhancement. The peak strength and corresponding strain are enhanced by the factor K. The interaction curve constitutes three zones. The first is a parabola as defined in CP110 up to 80% of the unconfined compressive strength. The second is a transitional parabola connecting the end of the first zone to the enhanced peak stress level. Finally, in the third zone, concrete is assumed to be fully plastic. The 122 modified CP110 stress-strain curve is illustrated in figure 3.5(h). For simplicity, no softening effect is considered in the third zone.
Equation 3-11, is easy to apply and so reduces a very complex problem to a simple one. When applied to spirally reinforced concrete section, no modification is needed. But, when applied to concrete section confined by rectilinear ties, the analytical model proposed here is used to assess the confining stress taking into consideration all the variables affecting the efficiency of ties in confining the concrete core; namely, tie spacing, distribution of longitudinal bars, diameter of tie steel, volumetric ratio of ties, and thickness of cover.
3.4••4- Application to specimens tested by Sheikh and Uzumeri.
To assess the adequacy of the K-N model and the A-S model, they were applied to specimens tested by Sheikh and Uzumeri. The analytical results were compared with the experimental ones reported in reference 3.29. Sheikh and Uzumeri measured strength enhancement by whichever of the following three methods was applicable
1- If concrete cover was intact at point of failure, then the load
carried by the core is,
Pcore = Ptotal-Psteel-Pcover
based on region 1 in figure 3*18. 2- If concrete cover separated from core and failed before the failure
load was attained, then, Pcore = Ptotal-Psteel
based on region 3 in figure 3.18.
3- If concrete cover partially failed when failure load was
attained,then the enhancement in concrete strength was assessed by
interpolation as shown in region 2 of figure 3.18. 123 where;
Pcore = load carried by confined core.
Pcover = load carried by cover; the strength of the cover is
considered the same as unconfined concrete.
Psteel = load carried by longitudinal steel.
Ptotal = total axial load carried by column.
Then, the strength of confined concrete is,
Pcore
fi = ------area of:----- core
and, strength gain is defined as,
unconfined strength
The strength gain was calculated for all twenty-four columns using both the K-N model and the A-S model. The results were compared with experimental values calculated as outlined above by Sheikh and Uzumeri
The computed values are summarized in table 3»3* For comparative purposes, these values are plotted in figures 3.19 and 3 -20. In most cases, the K-N model underestimated the strength gain, as illustrated in figure 3.19* This is clearly noticed when comparing specimens in which the only variable that changed was the yielding stress of the lateral reinforcement as in specimens 1 to 6 in table
3.4« While experimental results showed that strength gain increased with increase of yielding stress of ties, the K-N model gave no increase in strength. The lateral strains calculated from the K-N model were in all twenty-four specimens less than the yielding strain 8 1 . 3 e r u g i F contribution a> oceecnrbto uvs for curvescontributionConcrete calculating strengthcalculatinggain. 124 (3.29) Figure 3.19 Figure experimental tested by Sheikh &Uzumeri.Sheikh tested by The K-N model applied to specimens applied to model TheK-N 125 K- strength gain strength K- 126
K- strength gain
I i i » I i 1.0 1.1 1.2 1.3 1.4 1.5 1.6 J£ analytical
Figure 3.20 A-S model applied to specimens tested by Sheikh & Uzumeri. 127
Specimen K ^Park et al exp No. K1 K2
2A1 -1 1.22 1.26 1.29 1.18
2A1H-2 1.22 1.22 1.24 1.26 4C1 -3 1.24 1.29 1.29 1.21 4C1H-4 1.24 1.24 1.24 1.20 4C6 -5 1.41 1.57 1.54 1.64 4C6H-6 1.40 1.38 1.37 1.53 4A3 -7 1.26 1.32 1.39 1.28 4A4 -8 1.27 1.33 1.36 1.36 4A5 -9 1.29 1.33 1.40 1.23 4A6 -10 1.32 1.42 1.47 1.31 4C3 -11 1.26 1.30 1.34 1.37 4C4 -12 1.29 1.38 1.38 1.46 4A1 -13 1.22 1.29 1.31 1.30 2A5 -14 1.32 1.46 1.53 1.38 2A6 -15 1.36 1.48 1.52 1.47 2Cl -16 1.22 1.33 1.33 1.36 2C5 -17 1.41 1.41 1.45 1.36 2C6 -18 1.41 1.65 1.61 1.70 4B3 -19 1.29 1.36 1.42 1.43 4B4 -20 1.32 1.48 1.48 1.52 4B6 -21 1.39 1.54 1.55 1.54 4D3 -22 1.28 1.33 1.37 1.44 4D4 -23 1.38 1.47 1.46 1.54 4D6 -24 1.38 1.52 1.52 1.63
K = strength gain factor K^= strength gain factor from the K.-N model. K^= strength gain factor from the A-S model.
Table 3.3 Comparative values of strength gain factor for specimens tested by Sheikh & Uzumeri. 128
K-N Model A-S Model Specimen FO F2 Fl Fl Fl No. (ksi) FO FO FO FO
2A1 -1 5.44 0.006 1.04 0.026 1.07 2A1H-2 5.37 0.006 1.04 0.015 1.04 4Cl -3 5.28 0.008 1.05 0.035 1.09 4C1H-4 5.32 0.008 1.05 0.020 1.05 4C6 -5 5.07 0.032 1.20 0.116 1.33 4C6H-6 4.98 0.031 1.19 0.060 1.17 4A3 -7 5.93 0.010 1.07 0.049 1.13 4A4 -8 5.92 0.011 1.08 0.050 1.13 4A5 -9 5.88 0.015 1.10 0.051 1.13 4A6 -10 5.90 0.021 1.12 0.077 1.20 4C3 -11 5.90 o.olo 1.07 0.040 1.10 4C4 -12 5.92 0.015 1.10 0.066 1.17 4A1 -13 4.54 0.007 1.04 0.033 1.09 4A5 -14 4.57 0.021 1.12 0.080 1.24 2A6 -15 4.60 0.027 1.16 .0.088 1.26 2Cl -16 4.72 0.007 1.05 0.046 1.13 2C5 -17 4.77 0.032 1.20 0.068 1.20 2C6 -18 4.80 0.032 1.20 0.135 1.40 4B3 -19 4.85 0.015 1.10 0.055 1.16 4B4 -20 5.03 0.021 1.12 0.090 1.26 4B6 -21 5.15 0.029 1.18 0.107 1.30 4D3 -22 5.15 0.014 1.09 0.049 1.13 4D4 -23 5.20 0.028 1.17 • 0.088 1.25 4D6 -24 5.20 0.028 1.17 0.103 1.29
FO = unconfined concrete strength Fl = confined concrete strength F2 r confining stress
Table 3.4 Variation of triaxial stresses for specimens tested by Sheikh & Uzumeri. 129 of the ties, although, experimentally in almost all specimens yielding strains were measured. Such low values of lateral strains underestimated the stress in the ties and therefore underestimated the confining stress acting on the core. This phenomenon seemed to be the major reason for the discrepancy in results. Consequently, the K-N model is inadequate for evaluating the gain in strength of concrete members confined by rectilinear ties. From figure 3»19> the maximum strength gain obtained analytically, using this model, was 1.4-1 of the unconfined strength while the experimental value was as high as
1.70 of the unconfined strength. Such an error of nearly 20% makes this model justifiably unreliable especially since the trend of variation of the discrepancy has an exponential pattern as shown in figure 3•19•
Results of the A-S model predicted satisfactorily the experimental values of strength gain as shown in. figure 3»20. The strength gain of all the specimens was predicted with a maximum error of 10%. This model showed a proper indication of all the variables affecting the confinement of concrete and even for some values the prediction was better than that of Sheikh and Uzumeri.
For this study to be comprehensive, the model by Park et.al.
(refer to equation 3»5)> was also applied to the specimens tested by
Sheikh and Uzumeri. Results are shown in figure 3*21. The model predicted correctly the strength gain, with an error of 10%, for 80% of the specimens tested. As mentioned earlier, the only disadvantage of the model proposed by Park et.al. is that it does not take into consideration the spacing and size of lateral ties and longitudinal reinforcement. Table 3 »5 illustrates the discrepancy caused by keeping the volumetric tie steel ratio unchanged and varying the spacing of the ties. When the spacing is as high as 100mm, the model Figure 3.21 Figure experimental Park et al model applied to specimensal etapplied to Parkmodel tested by Sheikh &SheikhUzumeri tested by 130 K- strength gainstrength K- Variables Specimen No. £ Remarks ^experimental analytical
S = 3,3.75 inches 4 A3 -7 1.28 1.39 Although nearly same tie steel Psrl.66,1.62 4c3 -11 1.27 1.34 volumetric ratio,large spacing would lead to overestimation S =1,1.5,1.13 4C4 -12 1.46 1.38 of gain strength and inches 4B4 -20 1.52 1.48 vice-versa. P = 1.52,1.70 4D4 -23 1.54 1.46
S=3,4 inches 4A5 -9 1.23 1.40 P =2.39,2.37 2A5 -14 1.38 1.53 2C5 -17 1.36 1.45 Same as above.
S =rl. 50 inches 4C6 -5 1.64 1.54 131 P = 2.27,2.30 4C6H-6 1.53 1.37 2C6 -18 1.70 1.61 4D6 -24 1.63 1.52
S = spacing of ties. P — volumetric ratio of steel ties. K = strength gain factor.
Table 3.5 Effectiveness of Park et. al. model with respect to variation of tie spacing 132 overestimates the experimental results; while, when spacing is as low as 25mm, the model underestimates the experimental results. It is therefore logical that to achieve reliable results, this model needs to be supplemented by the following limitations for reliable results; the spacing of ties not to be smaller than 0.1 or larger than 0.4- of the core dimension, and the minimum number of longitudinal bars to be eight in the section with spacing not exceeding the specification in national codes. This conclusion is based on very little experimental results and more work is needed to justify it.
The comparative analysis discussed above showed that for levels of confinement used in the test programme by Sheikh and Uzumeri, the
A-S model and the model by Park et.al. assessed satisfactorily the strength gain of concrete members confined by rectilinear ties. Such levels of confinement cover a wide range, if not most, of the concrete structural elements normally used in the building industry. However, the models give a trend of continuous increase of concrete strength and thus do not predict the plateau as defined in figure 3•14-•
Therefore, for levels of confinement outside the range studied by
Sheikh and Uzumeri, the adequacy of these models is questionable and more experimental work is required if justified by practical needs. 133
3«5- Practical application of the confinement model.
Most national codes effectively ignore the effect of lateral reinforcement upon the behaviour of concrete, even though they contain clauses limiting the size and spacing of ties. Therefore, structural engineers are not provided with methods that enable them to exploit in their design procedures, the gain in strength of concrete elements confined by rectilinear ties, although it is well established that such a gain in strength exists. In the previous sections, review of many models was presented and a model to quantify the increase in concrete strength due to confinement by rectilinear ties was proposed.
This model can be utilised in detailing steel reinforcement especially in areas where stress concentration is expected, for example location of precast concrete connections. Such an approach in design, has been used on many construction sites. But overdesign due to lack of sufficient knowledge has always been the norm. The analytical model proposed here assists in quantifying the increase in concrete strength at any section along the structural member and hence will help in assessing the acting load that a concrete member can take without excessive damage or failure.
A typical application of the above mentioned concept has been used by Bobrowski in designing the H-frame[3.35]• Figure 3.22 shows the precast concrete column connection in the H-frame. In the connection zone the area of the section is reduced to accomodate the steel tube. Consequently, a smaller section has to carry the same load as the regular section of the column if the full capacity of the column is to be exploited. In that sense, the connection is a potential weak zone which might jeopardize the stability of the
concrete structure. The section in the connection zone is confined
such that the strength enhancement can counterbalance the effect of 134 the decrease in the sectional area of the column to avoid premature failure.
However, in the transition zone where the area narrows down from the regular section to the tube section, the change in stress distribution can cause bursting stresses. Therefore, extra steel ties are provided in this zone to offset the reduction in the size of the column section and resist the bursting stresses.
Figure 3*22 illustrates the change of spacing of the steel ties and the resulting change in the degree of confinement along the length of the jointed column. In the regular section of the column, the ties are spaced at 150mm.. In the transition zone and within 275mm of the joint, the ties are spaced at 75mmm; while within 50mm of the joint, heavy welded mat is added to provide an appreciable increase in confinement. The table in figure 3*22 shows that in areas of stress concentration along the length of the column, extra confinement has been provided accordingly.
Bobrowski used this approach qualitatively when detailing the H- frame connection and succeeded in getting all failures of the precast columns outside the connection region. The results of the H-frame test[3»35] will be analysed and presented in chapter 6.
The detailing of the grouted and dowelled connection in this test programme will be based on the confinement model proposed in this chapter and detailing technique used for the joint of the H-frame. Confinement Details
p f ^m r Ki K2 (ksi)
0.01002 0.0036 0.073 1.05 1.10
0.02004 0.01118 0.226 1.18 1.20 6. loTTo” 0.07815 1.581 2.33 2.07 0.1250 0.1250 2.53 3.17 not applicable 135 0.11284 0.11284 2.284 2.95 not applicable 0.10710 0.07815 1.581 2.33 2.07
0.o2004 0.01118 0.226 1.18 1.20
0.01002 0.0036 0.073 1.05 1.10
p -volumetric ratio of tie steel p -modified value for p m c -strength gain based on A-S model ^-strength gain based on Park's model (3.19) f^-confining stress (a) Longitudinal Section (b) Stress Distribution
Figure 3.22 Precast concrete column connection used in H-frame. 136
3.6- Summary.
A review of the various models describing the behaviour of concrete confined by rectilinear ties has been presented. A model has been proposed to predict the gain in strength of concrete members confined by rectilinear ties. The model is based on the concept of an effectively confined core combined with the relations defining the behaviour of cocrete confined by steel spirals or tubes. Such a model reduces the complexity of analysing confined concrete as it changes the problem of non-uniformly confined concrete to that of uniform confinement which is better understood and more easily defined.
The proposed model was used to predict strength enhancement of specimens tested by Sheikh and Uzumeri[3«29] and results were satisfactory. The model has the advantage of being applicable to any configuration of reinforcement layout within the section of a structural member, thereby reflecting all the factors affecting confinement.
Finally, the confinement model can be used for detailing connections in precast concrete structures where the drastic effect of stress concentration can be avoided by providing extra steel ties.
This concept was used by Bobrowski[3.35] in designing the H-frame.
Although the proposed model was tested by a small number of specimens, it does cover a whole range of concrete sections used in practice.
However, structural menubers outside the range of specimens tested by
Sheikh and Uzumeri require further investigation. 137
Chapter k - Description of the experiment.
4-.1- Introduction.
In chapter 2, various types of precast concrete column-to-column joints were presented, and the usefulness of investigating the behaviour of the dowelled and grouted column-to-column joint was discussed. Recommendations based on previous research reviewed in chapters 1-3 could be used to eliminate other parameters such as material properties and construction techniques. Hence, the principal objective of this research programme was to study the behaviour of the column-to-column joint with various combinations of loading patterns; i.e. different combinations of axial load, bending moment and shear to cover the whole range of the strength envelope of the joint. Nine precast specimens were allocated for this part of the research.
Another two precast specimens were reserved to study the sensitivity of the joint to errors of construction. Finally, three monolithic specimens were made to compare precast column behaviour to that of monolithic ones under the same boundary and laboratory conditions.
This was done to assist in relating analytical calculations to experimental values.
Also, the intent of this research programme was to compare results with those obtained from tests on the shoe joint at PCL
(introduced earlier in chapter 2). For the comparison to be effective, the dowelled and grouted columns must have the same length to width ratio of about 10 as the columns tested at PCL and the same normalized axial load-bending moment interaction diagram. The size of the section in this test depended on the jack capacity and the size of the steel moulds already available in the laboratory. The 200 ton jack together with steel moulds 200x200mm and 9 9 0 mm or 1980mm long, were considered 138 appropriate for this research. The precast columns were 990mm long.
The jointed precast columns and the monolithic ones were approximately
2000mm long. The column section was reinforced with four 16mm and four
10mm diameter mild steel bars to have approximately the same normalized strength envelope as the shoe joint column section. The diameter of the lateral ties and their spacing were based on the minimum requirements of CP110. In the precast columns only four 16mm diameter bars from the bottom column penetrated the top column in the form of dowels each accomodated in preformed 55mmm ducts. Also, the precast columns had double the amount of ties in the vicinity of the joint the quantity being based on the confinement model from chapter
3. Details of computations for detailing the joint region can be found in Appendix 1(a). The extra ties were intended to balance the decrease in axial load capacity due to discontinuity of the four 10mm diameter bars near the joint. However, the monolithic columns had ties spread evenly across the length of the column, except near the ends where,like the precast columns, the monolithic ones had double the amount of ties to prevent unwanted failure near the load platens.
Somerville[4*2] recommended that the joint thickness must not exceed 1/8 of the minimum dimension of the column section. Therefore, for the grouted and dowelled column specimens in the main test series, the thickness of the joint was 20-25mm. 139
4..2- Test rig.
A purpose built rig was used to study the behaviour of the dowelled and grouted column-to-column joint. The main criteria considered in the design of the rig were the following
(a) the safe provision of 200 tons axial load,
(b) the application of lateral loads,
(c) the accomadation of a test specimen 200x200x2000mm,
(d) the provision of appropriate axial stability and stiffness, and,
(e) the use, if possible, materials and equipment available in the
laboratory.
4-.2.1- Alternatives for the test rig.
Two alternative designs for the test rig were considered. One was to make use of the ground bolts in the floor of the laboratory which have capacity of 25 tons each and spacing of three feet in each direction. The idea was to use two concrete blocks stressed to the floor using the ground bolts as anchors so that the specimen and loading jack would react against the blocks as illustrated in figure
4-1. The other alternative was to use a self supporting system with the floor providing only dead load support. The two blocks would then need to be held together by tension bars. One of the blocks should be floating while the other supported on skates allowing sliding movement in the direction of the axial load. Figure 4*2 gives details of this arrangement.
Preliminary designs showed that massive end blocks (bearing area of approximately 3500mmx2500mm each) would be needed to provide
200 tons safe working load in shear at the interface with the test floor. Accordingly, the alternative shown in figure 4*1 was discarded at an early stage due to cost and lack of space. In pursuing the Fixed End Block
Figure 4.1 Test Apparatus Supported
By Ground Anchors 140 4-50mm diam Macalloy Bars
Figure 4.2 Self Supporting Arrangement
Of Test Apparatus 141
/ 142 second alternative, the largest available standard Macalloy bars (50mm diameter) were used as tie rods to provide axial stability and stiffness. Four such bars were used, each having a load capacity of
190 tons.
4-.2.2- Description of the test rig.
The test rig was made up of two rigs which were self supporting; as shown in figure 4-»3 and plate 4-.1. One rig was to provide axial compression whilst the other was to apply lateral loading.
4-.2.2.1- Axial load rig (plate 4-»2).
This part of the rig consisted of the following
(a) two concrete end blocks,
(b) 4--50mm diameter Macalloy bars with one metre threading each end,
(c) floating support for one end block, (d) moving support for the other end block,
(e) two 4-OOmm cubes as vertical supports for the specimen,
(f) one 200 ton jack, and
(g) two plates (1200x1120x10mm) to fit the inner face of each end
block with openings to accomodate the Macalloy bars.
4-.2.2.1.1- End blocks.
These blocks were designed to transfer the applied axial load through the jack and specimen to the Macalloy bars. The end blocks were designed in the same way as pile caps. Figure 4-*4- shows details of the end block.
The end blocks were cast in the vertical position. This made it possible for all bearing plates, on which the specimen and Macalloy bars reacted, to be accurately fixed to the side shutters of the
Plate 4.2 Details Of Axial Compression Rig *«y Number Description No. Pino** • Details
1 So m d im e te r 4 Nala a x ia l load tra n sfe r mechanism Macalloy bar 3 End block 3 Main a x ia l load c a rr ie r
TMt specimen 3 200CNa Long a 2ocw2oomneq*ats section, (fig.4.^)
4 □oncreta etude 3 Tmporary support for teat apecisan, (fig. I.Jf
5 Concrete etude 3 counterweights carrying lateral tiqr dead load, (fig. 4 ^ T
6 Spreader been 1 17ocma long a 20Ox20Cwtem thick box section,lateral load trananiaalon
7 200 tone jack l Applies axial load 8 3 In. bell seating 2 Axial load transmission, (fig. 4.*ft
9 R oller l Supports spreader bean, (fig.4.3? 145
10 Hinge l Supports spreader bean, (fig.4.jj)
U Re an 4 Soom long a lSOelSOxBaa thick box section, lateral load tran salssian
12 3 in . b a ll eeatlng 4 Lateral load transmission (flg.4.jt
U SO tons Jack 3 Applies lateral load
14 L iftin g hooka 4 Counterweight arrangaaent
IS 10 me ateel cable * Counterweight arrangmant
16 Pulleys 4 Counterweight arrangement
' i J B«M 1 Supports counterweight arrangeeant
18 Oolunn 2 Supports 17
19 P lates 4 Supports 17
20 Skates 1 Allows movement o f and block, ( f i g . 4.^)
21 Floating support 1 Carries weight of and block, (fig.4.^)
22 2S an dimeter 4 Main la te r a l load tra n sfe r each an lee Macalloy bar
23 Plataa 3 Locate Macalloy bars, (fig. 4.^1 Figure 4 . 4 Detail Of End Block 147 timber mould so achieving the best accuracy possible.
Dowels were left on the inner side of the end blocks to locate the loading plates, the ball seatings and the 200 tons jack. As problems of alignment were foreseen locating pins were used to ensure accuracy in the assembly stage. The ends of the specimens had locating pins embedded at the centroid of the section. The ball seating fitting the end of the specimen had 15nun deep holes to accomodate the locating pins. This arrangement made it possible to locate the specimen in place in less than 5 minutes.
During installation of the specimen, it was temporarily supported on the vertical supports. Once the ball seatings were in place and the end blocks had locked the specimen, the mechanical jacks on the vertical supports were lowered leaving the specimen suspended between the two ball seatings that were attached to the end blocks. Thus the specimen was located in the correct position.
4»2.2.1.2- Accessories.
The end blocks were supported by two frames made of welded steel angles. At one end the frame was supported on skates which run on a steel plate track. The frame at the other end was supported on steel box sections which were floating on the test floor, bringing it to the same height as the other block.
Load was applied to the specimen by a 200 ton Tangyes jack, which was attached to the floating end block. A 10000psi Walter+Baiag pump system supplied the jack with the required pressure. Ball seatings were attached to the jack at one end and to the end block at the other. The centre of the jack was coincident with the centre of the end block as the base plate of the jack slotted into dowels accurately located and embedded in the block. The ball seating was attached to 148 the centre of the ram by means of two locating threaded holes. While the ball seating at the other end was located by means of a locating stud that fitted into a threaded hole located accurately in the centre of the plate attached to the end block.
Two 400mm concrete cubes were cast to act as temporary supports for the specimens while they were fitted in the rig. These supports were plain concrete with an embedded plate 200x200x10mm that accomodated the mechanical jacks. Figure 4*5 illustrates details of the vertical supports and all attachments mentioned above.
The various parts of the rig were linked together by the Macalloy bars. These bars should carry equal loads to maintain equilibrium and stability of the rig during the test. To monitor forces in the bars, each was fitted with four electric strain gauges positioned at right angles to each other and equally spaced along the perimeter of the
Macalloy bar at midspan. Such positioning of strain gauges was wired in a load cell configuration measuring only axial deformation, i.e. cancelling any flexural or torsional effects. Details of the wiring scheme is illustrated in figure 4*6. The bars were "tuned'* by tightening or untightening of the nuts at the ends to get balanced tensile loads.
During the trial runs of the axial load rig, movement of each end block was closely monitored to ensure its safe performance.
4 . 2 . 2 . 2 - Lateral load rig (plate 4*3) •
It was decided not to support the lateral load rig on the laboratory floor. This was because an attachment to the floor would create relative movements between point of application of load on the specimen and point of reaction on the floor as the column would deform longitudinally due to the axial load imposed on it. Also, the Axial Load Ball Seating 149
Roller Detail Hinge Detail Counterweight
Figure 4.5 Miscellaneous Details. Electric Strain Gauge 150
(4.1) Figure 4.6 Strain Gauge Arrangement On Macalloy Bars. Plate 4.3 Details Of Lateral Load Rig 152
independent arrangement offered greater flexibility in applying various combinations of shear loads and bending moment.
For the tests envisaged two jacks of 15 ton capacity and 150mm stroke were required. In fact, 50 ton capacity jacks with the same stroke were employed as these were available in the laboratory.
Figure 4*3 shows details of this part of the test apparatus. The basic concept of design was that the jacks were supported on a spreader beam which applied downward load on two points of the specimen via the downward reaction of the two jacks. The upward movement of the ram was resisted by the saddle box section arrangement where the forces were transferred through the two 25mm diameter
Macalloy bars to the lower part of the beam column as upward loads.
The manner of the load application is shown in figure 4*7.
The most difficult part of this mechanism was to decide on how loads were transferred at the following locations (refer to figure
4.7);-
(a) the two ends of the main spreader beam where load was transferred
to the specimen, (locations 9 and 10),
(b) the points of the load transfer from jack to 25mm Macalloy bars,
(locations 12 top), and,
(c) the points of the load transfer from the 25mm Macalloy bars to the
specimen, (locations 12 bottom).
The main difficulty in designing the supports was to provide the freedom for the concrete specimen to deform whilst at the same time ensuring stability of the test assembly. This was done by providing rocker or pinned bearings at points 10 and 12 (top and bottom) and a roller at point 9* This roller allowed axial movement and so permitted contraction of the specimen. The length of the tie rods was such that a similar roller was not necessary at all points 12, - ball seatings 1 153
t 200Qno 1225 L 425 700 L 425 L225 •r *r i " ■■ f ’r L fL" Lateral Load J. A“ Axial Load l l : T, -* --- < ------
i ' Fiqmf ^ • 7 General Loading Arrangement Plate 4.4 Details Of Ball Seatings (Lateral Rig) Plate 4.5 Detail Of Roller.
Plate 4.6 Detail Of Hinge 156 at these points allowed the tie bars to rotate and move with the specimen under test. Plates 4«4> 4«5 and 4*6 illustrate the various details.
A steel frame was assembled from which the lateral load rig was suspended by counterweights to avoid loading the end blocks. Two specially cast concrete blocks 500x400x400mm were used as counterweights. Figure 4*3 and plate 4-1 illustrate the suspension arrangement.
Summary of the parts used for the lateral load rig;-
(a) main spreader square box section beam 200x200x8mm thick and
1700mm long,
(b) two 50 ton jacks with base plates to locate them on main
spreader beam,
(c) one roller and one hinge at the ends of the main spreader beam,
(d) four ball seatings 50mm diameter,
(e) four secondary spreader beams, each a square box section
150x150x8mm thick and 500mm long,
(f) four 25mm diameter Macalloy bars 2000mm long, threaded 750mm each
end ,
(g) two concrete counterweights 500x400x400mm,
(h) four steel pulleys 150mm diameter, for suspension, and,
(i) 10mm diameter steel cables to suspend counterweights and lateral
load rig.
4.2.3- Eccentricity of the test rig.
It was acknowledged that, regardless of the accuracy in the rig alignment achieved, some eccentricity was bound to exist. Instead of eliminating it altogether, it was decided to measure its effect at 157 midspan, i.e. the location of the joint in the column specimen.
It was recognized that there were two types of eccentricities.
One type resulted from rig imperfections and the other from the non uniformity of the concrete specimen itself. The first type was possible to measure while the second type was outside the scope of this research work.
To measure the eccentricity resulting from rig imperfection, the specimen had to be ’’homogeneous", so eliminating any eccentricity due to the specimen. Accordingly, a steel box section 200x200x8mm of the same length as the concrete column, was used in place of the concrete specimen in the calibrating tests. Twelve gauges in groups of four were located at each end and at midspan with one gauge in the centre of each face of the box section. Figure 4-.8 shows details of the calibrating specimen.
The box section was positioned and loaded under the same conditions as the concrete specimens. The test was made with only axial load not exceeding 800 kN.,i.e. the elastic range of the box section. The specimen was tested four times. Each time the box section was rotated 90 degrees to check whether the measured strains were due to local effects. The results are tabulated in table It was noticed that while strains varied at the ends, indicating local irregularities, the section at midspan was under concentric loading.
From table the variation of strains measured at midspan were within the recorded error of the voltmeter readings, namely +10us.,so that eccentricity in this region could be regarded as non existent.
It was not considered necessary to investigate the behaviour of the lateral load rig as the rig is self balancing and suspended with nothing to inhibit its ability to align itself as required by loading conditions.
159
Table 4.1 Loading Of Calibrating Specimen - Resulting Strains.
n. Gauge Location Strains Across Strains Across Strains AcrosS Load N. & End Section Midspan Other End Section Level \strains Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge Gauge (kN) 0 1 2 3 4 5 6 7 8 9 10 11 (us) (us) (us) (us) (us) (us) (us) (us) (us) (us) (us) (us)
Gauges 0 ,4 ,8 Top Su rface 0 O o 0 0 0 -10 0 0 10 10 0 0 104.3 -115 -87 -77 -19 -87 -87 -87 -87 -77 -77 -115 -10 208.7 -231 -193 -192 -48 -163 -163 -154 -163 -202 -173 -249 -57 313.0 -346 -298 -317 -135 -240 -240 -231 -260 -317 -298 -345 -144 417.3 -471 -394 -433 -212 -327 -317 -308 -336 -442 -384 -459 -249 521.6 -596 -490 -548 -289 -404 -394 -385 -423 -567 -471 -584 -335 625.9 -692 -596 -653 -375 -481 -471 -452 -500 -682 -567 -698 -412 834.6 -884 -807 -884 -548 -644 -644 -615 -663 -913 -769 -918 -612
GaUges 1 ,5 ,9 Top Su rface 104.3 -106 -91 -77 -19 -96 -86 -86 -86 -77 -96 -115 -10 208.7 -221 -191 -192 -38 -154 -163 -163 -163 -192 -192 -210 -57 417.3 -442 -385 -432 -202 -326 -317 -317 -326 -422 -394 -449 -248 625.9 -681 -580 -672 -365 -470 -480 -470 -499 -662 -576 -687 -420 834.6 -902 -790 -873 -538 -633 -633 -614 -662 -873 -777 -906 -611
Gauges 2,6,10 Top Surface. 104.3 -96 -96 -67 -19 -77 -86 -77 -86 -77 -86 -115 -20 208.7 -192 -192 -192 -38 -163 -154 -154 -173 -182 -182 -229 -67 313.0 -326 -298 -307 -125 -240 -240 -230 -250 -298 -288 -334 -153 417.3 -432 -394 -422 -202 -326 -317 -317 -336 -432 -384 -458 -248 521.6 -538 -480 -547 -269 -394 -403 -384 -422 -547 -470 -582 -334 625.9 -653 -576 -672 -355 -470 -470 -461 -509 -672 -566 -706 -420 730.3 -768 -672 -777 -442 -557 -557 -547 -586 -777 -662 -821 -515 834.6 -864 -777 -883 -537 -633 -633 -624 -672 -883 -768 -926 -620
Gauges 3 ,7 ,1 1 Top Surfac e. 104.3 -77 -77 -77 -2 0 -86 -77 -86 -77 -67 -77 -115 -10 208.7 -211 -192 -202 -58 -173 -154 -154 -163 -192 -182 -220 -67 417.3 -432 -384 -432 -211 -326 -317 -307 -346 -442 -384 -449 -248 625.9 -662 -566 -662 -384 -490 -470 -461 -509 -672 -576 -697 -420 834.6 -884 -807 -884 -548 -644 -644 -615 -663 -913 -769 -918 -613 160
4-.3- Test specimens.
4-.3.1- Formwork.
The columns used in this research were of three types, as shown in figure 4- • 9; —
(a) precast columns- top part, size 200x200x990mm,
(b) precast columns- bottom part, size 200x200x990mm, and,
(c) monolithic columns, size 200x200x1980mm.
The three types were cast in steel moulds with differently detailed timber end plates. Type (a) incorporated four 55mm diameter ducts at the joint each 575mm in length, with a 10mm diameter locating pin at the centre of the loading end. Type (b) had four 16mm diameter steel dowel bars protruding from the joint end, with a 10mm diameter locating pin at the centre of the loading end. Type (c) had two identical timber end plates that accomodated 10mm locating pins at the centre of the loading ends. All loading ends were shuttered with stiff and smooth timber end plates to provide even and smooth loading surfaces. Ducts in the top precast column were formed using rough surfaced PVC pipes, that were pulled out within two to three hours of casting. Plate 4-.8 shows details of this arrangement.
4-.3*2- Reinforcement.
For all the specimens 16mm and 10mm diameter mild steel bars were used as the main reinforcement. Mild steel was chosen in order to facilitate comparison with the earlier work at POL. The ties were 4-mm diameter (minimum requirement of CP110) and of high yield quality.
There was no specific reason for using such high tensile ties except that they were in abundance in the laboratory as leftovers from another project. Piat e 4.8 Details Of Top Precast Column Formwork Plate 4.9 Details Of Steel Reinforcement. 1980 mm 25 M3 LINKS + 50 M4 LINKS Centre to Centre as Shown 12.5■ j p g S O ^ g ^ l pO'jlOO . 1 0 0 , 1 0 0 , 1 0 0 1 0 0 100. 1 0 0 , loo loo , 1 0 0 1 0 0 1 0 0 , 100 75 50 50 50501 12.5 ¥------4------4------Jf------*------4------+------4------*----- 4------4------4-
MONOLITHIC COLUMN
990 mm 575 mm 7 f .... < l, 15 M3 LINKS + 30 M4 LINKS c.t.c. as Shown Bar Bending Schedule
12.5 . 505Q>5O1.65|,lOOaOO l 100L100 „ 100 ,50^0 ^50,50,-50 12.5 Rebar Diameter Shape T sf yf »r ?y~. -/f-— -■rf' f*' r f " jf— J- — * 21assifi (mm) \ catroi 1575 Ml 16 975 ’ M2 10 "T&o M3 4 160 160 PRECAST BOTTOM COLUMN M4 4 975 M5 16 975 M6 10 1975 M7 16 1975 M8 10
PRECAST TOP COLUMN
■7^
200
, SECTION A ( TOP COLUMN) SECTION B ( TYPICAL) N.T.S. N.T.S.
FIGURE 4 DETAILS OF SPECIMEN
I STRESS-STRAIN CURVE FOR STEEL REINFORCEMENT. dkjmtftr of bar It16 mm. 164 Table 4.2 Properties Of Reinforcement
Type Particulars Diameter Yield Stress (mm) (N/mm2)
Main Mild 16&10 300 Reinforcement Steel
Lateral Ties High Tensile 4 500 Reinforcement (plane) 166
The particulars of reinforcements are given in table 4»2 and details are shown in figure 4*9 and plate 4»9« Figure 4-10 shows the stress-strain curve of the steel used for the main reinforcement of the column. The various types of ties were bent accurately into required shapes (shown in figure 4»9) using purpose built jigs. The outside to outside dimension of the ties was 160mm allowing 24mm clear cover for the main steel reinforcement bars.
4.3«3- Concrete mix and casting of specimens.
The concrete mix adopted for this investigation was intended to give a cube strength of 40 N/mm2 at 28 days. Again this approximated to the concrete strengths employed in the tests at PCL.
The particular mix adopted has been used extensively in many projects at Imperial College and hence the various properties of the mix were well known. This allowed the use of a relatively small number of control specimens. The details of the mix proportions are shown in table 4*3* All the aggregates were Thames Valley river gravel.
Aggregates and sand were normally washed and dried by blowing air through, before storing in bins which allowed any moisture due to condensation to escape. Also, the sand supplied was separated into two categories, namely coarse (size 5mm to 600um) and fine (size less than
600um), before being stored. Ordinary Blue Circle Portland cement was stored in bulk in two four ton dry cement silos and blended by compressed air from the bottom. Unfortunately, when casting started the aggregate drier had broken down and the plant was in a lengthy period of repair. Only one specimen was cast using predried aggregate.
The coarse sand supply also ran short soon after the casting of the first specimen and wet sand had to be used, i.e. as delivered by supplier. The water content of the sand was checked and the 167 water/cement ratio adjusted accordingly. Also, the sand was checked for size grading. The fine and coarse sand ratios were combined as shown in table The grading and percentage weights of the new sand was equal to the original combination of the fine and coarse sands.
Hence no modification had to be introduced except that the independent ratios of coarse and fine sands had to be combined, and the amount of free water to be adjusted to keep the total amount of water unchanged.
At the time of casting the eighth specimen the supply of dry 10mm aggregates had also run short and wet 10mm aggregates had to be used.
So, a double adjustment of free water was made to maintain the same amount of total water. Tables 4-»5 and 4.6 show sieve analysis data for both the sand and the aggregate respectively. Water content of the sand was determined by means of a graduated glass tube, the "Gammon-
Morgan estimator for voids and moisture in sand", and was checked by oven drying 2000 grams of wet sand for 2J+ hours. The measured water content was about 5% in most cases. The void ratio of sand was found to be 32% as determined by the Gammon-Morgan technique. This way of determining the water content was very quick, (taking 5 minutes), and the error was only 0.5% when compared to the oven drying method. The water content of the aggregate was determined by oven drying 2000 grams for 2 A hours. This procedure was repeated every time concrete was cast. In general the water content of the aggregate ranged between
A.0-4.5%. Concrete was mixed in a 2 cu.ft. capacity Eirich counter rotating pan mixer. One batch was enough to fill the mould of a precast column unit plus three control cubes. The monolithic column required two batches to fill its mould. A one inch internal poker vibrator was used to vibrate both the bottom precast column and the monolithic column.
Filling was done in two stages; with the mould half filled and the 168 mould completely filled. The top column was vibrated using an Allam vibrating table with a continuously variable frequency control ranging from standstill to a maximum of 7000 cycles per minute and with an amplitude of 0.01 to 0.02 inches. To ensure proper vibration of the top column, the compaction was carried in three stages; with the mould filled to a third, to two thirds, and finally when the mould was completely filled. A special attachment was fitted to the top column mould to stop the PVC pipes moving while vibrating the specimen. (The poker could not be used for vibrating the top column because the PVG pipes congested the cross section. The other moulds could not be vibrated on the table because they exceeded its capacity.)
The tops of all specimens were levelled and finished with a trowel. Two to three hours after casting, the specimens were covered with wet hessian sacks and polythene sheets. After a maximum of three days, the columns were stripped from the moulds and again cured with wet hessian sacks and polythene sheets for a total of seven days.
Thereafter, the specimens were left to cure in the ambient atmosphere
of the laboratory until the day of testing. Plate 4*10 shows the precast columns before grouting.
For every top and bottom precast column three 102mm control cubes were cast, making six control cubes for every precast specimen. For
the monolithic specimens, only three control cubes were cast. Curing
of the control cubes was identical to that of the columns. Table 4*7
shows a summary of concrete cube strength for all the control cubes of
all specimens. 169
Table 4.3 Concrete Mix Details
Proportions Density By Weight (kg/m3)
Ordinary Portland Cement .1.00 940
10 mm Aggregate 2.80 610
Coarse Sand 1.82 285
Fine Sand 0.79 335
Total Water 0.69 225
Total= 2375 kg/m3
Table 4.4 Modification Of Concrete Mix
Proportions By Weight
Ordinary Portland Cement 1.00
aggregate & sand 170
Table 4.5 Sieve Analysis Of Sand
Sieve Size % Passing % Recommended . (microns) Table 5, BS882
10000 100 100
5000 loo 89-100
3180 91 -
2360 - 60-100
1180 71 30-100
600 35 15-100
300 22 5-100
150 5 0-15
Table 4.6 Sieve Analysis Of iQnm Aggregate
Sieve Size % Passing (microns)
12 500 100
lOOOO 87
5000 12
1180 1 171
Table 4.7 Summary Of Control Cubes Strength.
Specimen Concrete Grout No. Age Strength Age Strength (days) (N/mm2) (days) (N/mm2)
0 330 55.5 210 58.0
1 105 49.8 90 48.8
2 165 49.3 105 60.8
3 390 48.4 330 55.5
4 160 43.9 105 57.3
5 200 46.3 150 60.9
6 205 46.5 155 61.4
7 205 44.0 160 58.1
8 245 48.9 195 58.9
9 245 49.4 200 56.2
io 185 49.9 - -
11 310 43.5 - -
12 390 42.8 - -
13 -- - -
14 180 48.0 29 55.2
15 175 48.9 44 54.2 _ Plate 4.10 Top & Bottom Precast Columns Before Grouting With Section Showing Ducts For Dowels. 173
4- • 3 • 4-— Grouting.
4-.3.4*1- Introduction.
Initially it was planned to grout the column section 14 days after casting and to test the specimen when the concrete was 28 days old and the grout 14 days old. However, the difficulties of developing suitable test procedures had been underestimated and it was not convenient to keep to such a programme. Accordingly, the specimen preparation was continued whilst modifications were made to the test equipment. The control cubes could then be used to give the strength of the material. The main compromise was that, in most cases the grout would be stronger than the concrete rather than be of the same strength as originally planned.
Use of a proper grouting technique is critical in making the joint. If grouting is not effective then failure will almost certainly be attributable to the grouting method. The first step was to decide on the type of pump and the composition of the grout mix to be used.
4»3«4«2~ Pump.
An air pump for grouting was already available in the laboratory.
The pump is shown in figure 4-11 and plate 4*11• The only modification required to the existing pump was to change the size of the reservoir in order to accomodate all the grout needed for the top column. Plate 4.11 Grouting Process. Connection 175
Figure 4.11 Grout Pump Details. 176
4*3.4-.3- Trial mixes of grout.
The criteria for chosing the suitable grout mix were the following
(a) pumping ability,
(b) low bleeding or segregation as this would cause cavities that
would reduce effective area of the grouted section so causing
premature failure,
(c) dimensional stability by use of a suitable nonshrinking admixture,
(d) and, use of standard materials i.e. either cement or fine sand
and cement.
It was deemed important that the grout mix used should be representative of site practice. Consultation was made with precast manufacturers, site personnel and staff in the Concrete Section at
Imperial College (refer to the acknowledgement at the end of this chapter). A mix successfully used on site was a 1:1.75 cement/fine sand ratio and 0.5 water/cement ratio, together with Conbex admixture.
The mix was tried but the pump could not push it through the outlet since it was too stiff. Two other trials were made with lower sand content, namely 1.5 and 1.0 sand/cement ratios. Eventually, the 1:1 cement/fine sand ratio was chosen as it was suitable for the pump. The
14 days cube strength was 40N/mm2. Table 4*8 gives details of the strength of the various trial mixes. Table 4.8 Trial Mixes Of Grout
Mix No. Water Cement Sand Cement A d m i x t u r e D r y S t r e n g t h A g e R a t i o R a t i o Ddiisity (kg/m3) (N/mm2) (days)
1 0 . 5 0 C a b co 4 6 . 5 2 8 99grams/50 kg. c e m e n t
2 0 . 4 5 1 . 0 C o n b e x 2 1 6 0 3 0 . 1 7 227grams/50 kg. c e m e n t
3 0 . 5 1 . 5 C o n b e x 2 2 1 0 3 4 . 1 7 227grams/50 kg. c e m e n t
4 0 . 5 1 . 7 5 C o n b e x 2 2 2 0 3 9 . 8 7 454grams/50 kg. c e m e n t 178
4*3»4«4- Grouting technique.
A dummy minispecimen was used to test the grouting technique. The dummy was a 100mm square section and 700mm long plain concrete prism.
A duct 55mm in diameter and 550mm minimum length was preformed in the dummy specimen using PVC pipes. The dummy specimen was identical to one quarter of the grouted part of the top precast column. The bottom
column was simulated by a 100mm cube with a dowel steel bar 16mm in diameter protruding from it. To maintain verticality of the dowel it was welded to a plate 100mm square that fitted tightly inside the
100mm cube mould. The top element was placed on spacers (2 nuts) positioned on the bottom element. The height of the spacers was 20 to
25mm and the space created by the spacers was sealed by steel plates
clamped to the specimen. The clamp served to both hold the sealing plates in place, and to align the top and bottom elements. Grout was mixed in a small food mixer since only 12 kilograms were needed to grout the dummy specimen. One of the plates had a nozzle attached to
it through which the grout was pumped to make the joint. Pumping was
continued until the grout showed at the outlet at the top of the duct.
The whole operation took less than one minute from beginning of pumping. Plate shows details of the pump, sealing plates and
clamps.
Several trials were made using the above technique. Two days after grouting the dummy specimen, it was sliced along the grout
column to check the adequacy of the grout mix and the method of
grouting. Plate 4*12 shows some of these results. For the water cement mix, bleeding was a serious problem. However, the addition of sand to
the mix reduced the bleeding and it was demonstrated that an extension of the ouletb using perspex tube would solve completely the bleeding problem. The perspex tube acted as an external reservoir and since it 179 was the highest point in the grout column, it was the site for most of
the initial bleeding. Ideally, more sand should have reduced the bleeding to a minimum if not eliminated it altogether. However, the pumping capacity set a limit on the stiffness of the mix. A major problem in the grouting operation was that excessive pressure could
cause uplift of the top column. This was of practical importance. It was therefore decided that the applied pressure should not exceed 10
psi.. Also, the pressure should be maintained for at least one minute after the grout appeared at the outlet so as to avoid backflow due to
self weight.
Once satisfactory results had been produced in the trials,
grouting proceeded to the real specimens. Specimens were wetted and positioned vertically on spacers (4 nuts) of 20 to 25mm height. (Note
that for specimens with larger joint thickness, namely 50 and 75mm,
concrete spacers were specially made.) The special lifting studs
embedded in both top and bottom columns and shown in figure 4*12, were used to position both columns in place for grouting. Four plates, one with a nozzle, were used to seal the joint and align the two precast
columns when firmly clamped. The grout was mixed in the Eirich counter
rotating pan for five minutes and then sieved in a 5mm opening sieve
pan. Sieved grout was poured into the container of the pump and pumped
to form the joint. The fitted perspex tubes at the oulet were removed
after one hour. The four outlets were sealed with plasticine. The next
day the plasticine was removed and any cavity caused by settlement of
the grout column was topped by a dry mix. Such settlement never
exceeded 25mm in depth. Three 102mm grout control cubes were cast for
every specimen. These cubes were covered with wet hessian and
polythene sheets for one or two days. They were then removed from the
moulds and wrapped in wet hessian and polythene sheets for seven days 180 and left to cure in the ambient condition of the laboratory. It was hoped that, as far as possible, this curing would simulate the conditions inside the ducts.
4-.3»5- Stacking of the grouted specimens.
Once the grout, and joint in turn, had sufficient strength, the specimen was lifted from the vertical position to the horizontal one,
- the position of testing. A special timber cradle was made of two timber frames which clamped the specimen in between by means of 12mm diameter studs thereby distributing the stresses along the whole length of the column during tilting. Figure 1+A2 shows the various details involved. When in the horizontal position, the specimen could be moved as required since the joint could safely sustain the dead load of the column. lQnm dleun Studs*
See Detail A
loom diam
Studs*
Levelling Plate Specimen In Position For Grouting
* Studs embedded in specimens are usedf (a) to lift precast specimens frcm Detail B moulds, (b) and, to hold vertically while positioning for grouting. 00
Figure 4.12 Grouting Details. Trial A Mix: Cement Paste + Non-Shrinking Admixture Water/Cement = 0.50
Trial B Mix: Sand/Cement =1.0 + Non-Shrinking Admixture Water/Cement = 0.45
Trial C Mix: Same As Trial B Misc: Extended Tube Provided At Outlet And Pressure Maintained For At Least One Minute After Grout Appears At Outlet.
Plate 4.12 Trial Grouting Results 183
4.A- Instrumentation.
4..4-1- Measurements required.
To study the behaviour of the specimens the following measurements were required
(a) Measurement of applied loads.
(b) Measurement of lateral displacements relative to the centre line
of the specimen as this constitutes a source of bending moment and
shear along the length of the specimen.
(c) Measurement of axial displacements of the central span, which was
either 600mm or 4-50mm, to assess axial and flexural deformations.
(d) Measurement of strains on the dowels to check their state of
stress.
4-.4»2- Instruments.
The following instruments were used to make the above measurements;-
(a) The applied loads were measured by pressure transducers connected
to each pump system used.
(b) The displacements in the direction of the lateral load were
measured by three linear variable differential transducers (LVDT)
located at quarter, mid, and three quarters span as shown in
figure 4--13* The out of plane displacement, i.e. perpendicular to
axial and lateral loads, was measured by a dial gauge located at
mid-span.
(c) The axial displacement in the central span was measured by the
following two techniques
(i) A special extensometer device, which was made in the workshop,
on which four LVDT's were positioned two on the top and two on 184
the bottom as illustrated in plate 4-*7. Note that the springs
were incorporated primarily to hold the extensometer parts
together and to reduce the confining effect on the concrete
that could be caused by studs.
(ii)Electric resistance strain gauges (ERSG). The length of these
gauges was 10mm when fixed on a grout surface and 30mm when
fixed on a concrete surface. One layer of protective coating
was applied. Table 4*9 and figures 4*13 and 4*13A provide a
summary of the various configurations used in this research.
(d) The strains on the dowels were measured by 10mm electric
resistance strain gauges located 50mm from the end of the precast
columns as illustrated in figure The gauges were fixed in
pairs to each dowel. Three layers of protective coating were
applied.
Note that all electric resistance strain gauges in this research were wired in a quarter bridge circuit inside the Wheatstone Bridge unless otherwise mentioned[4*1]•
Measurement was achieved by connecting all the measuring devices, i.e. pressure transducers, LVDT's and ERSG’s, to a Hewlett-Packard data acquisition/control system (HP-3054A). This comprised of an automatic data acquisition and control unit (HP-3497A) and digital voltmeter (HP-3465A) interfaced with a computer (HP-85). The measuring devices were connected to the various appropriate channels in the
HP-3497A. The voltmeter can take readings when these channels are closed. The computer was programmed to initiate the voltmeter to take readings, by closing the required channels, whenever a set of readings was desired. 185 Table 4.9 Key to instrumentation of test specimens.
S p e c i m e n Acting Loads Surface T y p e •Value A x i a l No. G a u g e o f o f L o a d T y p e C o l u m n "a" (mm) (kN)
0 . A x i a l - P r e c a s t -
1 A x i a l - P r e c a s t -
2 A x i a l - P r e c a s t -
3 Axi al+Bending P3 P r e c a s t 1 1 2 . 5 2 5 0
4 Axial+Bending - P r e c a s t - 1 0 7 0
5 Axial+Bending PI P r e c a s t 0 2 5 0
6 Axi al+B ending P i P r e c a s t 0 5 0 0
7 Axial+Bending P i P r e c a s t 0 7 5 0
8 Axi al+Bending P 2 P r e c a s t 1 5 0 7 5 0 + S h e a r
9 Axi al+Bending P 2 P r e c a s t 1 5 0 2 5 0 + S h e a r
l o Axi al+Bending Ml M o n o - 1 0 7 0 l i t h i c
11 Axial+Bending M2 Mono 1 1 2 . 5 7 5 0 l i t h i c
12 Axial+Bending M2 M o n o 112.5 250 l i t h i c
13 - - P r e c a s t - -
14 Axi al+Bending P2 Precast 112.5 7 5 0
1 5 Axial+Bending P2 Precast 112.5 7 5 0
•
N o t e s ;
1- This table must be read in conjunction with figs. 4.13 and 4.13A 2- All precast specimens have joint thickness of max. 25mm except specimens 14 & 15 which have joint thicknesses of 75mm & 5Qnm respectively.
Plate 4.7 Detail Of Extensometer 189
4-«4«3- Calibration.
The ERSG’s did not require calibrating since the gauge factor was
readily obtained from the manufacturer. Resistance of all the gauges
was checked to be within an error of +0.5 ohm after installation.
The 200 ton Tangyes jack together with the pressure transducer of
the Walter+Baiag pump system were calibrated against an already
commissioned Amsler jack of 300 ton capacity. The results of the
calibration and accuracy are presented in Appendix 1(b).
The two 50 ton Enerpac jacks together with the pressure
transducer connected to the Amsler testing machine were calibrated
inside an already commissioned Amsler jack of 60 ton capacity.
Calibration was made to 15 tons which was the anticipated maximum load
to be applied. The results of the calibration and accuracy are
presented in Appendix 1(c).
The LVDT’s were calibrated using a comparator. Once the
transducers were mounted on the jig, a micrometer head was used to
control the travel starting from a zero output signal and moving in
both the positive and the negative directions. The stroke of the
micrometer was 25mm with an accuracy of +0.0005mm. All transducers
used had +25mm range. So, calibration was made in the following
ranges;-
(a) zero to +25mm.
(b) -25mm to zero.
(c) -12.5mm to +12.5mm.
The displacement versus voltage curves were represented as linear
relationships for each of the three ranges. Then the average of the
three curves was considered as the representative curve for the
specific transducer. This enabled the transducer to be used over its
whole range although whenever possible it was used in the ±10mm range. 190
4*5- Test procedure.
Once a specimen was in place and end blocks clamped in position, the mechanical jacks on the temporary supports were lowered leaving the specimen suspended between the blocks. Since the 200 ton jack was about 500mm long, the weight of the specimen tended to tilt the floating end block inward. A plumb was fitted to the edge of the end block to monitor the amount of tilt. The 200 ton jack was propped until the end block was in a vertical position. The end blocks were aligned using the centre line markings on the top surface. Up to this stage the Macalloy bars should not have been tight thereby allowing free movement of the end blocks so that they could take their aligned positions. The last step was to hand tighten all Macalloy bars.
Axial load was then applied to provide friction that could take the dead load of the specimen, allowing the vertical supports to be disengaged by lowering the mechanical jacks. During the experiment, the forces in the Macalloy bars needed to be in equilibrium. Such equilibrium of the tension bars was achieved by "tuning" them using the nuts.
Whenever lateral loads needed to be applied, the saddle suspension made up of items 11, 12 and 22 defined in figure 4*3 were positioned on the ball seatings on top of the 50 ton jacks. The roller at one end of the main spreader beam was positioned on the top surface of the specimen in assigned location and at the other end the hinge was positioned. The ram stroke of the 50 ton jacks engaged the spreader beam with hinge and roller. Pressure equivalent to 2.5 kN was enough to get the lateral load rig rigidly attached to the specimen.
After all the measuring devices had been connected to the data and acquisition/control system (HP-3497A), the axial load was applied in increments of 100kN. Each increment of axial load was applied in 191
approximately ten seconds. This rate of loading gave the same strain rate as in a standard cube testing machine. Although this was possible for axial loads up to 1000 kN, the control was impossible near failure load of specimens subjected to pure compression. For specimens
subjected to axial load and bending (with or without shear), the axial load was applied first. Then, the lateral load was increased in
increments of 10 kN up to peak load while maintaining axial load. At
every increment of either axial or lateral load all connected channels
of the data logger were scanned and the results stored. Once the lateral load capacity of the specimen had started decreasing, readings were taken at the maximum rate allowed by the data logger
(approximately one reading every ten seconds). The test was stopped when it was no longer possible to maintain the axial load.
Acknowledgement.
The following are gratefully acknowledged for their advice concerning
the production of* the test specimens j-
(a) Mr. B.K.Bardhan-Roy Jan Bobrowski & Partners.
(b) Dr. J. Bobrowski Jan Bobrowski & Partners.
(c) Mr. R. Loveday Imperial College.
(d) Dr. H.P.Taylor DowMac Concrete. 192
Chapter 5- Results of the main test series.
5.1- Introduction.
The object of the work reported in this chapter is to study the behaviour of the grouted joint under various combinations of axial load and bending moment covering the whole range of the interaction diagram of the jointed columns. The workplan for this research was left flexible. The intention was to study the results of each test and, depending on the conclusions, to determine the next step.
Nevertheless, the testing programme followed three main stages;
1- specimens subjected to pure axial load,
2- specimens subjected to axial load and flexure, and,
3- specimens subjected to axial load, flexure and shear.
The specimens were detailed with extra ties, as explained in
Appendix 1(a), in the joint zone to prevent premature failure of the jointed column. The number of extra ties was chosen to balance the reduction in strength caused by the discontinuity of some of the main steel reinforcement at the joint (the four 10 mm diameter bars were stopped near the joint interface). When the specimen was subjected to pure axial load, the failure was expected to occur at any section along the length of the column once the maximum predicted load capacity had been reached. Accordingly, axial loading provided a check on and also fixed one point on the interaction diagram. However, if the failure had always occurred away from the joint no information on the joint behaviour itself could have been obtained. As a result, in all other tests, the loading configuration was such that maximum stresses occurred at the joint thereby causing its failure. 193
Unlike specimens subjected to pure axial load, the ones also subjected to flexure depended very much on the location of the dowels in the joint section, as this determined the lever arm. The dowels defined the lower bound flexural capacity of the section. The upper bound was determined by the location of the four 16mm diameter reinforcement bars in the regular section of the column. It was expected that the interaction diagram for the specimens tested in this research programme would be controlled by these bounds.
The effect of shear is dependent on the applied axial load level, and on the shear span to effective depth ratio. The axial load mobilises a proportional amount of friction. Therefore, any shear is primarily resisted by this friction which inhibits any slip in the plane of the joint. Consequently, it was expected that the effect of shear, if any, would be more pronounced at low axial load levels. The shear span to effective depth ratio of about 4-, which is considered to be representative of typical structural conditions, was kept constant for all tests. To study the effect of shear, two specimens were loaded with an increasing lateral load while subjected to;
(a) a high axial load (750 kN), and,
(b) a low axial load (250 kN).
Experimental results are presented in the sequence in which work was done in the laboratory. This follows the development of ideas during the experimental programme, which are most clearly reflected in the revisions to the number and arrangement of surface gauges (refer to figures 4-»13 & 4-«13A).
As noted earlier, the specimens were detailed so that the ascending part of the loading curve would be similar to that of a monolithic column. However, it was not clear initially how the jointed 194
columns would behave once the peak load had been attained. Therefore,
observations concerning the behaviour of the specimen played a fundamental role in defining the mechanism of failure of the
specimens. The following measurements were made so that the behaviour
of the specimens at all stages of loading could be understood as far
as possible;-
1- Axial deformation; across the joint and along each side of the
joint, i.e. on the precast columns.
2- Lateral deformation; in both directions orthogonal to the axial
load.
3- Strains from the embedded gauges fixed to the dowels.
4- Indirect measurement of the local angular discontinuity at the
joint.
Methods of measurement and the interpretation of the results are
presented in the remainder of this chapter. The results which were
summarized in tabular form are located in Appendix 2.
Figure 5.0 provides a summary of the measured strength envelope of
the section at the joint for the various specimens tested in the main
test series. The bending moment reported is due to external loads
acting at the jointed column and lateral deflection at the joint, i.e.
the P-delta effect.
In all the tests presented in this report, a certain predetermined
level of axial load was maintained when the flexural stresses were
applied. The test was stopped when it was no longer possible to
maintain the load Axial Load /K (kN) Note: For specimens 8 and 9, shear is applied at the 1600 joint in conjunction with bending moment. 1(50) 2(49)
1200 Specimen No.(typ) © 2 4(44) Cube Strength - N/mm (typ) 800
© 195 7(44) 8(49)
6(47) © 400 © 0(55) © 3,5 & 9 (45-50)
-- 1-- 20000 40000 60000 Bending Moment (kN-mm)
Figure 5.0 Axial Load - Bending Moment Interaction Diagram For Precast Specimens In Main Test Series. 196
5.2- General observations.
For specimens tested under axial load, failure was sudden although internal cracking prior to failure could be heard. Invariably, all specimens failed away from the joint zone, as shown in plate 5.1. This proved the adequacy of the detailing in this zone but gave no indication of the strength of the joint itself. On the other hand, specimens subjected to a combination of axial load and flexure (with and without shear) , mostly failed in the vicinity of the joint. In considering behaviour, it is convenient to consider,
(a) behaviour up to peak load, and,
(b) post peak load behaviour.
The behaviour up to peak load was similar to that of a monolithic beam column (refer to figure 5.1) with the difference that cracks, if any, were mainly concentrated at the joint interface. This was
expected because the joint section was less strong than the normal
section as there is less reinforcement, and the interface between the
joint and the precast column represented a plane of weakness. No
effort was made to improve the strength at the interface, for example
by introducing keys, as this would not have affected the overall
behaviour of the beam column. If such an improvement had been
introduced, the crack would have shifted to the inside of the joint
rather than the interface. In this region of loading, the crack
opening at the joint (which was observed to occur at both interfaces) was a secondary effect that did not affect the overall behaviour of
the jointed column since the crack width was small. Visible cracking
at the joint depended on the applied axial load level. This could be
divided into two zones. One, when the axial load was larger than the
balanced condition; and two, when the axial load was controlled by
tension and the yield of the steel in tension. In the former case, 197 failure tended to be brittle with no visible distress until the peak load was attained. When failure was controlled by tension, the failure tended to be more ductile and cracks at both interfaces could be seen well before the peak load was attained. Figure 5-2 illustrates the difference in ductility between low and high axial load levels.
The post peak load behaviour of monolithic and precast columns was distinctively different. The secondary effect of joint opening, and the angular change across the joint thickness became more significant and dominated the behaviour of the specimen. The deformation of the specimen could be idealised as rigid body rotation of the two column components with a hinge forming at the joint. This required that the major part of the precast columns would be unloading while deformation became totally concentrated in the joint zone. Once the rotation became excessive the concrete at the extremities was subjected to high compressive stresses causing crushing. Total failure occurred when the compressive zone became ineffective. The failure mechanism observed is illustrated in figure 5-3- Plates 5.2-5.k show the shape of the specimens after failure. 198 Legend: Axial load load Axial kN. 750 load Axial kN. 250 P P --- M M = load. peak at Moment 0 = load. peak at Rotation © specimens. Monolithic £ specimens. Precast ------— — — > p e/e ------Normalized curves showing similar trends for monolithic & precast specimens. precast & monolithic for trends similar showing curves Normalized
a o 5.1 Figure 199
Figure 5.2 Variation of ductility with axial load level 200
-L
Smooth characteristic deflected shape.
Before Peak Load
Post Peak Load
Figure 5.3 Observed failure mechanism. Specimen No. 0
Specimen No. 1
Specimen No. 2
Note: Specimen No. 0 was first loaded axially to failure. It was repaired , notice the patch. Then loaded laterally , with axial load maintained at 300 kN , to failure.
Plate 5.1 Failure Mode Of Precast Columns Axial Loading. Specimen No. 3 Axial Load = 250 kN.
Specimen No. 4 Axial Load = 1070 kN.
Specimen No. 5 Axial Load = 250 kN.
Plate 5.2 Failure Mode Of Precast Columns Axial & Lateral Loading (Shear=0). Specimen No. 6 Axial Load = 500 kN.
Specimen No. 7 Axial Load = 750 kN.
Plate 5.3 Failure Mode Of Precast Columns Axial & Lateral Loading (Shear=0). Specimen No. 8 Axial Load = 750 kN.
Specimen No. 9 Axial Load =250 kN.
Plate 5.4 Failure Mode Of Precast Columns Axial & Lateral Loading (Shear^O). 205
5.3- Measurement of angular change across the thickness of the joint.
5.3*1- General.
From the observations presented in section 5.2, the angular change across the joint thickness was an important parameter as it characterized the behaviour of the joint itself. The significance of this angular change, and the accompanying localized angular discontinuity occurring during the post peak loading, was not fully recognized at first. As a result, the instrumentation used with the pilot specimen, i.e. specimen number 4» which had the central span monitored across the joint, was not sufficient to measure the constituent components of the total rotation. The measured rotation of the central span was due to the flexural rotation, both within the joint thickness and from the parts of the precast elements in this zone, together with the angular discontinuity at one or both interfaces of the joint thickness. Therefore, the angular change across the thickness of the joint involved a component caused by the flexural and axial deformation and another caused by a local angular discontinuity.
The first trial consisted of using surface gauges as illustrated in figure 4»13A type P1. The gauges were 10mm long and were fixed on the grout surface. The results showed that the angular change across the joint thickness was not significant up to peak load but no definite trends were obtained for the post peak load behaviour as all gauges became ineffective due to excessive damage at the joint.
Although this arrangement confirmed the observations presented earlier, it did not provide a technique to calculate the local angular discontinuity at the joint.
Direct measurement of the angular change across the joint 206 thickness was impractical because the concrete, in the joint vicinity, was excessively damaged once rotation of the joint becomes significant. Therefore, the incidence of concrete spalling, in areas where gauges measuring rotations were installed, was high so rendering these gauges ineffective. Accordingly, indirect measurements had to be used. The rotation obtained from the deformation of the extensometer, shown in plate 4»7, gave the total rotation of the central span monitored by the extensometer. The rotation of the central span due to beam column action could be obtained from the surface gauges.
Subtracting the two types of rotations gave the angular discontinuity at the joint.
It was decided to locate the surface gauges midway between the edge of the central span and the centre of the joint thickness, to avoid the damage experienced at the joint. This led to the P2 arrangement shown in figure 4»13A. This configuration gave clearer indications of behaviour. It was confirmed that, while the deformation became concentrated at the joint, after the peak load was attained, the other parts of the jointed column, i.e. the precast elements, unloaded as shown in figures 5*4 and 5-5. Also, the centre of rotation at the joint section shifted towards the mid-depth of the section as the rotation increased. This effect was confirmed by strain gauges positioned at mid-depth of the section which registered an increase in compressive strains when the beam column was unloading (refer to figure 5-6). The effect was not as prominent for specimen 9 (refer to figure 5»7), because the crack at the joint interface was deeper than the mid-depth of the section due to lower axial load. The shift in the position of the centre of rotation indicated crushing of the compressive zone and a reduction of its depth. However, some surface gauges were still affected by the concentration of stresses in their 207
Figure 5.4 Average surface gauge strain (top & bottom) - Specimen No. 8. 208
Figure 5.5 Average surface gauge strain (top & bottom) - Specimen No. 9. 209
Figure 5.6 Average surface gauge strain (centre) Specimen No. 8. 210
Figure 5.7 Average surface gauge strain (centre) - Specimen No. 9. 211 vicinity and some of the gauges were lost when crushing of the compressive zone occurred.
Finally, the type P3 arrangement of surface gauges, shown in figure 4-.13A, was adopted to confirm the exact path of the load-unload behaviour of the jointed elements. Strain gauges were positioned at quarter-span where no damage was expected. Although some gauges were still lost due to cracks, clear trends were obtained as illustrated in figure 5«8. This suggested that it was acceptable to assume that the load-unload interaction curves were identical within the column segments. This followed from the fact that most cracks were concentrated at the joint interfaces. Consequently, it was assumed that the jointed elements followed an elastic path of deformation, whilst all the inelastic deformation was concentrated in the region of the joint. This simplification which was justified experimentally, reduced the complexity of the measurement of the angular change across the joint thickness. The total angular change of the central span from readings of the extensometer was obtained for all levels of loading and unloading. Also, the angular change of the central span due to beam column action was obtained from the surface electric resistance
strain gauges for the first loading which was applicable to the post peak load. The local angular discontinuity at the joint was calculated by deducting the angular change due to beam column action from the total angular change of the central span obtained from the
extensometer 212
Figure 5.8 Elastic behaviour of precast elements - Specimen No. 3. 213
5*3*2- Exact Method.
Taking into consideration the discussion of section 5*3*1 the following assumptions were made when calculating the angular discontinuity at the joint;-
1- Up to peak load, the flexural deformation of the infill material in the joint was assumed to be the same as that of the precast elements in the vicinity of the joint. This assumption was valid as long as the joint thickness was small compared to the gauge length of the central span and the crack propagation was not excessive along the joint interface.
2- For the post peak load, the angular change due to flexural deformation of the infill material in the joint was small compared to that caused by the angular discontinuity at the joint interface, and can therefore be neglected. This assumption is justified as it was observed that both joint interfaces cracked although the angular discontinuity was normally concentrated at one interface only.
Consequently, part of the infill material in the joint unloaded depending on the depth of the crack.
The arrangement of the surface gauges is shown in figure 5.9-
Measurement from these gauges was used to give the curvatures for the elements marked sides A and B. The average of these two results was assumed to be equal to the rotation within the joint itself.
Therefore, the total angular change across the thickness of the joint is, 214
450 or 600 mm r✓ s Gauge length of central span= G
G/4 G/4 G/4 G/4 , L______L______1______t A a — * FT ’’b
75 Surface Gauge . 7 — 200 mm. (typ) 75 \ ^ 2 5 V ----,<■ Side A , Side B <4------joint
Arrangement of surface gauges outside the joint region.
G + At
Note; For the case of shear, load is applied on side A only.
Measurements using extensometer mounted across the central span- see plate 4.7.
Figure 5.9 Measurement Of Angular Change - Exact Method. 215
e. = e - (a.(f>A+ b.^lg ) ------(5.1) where; change 0 is angular''over the gauge length G.
= ( A t + A b )/276
<&A is curvature from side A
is curvature from side B
Therefore, the angular discontinuity at the joint due to crack opening and crushing is,
6jd = 6j -((0A + ^B)/2) ------(5-2)
Note that during the post peak loading and after cracking, the deformation of the material within the joint thickness is assumed to be negligible so that,
Having calculated the angular discontinuity the crack width at the joint can be found in the following manner,
At level of surface gauge (top side):
Change in gauge length is ^ T - 63 0
Crack opening width is ^ c g ~
(^T - 63 0) - (Eaverage.G) when below peak load
or (^T - 63 9) - (Eaverage.(a+b)) when post peak load
where,
Eaverage is the average strain of all surface gauges
at a particular level. 216
At concrete surface (elongation side):
Change in gauge length is - 38 ©
Crack opening width is A c =
A c g + 25 ejd ------(5.3)
where,
0 ^ is angular discontinuity, defined in earlier
in equation 5»2.
Tables 5«1 & 5*2 show the results of calculating the angular change across the thickness of the joint and angular discontinuity and crack width at the joint for all specimens. For specimens; 5,6 & 7 the values of 0 & 0 were deduced from the results for specimens 8 & 9«
Details of this are found in Appendix 2. Results for the specimens where measurements were made of the total angular change across the joint are plotted in figure 5.10. These results were normalized with respect to the peak load values. There was remarkably little scatter up to peak values with increasing scatter at large angular changes. M = Bending moment M/M Mp = Bending moment at peak load. 0 ^ = Angular discontinuity at joint. = Angular change across the joint © ▼ © thickness at peak load. 0.8 ^ w D v w □ ^ V v □ □V 0.6 H Q V Legend: O 3 © Specimen No. 217 □ Specimen No. 5 0.4 ▼ Specimen No. 6 • Specimen No. 7 ■ Specimen No. 8 0.2 V Specimen No. 9
n------1------1------1------r~ 1------1------> i.o 5:0 e. ,/e. jd jp
Figure 5.10 Normalized Angular Change - Exact Method 218
5.3*3- Approximate Method.
The plastic collapse theory was used to calculate the angular
discontinuity at the joint from lateral deflections measurements. This
approach was approximate because deflections in the direction of the
load causing bending were measured at only three locations; namely, quarter-span, mid-span and three quarter-span. The predominant angular
discontinuity that occurred once the peak load had been reached in the
beam columns tested, could be idealised as the rotation of a hinge which was formed during the failure at the joint. In figure 5.11(a)
the beam column is idealized and the deformation due to bending in the
column and from the local effect at the joint is shown in figure
5.11(b). Figure 5.11(c) shows the changes of deflection which are due
to rotation within the joint so that each half of the beam column is
straight as it rotates as a rigid body. The following basic
assumptions were made based on the experimental observations;
1- Before the peak load was reached, the beam column behaved uniformly
and there was no angular discontinuity at the joint. Therefore, the
lateral deflections were due to beam column action denoted by cL, and o defined by the smooth characteristic shape in figure 5.11(b)(i).
2- After the peak load had been achieved, the measured lateral
deflections were due to both bending in the column segments and a
localised rotation at the joint.
S t o t a l = £ B
where a is the deflection due to the angular discontinuity at the P joint alone as shown in figure 5.11(c).
3- Once the local, effect at the joint predominated, the rest of the
column was taken to unload elastically, as discussed in sections 5*3«1 219
Potential hinge- forms at peak moment.
p (a) P o i -- ■i ■ o <- r T
^ ^ =(L/ 2 )e y total p p
(b)
(c)
e 6 2 0 | 5 0 0 5 0 0 6 2 0 m m £______^ —3------7r— 7Z ----- ? L/2 L/2 7 ✓ < Figure 5.11 Measurement of Angular Change — Approximate method. 220 & 5.3.2. Therefore,the deflection due to beam column action occurring at a particular load during unloading, was the same as that observed during first loading and before failure occurred in the joint. c _ 5 _ 3 Q B loading aB unloading ” aB Based on these, the deflection due to the angular discontinuity at the joint can be defined as, ~ ^total ” ^B giving the angle (i ) P 1/2 6_ = (defined in figure 5.11). P L/2 If the average of the measured lateral deflections at the quarter-span (^„)and three quarter-spanare used, 9 can be calculated from, p 1/4 P 3/4 P 6p =<(ip ) + (Sp > )/(2x620)------(5*4) 1 ^ 3/4 Also, the angular discontinuity at the joint determined by the midspan deflection(°_) is defined by, p 1/2 6 = (d ) /11 2 0 ------(5.5) P P ij2 However, it is not always possible to use this expression as the deflection at mid-span could not always be measured because of spalling of the concrete. In spite of this, an estimate of the total mid-span deflection was required in order to obtain a value for the 221 additional bending moment caused by eccentricity of the applied axial load (i.e. the P-delta effect, with P shown in figure 5.11a). This was done in the following way. First the deflection at mid-span due to angular discontinuity at the joint was found using -0 from equation 5 «4 (based on the quarter P points) and 5*5. Second, the component of deflection due to bending of the column was considered as that measured during first loading and before failure occurred within the joint. Then the total lateral deflection at mid-span is, s = (Si) + (S ) 1/2 1/2 p 1/2 Results using the Approximate Method are tabulated in table 5-3 and shown in figure 5.12. Note that following the assumptions made with this approach there is no localised angular discontinuity at the joint prior to the achievement of the peak load. 5.3.4- Comparison between both methods. Results of angular change across the joint thickness by both methods are compared in figure 5*13. The Exact Method is dependent on readings obtained from the extensometer and the surface gauges, i.e. dependent on longitudinal strains. In contrast, the Approximate Method is dependent on lateral deflections. Although the two methods are based on different criteria, the results shown in figure 5*13 indicate close agreement. This justifies the assumptions made particularly in the region where the joint failure is fully developed and rotation is highly localised. M = Bending moment M/M P 11^ = Bending moment at peak load. 0 ^ = Angular discontinuity at joint. 1.0 0. = Angular change across the ioint JP thickness at peak load. o (from exact method).. 0.8 o 7 ! B V V 0.6 ° V V Q V nv Legend: 0 Specimen No. 3 0.4 □ Specimen No. 5 T Specimen No. 6 • Specimen No. 7 Specimen No. 8 0.2 ■ V Specimen No. 9 —,------!------r 1------J------T l.o 5.0 ® i j/0i 222 jd jp Figure 5.12 Normalized Angular Change- Approximate Method 223 Figure 5.13 Normalized Angular Change - Exact & Approximate Methods. 224 5*4“ Other measurements made during testing. 5.4*1- Lateral deflections. The main reason for measuring lateral deflections is to be able to calculate the total bending moment caused by the lateral loads and the P-delta effect. As explained in chapter 4* "the lateral deflections were measured in both directions at right angles to the direction of the applied axial load. In the direction parallel to the lateral load, deflections were measured by three transducers located at quarter-mid- and three quarter-span. In the other orthogonal direction, the deflection was measured by a dial gauge located at mid-span. In all specimens, the dial gauge reading never exceeded +. 1mm. Accordingly, out of plane displacements could be neglected in assessing the bending moment. The measured values of deflections, in the direction of lateral loads, are presented for all specimens, with the exception of those * subject to axial load only, in table 5*4* The deflection was negligible in specimens under axial load. * /o 2 225 5.4«2- Deformation of embedded strain gauges. The strain gauges located on the dowels and embedded in the concrete served two main purposes. One, during the pure axial load tests, any eccentric loading could be detected by both the transducers on the extensometer and these gauges. Second, the measured strain in the dowel indicated its state of stress which w>7/ be dependent on the state of bond with the grout. If dowels lost bond then the capacity of the section would be similar to that of an unreinforced one. Table 5.5 includes the strain values of all embedded gauges for the various specimens in the main test series. These values are plotted in the series of figure 5-14» For all the specimens, it appears that the bond between the dowels and the grout developed satisfactorily. Hence the column section would be expected to develop its full strength. 226 Figure 5.14A Strains Of Embedded Gauges On Dowels Specimens 0,1 & 2. 227 Figure 5.14 B Change Of Strain For Embedded Strain Gauges. Specimen No. 3 Axial Load =250kN. ^ Bending Moment (kN-m ) Average 0 & 1 or Average 4 & 5 Average 2 & 3 I n i ti a l Oaugo Mo. Strain Average 6 & 7 0 *' 1 1050 2 * 3 940 4 * 3 1130 228 6 * 7 1033 Note: The post peak load was not Avaraga 1040 Strain undar iii»l load measured due to brittleness but bafora application of banding no au n t. 1040 2000 1000 1000 2000 Strain(|is). Figure 5.14C Change Of Strain For Embedded Strain Gauges. Specimen No. 4 Axial Load =1070kN. I 229 Figure 5.14D Change Of Strain For Embedded Strain Gauges. Specimen No. 5 Axial Load =250kN. Average 0 & 1 Average 4 & 5 Bending Moment A Average 2 & 3 (kN-m ) Initial Gauga. No. Strain 230 ... ^ 0 & 1 2 4 3 575 . 4 4 5 575 6 4 7 550 Avaraga 575 Strain undar axial load but bafora application of banding aomant. 575 *<-- 1-- — r— — r— ..... I--- * 2000 1000 1000 2000 Extension Contraction Straintjus) . Figure 5.14E Change Of Strain For Embedded Strain Gauges. Specimen No. 6 Axial Load = 500kN. A Bending Moment ( k N - m ) 231 Initial Cauga No. Strain 0 & 1 770 2 4 3 675 4 & 3 730 6 4 7 705 --\~ Avaraga 720 1000 2000 Strain undar aalal load Strain(jiis). but bafora application Extension Contraction of banding «omant. Figure 5.14F Change Of Strain For Embedded Strain Gauges. Specimen No. 7 Axial Load =750kN. Average 0 & 1 232 Figure 5.14G Change Of Strain For Embedded Strain Gauges. Specimen No. 8 Axial Load =750kN. I v\ • ;V ho U> U) Figure 5.14 H Change Of Strain For Embedded Strain Gauges. Specimen No. 9 Axial Load =250kN 234 5*5- Effect of shear. As discussed in section 5*1, the effect of shear on load capacity might have been expected to be more pronounced when the axial load was low. Two specimens, Number 8 with axial load of 750 kN, and Number 9 with axial load of 250 kN, were tested to study the effect of shear. A comparison was made for specimens tested under the same axial load levels with and without shear. In general, direct comparison was not possible since the specimens were of different strengths, varying between 4-5 & 50 N/mm2 cube strength. This variation was not critical for low axial load level, e.g. 250 kN, (will be discussed in chapter 6); but the peak loads differed significantly when the axial load level was higher than that for the balanced condition, e.g. 750 kN. Accordingly, data for specimens 3,5 & 9 (axial load = 250 kN) are presented in their original form. On the other hand, normalization of data with respect to cube strength was necessary for specimens 7 and 8 (axial load=750kN) to enable a direct comparison to be made. The results of the comparison, which are summarized in table 5.6 in Appendix 2, indicate that the effect of shear on load capacity was insignificant• 235 5.6- Summary, The behaviour of the specimen under pure axial load showed that the detailing in the joint zone was satisfactory since failure always occurred away from the joint. The behaviour, when axial load was coupled with lateral loads, can be classified as, (a) behaviour up to peak load, with the specimen exhibiting a smooth displacement profile, and, (b) post peak load behaviour, with the specimens deformation becoming progressively more localised. Two independent techniques were used to measure the angular change across the thickness of the joint. The results from both techniques were very similar proving the success of the method used to measure the angular discontinuity at the joint. Shear proved not to have any significant effect on the load capacity of the section at the joint. 236 Chapter 6- Analytical view of behaviour. 6.1- Introduction. As noted in chapter 5, the specimens exhibited two distinctive modes of behaviour. The first mode, up to peak load, was similar to that of a monolithic element. This could be explained by the conventional column theory. The second mode, concerned with post peak load behaviour, was characterized by unloading away from the joint and localised rotation in the joint itself. The objective of developing an analytical view of this behaviour is to be able to make prediction for the purpose of analysis and design. The shoe joint was also analysed. Its behaviour was studied using the same column theory applied to the grouted joint. Behaviour of both types of joints were compared and factors of safety were considered for the two types of joints. 237 6.2- Behaviour to peak load. 6.2.1- Introduction. The behaviour to peak load of the precast specimens has been noted to be similar to that of a monolithic beam column. The latter is well defined by the available literature, e.g. Cranston[6.1]• Therefore, existing column theory can be applied to specimens in the main test series to predict their behaviour to peak load. 6.2.2- Column Theory. 6.2.2.1- Assumptions. The following assumptions were proposed by Cranston[6.1] when analysing a column section;- (a) The strain distribution in the concrete in compression and the strain in the reinforcement, whether in tension or compression, are derived from the assumption that plane sections remain plane and that there is no bond-slip between the reinforcement and the concrete. (b) The cross section can be idealised into a number of elements within which the stresses and strains can be taken to be constant. (c) The lateral deflections of the beam column are small in comparison to its length. (d) The overall shortening of the column along its axis is negligible compared to its length. (e) The shear and torsional deformations are negligible. 238 6.2.2.2- Mathematical formulation. At any section along the length of the column the matrix of stress resultants can be defined as, ( 6. 1) x ) where, the subscript "a'1 denotes applied stresses, axes x and y are defined in figure 6.0, P is axial force, and M & M are moments about ° x y x and y axes respectively due to end eccentricities, P-delta effect, lateral loads and other effects. Any section can be divided into MnM discrete elements and the strain th in the i— element with coordinates (x,y) is given by, £ = a+ bx + cy ( 6. 2) where a, b and c are parameters governing the strain distribution, and i varies from 1 to n. Clearly the strain in the column is known if the parameters a,b,c are known for all elements i=l,n. It should be noted that when the column theory is applied,the deflected shape of the column is initially assumed and then corrected on an iterative basis.However, in this work the deflection at the joint is measured and then fed into the analysis so giving the stress resultant acting on the section in the joint region.Hence, only the section in the joint region is analysed and not the beam column as a whole. In the analysis an estimate is made of a,b,c at each cross section which is corrected on an iterative basis. An adequate initial estimate of a,b,c can be obtained by elastic analysis assuming both concrete and steel have constant Young's moduli. Alternatively it would be possible to set a=b=c=0, which would result with few more iterations. In either case the assumed values of a,b,c lead to the following values for the stress resultants;- 239 Figure 6.0 Definition of axes. 240 P = Y f.-A. •-----(6.3) c Z_ 1 i M = Y f. .A. .x ------(6.4) yc c— i i M = Y f . .A. .y ------(6.5) xc l l where, f. is the stress of element i. l A. is the area of element i. l and the subscript c denotes a calculated value of the stress resultant. Additionally, f. = E . £. ( . ) 1 s i 6 6 where, E is the secant modulus of the material in the s ^ i— element. Reorganizing these relations leads to, Y e a . Y e A.x s i Z_ s i I EsA i^ Y e a . x Y e a .x 2 Z_ s i 1— S 1 L EsA ixy Y e a . y Y e A.y2 X _ S 1 s V y or (6.7) H < ■ M M le section stiffness matrix. and ’ w represents the section deformation matrix. The next step would be to calculate the out of balance where, ------( 6. 8) 241 Let the required^ corrections to a,b,c be a m ,b m ,c m , then, d«< dw(. d«* m - da db dc ) d/3 d * \ -- (6.9) m V da db dc d V d V d V c m - da db dc J L V• J Or, m w ■ - w where, IS the correction matrix. On differentiating equation 6.8, [cl becomes, 1 ___ X>!Od oi dP dP c c da db dc dM dM dM yc yc yc -----(6.10) da db dc dM dM dM xc xc xc da db dc _ - Now differentiate equations 6.3, 6.4 and 6.5 whilst noting that, df . df. df . l 1 E E x and t 9 t 1 = V da db dc where E^ is the tangent modulus which is taken as constant during changes in a,b,c to obtain, Y e a . Y e a .x t i Z_ t i ZXv Z?tAiX I^v 2 ZEtAixy ------( 6. 11) IEtV ZEtAixy Zav 2 242 Clearly, the correction matrix is another form of the section stiffness matrix. The modification to can written from equation 6.9, as [ DmJ = [ C1 [ ‘"I ( 6. 12) and the new deformation matrix is, KJ - H • { “•] (6.13) where; th is the deformation matrix in the n: iteration, and th £ - * ] is the deformation matrix in the (n+1)— iteration. The iteration continues until £wj becomes acceptably small, making approach zero. Once the solution converges, then the deformation matrix gives the deformations corresponding to the applied stress resultants. From the previous presentation it is noticed that the matrices [ c ] and [ s ] are identical except for the different moduli used, namely and Eg. Applying the Newton-Raphson method for the solution of nonlinear equations, then equation 6.7 can be rewritten as, H = H i d (6.14) with the rest of the solution remaining the same.The calculations involved are obviously reduced except that more iterations might be needed for convergence. 243 6.2.3- Application to specimens in the main test series. To apply the column theory to the specimens in the main test series, it was necessary to establish or define; (a) the stress resultants at the section, (b) the material properties in the section, and, (c) the optimal discretisation of the section. The stress resultants were determined by measuring the lateral deformation of the specimen. The axial stress was directly measured and the flexural stresses were the sum total of the moment created by both the lateral load and the P-delta effect. The material properties were determined based on control tests for concrete and steel (refer to tables 4*2 and 4»7 and figure 4*10). The tensile strength of concrete was assumed to be negligible. The stress- strain curves of both concrete and steel were considered as shown in figures 6.1 & 6.2 respectively. No safety factors were included since material properties were controlled in the laboratory. The general shape of the stress-strain curves was in accordance with CP110 except for the maximum compressive strength of concrete taken as 0.72 of the cube strength. This followed data from Neville[6.5] giving the cylinder strength as 85% of the cube strength for grade 40 concrete. A confinement factor was also incorporated in the concrete stress-strain curve based on the model proposed by Park et.al.[6.6]. The confinement factor was calculated using the equations presented earlier in chapter 3. The stress-strain curve of steel was considered to be identical in compression and tension, as determined by figure 4»10, so neglecting the Bauschinger effect. Equations of parabolas: 244 Figure 6.1 Assumed stress-strain curve of concrete. 245 Figure 6.2 Assumed stress-strain curve of steel reinforcement 246 The column section tested can be divided into three types; (a) column section with a minimum amount of stirrups, with an enhancement factor of 1.0; section Type A in figure 6.3* (b) column section at the joint reinforced with four 16mm diameter bars 55mni from the edge of the section and having an enhancement factor of 1.1-4; section Type B in figure 6.3, and, (c) column section at the joint reinforced with four 16mm diameter bars 30mm from the edge of the section and having an enhancement factor of 1.14? section Type G in figure 6.3. Discretisation of the three types of sections A,B & C is also shown in figure 6.3. Two levels of discretisation were tried for type A; one with 408 elements and the other with 28 elements. For uniaxial bending, there was no difference in the accuracy of the solution between the two trials although the computer time used for the 408 elements was much more than for only 28 elements. Therefore, it was decided that using 28 elements was satisfactory. To apply the column theory to the three types of sections a computer programme was written based on the algorithm and flow chart shown in figure 6.4. The programme is listed in Appendix 3(a). The computer programme can accomodate steel, concrete and/or grout elements. The section was taken to have reached its ultimate capacity when the concrete strain was 0.0035.The data input to the programme included the following; (a) Number of loading cases that needed to be considered. (b) Number of elements in the section. (c) Physical and geometrical properties of every element. (d) Various cases of acting loads. Total number of elements = 408 Total number of elements = 28 F i g u r e 6.3 Grouted Joint - Type A 248 2 0 0 m m ->u -7*- - " “ 10 -7*-(typ) 200 7 t " No. of concrete elements = 20 No. of steel elements = _ A _ T o t a l 24 Figure 6.3 (cont'd) Grouted Joint - Type B 249 No. of concrete elements = 20 No. of steel elements = 4 T o t a l 24 Figure 6.3 (cont’d) Grouted Joint - Type C 0 5 2 F i g u r e 6 . 4 Flow chart for Column Theory computer programme. 251 The properties of the materials, e.g. concrete, grout or steel, are stored in a subroutine in the main programme and coded in the input file in the form of; (a) 0 for concrete, (b) 1 for steel, and, (c) 2 for grout. An example of the input file is listed in Appendix 3(b). 6.2.4- Comparison with experimental results. Comparison is valid only up to peak load because the specimens, in the main test series, were not expected to comply with the column theory during the post peak load. The ability of the column theory to predict the behaviour of the various specimens, depended on the validity of both the assumed shape of the stress strain curve of concrete and the idealisation of the column section. Three monolithic columns were cast and tested under different loading patterns using the same basic instrumentation as for the specimens in the main test series. (A summary of the location of the electric resistance strain gauges is given in table 4-9 and shown in figure 4-13-) The objective was twofold. Firstly, was to compare the behaviour of the precast columns with monolithic ones under the same loading conditions. Secondly, to "calibrate" the various assumptions made in the column theory presented earlier in section 6.2.3- The ultimate strength results of the three monolithic specimens (numbers 10,11 & 12) are plotted on the strength envelope (or interaction surface) as obtained by the column theory in figure 6.5 and presented in table 6.1. Although the concrete mix was intended to be a grade 40* the specimens were tested when their age was more than 2 5 2 Figure 6.5 Axial Load - Bending Moment Interaction Diagram For Monolithic Specimens Table 6.1 A Axial load and bending moment values for section type A (b = h = 200mm) G r a d e 45 G r a d e 50 A x i a 1 B e n d i n g Normalized Values Axia 1 Bending Normalized Values Lo a d M o m e n t P M , Load Moment P M (kN) (kN-mm) f bh t bh^ (kN) (k N - m m ) f bh f bh* cu cu cu cu 0 2 5 0 0 0 0 0 0 2 5 0 0 0 0 0 253 2 5 0 4 1 0 0 0 0 . 1 3 9 0 . 1 1 4 250 4 2 0 0 0 0 . 1 2 5 0 . 1 0 5 5 0 0 4 8 2 5 0 0 . 2 7 8 0 . 1 3 4 5 00 5 0 5 0 0 0 . 2 5 0 0 . 1 2 6 6 5 0 49500 0.361 0.138 6 0 0 5 2 5 0 0 0 . 3 0 0 0 . 1 3 1 7 00 4 8 0 0 0 0 . 3 8 9 0 . 1 3 3 7 00 5 3 0 0 0 0 . 3 5 0 0 . 1 3 3 7 5 0 4 6 5 0 0 0 . 4 1 7 0 . 1 2 9 750 5 2 0 0 0 0 . 3 7 5 0 . 1 3 0 1 0 0 0 3 5 5 0 0 0 . 5 5 6 0 . 0 9 9 1 0 0 0 4 3 2 5 0 0 . 5 0 0 0 . 1 0 8 1 2 0 0 2 6 5 0 0 0 . 6 6 7 0 . 0 7 4 1 2 0 0 3 5 5 0 0 0 . 6 0 0 0 . 0 8 9 1 5 7 0 0 0 . 8 7 2 0 1 7 2 0 0 0 . 8 6 0 0 H-jjK Table 6. IB Axial load and bending moment values for section type B (b = h = 200mm) G r a d e 45 G r a d e 50 Axial Rending Normalized Values A x i a l B e n d i n g Normalized Values L o a d M o m e n t P M , L o a d M o m e n t P M (kN) (kN-mm) f bh f b h * (kN) ( k N - m m ) f bh f bh^ cu cu c u cu 4 5 2 0 1 9 0 0 0 0 0 . 0 5 3 0 1 9 0 0 0 0 0 . 0 4 8 2 5 0 3 2 0 0 0 0 . 1 3 9 0 . 0 8 9 2 5 0 3 3 2 5 0 0 . 1 2 5 0 . 0 8 3 5 0 0 4 2 5 0 0 0 . 2 7 8 0 . 1 1 8 500 4 4 0 0 0 0 . 2 5 0 0 . 1 1 0 6 5 0 4 4 2 5 0 0 . 3 6 1 0 . 1 2 3 7 50 4 8 0 0 0 0 . 3 7 5 0 . 1 2 0 7 5 0 4 3 0 0 0 0 . 4 1 7 0 . 1 1 9 1 0 0 0 4 4 0 0 0 0 . 5 0 0 0 . 1 1 0 1 0 0 0 3 7 5 0 0 0 . 5 5 6 0 . 1 0 4 12 0 0 38000 0.600 0.095 1 2 0 0 2 8 0 0 0 0 . 6 6 7 0 . 0 7 8 18 0 0 0 0 . 9 0 0 0 1 6 5 0 0 0 . 9 1 7 0 Tabic 6.1c Axial load and bending moment values for section typeC (b = h = 200mm) G r a d e 45 G r a d e 50 Ax i a 1 B e n d i n g Normalized Values Axial Bending Normalized Values Lo a d M o m e n t P . M K L o a d M o m e n t - P M (kN) (kN-mm) f bh f b h^ (kN) ( k N - m m ) f b h f b h z cu cu c u cu 5 5 2 0 1 9 2 5 0 0 0 . 0 5 3 0 1 9 2 5 0 0 0 . 0 4 8 2 5 0 3 6 3 0 0 0 . 1 3 9 0 . 1 0 1 2 50 3 6 7 5 0 0 . 1 2 5 0 . 0 9 2 5 0 0 4 7 7 5 0 0 . 2 7 8 0 . 1 3 3 5 0 0 4 9 5 0 0 0 . 2 5 0 0 . 1 2 4 7 0 0 5 0 0 0 0 0 . 3 8 9 0 . 1 3 9 7 50 5 5 0 Q 0 0 . 3 7 5 0 . 1 3 8 •750 4 9 7 5 0 0 . 4 1 7 0 . 1 3 8 1 0 0 0 4 9 0 0 0 0 . 5 0 0 0 . 1 2 3 1 0 0 0 4 1 5 0 0 0 . 5 5 6 0 . 1 1 5 1 2 0 0 4 1 0 0 0 0 . 6 0 0 0 . 1 0 3 1 2 0 0 3 2 0 0 0 0 . 6 6 7 0 . 0 8 9 1 8 0 0 0 0 . 9 0 0 0 1 6 5 0 0 0 . 9 1 7 0 256 Table 6.ID Experimental Values (b=h=200mm) S p e c i m e n C u b e A x i a l B e n d i n g Normalized Values No. S t r e n g t h L o a d M o m e n t P M f b h f b h ^ ( N / m m ^ ) (kN) ( k N - m m ) cu cu 0 55 3 0 0 4 6 5 0 0 0 . 1 3 6 0 . 1 0 6 1 50 1 5 8 0 0 0 . 7 9 0 0 2 49 1 5 5 0 0 0 . 8 0 7 0 3 48 2 5 0 35500 0.130 0.092 4 4 4 1 0 7 0 3 4 5 0 0 0 . 6 2 2 0 . 1 0 0 5 47 2 5 0 3 5 0 0 0 0 . 1 3 4 0 . 0 9 4 6 47 500 44500 0.269 0 . 1 2 0 7 44 7 5 0 4 2 5 0 0 0 . 4 2 7 0 . 1 2 1 8 49 7 5 0 5 0 0 0 0 0 . 3 8 3 0 . 1 2 8 9 49 2 5 0 3 5 0 0 0 0 . 1 2 8 0 . 0 8 9 10 50 1070 42000 0 . 5 3 5 0 . 1 0 5 11 44 7 50 4 7 0 0 0 0 . 4 2 6 0 . 1 3 4 12 43 250 46500 0.145 0 . 1 3 5 Specimen 0 failed prematurely near loading end when loaded axially. It was repaired and then loaded under axial & lateral loads. 257 28 days and all specimens had cube strengths between 43 & 50 N/mm2. This explains the reason for drawing two strength envelopes, corresponding to 45 & 50 N/mm2 cube strength. Figure 6.5 shows a satisfactory prediction of the strengths of the specimens. The calculated moment curvature relationship was compared with the experimental values and shown in figures 6.6. The curvature was calculated using the difference in the axial deformation of top and bottom transducers of the extensometer and, alternatively, using the lateral deflection assuming the beam column followed a smooth characteristic deflected shape. For specimens 10 & 11 (axial loads 1070 & 750 kN respectively), the prediction by the column theory was almost exact, refer to figures 6.6 A & B. For specimen 12 (axial load 250 kN), the theory underestimated the ultimate strength although the predicted moment curvature relationship was satisfactory up to 85% of the peak load. This is shown in figure 6.6C. The calculation of the curvature using the results from the transducers mounted on the extensometer (i.e. axial deformation) and the lateral deflection gave similar results, as indicated by values plotted in figures 6.6. The appearance of the specimens after testing is shown in plate 6.1. It is concluded that the column theory provided a reasonable prediction of the beam column behaviour of the monolithic specimens tested in this experimental programme. The next step was to apply the column theory to the precast specimens, i.e. specimens number 3>4»5,6,7,8 & 9» Unlike the monolithic specimens, the ultimate strength of the precast specimens was controlled by sections Types B & C (refer to figure 6.3) at the joint, a lower and upper bound respectively. For these specimens, the strength was controlled by the section at the joint. The ultimate Specimen No. 10 Axial Load = 1070 kN. Specimen No. 11 Axial LOad = 750 kN. Specimen No. 12 Axial Load =250 kN. P la te 6 .1 Failure Mode Of Monolithic Columns Axial & Lateral Loading (Shear=0) . L e g e n d : 9 5 2 based on axial deformation based on lateral deformation Figure 6.6A Bending Moment - Curvature Interaction Diagram Specimen No. 10 (Axial load = 1070kN). 260 Figure 6.6B Bending Moment - Curvature Interaction Diagram Specimen No. 11 (Axial load = 750kN). 261 Figure 6.6C Bending Moment - Curvature Interaction Diagram Specimen No. 12 (Axial load = 250 kN). 262 strengths are plotted in figure 6.7, and presented in table 6.1, together with the theoretical strength envelopes based on sections Types B or C. The strength of most specimens was adequately determined by the lower and upper bounds although for design purposes the lower bound should be used as a criterion. The moment-curvature relationship is shown for all precast specimens in figures 6.8. Curvature was calculated using values from both lateral deflection and axial deformation. The results showed very close agreement indicating that up to peak load the precast specimens followed a smooth characteristic deformed shape. For all specimens, the lower bound predicted conservatively the moment curvature relationship. The results of all specimens, except for specimen 8, were contained between the lower and upper bounds. No special consideration was taken for the material properties of the grout in the analysis of the moment curvature relationship.Assuming that the grout had the same properties as the concrete reduced the complexity of the analysis and was justified by the results of figures 6.7 & 6.8. 6.2.5- Conclusion. The behaviour, up to peak load, of the joint tested in this research programme was adequately determined by the column theory presented. The flexural capacity was controlled by the location of the dowels (section type B - figure 6.3)* Therefore, the column theory provided a convenient analytical tool to predict the behaviour of the grouted precast specimens up to peak load. 3 6 2 Figure 6.7 Axial Load - Bending Moment Interaction Diagrams For Precast Specimens. 4 6 2 Figure 6.8A Bending Moment - Curvature Interaction Diagram Specimen No. 3 (Axial load = 250 kN). 5 6 2 Figure 6.8B Bending Moment - Curvature Interaction Diagram Specimen No.4 (Axial load = 1070 kN). 266 Figure 6.8C Bending Moment - Curvature Interaction Diagram Specimen No,5 (Axial load = 250 kN). Bending Moment ( k n - m ) 40 3 0 7 6 2 20 10 Figure 6.8D Bending Moment - Curvature Interaction Diagram Specimen No.6 (Axial load = 500 kN). 268 Figure 6.8E Bending Moment - Curvature Interaction Diagram Specimen No.7 (Axial load = 750 kN). 69 2 Figure 6.8F Bending Moment - Curvature Interaction Diagram Specimen No.8 (Axial load = 750 kN). 0 7 2 Figure 6.8G Bending Moment - Curvature Interaction Diagram Specimen No.9 (Axial load = 250 kN). 271 6.3- Post peak load behaviour. 6.3.1- Introduction. The post peak load behaviour represented the ductility and energy absorption capacity of the joint. The experimental observations indicated that this behaviour was, largely, concentrated in the joint zone. A local effect predominated in the form of rigid rotation of the precast columns about the joint. The variation of the bending moment with angular change across the thickness of the joint, showed decreasing ductility with increasing axial load levels, for the same detailing of the connection. However, when values of bending moment and angular change were normalized with respect to corresponding values at peak load, they yielded the same variation for all levels of axial load (refer to figure 5•13)* The objective of this section was to study the various controlling factors that affected the post peak load behaviour. 6.3•2- Failure mechanism. The stability of the connected precast columns, once the peak load has been attained, depended on the following factors; (a) The depth of the compressive zone; this depended mainly on the applied axial load. (b) The ability of the compressive zone to resist crushing; this depended on the concrete strength and the confinement provided in the connection zone. (c) The anchorage capacity of the dowels. The failure mechanism was discussed in detail in section 5*2. It was considered that the flexural capacity of the beam column was 272 maintained until crushing of the compressive zone occurred. The drop in the flexural capacity depended on the reduction of the effective section at the joint. When part of the section was lost due to surface spalling, the lever arm became smaller causing a reduction of the bending moment. This mechanism must be taken into account in the analysis. 6.3«3- Literature review. A review of the literature indicated that precast and brickwork panels showed similar behaviour ^5 the grouted precast columns. For normal applications the joint interfaces are weak compared with the panel sections. Consequently, the panels could be regarded as rigid and thus the angular deformations would be concentrated at the transverse joint. Engstrom[6.2] did extensive research on precast concrete panel slabs. The slab could be considered as a limiting case in the sense that the axial load was zero. The main emphasis of Engstrom’s work was on the anchorage of the ties across the joint (i.e. the dowels). Flexural cracks occurred only in the interfaces between the joint concrete and the end surface of the slab panels. In all of the tests it was possible to anchor the ties until fracture and the deformation capacity was large, especially when using smooth mild steel bars. From the observation of the strain distribution in the ties, it was clear that the end hooks on the ribbed bars were never strained. Thus, the bond capacity along the embedded length was sufficient for anchorage at fracture load. On the other hand, the main part of the load at fracture was taken by the end hooks on the smooth bars. In Engstrom’s work, the relation between the bending moment and rotation of the joint was obtained by assuming that the depth of the 273 compressive zone was negligible due to the small reinforcement content in the joint section. However, a major difference between the behaviour of the precast panel slabs and the grouted columns, was the axial load. The behaviour of the panels became relevant only when the axial load in the main test series was low. The simplification made by Engstrom, namely that the depth of the compressive zone was negligible, was not applicable when analysing the precast grouted columns (refer to table 5*2). Brickwork panels and columns tested by Hendry et.al.L6.2&6.3] showed the same local effect of angular discontinuity at the joint, as the grouted columns, when subjected to precompression and lateral loads. Failure of the brickwork column took place when the cracked zone reached the line of thrust; at the moment of collapse, a hinge formed at mid-height of the column, and the line of thrust passed through it as shown in figure 6.9» The main assumption of the analysis was that rotation took place about point A (in figure 6.9)• In the case of unreinforced brickwork, failure at ultimate load was brittle, and the post peak load behaviour was virtually nonexistent. The analysis of brickwork columns avoided the fact of crushing of the concrete in the compression zone. The analysis was simplified by the introduction of a hinge at point A although this required that the section at A did not crush before the crack propagated across the section. This assumption was justified, from experimental observations, up to peak load but not beyond. Although the two structural members presented above are differrent in nature from the grouted columns, they indicate the difficulties involved when trying to analyse the specimens tested in this experimental programme. 274 F i g u r e 6 . 9 Eccentrically loaded pinned-end column of brittle material 275 6.3.4- Analysis of. angular change across the joint thickness. The experimental observations suggest that the angular discontinuity at the joint occurs for the first time at peak load. Calculation of the depth of the crack caused by the angular discontinuity (refer to table 5.2), has indicated that the depth of the crack and hence the location of the neutral axis (N.A.) keeps increasing. However, when the flexural capacity declines, the shift of the neutral axis is negligible. Therefore, it can be assumed that the location of the neutral axis during the post peak load phase is defined by peak load conditions. From the previous discussion of section 6.3.3, it is concluded that the analysis of the angular discontinuity at the joint must include the following factors;- (a) the depth of the compression zone, which depends on the axial load level, (b) the top and bottom reinforcement of the section, and, (c) the fact that part of the section is lost once the peak load is reached thus reducing the flexural capacity of the section. In the analysis of the joint region, the axial load is assumed to be maintained and the dowels yield without losing anchorage. A freebody diagram of the joint is shown in figure 6.10. At peak load, M = a.F + C.s. - P.(d -d/2) ------( 6 . 1 5 ) p l N w h e r e , is the bending moment at peak load, and F is the force in the top and bottom reinforcement bars assuming both lots at yield to make solution simpler. All terms are defined in figure 6.10. In the post peak load freebody diagram, part of the section is crushed and therefore, M = a.F + C.s - P.(d -d/2) ------( 6 . 1 6 ) the reduction of the compressive zone and the resulting reduction in the lever arm is reflected in the value of "s". 276 F o r c e D i a g r a m Joint thickness F t N. A. ^ 7 d N ' d / 2 s.u £ 1 M d / 2 * C C =Resultant of concrete compression. Ft=Tension force in dowel. Fc=Compression force in dowel (a) At Peak Load Figure 6.10 Failure of joint zone. 277 Generally, S = ^ • (djq~x) ------— (6.17) where, is a dimensionless factor determining the centroid of the compressive zone. A special case of equation 6.17 is when x=0 resulting with, S1 - > V dN therefore, s = — --- s . ------(6.18) dN 1 from figure 6.10(a), the angular discontinuity at peak load can be defined as, 0- = ^ 2 ------(6.19) P dN where is the deformation at concrete surface of the section P at the peak load conditions. Similarly, from figure 6.10(b) the angular discontinuity is, m. A. -6- = ---- 2------(6.20) dN'X where, Mm" is a multiplier that measures the increase in deformation causing crushing of concrete and depends mainly on;- (a) axial load level, (b) degree of confinement, and, (c) value of Mx". Combining equations 6.19 and 6.20 and substituting in equation 6.18, m s = ------s. ------(6.21) (e/e ) 1 P Substituting for the value of "s" in equation 6.16, yields, m M = a.F + (C. s. ) ------P. (d..-d/2) 1 (e/e ) N p 278 Therefore, a .F - P.(dN-d/2) C. s m M M M m ( e / e ) p p m ( 6 . 22) (e /e ) p where and k£ are constants. Rearranging, and bearing in mind that k^ + = 1j (6.23) m “ 1 k 2 1 e /e p p In the expression, k^ represents the contribution of the compressive zone to >1^ at peak load. For example for pure bending, k^ = 0. Equation 6.23 can represent the post peak load curve shown in figure 5.13. Note that at peak load m=l and &/Q- =1 giving M/M =1 as P P expected. Therefore, the declining slope in figure 5.13 has two components; one attributed to confinement by various effects, e.g. stirrups, curvature, etc..., in the form of "m", and the other attributed to the axial load level in the form of A special case of interest is when the core is of the same strength as the surface, for example the cover concrete, i.e. m=l. Therefore, equation 6.23 can be written as, M = 1 - k2 ( 1- — --- ) ------(6.24) m e /e P P Equation 6.24 can be illustrated in the following diagram, Ductility is improved if curve (ii) approaches curve (i).0ne way to do this is to increase the value of confinement. 279 6.3-5- Discussion of results and conclusion. The experimental results of the main test series were explained by- equation 6.23. The analysis presented in section 6.3.4- showed that confinement of concrete in the joint zone, e.g. by rectilinear ties, could reduce the slope of the declining part of the normalized relationship of the bending moment-angular change at the joint. This resulted in a higher value of the multiplier T,m" which signified that the local failure tended to be spread over a greater depth of section. Although this cannot be considered as a general solution, it does provide a physical explanation for the results obtained in figure 5.13. 280 6.4- Analysis of the shoe joint. 6.4.1- Introduction. The shoe joint[6.7], tested at the Polytechnic of Central London (PCL), and designed by Jan Bobrowski & Partners, was discussed in detail when the confinement model was developed in chapter Figure 6.11 is reproduced here for comprehensiveness of the discussion. The shoe joint was tested with two main variations of loading; namely, pure axial load and axial load combined with flexure. In all tests, the joint remained intact. Invariably, failure occurred either in the zone near the interface of the steel tube section and the column, or in the column section with maximum spacing of steel stirrups. 6.4»2- Analysis of the various sections. From the results given in figure 6.11 it was decided to classify the column into sections according to the volumetric ratio of the steel ties and the resulting gain in concrete strength defined by the value of K. These sections were; 1) A section where the spacing of ties was 150 mm with K = 1.0; referred to as section A in figure 6.12. 2) A section where the spacing of ties was 75 mm with K = 1.2; referred to as section B in figure 6.12. 3) A section near the joint interface where concrete cover was considered to be ineffective, due to bursting stresses from abrupt change in the section dimensions, with K = 2.3; referred to as section G in figure 6.12. 4) Finally, a section at the joint in the steel tube with K = 3»2, referred to as section D in figure 6.12. I *!• ; i : / J *! i Confinement Details p pm fr Ki *2 (ksi) 0.01002 0.0036 0.073 1.05 1.10 0.02004 O.olllS 0.226 1.18 1.20 ”0.10716’ 0.07QlS 1.581 2.33 2.07 0.1250 0.1250 2.53 3.17 not applicable 0.11284 0.11284 2.284 2.95 IQZ O.10710 0.07815 1.581 2.33 2,07 0.O2004 0.01118 0.226 1.18 1.20 0.01002 0.0036 0.073 1.05 1.10 p -volumetric ratio of tie steel p -modified value for p -strength gain based on A-S model ^-strength gain based on P ark 's model (3.19) f^-confining stress (a) Longitudinal Section (b) Stress Distribut ion Figure 6.11- Precast concrete column connection used in H-frame 282 300 ------:------* i 2 2tyTN 3 22/<^\ 23 /tn 2 f 12 1 # 25 © 4 © 8 • 7 • 8 2 f> 25 2< /TN 10 2S/TN 300 mm 11 12 t15 13 14 1S 16 2 t 12 2 £ 25 2 6 /e . 17 27 / C S \ 2 8 ^ © ie v ^ y © 19 20 T S e c tio n A o r 8 No. of concrete eleeents • 20 Mo. of steel elsnents * 8 T b t e l - 28 2 4 12 1 i 25 2 #25 2 l 12 1#25 No. of concrete elements - 16 NO. of steel elencats » 8 f e t a l - 24 Figure 6.12 Shoe Joint - Sections A,B & C 283 Concrete •laments 12-22 Tuba elorn anta 46-68 Figure 6.1 2(coat'd) Shoe Joint - Section D 284 The four sections were divided into discrete elements as shown in figure 6.12. The column theory, presented earlier in section 6.2.2, was applied to the various sections. Different interaction diagrams (axial load-bending moment) were obtained for the jointed column depending on the section which was assumed to be controlling its failure. Figure 6.13 shows the different interaction diagrams which were obtained by this analysis. In addition, the results of the analysis are presented in table 6.2. For simplicity of the discussion the part of the interaction diagram below the balanced point is referred to as Zone 1 and above it as Zone 2. It is important to note that failure, as defined by the envelopes presented in figure 6.13 > depended on the maximum assumed strain of concrete, i.e. 0.0035* Experimentally, higher strains were measured. This fact had no effect on the shape of the failure envelope when in Zone 1 and with a K-value of 1. However, when in Zone 2 and for higher values of K, especially when K is larger than 2, the peak of the concrete stress-strain curve, I i.e. Kf , was never attained. Therefore, for section D which has K = 3.2, the failure envelope underestimated the real strength of the section in Zone 2. 6.4-*3- Comparison with experimental results. The experimental results of the various specimens have been plotted on figure 6.13, and presented in table 6.3* The results of pure axial load form an acceptable scatter about the theoretical maximum axial load capacity of section A; bearing in mind that secondary moment effects originating from specimen imperfections, e.g. due to the method of casting, were detected. Invariably, in all specimens, failure occurred in section A as predicted in the previous p LEGEND Section A Section B Section C Section D 285 Figure 6.13 Normalized Bending Moment-Axial Load Interaction Diagram For Shoe Joint. 286 Table 6.2 Values based on section A of shoe joint. Axial Bending Normalized Values based on f based on f' load Moment cu c PMPM (kN) (kN-mm) f bh f bh2 f ’bh f'bh^ cu cu c c 0 80000 0 0.074 0 0.103 200 100000 0.056 0.093 . 0.077 0.129 400 115000 0.111 0.107 0.154 0.148 600 124750 0.167 0.116 0.232 0.160 800 129250 0.222 0.120 0.309 0.166 1000 133000 0.278 0.123 0.386 0.171 1200 135250 0.333 0.125 0.463 0.174 1275 135750 0.354 0.126 0.492 0.175 1400 136000 0.389 0.126 0.540 0.175 1800 122000 0.500 0.113 0.694 0.157 2000 133000 0.556 0.105 0.772 0.145 2400 88000 0.667 0.082 0.926 0.113 2750 51750 0.764 0.048 1.061 0.067 3180 0 0.883 0 1.227 0 (see notes at end of table) 287 Table 6.2 (cont'd) Values based on section C of shoe joint. Axial Bending Normalized Values based on f based on f* Load Moment cu c P M P M (kN) (kN-mm) f bh f bh2 f'bh f'bh^ cu cu c c 0 73000 O 0.068 0 0.094 400 106000 0. Ill 0.098 0.154 0.136 800 122000 0.222 0.113 0.309 0.157 1200 133000 0.333 0.123 0.463 0.171 1600 139000 0.444 0.129 0.617 0.179 2000 135000 0.556 0.125 0.772 0.174 2400 120000 0.667 0.111 0.926 0.154 3000 88000 0.833 0.082 1.157 0.113 4300 0 1.194 0 1.659 0 (see notes at end of table) 288 Table 6.2 (cont'd) Values based on section D of shoe joint. Axial Bending Normalized Values based on f based on f ' Load Moment cu c PM PM (kN) (kN-mm) f bh f bh2 f'bh f'bh^ cu cu c c 0 109000 0 0.101 0 0.140 200 116000 0.056 0.107 0.077 0.149 400 123000 0.111 0.114 0.154 0.158 600 130000 0.167 0.120 0.232 0.167 800 132000 0.222 0.122 0.309 0.170 1000 133000 0.278 0.123 0.386 0.171 1200 131000 0.333 0.121 0.463 0.169 1400 125000 0.389 0.116 0.540 0.161 1600 120000 O. 444 0.111 0.617 0.154 2000 lOOOOO 0.556 0.093 0.772 0.129 2400 82000 0.667 0.076 0.926 0.106 4100 0 1.139 0 1.582 0 Notes: 1- Above values plotted in figure 633. 2- Sections A , C & D are defined in text and in figure 6.13. 3- f =40N/mn 2 f'=28.8N/mm 2 b=h=30Qmn cu c * 289 Table 6.3 Experimental results of shoe joint tests. Specimen Concrete Strength Acting Loads Normalized Values No. f f ' Axial Lateral Bending P M cu c Loads Loads Moment f bh f bh^ (N/ram^) (N/mm2) cu cu (kN) (kN): (kN-mm) 2A 38.1 33.5 2550 0 76500 0.728 0.073 2B/1 32.9 35.3 3530 0 105900 1.193 0.119 2B/2 46.9 35.5 3240 0 97200 0.767 0.077 3A 33.6 27.4 1325 12 123600 0.438 0.136 4A 33.8 29.5 1815 14.5 149360 0.597 0.164 5A 39.0 40.0 150 13 133905 0.042 0.127 5B 35.0 33.0 1765 10 103000 0.561 0.109 3B/1 36.0 38.0 1765 15 154510 0.545 0.159 3B/2 39.0 32.5 150 15 154510 0.042 0.147 4B/1 34.6 30.0 150 11 113305 0.047 0.121 1A 35.0 30.0 3040 0 0 0.965 0 1B/1 38.1 43.3 2610 0 0 0.761 0 1B/2 44.0 40.2 2945 0 0 0.743 0 3A/1P* 32.2 31.7 3405 0 0 1.175 0 3A/2P* 33.0 31.7 2925 0 0 0.984 0 3A/3P* 47.1 40.7 3090 0 0 0.728 0 3A/1E* 33.5 28.0 2710 0 0 0.898 0 3A/3E* 43 .0 48.0 3365 0 0 0.869 0 3A/2E* 34.0 28.0 2510 0 0 0.821 0 * Monolithic Specimens 290 section. For specimens subjected to flexural and axial load, the failure mode depended on whether the loading configuration was in Zone 1 or 2 of the interaction diagram. When in Zone 1, the specimens failed either in the area near the column-tube section interface or at the interface, depending on the level of axial load. For low axial loads, i.e. 150 kN, the cracks were concentrated at the joint interface, and the collar pulled away from the main column. Although it is not clear from the report, it can be concluded from the shape of the failed column that the failure was local at the joint with the rest of the column unloading. This type of failure is identical to the failure experienced in the grouted joint. On the other hand, for higher axial loads, i.e. 1800 kN, the failure occurred in the joint vicinity but away from the interface. For both cases of axial load levels, the failure seems to have depended on the capacity of section G where most of the damage occurred. For specimens subjected to both axial and flexural stresses in Zone 2, the failure was observed to occur in sections A & B. In fact, the strength of specimens 2A & 5B was predicted by the theoretical interaction diagram based on section A. In general, all specimens subjected to axial and flexural stresses (except 2A and 5B) had higher load capacity than that predicted by the column theory. One of the reasons for this discrepancy was the characteristic strength of concrete reported. For many specimens, e.g. 2B/1,5A,3B/1,1B/1 and 3A/3E, the measured cube strength was lower than the reported cylinder strength which is difficult to explain. However, the above analysis is intended to be qualitative rather than exact and on this basis the comparison of the shoe joint and the grouted joint will be made 291 The experimental values presented in table 6.3 do not include secondary moment effects, e.g P-delta effect, because of the difficulty of assessing these effects with certainty. Nevertheless, it is believed that the qualitative analysis is still valid since all precast specimens were produced and tested under the same conditions. (Note that intentionally, the monolithic specimens were compacted differently.) 6.4 .4.“ Discussion of the shoe and grouted joints results. The behaviour of both types of joint generally followed the same trend. In Zone 1 of the interaction diagram they showed relative ductility, as observed experimentally. In Zone 2, the failure was sudden and brittle. The grouted joint showed the same post peak load behaviour for all specimens except the ones subjected to pure axial load, i.e local angular discontinuity at the joint. The same behaviour seemed to have occurred in the shoe joint at low axial load as indicated by some reported photographs. However, it was not clear, from the description of the shoe joint tests, whether the significance of the local behaviour was recognized since tests were stopped once peak load was reached. Considering the interaction diagrams of both types of joints, (figures 6.13 & 6 .14)» it was noted that under pure axial load the full capacity of the column was achieved since the failure occurred in the precast columns rather than in the connection. In Zones 1 & 2 of the interaction diagram, the column theory predicted safely the strength envelope of the shoe joint. While for the grouted joint, the column theory predicted the lower and upper bounds. For the shoe joint, basing the design on the column section (type A) yielded a p K - 1.0 K - 1.14 292 K - 1.14 Figure 6.14 Normalized Bending Moment-Axial Load Interaction Diagram For Grouted Joint 293 conservative prediction of the strength for all specimens. Therefore, the factors of safety included in the Codes of Practice, in this case, did not need any modification. So, the shoe joint proved to be adequate when full moment continuity at the joint is desired. On the other hand, for the grouted joint, the design based on the regular column section Type A failed to predict safely the failure envelopes. Therefore, the design should be based either on the lower bound criterion with no modification of the factors of safety; or, on the regular column section with a new cumulative factor of safety of about "4-/3 x regular load factor" amounting to a value of 2 as shown in figure 6.15. This same value was proposed by Raths as mentioned in section 2.5 of chapter 2. Hence, it is adequate to incorporate a safety factor of two in the design of connections in precast structures. 294 Figure 6.15 Comparative Interaction Diagrams For Grouted Joint. 295 6.5- Summary and conclusions. The behaviour of the grouted joint has been fully explained. The column theory, which included discretisation of the section, predicted satisfactorily the behaviour of the various specimens up to peak load. However, the post peak load behaviour was examined by analysis of the angular change across the joint thickness. The change of the bending moment curvature relationship for the post peak load depended on the applied axial load and the confinement level in the section under consideration, (the k2 and m factors respectively as defined in equation 6.23). The confinement model when combined with the column theory predicted satisfactorily the lower bound failure envelope of the jointed precast columns. This allowed adequate detailing of the various sections of the column including the joint zone. The detailing of the shoe joint was very successful in attaining the full strength capacity of the column section. The same results could have been obtained for the grouted joint if more steel ties had been provided in the joint zone. However, more stirrups would have congested the column section and hindered the flow of concrete. In conclusion, the analysis of the grouted joint has shown that a safety factor of 2 needs to be incorporated in the design of connections in precast concrete structures. Also, the study of the strength capacity of the shoe joint showed that the strength of the joint matched the strength of the column section. This proved the adequacy of the detailing of the shoe joint. However, more experimental work is required to fully understand the behaviour of the shoe joint. 296 Chapter 7- Results of tests on the influence of joint thickness. 7.1- Introduction. The specimens in the main test series had a joint thickness varying between 20-25nun. In real construction practice a much greater variation in thickness could be expected due to tolerances and imperfections in production and erection of precast elements. Somerville[7.1], indicated that the influence of joint thickness depends primarily on the ratio of the grout to concrete strength and on the ratio of the section dimension to joint thickness. Figure 7.1 illustrates the sensitivity of the joint strength to its thickness as observed by Somerville. In the main test series the ratio of the column section dimension to joint thickness was about 8 ; also, the minimum grout strength to concrete strength ratio was 1.0. Thus if the data in figure 7.1 were applicable, the reduction in strength would be negligible even if the joint thickness was twice that used in the specimens of the main test series. Somerville made his conclusions from results of cubes (100mm) jointed together by grout of varying thicknesses. Although model tests in most cases are indicative of true behaviour, in the present work it was considered appropriate to study the influence of joint thickness on full size columns, of the form used in the main test series. From the analysis presented in chapter 6, it was expected that increasing the joint thickness would tend to reduce the confinement in the joint zone. This effect would be more pronounced when the size of the compressive zone is significant. A low axial load would require only a small compressive zone and the change of the joint thickness would have little effect on the overall behaviour of the column. On the other hand, if the specimen was subjected to a high axial load, 297 Grout Strength Concrete Strength (7.1) Figure 7.1 Sensitivity To Joint Thickness 298 any reduction of the confinement would affect the behaviour and might cause premature failure. Accordingly, a load above the balanced condition was used in these tests, i.e. with the section controlled by compression. The load used 750kN allowed direct comparison with specimens 7 and 8. 7.2- Tests undertaken. Two specimens, numbers 14 & 15, were cast to study the influence of joint thickness. The specimens were identical to the ones in the main test series except that the joint thickness were 75 mm (No.14) and 50 mm (No.15). The testing procedure was identical to that presented in chapter 5. The same measurements were made to permit comparison with results of specimens 7 & 8. The connection was tested under axial load (750 kN) combined with flexure (without shear). The central monitored span was 450 mm. The failure mode was similar to that of specimen No.7 (axial load 750 kN) except that the joint zone failed at lower peak load which decreased with increasing joint thickness. Plate 7.1 shows both specimens after failure. 7.3- Presentation and discussion of experimental results. The presentation of results in this test series followed the same pattern as in chapter 5« To make comparison easier, some of the results were normalized with respect to peak load conditions of specimen No.8 because of the similarity of cube strengths. The local angular discontinuity across the joint thickness was calculated following the same techniques used in sections 5«3*2 & 5.3*3, namely the Exact & Approximate Methods. The change of bending moment with rotation of the joint is shown in figure 7.2 and tables 7.1-7.3. Specimen No. 14 Axial Load = 750 kN. Joint Thickness = 75 mm. Specimen No. 15 Axial Load =750 kN. joint Thickness = 50 mm. Plate 7.1 Failure Node Of Precast Columns With Variable Joint Thickness. Exact Method. Approx. Method. Exact Method. Approx* Method. 300 peak load at peak load Figure 7.2 Normalized Change Of Bending Moment With Angular Change For Various Joint Thickness (Axial Load = 750 kN). Table 7.1A Angular change Specimen No. 14 Bending Total Components (rad) *10“3 Angular Moment Rotation ( a = b = 1875mm) Distontinuity (kN-mm) *10 Side A Side B Joint *10 (rad) (rad) 0 0.685+ 0.300+ 0.300+ 0.120+ 0 1460 0.495 0.150 0.150 0.195 0.135 7900 1.260 0.340 0.340 0.580 0.450 12305 2.025 0.600 0.600 0.825 0.585 17440 3.195 0.900 0.900 1.395 1.035 19425 3.420 0.920 0.920 1.580 1.210 21325 4.005 1.050 1.050 1.905 1.485 24110 5.135 1.160 1.160 2.810 2.340 26815 6.750 1.125 1.125 4.500 ' 4.050 25300 10.035 0.950 0.950 8.135 7.745 20020 14.985 - - 14.985 14.985 19775 25.335 — 25.335 25.335 + initial values are suppressed. 302 Table 7 .1B Angular change - Specimen No. 15 V _3 Bending Total Components (rad) *10 Angular Moment Rotation ( a = b = 18^5mm) Discontinuity (kN-mm) *io-3 Side A Side B Joint *10 3 (rad) (rad) 0 0.430+ -0.200+ -0.200+ — 0 2785 0.315 0.140 0.140 0.035 0 7320 1.035 0.300 0.300 0.435 0.360 11590 1.800 0.540 0.540 0.720 0.585 12795 1.935 0.560 0.560- 0.815 0.675 15150 2.610 0.760 0.760 1.090 0.900 16810 2.700 0.760 0.760 1.180 0.990 20670 3.285 0.920 0.920 1.445 1.215 22570 3.825 1.040 1.040 1.745 ' 1.485 26700 4.635 1.200 1.200 2.235 1.935 29360 7.065 1.360 1.360 4.345 4.005 31350 8.055 1.420 1.420 5.215 4.860 34195 11.115 1.520 1.520 8.075 7.695 30720 17.370 1.280 1.280 14.810 14.810 30150 25.560 0.960 0.960 23.640 23.640 23600 34.695 0.840 0.840 33.015 * 33.015 23000 46.260 0.760 0.760 44.740 44.740 + initial values are suppressed. 303 Table 7.2A Crack Opening at Joint - Specimen No^14 Bending Elongation Angular Crack Op ening Moment Discontinuity Depth *CG (kN-mm) (mm) '0 *10~3 (rad) (mm) (mm) . Jd ST (nan) V 24110 0.207 2.340 0.0 0.0 24 26815 0.399 4.050 0.1 0.2 44 25300 0.722 7.745 0.2 0.4 50 20020 1.429 14.985 0.5 0.9 57 19775 2.461 25.335 0.9 1.5 59 >e Table 7 .2B Crack Opening at Joint - Specimen No. 15 Bending Elongation Angular Crack Opening Moment Discontinuity Depth ^CG (kN-mra) (mm) 9 . *10 ^(rad) (mm) As , . Jd — (mm) jd 26700 0.204 1.935 0.1 0.2 103 29360 0.506 4.005 0.2 0.3 83 31350 0.632 4.860 0.3 0.4 81 34195 0.993 7.695 0.4 0.6 77 30720 1.705 14.810 0.7 1.0 70 30150 2.604 23.640 1.0 1.6 67 23600 3.564 33.015 1.4 2.2 67 23000 4.799 44.740 1.9 3.0 67 Table 7.3 A Angular change by lateral deflection including estimate of deflection at midspan and corresponding bending moment. Specimen No. 14 Bending Lateral Deflection (mm) Lateral Deflection (mm) Angular Dis- Moment Average of quarter & three quarter span Midspan continuity (kN-mm) r © = ^ 9 = ^ 2© *10-J °total ^bending p 620 ^total ^bending JP p 1120 P (rad) * 10 Uad) ^ " I r a d ) 26815 3.021 3.021 0.0 0.0 4.361 4.361 0.0 0.0 0.0 305 25300+ 4.068 2.6 1.5 2.4 7.00 4.0 3.0 - 5o 20020+ 6.282 1.8 4.5 7.2 11.0 2.6 8.0 - 14. 5 19775+ 9.560 1.8 7.8 12.5 16.5 2.6 14.0 — 25.0 + based on estimated midspan deflection. * * * Table 7.3 B Angular change by lateral deflection including estimate of deflection at midspan and corresponding bending moment. Specimen No. 15 Bending Lateral Deflection (mm) Lateral Deflection (mm) Angular Dis Moment Average of quarter & three quarter span Midspan continuity (kN-mm) r e _ Se C e = 20- *10“3 °total ^bending p 620 ^total ° bending JP p 1120 P *10~3(rad) *10_3(rad) (rad) 34195 4.462 4.462 0.0 0.0 6.891 6.891 0.0 0.0 0.0 306 30720+ 6.312 3.2 3.1 5.0 11.0 5.0 6.0 - 10.0 30150+ 8.792 2.8 6.0 9.7 1 6.0 4.7 11.0 - 19.5 23600+ 11.558 1.9 9.7 15.6 20.5 2.9 17.5 - 31.5 23000+ 15.107 1.9 13.2 21.3 2 7.0 2.9 24.0 - 42.5 + based on estimated midspan deflection. • * 307 Similarly, the change of bending moment with lateral deflection is presented in figure 7.3 and table 7.4-* The results showed that there was a significant reduction in strength and ductility, i.e area under the moment-rotation curve, with increase in joint thickness. For example, the strength declined to 69% and 54-% > of the maximum strength of specimen No.8, when the joint thickness was increased to 50 mm and 75 mm respectively. This reduction in strength can be attributed to reduction in confinement, i.e. reduction of the nmn factor defined in equation 6.20 and figure 6.10(b). Analysis of the embedded gauges and the extensometer readings (refer to figure 7.4- and tables 7.5 & 7.6) indicated increasing axial deformation with increasing joint thickness under axial load, but before application of bending moment. This could have been caused by the bleeding of the grout within the joint thickness that increased with increasing joint thickness. In turn, this bleeding may have created cavities at the joint interface. Such cavities, if large enough could reduce the capacity of the section because of the imposed extra compressive strains. The problem of bleeding, in this case could possibly be overcome by using more sand in the grout mix, e.g. 1.75 instead of 1.0 sand/cement ratio. The pump used in this experimental programme could not accomodate a high sand content. However, pumps normally used on site can pump a grout mix with minimal bleeding. The excessive deformation at pure axial load (table 7.6) explained the deterioration of bond for some of the dowels (refer to figure 7.4-) when bending moment was applied. Plate 7.2 illustrates the difference in the damage of the bond between grout and dowel, for specimens 7 and 15. The cut was taken midway along the height of the grout duct. It might have been expected that if bond was lost between the dowels and the grout, then the column section would act as an 0.2 0.6 0.4 0.8 2 2 iue 7.3 Figure For Various Joint Thickness (Axial Load = 750 kN). 750 = Load (Axial Thickness Joint Various For Deflection Lateral With Moment Bending Of Change Normalized . a - © on Tikes 75mm = Thickness Joint 25mm = Thickness Joint ------0 ^> 2 =Mdpn elcina pa load *2) peak at deflection Midspan = Bnigmmn a pa load peak at moment Bending = M fr pcmnn. 8 no. specimen for ^ fr pcmnn. 8 no. specimen for ^ 2 isa deflection. Midspan = pcmnN. 14 No. Specimen © pcmnN. 15 No. Specimen £ Legend; 308 309 Table 7.4 A Lateral Deflections - Specimen No. 14 Load (Axial = 750 kN) Lateral Deflections (mm) Lateral Bending Moment Transducer 1 Transducer 2 Transducer 3 (kN) (kN-mm) quarter-span mid-span 3quarter-span 0.0 0 0.0 0.0 0.0 2.8 1460 0.245 0.356 0.255 16.9 7900 0.653 0.957 0.680 26.2 12305 1.061 1.561 1.105 37.0 17440 1.544 2.282 1.596 41.4 19425 1.636 2.440 1.707 45.2 21350 1.904 2.848 1.993 50.5 24110 2.341 3.530 2.478 55.4 26815 2.945 4.361 3.097 47.2 25300 4.009 7.0+ 4.127 28.0 20020 6.291 11 .0+ 6.272 17.7 19775 9.556 16.5+ 9.571 + calculated as explained in section 3.3.3 310 Table 7,4 B Lateral Deflections - Specimen No. 15 Load (Axial = 750 kN) Lateral Deflections (mm) Lateral Bending Moment Transducer 1 Transducer 2 Transducer 3 (kN) (kN-mm) quarter-span mid-span 3quarter-span 0.0 0 0.0 0.0 0.0 6.0 2785 0.216 0.312 0.201 15.7 7320 0.574 0.858 0.587 24.7 11590 0.962 1.452 0.986 27.4 12795 1.008 1.533 1.052 32.0 15150 1.322 2.065 1.447 35.8 16810 1.365 2.129 1.488 44.3 20670 1.525 2.457 1.736 48.1 22570 1.729 2.840 2.060 56.9 26700 1.998 3.357 2.460 60.7 29360 2.642 4.748 3.533 64.5 31350 2.891 5.253 3.927 68.3 34195 3.810 6.891 5.114 52.5 30720 5.556 11.0+ 7.067 43,4 30150 7.931 16.0+ 9.652 19.5 23600 10.605 20.5+ 12.512 9.3 23000 14.046 2 7.0+ 16.168 + calculated as explained in section 5.3.3 Bending Moment (kN-m ) Average 0 & 1 Average 4 & 5 Average 6 & 7 311 Initial Cauge No'. Strain 0 A 1 1 2 3 0 2 A 3 1 4 7 0 4 A 5 9 6 0 6 A 7 8 1 0 Average 1 1 2 0 Strain under axial load 10000 us byt before application of> bending moment. t peak load. ?000 1000 2000 Straln(jJB). Figure 7.4A Change Of Strain For Embedded Strain Gauges. Specimen No. 14 Bending Moment (kN-m ) Average 2 & 3 Average 6 & 7 20000 us at M=23000 kN. 312 Initial Caugc N o . Strain 0 & 1 1 2 7 0 2 & 3 8 9 0 <, & 1 1 00 0 b & 7 7 8 0 Avaraga 9 8 5 Strain under axial load but bafora application ol banding aoaant. < -- ,-- 2000 St rain(|is). Figure 7.4B Change Of Strain For Embedded Strain Gauges. Specimen No. 15 313 Table 7.5 A Strains of embedded gauges on dowels. Specimen No. 14 Axial Bending Position of gauge (refer to fig. 7. 4 for Location) Load Moment 0 1 2 3 4 5 6 7 (kN) (kN-mm) (us) (us) (us) (us) (us) (us) (us) (us) 750 0 1140 1320 1670 1265 845 1080 820 800 1460 1110 1315 2160 1350 800 1070 820 830 7900 830 1275 3660 2080 710 1070 820 875 12305 790 1265 5445 3080 605 1080 820 915 17440 630 1215 7630 4285 460 1080 830 965 19425 460 1185 8400 4710 420 1100 810 955 21350 275 1140 9280 5290 320 1100 800 990 24110 235 1120 10700 6340 185 1130 840 1080 26815 160 1010 12185 7700 30 1180 885 1200 25300 275 1150 14950 10815 320 1430 1020 1450 20020 1280 1420 16030 - 815 1780 - 1300 19775 2045 1785 -- 1290 2610 - 3125 * Values are tensile strains. 314 Table 7 .5 B Strains of embedded gauges on dowels. . Specimen No. 15 Axial Bending Position of gauge (refer to fig. .7A for location) Load Moment 0 1 2 3 ' 4 5 6 7 (kN) (kN-mm) (us) (us) (us) (us) (us) (us) (us) (us) 750 0 1230 1305 805 970 1035 980 725 835 2785 990 1190 765 960 950 930 705 850 7320 1210 1300 825. 1075 910 950 715 930 11590 1150 1290 815 1140 815 940 680 995 12795 795 1170 730 1085 755 920 620 960 15150 980 1220 775 1180 670 910 650 1055 16810 765 1120 700 1130 640 890 620 1055 20670 900 1190 745 1200 600 910 640 1115 22570 880 1190 755 1270 495 910 610 1160 26700 550 1095 700 1315 340 880 550 1220 29360 80 950 630 1500 70 860 515 1460 31350 105 900 610 1590 225 850 505 1550 34195 550 850 715 1675 650 920 320 1800 30720 775 1140 185 1710 1300 1260 1065 5540 30150 1620 1480 525~~ 1945 2320 1685 7775 16525 23600 1850 2320 1220 - 3250 2280 8270 21440 23000 3080 3065 - - 4450 2825 9090 25300 * Values are tensile strains. 315 unreinforced one. However, figure 7.5 shows that the strength of both specimens 14 & 15 falls short of that of an unreinforced section indicating the occurrence of premature failure. It is worthwhile noting from plate 7.2 the random location of the dowels which justified the generous tolerance used for the size of the preformed duct. 7.4- Summary and conclusions. The sensitivity of the joint performance to errors in construction was examined by varying the joint thickness. The resulting decrease in confinement due to increase in joint thickness, led to significant reduction in strength. The excessive measured axial deformation indicated that the reduction in strength might be a result of the interactive effects of both the joint thickness and the quality of the grout which caused cavities at the joint interface. The bleeding effect was not significant when the joint thickness was 25 mm.. Therfore, in practical application, the sand ratio in the grout mix should not be such that it causes unacceptable bleeding especially if the joint thickness exceeds 1/8 the minimum dimension of the column section. The loss of bond of some of the dowels implied that it could have been the main cause for the reduction in strength. If this was the case then the lower bound of the strength of specimens 14 & 15 would have been the interaction diagram of an unreinforced section. However, the strength of the specimens was less than that of an unreinforced section suggesting the occurrence of premature failure. It is recommended that care must be taken in construction of this type of joint to control the quality of the grout and the thickness of the joint to avoid premature failure. 200 Axial (kN) 316 Figure 7.5 Change Of Strength With Joint Thickness. 317 Table 7.6 Change of axial deformation with joint thickness. Axial Load = 750 kN , Bending Moment = 0. Specimen Joint Average strain of Average axial deformation No. thickness embedded gauges from axial transducers, (mm) (us) (mm) 7 25 720 0.345 8 25 810 0.331 15 50 985 0.406 14 75 1120 0.468 Specimen No. 7 Axial Load = 750 kN. Joint Thickness = 25 mm. Specimen No. 15 Axial Load = 750 kN. Joint Thickness = 50mm. Note: The above sections are cuts at about 400mm. from joint. Other cuts along the length of the grouted ducts show the same damage. Plate 7.2 Damage In Grouted Ducts 319 Chapter 8- Discussion and conclusions. 8.1- Summary and general discussion. The work undertaken has involved a study of the behaviour of the grouted dowelled connection between precast concrete columns and a review of the various types of column-to-column connections most commonly used in precast structures. The efficiency of the connection relates to its dimensional accuracy, i.e. tolerance, which in turn can only be obtained by using a suitable manufacturing process. It is concluded that there are only two practical approaches to this fundamental problem of tolerances; (a) connections with near perfect fit, or, (b) connections with generous tolerances. The grouted dowelled connection is of type(b) and so provides both the tolerance and continuity required in most structures (chapter 2). A confinement model, based on the work of Sheikh and Uzumeri[8.3] and Ahmad and Shah[8.1] (chapter 3) > has been used to detail the various specimens as explained in Appendix 1. Under pure axial load, the specimen failed outside the connection zone, thus proving the adequacy of the detailing (chapter 5)• However, for axial load combined with bending, the connection behaved similar to a monolithic section up to peak load. The moment curvature relationship for the joint region was predicted satisfactorily by the column theory (chapter 6). The post peak load behaviour was characterized by a rigid body rotation of the column elements about the jointed region.The analysis of the angular discontinuity at the joint indicated that the load capacity of the connection depends on the ability of its compressive zone to resist crushing, which can be enhanced by confining concrete, for example with rectilinear ties. The concept of 320 confinement was used very effectively in this research programme to prevent premature failure of the connected columns. Similarly, Bobrowski[8.2] used the concept of confinement when designing the shoe connection. The strength envelope of the shoe connection, predicted by the column theory, proved to be a lower bound for all combinations of axial and bending loads applied to the connection (chapter 6). The specimens subjected to bending moment or bending moment and shear, under same axial load, behaved similarly. The effect of shear on the load capacity of the relevant specimens was not significant when the shear span to effective depth was about J+ (chapters 5 & 6). The sensitivity of the joint performance to errors in construction was examined by varying the joint thickness (chapter 7). The resulting change in confinement led to a significant reduction in strength with increase in joint thickness. Also, it was concluded that the quality of the grout must be such as to minimize bleeding; otherwise, the resulting cavities, which were measured in some specimens (14- & 15), contributed to the occurrence of premature failure. The excessive deformation caused by bleeding and by reduction of confinement due to increasing joint thickness, helped the deterioration of bond between the grout and the dowels. It is recommended that bond must be given due consideration (chapter 7). The post peak behaviour of the jointed columns which was observed during the test, depended on the overall length and stiffness of the columns as well as the performance of the joint itself. Successive modification of the instrumentation led to techniques by which the behaviour of the joint itself could be isolated. In considering structural behaviour, there must be recognition of the possibility of localisation of failure and possibly the adoption of higher factors of safety to avoid failure in the joint itself. 321 8.2- Conclusions. The principal conclusions, relating to the behaviour of the grouted dowelled connections between precast concrete columns, are summarized in this section under the following headings; (a) Tolerances in precast concrete structures (chapter 2). (b) Confinement of concrete by rectilinear ties (chapter 3)• (c) Application- design and construction (chapters 5,6 & 7). Suggestions for further work are incorporated with the conclusions where these are appropriate. Tolerances (chapter2). 1) The conceptual design of a precast project is the place to begin to deal with dimensional control considerations. Architectural and structural concepts should be developed with the practical limitations of dimensional control in mind. 2) The practical approach to tolerances is one in which allowance is made for the elimination of the various constraints. This can be achieved by judicial detailing. The opposite course of action, i.e. one of accomodating all the constraints simultaneously, would result in very small tolerances approaching perfect fit design. 3) Actual geometric imperfections in prefabricated structures need to be studied, by investigating existing structures, to establish a guide to "erection tolerance". Confinement of concrete (chapter 3)• 4) The detailing of concrete in the connection zone requires special consideration, for example the use of rectilinear ties for confinement in order to avoid premature failure of the jointed structural elements. 322 5) The confinement model developed in this text provides a useful and practical design tool for detailing connections in concrete structures. 6) The equation for the ’’effectively confined" area, used in the confinement model, has been determined from a limited number of experiments. Consequently, more work needs to be done to define the empirical values in the equation with better certainty and possibly in an easier form. Application (chapters 5*6 & 7). Design. 7) The specimens in the main test series, which were detailed using the proposed confinement model, achieved their full predicted strength. 8) The behaviour up to peak load was adequately predicted by the column theory, therefore, providing a convenient analytical tool for design purposes. 9) For uniaxial bending, discretization of the column section into more than 28 elements had little effect on the accuracy of the results. 10) The stability of the post peak load behaviour, which was localized at the joint, depended on the capacity of the compressive zone to resist crushing. The addition of steel ties in the joint zone, i.e. increasing confinement, enhanced the resistance to crushing and hence improved the ductility of the specimens. 11) The study of the shoe joint designed by Bobrowski[8.2] showed that all tested specimens achieved full strength. However, more detailed experimental investigation of the shoe joint may lead to even further economies in detailing column-to-column connections in precast 323 structures without sacrificing the main advantage of attaining the full strength capacity of the column section. 12) The behaviour of the grouted dowelled and the shoe connections was studied under monotonic loading. The work needs to be extended to study the behaviour under cyclic loading to cover the full scope of applications. 13) Precast concrete structures require a higher factor of safety than reinforced concrete structures due to the presence of the connections. A value of 2 (= 4/3 x regular load factor) is recommended, as a result of the present research work, to be suitable. However, more work needs to be done on full size structural members to confirm this conclusion. Construction 14) The grouted dowelled connection showed sensitivity to workmanship. Increasing the joint thickness reduced the strength significantly. The joint thickness of 1/8 the length of the jointed column, determined by Somerville[8 .4 ] and tried in this research work, appears to be a satisfactory limitation provided there is adequate control on grout properties. 15) The grout used on site must be of a quality that does not result in excessive bleeding. Cavities created by bleeding can contribute to the occurrence of premature failure. 16) Bond deterioration proved to be an important consideration. Therefore, the use of deformed, rather than plain, steel bars is recommended. This, however could affect the results obtained on joint ductility. 17) The provision of ample tolerance when determining the size of the grout ducts is recommended due to lack of alignment of the dowels (refer to plate 7.2), which is typical of site conditions. 324 List Of References. Chapter 1• 1.1- The Institution of Structural Engineers. "Structural joints in precast concrete - Manual." Institution of Structural Engineers, August 1978, London. 1.2- The Polytechnic of Central London. "Report on column joint performance." Department of Civil Engineering. Project 38CH1P,Dec.1971,London. 1.3- Somerville, G. "Horizontal compression joints in precast concrete framed structures." Ph.D. dissertation submitted at the City University, Dec.1971,London. Chapter 2. 2.1- Bobrowski, J. "Tolerances and accuracy in buildings." CIB Report No. 16. Colloquium organized by CIB Working Commission W49 in collaboration with FIG. Copenhagen 1972. 2.2- Bobrowski, J. "Accuracy in precast structures." Financial Times. Feb.15»1973« 325 2.3- Danish Concrete Society. "Tolerances for main dimensions of concrete components." Revised edition 1975* 2.4- - Eriksson,0. "Sleeve method of splicing reinforcing bars." Ingenion (Copenhagen) International Edition.Vol4,No.4»Dec.1960,pp136 2.5- Fiorato, A.E. "Geometric variations in the columns of a precast concrete industrial building." PCI Journal, Vol.18,No.4»July/August 1973,pp.50-60. 2.6- Gergely, P. & Sozen, M.A. "Design of anchorage zone reinforcement in prestressed beams." PCI Journal, Vol.12,No.4,April 1967, pp.63-74. 2.7- Gurskii, A.F. & Fedotycheva, V.S. "Joints in precast reinforced concrete columns in multi-storey buildings." Beton i Zhelozonbetton, No.5, 1964* pp.207-211. 2.8- Hartland, R.A. "Design of precast concrete." Surrey University Press, 1975* 326 2.9- Heynisch, V. nA new type of reinforced concrete butt joint of VEB.n Bauplan-Bautechnic, Vol.16,No.9 > Sept.19&2• 2.10- Igonin, L.A. nGlued joints for reinforcing bars and precast reinforced concrete units." Civil Engineering Research Association (CIRA), Trans.No.1,Sept.19&4-• 2.11- The Institution of Structural Engineers. "Structural joints in precast concrete - Manual." The Institution Of Structural Engineers, Aug.1978, London. 2.12- Ivey, D.L. "Fatigue of grouted sleeve reinforcing bar splices." ASGE Journal,Structural Division,Jan.1968,pp.199-210. 2.13- Johnston, R.P. "Creep tests on glued joints." Institution of Structural Engineers Journal, May19&6, pp. 14-3-14-7. 2.14- - Kriz, L.B. & Raths, C.H. "Connections in precast concrete structures; bearing strength of column heads." PCI Journal, Vol.8,No.6,1963,pp*45-55» 327 2.15- Korolev, L.V. & Korovin, N.N. "Joints between prefabricated reinforced concrete columns and foundations.n Prom.Strout. Vol.4.1 ,pp.64.-68. 2.16- Laursen, F.B. "Tolerances for main dimensions of concrete components." Build International,May/June 1971. 2.17- Martin, L.D. & Korkosz, W.J. "Connections for precast prestressed concrete buildings including earthquake resistance." PCI Technical Report No.2, March 1982. 2.18- Niyogi, S.K. "Concrete bearing strength - support,mix,size effect." ASCE Journal, Vol.100,No.ST8,Aug.1974,pp.1685-1702. 2.19- Pfister, J.F. "High strength bars as concrete reinforcement." PCA Journal, Vol.5,No.2,May1963,pp.27-4-0. 2.20- The Polytechnic of Central London. "Report on column joint performance." Department of Civil Engineering. Project 38CH1P.Dec.1971.London. 328 2.21- Prestressed Concrete Institute (PCI). nPCI design handbook.n Second edition.1978. 2.22- PCI Committee on Tolerance. "Tolerances for precast and prestressed concrete." PCI Journal, Vol.30,No.1,Jan/Feb 1985,pp.26-112. 2.23- Somerville, G. "The behaviour of mortar joints in compression." C&CA Technical Report 4-2.4-76, Nov. 1972. 2.24- Somerville, G. "The influence of percentage reinforcement on mortar compression joints for framed structures." C&CA Technical Report 42.477, Dec.1972. 2.25- Somerville, G. "Horizontal compression joints in precast concrete framed structures." Ph.D. dissertation submitted at the City University,Dec.1972,London. 2.26- Somerville, G. & Burhouse, P. "Tests on joints between precast concrete members." Engineering Papers 45. BRS. August 1967. 329 2.28- Spyra, J.J. & Smith, R.B.L. "The development of a new method of jointing precast concrete members in buildings." Civil Engineering & Public Works Review. March 1965«pp»331-335« 2.29- Stupre-Society for Precast Concrete, Netherlands. "Precast concrete connection details - Design Manual." Beton-Verlag GmbH 1978. 2.30- Utescher, G. "Tests to failure of connections between precast and insitu concrete." C&CA Library Translation No.96. 2.31- Volbeda, A. "Tolerance systems - Comparison between four systems." CIB Report No.16. Colloquium organized by Working Commission W49 in collaboration with FIG.Copenhagen 1972. 2.32- Yee, A.A. & Chang, N.K. ""One Hundred Washington Square" office tower." PCI Journal, Vol. 29, No.1,Jan/Feb 1984-,pp. 18-63. 330 Chapter 3. 3.1- Ahmad,S.H. & Shah,S.P. "Complete triaxial stress-strain curves for concrete." ASCE , Vol.108 , No.ST4 , April 1982 , pp.728-742. 3.2- Ahmad,S.H. & Shah,S.P. 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Urbana,Univ.of Illinois,Eng'g Experiment Station,1928,Bulletin No.185. 333 3*22- Richart,F.E.;Brandtzaeg,A.;&Brown,R.L. "The failure of plain & spirally reinforced concrete in compression." Urbana,Univ.of Illinois,Eng'g Experiment Station, 1 929,Bulletin No. 190. 3.23- Roy,H.E.H. & Sozen,M.A. "Ductility of concrete." ACI Publication,SP-1 2,1965,pp.213-224. 3.24- Sargin,M.;Ghosh,S.K.;&Handa,V.K. "Effects of lateral reinforcement upon strength & deformation properties of concrete." MCR ,V.23,No.75-76,Jun/Sept.1971 ,pp.99-110. 3.25- Scott,B.D.;Park,R.;& Priestley,M.J.N. "Stress-strain behaviour of concrete confined by overlapping hoops at low and high strain rates." AC I Journal,V.79,No.1,Jan./Feb. 1982,pp.13-27. 3.26- Shah,S. & Rangan,B.V. "Effects of reinforcements on ductility of concrete." ASCE Journal,V.96,No.ST6,June 1970,pp.1167-1184. 3.27- Sheikh,S.A. "A comparative study of confinement models." ACI Journal,V.79,No.4,July/Aug. 1982,pp.296-306. 3.28- Sheikh,S.A. "A comparitive study of confinement models." Discussion bY R. Park,A.Fafitis and S.P.Shah,and Author ACI Journal,May/June 1983,pp260 334 3.29- Sheikh,S.A. & Uzumeri,S.M. "Strength and ductility of tied concrete columns." ASCE Journal,V.106,No.ST5,May 1980,pp.1079-1102. 3.30- Sheikh,S.A. & Uzumeri,S.M. "Analytical model for concrete confinement in tied columns." A S C E Journal,V.10 8 ,No.ST 12 ,Dec.1982,pp.2703-2722. 3.31- Soliman,M.T.M. & Yu,C.W. "The flexural stress-strain relationship of concrete confined by rectangular transverse reinforcement." MCR ,V.19,No.61 ,Dec.1967,pp.223-238. 3.32- Somes,N.F. "Compression tests on hoop-reinforced concrete." ASCE Journal,V.96,No.ST7,July 1970,pp.1495-1509. 3*33- Vallenas,J.;Bertero,V.V.;& Popov,E.P. "Concrete confined by rectangular hoops and subjected to axial loads." Report No.UCB/EERC-77/1 3,Earthquake Engineering Research Center, Univ.of California,Berkeley,Aug.1977,114pp. 3*34- Watstein,D. "Effect of straining rate on the compressive strength and elastic properties of concrete." ACI Journal proceedings V.49,No.8,April 1953,pp.729-744. 3-35- The Polytechnic of Central London. Report on Column Joint Performance in H-Frame. Dept, of Civil Engineering, Project 38CH1P, Dec.1971. 335 3*36- Dilger, W.H. ; Koch, R. & Kowalczyk R. "Ductility of plain & confined concrete under different strain rates" AGI Journal, Jan/Feb 1984> pp.73-81. Chapter 4 4.1- Dally, J.W. & Riley, W.F. "Experimental stress analysis." McGraw-Hill 1978, Second Edition, pp.229. 4-2- Somerville, G. "Horizontal compression joints in precast concrete framed structures." Ph.D. dissertation submitted at the City University, Dec.1972,London. Chapter 6 6.1- Cranston, W.B. "A computer method for the analysis of restrained columns." Technical Report. TRA 402. Cement & Concrete Association. April 1967. 6.2- Engstrom, Bjorn. "Ductility of tie connections for concrete components in precast structures." FIP Technical Report 1982. 336 6.3- Hendry,A.W. "Structural Brickwork." Macmillan Press Ltd. 1981. 6.4- Hendry, A.W.; Sinha B.P. & Davies A.B. "An introduction to load bearing brickwork design." Ellis Horwood Series in Engineering Science. 1981. 6.5- Neville, A.M. "Properties of Concrete." Pitman. Third Edition. London:1981. 6.6- Park, R. ; Priestley, M. & Gill, W.D. "Ductility of square-confined concrete columns." ASCE Journal, V.108, N0 .ST4 , April 1982, pp.929-950. 6.7- The Polytechnic of Central London. "Report on column joint performance." Dept, of Civil Engineering. Project 38CH1P, Dec. 1971, London. Chapter 7 7.1- Somerville, G. "Horizontal compression joints in precast concrete framed structures. Ph.D. dissertation submitted at the City University, Dec.1972, London 337 Chapter 8 8.1- Ahmad, S.H. & Shah, S.H. "Stress - strain curves of concrete confined by spiral rebars." ACI Journal, Vol.79>No.6,Nov./Dec. 1982,pp.4-84-490. 8.2- Sheikh, S.A. & Uzumeri, S.M. "Strength and ductility of tied concrete columns." ASCE Journal, Vol.106,No.ST5,May1980,pp1079-1102. 8.3- Somerville, G. "Horizontal compression joints in precast framed structures." Ph.D. dissertation submitted at the City University, Dec.1972,London. 8.4- The Polytechnic of Central London. "Report on column joint performance." Department of Civil Engineering.Project 38CH1P.Dec.1971. 338 Appendix 1 - Chapter 4 (a) Calculation of the amount of ties in the joint region. The amount of the ties in the joint region must balance the reduction in strength due to discontinuity of the 4 (j) 10mm mild steel bars within the joint. The bearing capacity of these bars is approximately 90 kN.. The following steps were followed for calculating the strength gain of the column section when the spacing of the ties was reduced from 100mm in the regular section of the column to 50mm in the joint region, 1- calculate the volumetric ratio of the column section,p, when the spacing of the ties,s, is 100mm p=0.00662 and when s=50mm p= 0.01323, 2- calculate the effectively confined area and the lateral confining pressure using equation 3.10 and figures 3.10 & 3.15 of the main text, therefore, effectively confined area= 2 A = 8130mm when s= 100mm e n=8 and A =12420mmi when s= 50mm e C=68 mm (for notations refer to figure 3.10) the modified confinement= p =0.00221 when s=100mm m and p =0.00671 when s= 50mm m this results in a confining pressure, 2 f = 0.5x0.00221x500 = 0.55 N/mm (0.078 ksi) when s=100mm r and f = 0.5x0.00671x500 = 1.69 N/mm (0.240 ksi) when s= 50mm r 3- calculate the strength gain factor,K, using equation 3.11 of main text, and bearing in mind that the cylinder strength 2 of concrete,f , is 35 N/mm (5.0ksi),approx. 0.85 of cube strength, o for s=100mm K^q q =1.04 ; and, for s=50mm K^q =1.14 So, the gain in bearing strength of the column section due to provision of extra ties in the joint region is, area of the concrete bounded by the ties)*f = jU 1 uu o (1.14-1.04)x 1562x 35 90 kN. which is enough to offset the loss in strength due to discontinuity of the 4 (f) 10mm bars when pure axial load is acting. 339 T (b) Calibration of 200 jack Load=L Pressure Voltage=V (kN) (psi) (volts) 0 0 0 95 290 0.20145 190 580 0.40290 285 870 0.60295 380 1160 0.80470 480 1450 1.00430 580 1740 1.20120 690 2030 1.40330 785 2320 1.60240 885 2610 1.80140 980 2900 2.00275 1080 3190 2.20325 1180 3480 2.40325 1280 3770 2.60275 1380 4060 2.80410 1480 4350 3.00300 1580 4640 3.20325 1680 4930 3.40290 1780 5220 3.60425 1885 5510 3.80340 The above data are average of three sets of readings. Equation: L = -9.4 + 496.5 * V Error was + 0.001 volts resulting with + 0.5 kN error in load readings. 340 (c) Calibration of 50 jack. Load=L Pressure Voltage=V (kN) (psi) (volts) 0 0 0 10 260 0.00043 20 460 0.00076 30 675 0.00110 40 885 0.00144 50 1100 0.00178 60 1320 0.00213 70 1535 0.00250 80 1745 0.00282 90 1960 0.00316 100 2175 0.00350 110 2390 0.00385 120 2600 0.00420 130 2800 0.00452 140 3020 0.00487 150 3220 0.00520 The above data are average of minimum six readings. Equation: L = -2.1 + 29215 * V Error was +0.00001 volts resulting with + 0.3 kN error in load readings. 341 Appendix 2 - Chapter 5 Estimate of rotation of the precast columns near the joint. Specimens 5,6 & 7 had a PI surface gauge configuration (refer to figure 4.10a). The objective was to determine the rotation of the joint thickness, as explained in the main text of chapter 5. The surface gauges were effective up to the cracking of the joint interface. It is discussed that the cracks would be concentrated at the joint interface. Consequently, the precast parts of the connected columns would follow an elastic linear path. Therefore, rotation of the precast columns in the vicinity of the joint zone, within the monitored central span, would be estimated based on an elastic linear behaviour. Figures A.5.1,A.5.2 & A.5.3 show both the curvature as obtained from the change of strains across the depth of the section and the linear trend representing an estimate of the behaviour of the precast elements. It is worthwhile noting that before the cracks propagate across the joint interface, the curvature was obtained by considering the average of the change of strains between top (i.e. gauges 1 & 4 in figure 4.13 ) and centre (i.e. gauges 2 & 5 in figure 4.13 ),and between centre and bottom (i.e. gauges 3 & 6 in figure 4.13 )• However, when cracks reach the level of the top gauges, the curvature was calculated from the change between the centre and bottom gauges only. Therefore, in this case, 0. or = 215 * (J) A B where; where; ■9- , ©„ = rotation of side A & B respectively, A B in table 5.1 for specimens 5,6 & 7. (|) = curvature as obtained from the linear trend in figures A.5.1 - A.5.3 for relevant specimens. Bending Moment *10^ (kN-mm) 40 30 20 342 10 Figure A.5.1 Estimate of rotation of the precast columns near the joint Specimen No. 5 (Axial load = 250 kN). 343 Figure A.5.2 Estimate of rotation of the precast columns near the joint Specimen No. 6 (Axial load = 500 kN). I 344 Figure A.5.3 Estimate of rotation of the precast columns near the joint Specimen No. 7 (Axial load = 750 kN). 345 Table 5.1A Angular Change — Specimen No.3 Components Bending Total (rad) *10“3 Angular Moment Rotation ( a = b =215 mm) Discontinuity (kN-mm) *10 Side A Side B Joint *10‘J (rad) (rad) 0 0.1 + 0.1 + 0 0 0 1750 0.304 0.030 0.070 0.204 0.200 6165 0.717 0.250 0.240 0.227 0.200 10680 1.286 0.520 0.415 0.351 0.300 15150 2.181 0.810 0.610 0.761 0.700 19690 3.406 1 .190 0.790 ' 1.426 1.340 24430 4.917 1.685 0.970 2.262 2.140 29150 7.069 2.170 1.120 3.779 3.630 31630 8.322 2.300 1.170 4.852 • 4.700 31790 6.605 2.300 1.170 5.135 4.985 34425 11.014 2.500 1.270 7.244 7.085 34540 11.685 2.515 1.285 7.885 7.705 35590 12.572 2.600 1.310 8.662 8.480 35125 18.051 3.490 1.575 12.986 12.750 33990 21.975 3.110 1.140 17.725 17.500 32980 25.830 2.820 0.860 22.150 . 22.000 31880 32.786 2.565 0.775 29.446 29.300 30995 38.641 2.450 0.565 35.626 35.500 29735 59.620 1.480 0.540 57.600 57.510 27595 112.243 - - 112.243 112.243 19000 142.899 -- 142.899 142.899 + initial values are suppressed. 346 Table 5.1B Angular Change — Specimen No.5 -3 Bending Total Components (rad) ~10 Angular Moment Rotation ( a = b =215 mm) Discontinuity -3 (kN-mm) *10 Side A Side B Joint *10 ^ (rad) (rad) 0 0.015+ 0.1 + 0.1 + 0 0 4160 0.395 0.130 0.130 0.135 0.120 8630 0.855 0.300 0.300 0.255 0.255 11370 1.485 0.388 0.388 0.710 0.670 18400 3.555 0.645 0.645 2.265 2.205 20670 4.410 0.690 0.690 3.030 2.965 27100 6.570 0.925 0.925 4.720 4.630 32540 8.505 1.120 1.120 6.265 6.160 34530 10.710 1.200 1.200 8.310 • 8.200 34863 21.915 1.200 1. 200 19.515 19.405 30518 38.475 1.050 1.050 36.375 36.375 27100 53.640 0.900 0.900 51.840 51.840 26400 68.400 0.850 0.850 66.700 66.700 23500 86.000 0.775 0.775 84.450 84.450 23000 107.975 0.775 0.775 106.425 106.425 + initial values are suppressed. 347 Table 5.1c Angular Change” Specimen No.6 Bending Total Components (rad) *10~3 Angular Moment Rotation a = b =215 mm) Discontinuity (kN-mm) *10 Side A Side B Joint *10 (rad) (rad) 0 0.090+ 0.068+ 0.068+ 0.004+ 0 2665 0.270 0.100 0.100 0.070 0.065 7241 0.620 0.225 0.225 0.170 0.150 11572 1.080 0.335 0.335 0.410 0.380 16231 1.690 0.500 0.500 0.690 0.640 21000 2.150 0.690 0.690 0.770 0.705 25476 3.090 0.840 0.840 1.410 1.330 27916 3.720 0.905 0.905 1.900 1.820 30496 4.545 0.990 0.990 2.565' 2.470 33066 5.355 1.075 1.075 3.205 3.105 34193 5.670 1.120 1.120 3.430 3.325 35562 6.480 1.160 1.160 4.160 4.050 36876 6.885 1.205 1.205 4.475 4.360 38241 7.605 1.270 1.270 5.065 4.945 39372 7.965 1.290 1.290 5.385 5.265 40954 9.225 1.355 1.355 6.515- 6.390 4 42356 9.990 1.375 1.375 7.240 7.110 44015 11.655 1.500 1.500 8.655 8.515 44368 13.275 1.500 1.500 10.275 10.135 43712 17.370 1.450 1.450 14.470 14.470 38566 25.560 1.275 1.275 23.010 23.010 38500 31.-750 1.205 1.205 29.340 29.340 39000 41.230 1.210 1.210 38.810 38.810 26000 97.280 0.730 0.730 95.820 95.820 +. initial values are suppressed. 348 Table 5.1 D Angular Change - Specimen No. 7 Bending Total Components (rad) *10~3 Angular Moment Rotation a = b =215 mm) Discontinuity (kN-mm) *10 Side A Side B Joint *10 3 (rad) (rad) 0 0.230+ 0.100+ 0.100+ 0 0 3186 0.240 0.150 0.150 0.015 0 7784 0.900 0.300 0.300 0.300 0.270 12995 1.305 0.500 0.500 0.305 0.270 17315 1.800 0.600 0.600 0.600 0.540 22205 2.475 0.775 0.775 ' 0.925 0.850 26920 3.015 0.925 0.925 1.165 1.075 32030 4.140 1.100 1.100 1.940 1-.640 34318 4.770 1.180 1.180 2.410 • 2.295 36765 5.310 1.400 1.400 2.510 2.380 39820 6.525 1.570 1.570 3.385 3.235 40230 7.110 1.640 1.640 3.830 3.685 40810 7.965 1.655 1.655 4.655 4.500 42555 9.405 1.765 1.765 5.875 5.710 36907 18.585 1.400 1.400 15.785 15.785 31652 39.690 1.000 1.000 37.690 . 37.690 + initial values are suppressed. 349 Table 5.IE Angular Change - Specimen No.8 Bending Total Components (rad) *10"3 Angular Moment Rotation ! a = b =290 mm) Discontinuity n (kN-mm) *10 Side A Side B Joint *10 (rad) (rad) 0 0.020+ 0.300+ 0.600+ __ 1770 0.240 0.115 0.090 0.035 - 5085 0.540 0. 260 0.205 0.075 - 8535 0.900 0.495 0.375 0.030 - 10195 1.140 0.580 0.465 0.095 - 15610 1.860 0.960 0.670 0.230 - 18330 2.220 1.130 0.815 0.275 - 21585 2.580 1.365 0.960 0.255 - 24750 3.000 1.540 1.100 0.360 - 28150 3.600 1.770 1.275 0.555 - 31315 4.080 2.150 1.420 0.510 . 34880 4.860 2.755 1.680 0.430 - 38380 5.880 3.420 1.800 0.660 0.480 42040 7.200 4.120 2.000 1.080 0.870 46400 9.600 4.785 2.235 2.580 2.340 48280 11.040 5.335 2.550 3.155 ’ 2.880 49785 12.900 5.655 2.550 4.695 4.410 49925 13.980 5.745 2.525 5.710 5.425 48550 17.160 5.510 2.090 9.560 9.560 42255 24.420 5.045 1.565 17.810 17.810 40690 30.180 4.900 1.365 23.915 23.915 39100 42.120 4.175 1.190 36.755 36.755 35860 54.780 3.480 1.190 50.110 50.110 33000 68.400 2.870 0.755 64.775 64.775 -f initial values are suppressed. 350 Table 5.1 F Angular Change - Specimen No.9 Bending Total Components (rad) *10 3 Angular Moment Rotation a = b =290 mm) Discontinuity (kN-mm) *10 Side A Side B Joint *10"3 (rad) (rad) 0 0.280+ 0.200+ 0.100+ -- 4640 0.660 0.290 0.230 0.140 0.120 7860 1.140 0.495 0.350 0.295 0.265 10910 1.560 0.670 0.465 0.420 0.385 14085 2.040 0.900 0.580 0.560 0.510 17455 2.940 1.190 0.695 ' 1.055 0.985 20670 3.960 1.450 0.810 1.700 1.620 23790 5.520 1.710 0.930 2.880 2.790 27025 7.440 2.030 0.985 4.425 • 4.320 28930 9.360 2.260 0.985 6.115 6.005 30720 10.800 2.380 1.015 7.405 7.290 31610 12.360 2.525 1.045 8.790 8.665 32350 13.200 2.550 1.075 9.575 9.450 34285 16.800 2.755 1.075 12.970 12.840 34890 21.600 2.870 1.190 17.540 17.400 34935 25.920 2.870 1.220 21.830 . 21.690 34625 31.260 2.840 1.335 27.085 27.085 34055 36.540 2.815 1.450 32.275 32.275 32650 42.660 2.580 1.075 39.005 39.005 28100 51.660 2.495 0.755 48.410 48.410 27100 57.480 2.495 0.755 54.230 54.230 26700 62-. 940 2.465 0.755 59.720 59.720 26350 70.140 2.440 0.695 67.005 67.005 26160 79.380 2.405 0.695 76.280 76.280 25420 87.600 2.380 0.665 84.455 84.455 25100 95.040 2.350 0.610 92.080 92.080 22640 121.440 2.205 0.610 118.625 118.625 21720 127.320 2.115 0.520 124.685 124.685 + initial values are suppressed. . 351 Table 5.2a Crack Opening at Joint - Specimen No. 3 Bending Elongation Angular Crack Opening Moment Discontinuity Depth a c g (kN-mm) (mm) 6 *10-3(rad) (mm) (mm) Ac , . Jd — (mm) jd 15150 0.186 0.7 0.1 0.1 94 19690 0.385 1.3 0.2 0.2 152 24430 0.632 2.1 0.3 0.4 175 29150 0.999 3.6 0.6 0.6 178 31630 1.211 4.7 0.7 0.8 171 31790 1.257 5.0 0.7 0.8 168 34425 1.680 7.1 1.0 1.2 164 34540 1.804 7.7 1.1 1.3 164 35590 1.928 8.5 1.1 1.3 159 35125 2.902 12.8 1.8 2.1 163 33990 3.581 17.5 2.2 2.6 150 32980 4.228 22.0 2.6 3.2 143 31880 5.408 29.3 3.3 4.1 140 30995 6.369 35.5 3.9 4.8 136 29735 9.759 57.5 6.0 7.4 130 27595 17.792 112.2 10.7 13.5 120 19000 22.129 142.9 13.1 16.7 116 352 Table 5.2b Crack Opening at Joint - Specimen No. 5 Bending Elongation Angular Crack Op ening Moment Discontinuity Depth ^CG (kN-mm) (mm) 6 . *10_3(rad) (mm) (ram) AC , V Jd — (ram) 6 jd 11370 0.080 0.7 0 0 4 • 18400 0.432 2.2 0.2 0.3 120 20670 0.563 3.0 0.3 0.4 121 27100 0.942 4.6 0.5 0.6 139 32540 1.261 6.2 0.7 0.9 143 34530 1.654 8.2 1.0 1.2 144 34863 3.655 19.4 2.3 2.8 142 30518 6.448 36.4 4.0 4.9 136 27100 8.945 51.8 5.6 6.9 132 26400 11.379 66.7 7.1 8.7 131 23500 14.422 84.5 9.0 11.1 131 23000 18.107 106.4 11.3 14.0 131 353 Table 5.2C Crack Opening at Joint - Specimen No.6 Bending Elongation Angular Crack Op ening Moment Discontinuity Depth a c g (kN-mm) (mm) 0 . *10 ^(rad) (mm) (mm) A: . . Jd Z ~ On™) e jd 25476 0.202 1.3 0 . 0 . 31 27916 0.315 1.8 0.1 0.1 69 30496 0.433 2.5 0.1 0.2 84 33066 0.565 3.1 0.2 0.3 98 34193 0.617 3.3 0.3 0.3 103 35562 0.748 4.1 0.3 0.4 109 36876 0.816 4.4 0.4 0.5 113 38241 0.923 4.9 0.4 0.6 115 39372 0.988 5.3 0.5 0.6 117 40954 1.190 6.4 0.6 0.8 120 42356 1.323 7.1 0.7 0.9 123 44015 1.596 8.5 0.9 1.1 126 44368 1.852 10.1 1.0 1.3 125 43712 2.491 14.5 1.4 1.8 122 38566 3.771 23.0 2.2 2.7 119 38500 4.644 29.3 2.6 3.4 115 39000 6.076 38.8 3.5 4.4 114 26000 13.863 95.8 7.7 10.1 105 L.. ______354 Table 5.2D Crack Opening at Joint - Specimen No. 7 Bending Elongation Angular Crack Op ening Moment Discontinuity Depth ^CG (kN-mm) (mm) 6 *10~3(rad) (mm) (mm) Ac , v Jd — (mm) jd 36765 0.356 2.4 0. 0.1 34 39820 0.561 3.2 0.2 0.2 71 40230 0.656 3.7 0.2 0.3 82 40810 0.779 4.5 0.3 0.4 87 42555 1.015 5.7 0.4 0.6 99 36907 2.282 15.8 1.1 1.5 95 31652 4.732 37.7 2.2 3.2 84 * Table 5.2E Crack Opening at Joint - Specimen No. 8 Bending Elongation Angular Crack Opening Moment Discont inuity Depth AT ^CG (kN-mm) (mm) 9 *10“3(rad) (mm) (mm) A c , ) Jd 7T- (mm) ejd 42040 0.681 0.9 0 . 0 . 43 46400 1.058 2.3 0.2 0.2 101 48280 1.282 2.9 0.2 0.3 105 49785 1.562 4.4 0.4 0.5 108 49925 1.739 5.4 0.5 0.6 112 48550 2.185 9.6 0.8 1.0 105 42225 3.141 17.8 1.3 1.8 100 40690 3.902 23.9 1.8 2.4 98 39100 5.389 36.8 2.6 3.5 95 35860 6.730 50.1 3.2 4.4 88 33000 8.243 64.8 3.9 6.4 98 356 Table 5.2F Crack Opening at Joint - Specimen No. 9 Bending Elongation Angular Crack Opening Moment Discontinuity Depth AT ^CG (kN-mm) (mm) 0 . *10~3 (rad) (mm) (mm) A c , . Jd — (mm) e jd 17455 0.235 1.0 0.1 0.1 74 20670 0.413 1.6 0.2 0.2 128 23790 0.686 2.8 0.3 0.4 146 27025 1.024 4.3 0.6 0.7 154 28930 1.366 6.0 0.8 0.9 154 30720 1.640 7.3 1.0 1.1 156 31610 1.918 8.7 1.1 1.4 156 32350 2.091 9.5 1.3 1.5 157 34285 2.758 12.8 1.7 2.0 158 34890 3.668 17.4 2.3 2.7 158 34935 4.459 21.7 2.8 3.4 155 34625 5.434 27.1 3.5 4.1 153 34055 6.357 32.3 4.1 4.9 151 32650 7.362 39.0 4.7 5.7 145 28100 8.716 48.4 5.5 6.7 138 27100 9.662 54.2 6.0 7.4 136 26700 10.561 59.7 6.6 8.1 135 26350 11.762 67.0 7.3 9.0 135 26160 13.287 76.3 8.3 10.2 134 25420 14.632 84.5 9.1 11.2 133 25100 15.861 92.1 9.9 12.2 132 22640 20.196 118.6 12.5 15.5 131 21720 20.823 124.7 12.8 15.9 128 I..,— — Table 5.3 A Angular change, by lateral deflection including estimate of deflection at midspan and corresponding bending moment. Specimen No. 3 Bending Lateral Deflection (mm) Lateral Deflection (mm) Angular Dis- . Moment Average of quarter & three quarter span Midspan concinuity (kN-mm) e = £e c 20> *10‘3 ^total ^bending h p 620 ^total ° bending p 1120 P *10~3(rad) *10 3(rad) (rad) 35590 5.833 5.833 0 0 8.893 8.893 0 0 0 35125+ 7.371 5.4 2.0 3.2 12 .0 8.5 3.5 - 7 357 33990+ 8.471 5.0 3.5 5.6 14.0 7.5 6.5 - 12 32980+ 9.559 4.5 5.0 8.1 16.0 7.0 9.0 - 17 31880+ 11.585 4.0 7.5 12.1 20.0 6.0 14.0 - 25 30995+ 13.245 3.5 9.7 15.7 23.0 5.5 18.0 - 32 29735+ 19.359 3.3 16.0 25.8 34.0 5.2 29.0 - 52 27595+ 35.433 2.8 32.6 52.6 63.0 4.2 59.0 105 ______i + based on estimated midspan deflection. * / Table 5 . 3 b Angular change by lateral deflection including estimate of deflection at midspan and corresponding bending moment. Specimen No. 5 Bending Lateral Defl ection (mm) Lateral Deflection (mm) Angular Dis- . Moment Average of quarter & three quarter span Midspan continuity (kN-mm) e = is. C e = 29> *10~3 ^total ^bending p 620 ^tota1 ° bending p 1120 P *10'3(rad) *10_3(rad) (rad) 34863 9.233 9.233 0.0 0.0 14.332 14.322 0.0 0.0 0.0 358 30518 13.772 4.2 9.6 15.5 23.332 6.2 17.1 15.3 31.0 27100+ 18.085 3.5 14.6 23.5 3 2.0 5.5 2 6.5 - 48.0 26400+ 22.372 3.3 19.0 30.5 4 0.0 5.4 3 4.5 - 62.0 23500+ 27.572 2.6 25.0 40.3 5 0.0 4.2 4 5.0 - 82.0 23000+ 34.041 2.5 31.5 50.8 60.0 4.0 5 7.0' - 100.0 + based on estimated midspan deflection. « / ..... h I Table 5.3 C Angular change by lateral deflection including estimate of deflection at midspan and corresponding bending moment. Specimen No. 6 Angular Bending Lateral Deflection (mm) Lateral Deflection (mm) Dis- . continuity Moment Average of quarter & three quarter span Midspan (kN-mm) T e = r e = € e - 20- *10-3 °total ^bending p 620 ^total ° bending p 1120 P * 10~3(rad) *10"3(rad) (rad) 44368 6.669 6.669 0.0 0.0 10.010 10.010 0.0 0.0 0.0 43712 7.899 5.700 2.2 3.6 11.909 8.5 3.4 3.0 7.0 359 38566 10.163 4.2 6.0 9.7 15.017 6.0 9.0 8.0 18.0 38500+ 11.768 4.1 7.6 12.3 20. 0 6.0 14. 0 - 25.0 39000+ 14.408 4.5 10.0 16.0 25.0 6.5 18. 0 - 32.0 26000+ 30.601 2.0 28.6 46.1 5 5.0 3.0 5 2.0 - 90.0 + based on estimated midspan deflection. I ♦ i ./ t I Table 5.3D Angular change by lateral deflection including estimate of deflection at midspan and corresponding bending moment. Specimen No.7 Bending Lateral Deflection (mm) Lateral Deflection (mm) Angular Dis- . Moment Average of quarter & three quarter span Midspan continuity (kN-mm) r e = ^ r e = 5jl_ 20 *10~3 °total ^bending p 620 ^tota 1 ° bending p 1120 P *10'3(rad) *10 3(rad) (rad) 42555 5.150 5.150 0.0 0.0 7.610 7.610 0.0 0.0 0.0 360 36907 7.90 3.3 4.6 7.4 11.696 4.7 7.0 6.3 14.0 31652 13.7 2.5 11.2 18.0 19.763 3.7 16.0 14.3 32.0 * / / I Table 5.3 E Angular change by lateral deflection including estimate of deflection at midspan and corresponding bending moment. Specimen No.8 Bending Lateral Deflection (mm) Lateral Deflection (mm ) Angula r Dis- . Moment Average of quarter & three quarter span Midspan continuity (kN-mm) e = *£ r 0 - 20 *10-3 ^total ^bending p 620 ^tota 1 0 bending JP 0p~l120 P ^ ( r a d ) *10_3(rad) (rad) 49925 5.441 5.441 0.0 0.0 8.164 8.164 0.0 0.0 0.0 361 48550 6.348 4.5 1.85 3.0 9.488 6.700 2.8 2.5 5.5 42255 8.450 3.1 5.4 8.6 12.660 4.6 8.1 7.2 15.7 40690 10.193 2.9 7.3 11.8 15.250 4.0 11.3 10.0 21.8 39100+ 13.8 2.7 11.1 18.0 24.0 3.7 20.3 - 36.0 35860+ 17.6 2.4 15.2 24.5 30.8 3.4 27.4 - 49.0 33000+ 21.8 2.1 19.7 31.8 3 9.0 3.0 3 6.0 - 6 4.0 + based on estimated midspan deflection. / I Table 5.3F Angular change by lateral deflection including estimate of deflection at midspan and corresponding bending moment. Specimen No. 9 Bending Lateral Deflection (mm) Lateral Deflection (mm) Angular Dis- '. . . . Moment Average of quarter & three quarter span Midspan continuity (kN-mm) T e - c e = £e _ 2e no"*3 °total ^bending p~ 620 ^total 0 bending JP p 1120 p * 10'3 34935 8.720 8.720 0.0 0.0 13.979 13.979 0.0 0.0 0.0 34625 10.340 6.7 3.6 6.0 16.585 10.5 6.1 5.4 11.4 362 34055 11.874 5.5 6.4 10.5 18.855 9.0 9.9 8.8 19.3 32650+ 13.684 5.0 8.7 14.0 24. o 7.8 16. o — 2 8.0 28100+ 16.315 3.3 13.0 21.0 29. 0 5.0 23.5 - 42. o 27100+ 18.065 3.0 15.0 24.2 32.0 4.4 2 7.0 - 49. 0 26700+ 19.674 2.9 16.8 27.1 35. 0 4.3 30.5 - 54. 0 26350+ 21.865 2.8 19.0 30.7 39. 0 4.2 3.4.5 - 62.0 26160+ 24.607 2.6 22.0 35.5 44. 0 4.2 40.0 - 71.0 25420+ 27.048 2.5 24.5 39.5 48. 0 3.8 44. 5 - 79. 0 25lOO+ 29.263 2.5 26.8 43.2 52. 0 3.8 48. 5 - 87.0 24100+ 32.050 2.4 29.6 47.7 57.5 3.5 54.0 - 96.0 23160+ 34.922 2.3 32.6 52.6 62. 6 3.4 59. 0 - 105. 0 22640+ 37.237 2.2 35.0 56.5 6 7.0 3.2 63. 5 - 113. 0 21720+ 39.850 2.0 37.9 61.1 71.5 3.0 68.5 - 122. 0 + based on estimated midspan deflection. « 363 Table 5.4 A Lateral Deflections - Specimen No. 3 Load (Axial = 250 kN) Lateral Deflections (mm) Lateral Bending Moment Transducer 1 Transducer 2 Transducer 3 (kN) (kN-mm) quarter-span mid-span 3quarter-span 0.0 0 0.000 0.000 0.000 4.0 1750 0.140 0.201 0.140 14.2 6185 0.404 0.603 0.438 24.5 10680 0.689 1.066 0.791 34.7 15150 0.991 1.626 1.253 44.9 19690 1.393 2.418 1.856 55.4 24430 1.992 3.546 2.700 65.6 29150 2.874 5.098 3.804 70.9 31630 3.437 5.997 4.414 71.2 31790 3.512 6.129 4.509 76.4 34425 4.559 7.820 5.611 76.4 34540 4.848 8.294 5.925 78.5 35590 5.291 8.893 6.374 75.0 35125 6.798 1 2.0+ 7.944 71.2 33990 7.890 14. 0 + 9.051 67.7 32980 8.972 16. 0 + 10.146 63.0 31880 10.964 20. 0 + 12.205 59.2 30995 12.567 23.0 + 13.923 49.9 29735 18.454 34. 0 + 20.263 28.2 27595 34.050 63.0 + 36.816 0.0 19000 41.701 77.0 + 44.820 + calculated as explained in section 5.3.3 364 Table 5.4 B Lateral Deflections - Specimen No. 4 Load (Axial = 1070kN) Lateral Deflections (mm) Lateral Bending Moment Transducer 1 Transducer 2 Transducer 3 (kN) (kN-mm) quarter-span mid-span 3quarter-span 0.0 0 0.0 0.0 0.0 6.5 3030 0.171 0.248 0.174 17.0 7920 0.445 0.651 0.457 27.0 12655 0.798 1.103 0.790 38.0 17920 1.188 1.655 1.177 48.5 22980 1.566 2.213 1.545 59.0 28320 2.071 3.031 2.166 69.5 33760 2.530 3.944 2.925 69.5 34445 2.833 4.584 3.453 365 Table 5.4 C Lateral Deflections - Specimen No. 5 Load (Axial = 250 kN) Lateral Deflections (mm) Lateral Bending Moment Transducer 1 Transducer 2 Transducer 3 (kN) (kN-mm) quarter-span mid-span 3quarter-span 0.0 0 0.0 0.0 0.0 9.6 4160 0.243 0.313 0.238 19.9 8650 0.542 0.774 0.578 26.0 11370 0.868 1.288 0.955 41.5 18400 1.896 3.055 2.287 46.4 20670 2.362 3.795 2.785 60.5 27100 3.513 5.573 4.013 72.4 32540 4.489 7.088 5.012 76.2 34530 5.441 8.588 '5.977 73.6 34863 8.911 14.332 9.555 58.1 30518 13.414 23.332 14.129 44.1 27100 17.630 32.0+ 18.539 37.7 26400 21.783 40.0+ 22.960 25.4 23500 26.890 50.0+ 28.254 19'. 9 23000 33.180 60.0+ 34.901 + calculated as explained in section 5.3.3 366 Table 5.4D Lateral Deflections - Specimen No.6 Load (Axial = 500 kN) Lateral Deflections (mm) Lateral Bending Moment Transducer 1 Transducer 2 Transducer 3 (kN) (kN-mm) quarter-span mid-span 3quarter-span 0.0 0 0.0 0.0 0.0 6.0 2665 0.166 0.229 0.161 16.3 7241 0.435 0.621 0.423 26.0 11572 0.721 1.033 0.724 36.4 16231 1.038 1.507 1.074 46.9 21000 1.415 2.112 1.514 56.6 25476 1.867 2.814 2.043 61.8 27916 2.140 3.270 2.372 67.1 30496 2.544 3.918 2.826 72.4 33066 2.920 4.546 3.278 74.7 34193 3.090 4.842 3.496 77.3 35562 3.430 5.366 3.866 80.0 36876 3.607 5.695 4.095 82.6 38241 3.954 6.209 4.446 84.9 39372 4.136 6.513 4.646 87.6 40954 4.721 7.374 5.220 90.2 42356 5.123 7.963 5.594 92.8 44015 5.841 9.059 6.295 92.5 44368 6.438 10.010 6.900 88.7 43712 7.659 11.909 8.139 72.9 38566 9.872 15.017 10.453 66.5 38500 11.447 20.0+ 12.089 62.7 39000 14.071 25.0+ 14.746 6.0 26000 29.879 55.0 + 31.322 + calculated as explained in section 5.3.3 367 Table 5.4E Lateral Deflections - Specimen No. 7 Load (Axial = 750 kN) Lateral Deflections (mm) Lateral Bending Moment Transducer 1 Transducer 2 Transducer 3 (kN) (kN-mm) quarter-span mid-span 3quarter-span 0.0 0 0.0 0.0 0.0 6.9 3186 0.277 0.338 0.277 16.9 7784 0.598 0.802 0.624 28.2 12995 0.979 1.347 1.013 37.6 17315 1.304 1.780 1.335 48.1 22205 1.710 2.351 1.722 58.3 26920 2.069 2.859 2.082 68.6 32030 2.629 3.831 2.753 73.2 34318 2.914 4.278 3.071 78.2 36765 3.191 4.706 3.352 83.8 39820 3.788 5.605 3.953 84.0 40230 4.072 6.037 4.216 84.3 40810 4.487 6.640 4.584 86.7 42555 5.143 7.610 5.195 66.2 36907 8.017 11.696 7.829 39.6 31652 14.012 19.763 13.379 368 Table 5.4F Lateral Deflections - Specimen No. 8 Load (Axial = 750 kN) Lateral Deflections (mm) Lateral Bending Moment Transducer 1 Transducer 2 Transducer 3 (kN) (kN-mm) quarter-span mid-span 3quarter-span 0.0 0 0.0 0.0 0.0 5.5 1770 0.118 0.158 0.126 16.0 5085 0.243 0.381 0.294 26.8 8535 0.424 0.659 0.502 32.0 10195 0.496 0.791 0.615 49.0 15610 0.765 1.213 0.921 57.5 18330 0.902 1.438 1.089 67.7 21585 1.065 1.700 1.283 77.6 24750 1.232 1.963 1.488 88.1 28150 1.443 2.294 1.719 97.8 31315 1.674 2.634 1.961 108.3 34880 2.053 3.187 2.332 118.5 38380 2.454 3.776 2.736 128.7 42040 2.979 4.569 3.270 139,8 46400 3.846 5.950 4.182 144.2 48280 4.326 6.696 4.677 146.9 49785 4.919 7.618 5.269 146.0 49925 5.271 8.164 5.610 138.1 48550 6.169 9.488 6.526 109.2 42255 8.293 12.660 8.634 97.5 40690 10.019 15.250 10.366 70.0 39100 13.687 24.0+ 13.924 42.6 35860 17.567 30.8+ 17.613 14.8 33000 21.892 3 9.0+ 21.747 + calculated as explained in section 5.3.3 369 Table 5.4 G Lateral Deflections - Specimen No. 9 Load (Axial = 250 kN) Lateral Deflections (mm) Lateral Bending Moment Transducer 1 Transducer 2 Transducer 3 (kN) (kN-mm) quarter-span mid-span 3quarter-span 0.0 0 0.0 0.0 0.0 15.1 4640 0.272 0.424 0.329 25.6 7860 0.472 0.728 0.567 35.5 10910 0.664 1.037 0.795 45.8 14085 0.900 1.381 1.048 56.5 17455 1.245 1.894 1.367 66.8 20670 1.629 2.519 1.821 76.5 23790 2.124 3.348 . 2.401 86.4 27025 2.715 4.422 3.114 91.9 28930 3.307 5.445 3.823 97.2 30720 3.781 6.241 4.357 99.5 31610 4.231 7.042 4.893 101.6 32350 4.477 7.465 5.170 106.5 34285 5.522 9.339 6.392 106.5 34890 6.897 11.765 7.941 104^8 34935 8.132 13.979 9.309 101.6 34625 9.697 16.585 10.983 97.8 34055 11.185 18.855 12.562 88.4 32650 13.021 24. 0+ 14.347 69.2 28100 15.754 29. o" 16.877 63.3 27100 17.511 32. o+ 18.619 59.5 26700 19.112 35.0+ 20.236 55.1 - 26350 21.279 39.0+ 22.450 50.4 26160 23.987 44. o+ 25.227 44.3 25420 26.405 48.0+ 27.691 39.9 25100 28.595 52. o+ 29.931 32.3 24100 31.347 57.5+ 32.752 25.0 23160 34.197 62. 5+ 35.646 19.8 22640 36.478 6 7.0+ 37.996 12.8 21720 39.076 71.5+ 40.643 + calculated as explained in section 5.3.3 370 Table 5.5A Strains of embedded gauges on dowels. Spec imen No. 0 Axial Bending Position of gauge (refer to fig.5.14 for location) Load Moment 0 1 2 3 4 5 6 7 (kN) (kN-mm) (us) (us) (us ) (us) (us) (us) (us) (us) 0 - 0 0 0 0 0 0 0 0 105 - . 90 80 115 125 90 70 105 115 210 - 165 165 200 195 185 135 165 165 315 - 230 230 260 260 250 195 205 220 415 - 310 310 330 340 320 250 260 270 520 - 395 385 395 405 395 330 330 340 625 - 460 475 470 480 460 395 395 405 730 - 530 540 540 550 540 460 450 470 835 - 600 615 615 630 615 540 520 540 940 - 675 685 685 695 685 600 580 600 1045 - 740 760 750 770 750 675 655 665 1150 - 820 850 830 840 820 730 715 720 1250 - 885 925 885 915 895 810 780 800 1360 - 960 1000 960 980 960 875 840 865 Note: Specimen 0 was repaired and tested under bending moment and constant axial load of 300 kN. The embedded gauges were not working during this test. 371 Table 5.5B Strains of embedded gauges on dowels. Specimen No.1 Axial Bending Position of gauge (refer to fig.5.14 for location) Load Moment 0 1 2 3 4 5 6 7 (kN) (kN-mm) (us) (us) (us) (us) (us) (us) (us) (us) 0 --- 0 0 0 - 0 0 105 - . - - 275 260 190 - 210 210 210 -- - 365 350 265 -• 305 305 315 - - - 425 420 340 - 375 375 420 - -- 495 480 410 - 440 430 520 - -- 580 560 490 - 530 525 625 - - - 625 620 580 - 615 610 730 - - - 725 700 655 - 700 695 835 - -- 760 725 730 - 780 775 940 -- - 800 825 815 - 860 855 1045 -- - 920 925 940 - 960 960 1150 -- - 975 975 990 - 1050 1035 1250 - -- 1065 1070 1090 - 1165 1105 1360 --- 995 1120 1135 - 1225 1290 1460 - -- 1230 1210 1230 - 1370 1660 1565 - - - 1140 1280 1275 - 1980 2000 Note: Gauges 0,1 & 5 failed. 372 Table 5.5C Strains of embedded gauges on dowels. Specimen No.2 Axial Bending Position of gauge (refer to fig.5.14 for location) Load Moment 0 1 2 3 4 5 6 7 (kN) (kN-mm) (us) (us) (us ) (us ) (us ) (us) (us) (us) 0 - 0 0 0 0 0 0 0 0 100 - 135 155 220 200 145 135 180 165 210 - 220 240 315 300 230 220 290 260 315 - 295 315 395 365 315 300 365 335 425 - 385 395 470 430 395 395 450 410 530 - 490 500 545 530 490 490 545 520 640 - 530 585 630 605 575 585 625 595 745 - 615 660 720 680 670 670 720 690 855 - 710 765 815 775 765 775 835 785 960 - 555 625 910 870 870 870 940 890 1070 - 630 700 1005 960 965 975 1035 985 1175 - 605 785 1090 1050 1050 1060 1120 1070 1285 - 890 930 1195 1175 1165 1175 1245 1205 1390 - 995 1050 1310 1290 1280 1300 1370 1320 1500 - 1080 1120 1380 1380 1370 1390 1445 1400 1510 - 1090 1150 1400 1400 1350 1400 1465 1400 1550 - 1050 1120 1425 1435 1340 1400 1520 1425 373 Table 5.5D Strains of embedded gauges on dowels. Specimen No. 3 A x i a l B e n d i n g Position of g a u g e ( r e f e r to note below) L o a d M o m e n t 0 1 2 3 4 5 6 7 (kN) (kN-mm) (us) (us) ( u s ) ( u s ) (us) (us) (us) (us) . 2 5 0 0 3 5 0 3 5 0 3 6 0 4 0 0 4 0 0 3 8 0 4 1 0 4 1 0 1 7 5 0 3 2 5 325 3 4 0 3 8 0 4 3 0 4 0 0 4 2 0 4 3 0 6 1 8 5 2 7 5 275 2 8 5 3 3 0 480 4 5 0 4 6 0 4 8 0 1 0 6 8 0 2 0 5 225 2 25 275 5 30 5 0 0 5 1 0 5 2 0 1 5 1 5 0 70 100 6 0 1 40 5 80 5 6 0 5 5 0 5 6 0 1 9 6 9 0 175 .90 2 9 0 90 6 4 0 6 2 0 5 8 0 5 8 0 2 4 4 3 0 5 1 0 310 730 3 4 0 650 6 8 0 5 9 0 6 0 5 2 9 1 5 0 8 8 0 615 1 2 9 0 590 630 760 550 620 3 1 6 3 0 1 0 6 0 790 1 5 8 0 6 2 0 560 7 9 0 4 7 0 5 8 0 3 1 7 9 0 10 7 5 8 3 0 1 6 3 0 6 15 565 8 2 0 4 6 0 5 7 0 3 4 4 2 5 1 2 3 0 1150 .2110 600 500 870 390 4 9 0 hi. 34540 1250 1220 2 1 3 0 625 510 9 1 0 3 9 0 5 0 0 3 5 5 9 0 1 3 1 0 1360 2 1 9 0 700 460 920 340 460 JU 3 5 1 2 5 1 2 6 0 1690 2 0 0 0 2 2 0 0 440 1 1 0 0 3 2 0 5 2 0 3 3 9 9 0 1 3 4 0 1680 2 0 1 0 3 0 4 0 4 80 1 2 2 0 3 2 0 6 0 0 3 2 9 8 0 1 3 7 0 1680 2 0 6 5 3 5 2 0 530 1 2 9 0 3 4 0 7 3 0 3 1 8 8 0 1 3 8 0 1740 1 8 3 0 4550 570 1410 4 4 0 9 6 0 3 0 9 9 5 1 3 4 0 1760 1 3 4 0 5 4 8 0 615 1 4 8 0 5 7 0 1 1 1 0 2 9 7 3 5 1 4 2 0 6 0 4 0 615 8 3 3 0 1150 1590 1690 3 4 3 0 27595 20300 large 2 50 large 1 9 7 3 0 large large large * Values are tensile strains. Notes: 1) Gauges 0,1,2 & 3 are at same level located 55mm from top of section. 2) Gauges 4,5,6 & 7 are at same level located 55mm from bottom of section. 3) In figure 5.14B the naming of gauges 2 & 3 and 4 & 5 are interchanged for convenience of presentation. 374 Table 5.5E Strains of embedded gauges on dowels. Specimen No.4 A x i a l B e n d i n g Position of g a u g e (refer to fig.5.14 for L o c a t i o n ) L o a d M o m e n t 0 1 • 2 3 4 5 6 7 (kN) ( k N - m m ) ( u s ) ( u s ) (us ) ( u s ) ( u s ) ( u s ) (us) (us) 10 7 0 0 1 0 2 5 10 8 5 9 5 0 9 2 0 1115 11 4 5 1 0 5 5 1 0 1 0 3030 1010 1060 9 7 0 9 5 0 1100 1 1 4 5 1 0 7 5 1 0 3 0 7 9 2 0 9 8 0 1 0 3 0 1000 990 1060 1 1 1 5 1 1 1 5 1 0 9 0 1 2 6 3 5 9 3 0 1 0 0 0 1050 1050 1020 1 0 9 0 1 1 4 5 1 1 2 5 1 7 9 2 0 8 9 0 9 7 0 1075 1105 990 1 0 5 0 1 1 7 5 1 1 6 5 2 2 9 8 0 8 3 5 9 3 0 1125 11 5 5 930 1 0 3 0 1 1 9 5 1 2 0 0 2 8 3 2 0 785 9 0 0 1165 1220 890 990 1225 1 2 5 0 3 3 7 6 0 6 9 0 825 1230 1310 815 940 1 2 5 0 1 2 9 0 34445 640 795 1270 1320 790 940 1 2 7 0 1 2 9 0 375 Table 5.5F Strains of embedded gauges on dowels. Specimen No. 5 A x i a l B e n d i n g Position of g a u g e (refer to fig.5.14 for Locat ion) L o a d M o m e n t 0 1 2 3 4 5 6 7 (kN) ( k N - m m ) (us) (us) ( u s ) ( u s ) ( u s ) (us) (us) (us) 2 50 0 155 2 8 0 310 310 260 280 3 0 0 3 2 0 4 1 6 0 155 250 3 4 0 3 4 0 2 20 2 4 0 3 2 0 3 5 0 8 6 5 0 40 185 3 5 0 3 9 0 155 195 3 5 0 3 9 5 1 1 3 7 0 125 85 3 8 0 425 70 1 05 3 7 5 4 5 5 1 8 4 0 0 475 3 2 0 4 7 5 6 0 0 2 4 0 2 6 0 4 4 5 6 0 0 20670 810 530 4 4 5 6 3 0 425 4 5 0 4 4 5 6 4 0 2 7 1 0 0 12 75 9 40 3 9 0 685 8 0 0 8 3 0 4 2 5 7 05 3 2 5 4 0 1325 1 2 6 0 3 3 0 765 995 1 0 8 5 3 9 5 7 15 3 4 5 3 0 1 2 2 0 1615 2 3 0 7 90 1 0 5 0 1 3 8 0 3 5 0 725 31360 1270 1770 155 8 4 0 1005 1 6 1 5 3 3 0 7 7 0 32170 1270 1820 1 0 0 8 8 0 965 1 7 7 5 2 6 0 8 2 0 3 4 8 6 3 1 5 1 0 19 3 0 95 1140 1235 3000 8 0 1 0 1 0 3 0 5 1 8 7 1 3 0 5 8 0 0 130 1850 1965 4460 475 1 2 8 0 2 7 1 0 0 1 6 5 7 0 19790 700 2080 5 7 3 0 9 0 8 0 7 5 5 1 2 8 0 2 6 4 0 0 1 8 1 8 0 2 2 5 7 0 1 2 7 5 2340 10295 13800 940 1 2 6 0 2 3 5 0 0 1 9 2 5 0 large 1775 2550 10650 13240 9 7 0 1 1 3 5 2 3 0 0 0 2 3 0 0 0 --- 1 1 0 9 0 1 2 8 0 0 1 1 1 5 1 0 2 0 Values are tensile strains. 376 Table 5.5G Strains of embedded gauges on dowels. Specimen No. 6 A x i a l Bending Position of g a u g e (refer to fig.5.14 for l o c a t i o n ) L o a d M o m e n t 0 1 2 3 4 5 6 7 (kN) (kN-mm) (us) ( u s ) (us) (us) (us) (us) (u s ) (us) 5 0 0 0 5 7 0 6 2 0 5 40 6 1 0 5 70 5 8 0 5 4 0 5 6 0 2 6 6 5 5 5 0 5 90 5 70 6 4 0 540 5 6 0 5 7 0 5 8 0 7241 5 0 0 5 7 0 6 1 0 7 00 5 15 5 3 5 5 9 0 6 4 0 11572 465 540 650 745 465 5 1 0 6 3 0 6 9 0 16231 420 505 6 7 0 8 0 0 4 25 4 7 5 6 7 5 7 2 5 2 1 0 0 0 3 3 0 445 725 8 8 0 3 4 0 4 2 0 7 0 5 7 95 2 5 4 7 6 145 3 2 0 785 9 5 0 220 3 1 0 7 5 5 8 5 0 2 7 9 1 6 20 2 3 0 790 1005 135 220 7 7 0 9 1 0 30496 175 100 8 2 0 1 0 7 0 0 1 0 0 8 0 0 9 6 5 «JL» 3 3 0 6 6 3 3 0 50 8 6 0 1 1 3 0 135 30 8 3 0 1 0 1 5 3 4 1 9 3 3 9 5 120 8 7 0 1 1 5 0 215 85 8 4 0 1 0 3 5 35562 530 215 8 9 0 1 2 1 0 3 2 0 175 8 6 0 1 0 8 5 3 6 8 7 6 6 2 0 2 8 0 8 9 0 1 2 4 0 405 2 4 0 8 7 0 1 1 2 0 3 8 2 4 1 745 3 7 0 9 2 0 1 2 8 5 525 3 4 0 8 9 0 1 1 5 0 3 9 3 7 2 8 3 0 435 9 2 0 1 3 1 5 5 80 4 05 9 0 0 1 1 8 0 4 0 9 5 4 1 0 4 0 550 9 5 0 1 4 0 0 765 5 4 0 9 5 0 1 2 6 0 4 2 3 5 6 1 1 6 5 6 3 0 9 7 0 1440 890 650 960 1 2 9 5 4 4 0 1 5 1 3 3 0 795 985 1595 1075 805 1 0 2 5 1 4 0 0 4 4 3 6 8 1 4 0 0 1 2 0 0 1 1 0 0 2 2 0 0 1 1 0 0 1 0 0 0 1 1 0 0 1 5 0 0 4 3 7 1 2 1 6 1 5 14 8 0 12 0 0 2 8 9 5 11 5 0 1 2 0 0 1 2 0 0 1 6 7 0 3 8 5 6 6 1 5 3 5 2 1 0 0 4 0 5 0 7 5 1 5 1 1 1 0 1 4 6 0 1 2 7 5 2 0 8 5 3 8 5 0 0 1 6 2 5 2 2 5 0 6 1 5 0 9 3 0 0 1 0 8 0 1 5 9 0 1 3 0 5 2 9 7 0 3 9 0 0 0 2 2 1 5 3 2 0 5 8 6 5 0 1 1 1 0 0 1 1 0 0 3 3 3 0 1 3 8 0 3 9 4 0 2 6 0 0 0 1 4 5 5 0 2 2 0 1 0 - - 8 2 0 0 2 1 1 3 0 - - * Values are tensile strains 377 Table 3.5H Strains of embedded gauges on dowels. Specimen No. 7 Axial Bending Position of g a u g e (refer to fig.5.14 for l o c a t i o n ) L o a d M o m e n t 0 1 2 3 4 5 6 7 (kN) ( k N - m m ) ( u s ) (us) (us) ( u s ) (us) (us) (us) (us) • 7 5 0 . 0 7 8 0 7 6 0 6 8 5 6 6 5 745 7 15 7 1 5 695 3 1 8 6 7 50 7 5 0 7 1 5 7 2 5 705 6 9 5 7 5 0 745 7 7 8 4 705 7 1 0 7 6 5 7 8 0 6 55 6 5 5 8 0 0 790 1 2 9 9 5 6 65 6 8 5 8 2 0 8 5 0 6 0 0 6 3 0 8 5 0 8 4 0 1 7 3 1 5 615 6 6 0 8 6 0 9 1 0 550 5 9 0 8 8 0 9 0 0 2 2 2 0 5 5 7 0 6 1 5 9 2 0 9 8 5 475 5 4 0 9 3 5 965 2 6 9 2 0 5 10 5 70 9 7 5 1 0 4 0 3 95 4 9 5 985 1 0 1 5 3 2 0 3 0 3 7 5 4 6 0 1 0 6 0 1 1 7 5 2 60 3 9 5 1 0 5 0 11 2 0 3 4 3 1 8 3 0 0 405 1100 1225 185 3 47 1 0 8 0 11 5 0 3 6 7 6 5 2 15 320 1130 1265 1 2 0 2 9 0 1 1 0 0 1 1 9 5 3 9 8 2 0 10 155 1195 1340 20 175 1 1 3 0 1245 4 0 2 3 0 80 90 1 2 2 5 1 3 7 8 60 155 1 1 4 0 1275 4 0 8 1 0 195 10 1 2 4 5 1 3 9 8 105 105 1 1 6 0 13 0 0 00 4 2 5 5 5 3 8 5 1 2 2 5 1 4 6 5 2 15 20 1 2 0 5 13 7 0 3 6 9 0 7 965 9 75 1 1 7 5 1 5 9 0 4 05 3 9 5 1 4 0 5 14 4 0 Jt. 3 1 6 5 2 922 1 5 9 0 1 1 6 0 - 4 5 0 10 8 5 1 3 0 0 1 3 3 0 2 5 0 0 0 1 9 5 0 2 5 6 0 165 - 575 6 7 0 8 9 5 3 6 0 Values are tensile strains. 378 Table 5.5J Strains of embedded gauges on dowels. Specimen No.8 A x i a l B e n d i n g Position of g a u g e (refer to f ig.5.14 for L o c a t i o n ) L o a d M o m e n t 0 1 2 3 4 5 6 7 (kN) ( k N - m m ) ( u s ) (us) ( u s ) ( u s ) ( u s ) (us) (us) (us) 7 5 0 0 8 1 5 785 775 775 890 850 795 795 1 7 7 0 795 785 785 795 8 6 0 8 4 0 8 2 5 8 0 5 5 0 8 5 755 775 8 15 835 8 3 0 8 2 0 8 3 5 8 4 5 8 5 3 5 7 3 0 745 845 8 8 0 795 8 0 0 8 7 5 8 8 0 1 0 1 9 5 7 2 0 735 8 6 0 8 9 0 775 7 85 8 7 5 9 0 0 1 5 6 1 0 6 7 0 7 10 9 1 0 9 7 0 710 7 5 0 9 2 0 9 6 0 1 8 3 3 0 6 3 0 6 8 0 940. 1 0 0 0 680 7 2 0 9 3 0 9 9 0 2 1 5 8 5 5 9 0 6 5 0 9 60 1045 640 6 9 0 9 5 0 1 0 3 0 2 47 50 5 5 0 6 3 0 9 90 1 1 0 0 590 6 5 0 9 8 0 1 0 6 5 2 8 1 5 0 505 580 1030 11 4 5 515 6 1 0 1 0 1 0 1 1 1 5 3 1 3 1 5 4 3 5 545 1045 1 1 9 0 455 5 7 0 1 0 3 0 1 1 5 0 3 4 8 8 0 3 0 0 4 45 1105 12 9 0 3 30 4 9 5 1 0 5 5 1 2 7 0 3 8 3 8 0 125 3 5 0 1145 1385 155 4 0 5 1 0 6 5 1 3 5 5 4 2 0 4 0 175 2 15 1180 1 5 1 0 90 3 0 0 1 1 0 5 1 5 0 0 JL 4 6 4 0 0 6 2 0 0 1270 1665 525 195 1 1 2 5 1 7 3 0 4 8 2 8 0 8 4 5 85 1230 1715 700 175 1 1 1 5 1 8 1 0 JL 4 9 7 8 5 1 1 4 5 165 11 9 0 1 8 0 0 9 2 0 135 1 1 5 5 1 9 0 5 4 9 9 2 5 1 3 0 0 205 1190 1740 1010 95 1 1 8 0 1 9 7 5 4 8 5 5 0 1 7 1 0 2 9 0 1115 3 9 2 0 1 2 5 0 95 1 3 9 5 2 1 5 0 4 2 2 5 5 2 3 0 5 3 6 0 3600 9780 1575 95 1 7 6 0 2 2 8 0 4 0 6 9 0 3 0 0 5 6 4 0 5435 12465 1710 8 0 2 0 1 0 2 7 9 5 JL •JL. JL 3 9 1 0 0 3 2 6 0 1 3 7 0 86 6 5 1 6 1 7 0 1 7 4 0 1 7 5 3 4 2 0 5 1 0 0 3 5 8 6 0 3 2 6 5 1 9 1 0 large - 1 7 1 0 3 3 5 9 9 2 0 1 3 4 0 0 JL 3 3 0 0 0 3 2 5 0 2 3 2 0 large - 1 7 1 5 4 8 5 1 4 1 6 0 - Values are tensile strains. 379 Table 5.3 K Strains of embedded gauges on dowels. Specimen No. 9 Axia 1 Bending Position of g a u g e (refer to fig.5.14 for L o c a t i o n ) L o a d M o m e n t 0 1 2 3 4 5 6 7 (kN) (kN-mm) ( u s ) ( u s ) (us) ( u s ) ( u s ) (us) (us) (us) • 2 5 0 0 2 9 0 3 0 0 225 2 3 5 3 2 0 3 1 0 3 2 0 3 4 0 1 4 7 0 2 75 285 235 2 4 5 3 1 0 2 80 3 4 0 3 6 0 4 6 4 0 2 5 0 2 50 2 70 2 7 0 280 250 390 380 7 8 6 0 2 25 205 3 2 0 3 0 0 2 6 0 215 4 5 0 4 1 0 1 0 9 1 0 175 135 3 5 0 3 3 0 2 1 5 160 4 8 5 43 5 1 4 0 8 5 1 00 40 4 0 0 3 5 0 1 45 100 5 3 5 4 6 0 1 7 4 5 5 30 90 465 3 7 0 60 10 5 9 5 4 8 5 2 0 6 7 0 175 275 515 3 7 0 70 145 670 495 2 3 7 9 0 3 7 0 595 595 3 2 0 185 525 7 6 0 4 7 5 «JL 2 7 0 2 5 555 10 5 0 650 185 2 6 5 945 8 2 5 4 2 5 2 8 9 3 0 7 70 1265 710 3 0 ’ 34 0 11 6 0 8 9 5 3 0 0 3 0 7 2 0 965 1375 730 125 420 1305 905 185 3 1 6 1 0 1120 1415 770 2 1 5 5 1 5 1395 9 5 0 9 0 3 2 3 5 0 1 2 1 5 1 4 4 0 775 3 0 0 5 7 5 1440 9 6 0 2 0 3 4 2 8 5 1560 1345 895 6 8 0 860 1520 1080 3 4 0 3 4 8 9 0 1 8 1 0 1 2 0 0 1155 1 1 6 0 1240 1420 1370 7 9 0 3 4 9 3 5 1870 1200 1455 1570 1550 1385 1640 1 1 7 0 3 4 6 2 5 1870 1300 1900 2020 1745 1375 2 3 6 0 1 6 4 0 3 4 0 5 5 2250 1410 2530 2320 1850 1430 3355 2025 3 2 6 5 0 6550 1480 4060 2330 1820 1345 4790 2 1 1 5 aJL 2 8 1 0 0 15050 1870 8740 1950 1 3 2 5 1420 6760 2145 2 7 1 0 0 20250 7710 9850 1285 1 1 4 0 1500 7 5 2 0 2 3 4 0 «IU 2 6 7 0 0 21140 12830 10980 1020 1 0 0 0 16 0 0 7 9 7 0 2 6 7 0 2 6 3 5 0 21660 7750 13600 550 410 2115 8 3 5 0 3 0 1 5 * 2 6 1 6 0 - - -- 1 15 2 7 5 5 8 8 5 0 3 5 2 0 2 5 4 2 0 - --- 15 2990 9240 3825 2 2 6 4 0 - - - - - 9000 9280 3885 Values are tensile strains. Table 5.6 Effect of shear on load capacity of the joint section. S p e c i m e n Axial Load M a x i m u m Shear Cube Strength P /f M / f cu cu No. Bending Moment P M f cu (kN) ( k N - m m ) ( N / m m 2 ) 3 2 5 0 3 5 5 0 0 0 48 5 2 50 3 5 0 0 0 0 47 9 2 5 0 3 5 0 0 0 * 0 49 7 750 4 2 5 0 0 0 44 1 7 . 0 965 8 750 5 0 0 0 0 1 o 49 15.3 1 0 2 0 381 Appendix 3 - Chapter 6. (a) Listing of computer programme for column theory. F E a£E xI 50(!)^?( 5ubiySihfl{ 500) , IXY(500), IYX( 500) INTCGER C 00 E(500) BEAL K <3,3 >, IK (2 ,3 ), S ( 3, 3) NSION- AAP{500)(500)»AMV(50Q)»AMX(500)» ' >6), fjMon r 15 - CAP(500),CHY(500),CMX(500) 5,*)NUMB CP N 8 P , £ E J a ? S ? ^ S H ? ? 8 A i CALALL I T " N " INPUT $PnPEP.TIE: UF ELEMENTS/SECTION ICGCND» :(10)» X COORDINATE OF ELEMENT 10 ’c f o ) - r c o o r d i n a t e o f e l e m e n t 10 ii? i- ______AXIS___ OF ELEMENT 10 ELEM EN T 10 rKtm ^ n2H\ r z ? w Ru A itToiciviw IF ST E E L OR 2 IF GROUT. N rEaJ?5,*) X {I ) , Y (I ),AR EA (I),IXY(I),IYX(I),CO D E(I) 10 C O N T IN U - 300 FfnPNAT(5X,“NOTE:------ALL DIMENSIONS G LQAOS IN MM G KN ■ FESPECTIVELY.",// / ) rOPKAT(5X,"NUMDC «s:fSfe55P®°f°>OUT ^ Y-AXIS",/) - L- '2X'”M0MENT AB0U1 *-a5is"' 315 F ORMAT(6X,13» 15X,I3,12X,F5.1,0X,F5.1,6X,F8.2,AX,F12.2,9X,F12.2) 330 F OR HA T.. ( 5 X - , " AC -“ING AXIAL LOAD",F10.2,MKN",/,5X,"ACTING Y-MOMENT", ♦ F 1 0 .2, "Kfl-MH", /, 5X, "AC TIIIG X-MOMENT ", F 10.2 , "KN-MM" ) 3fc0 TORNAT( 5X»"NO• OF ELEMENT ",5X, "SIP. AIN (US )" ) 350 FnRMAT(l2fc,I3,5X,F10.?l 360 FOPMATtlOX,"A-", FI 0.8,5X,"B* ", F10.8,5X, "C ■ F I0.8, 5X, ♦"NO. nr ITERATIONS * ",110 ) 370 FORMAT(5X»"END OF CALCULATIONS FOR SPECIFIED LOAD LEVEL",////) * 380 FOPMAT j 5X,"LOAD APPLIED EXCEEDS CAPACITY OF SECTION,",///) 300 FORMAT(5X,»$TRMAX*",F6.V,5X,»C1•",F8.2,5X,"C2«" , F8.2,5X, ♦ " C 3 - " , F 6 . A, 5X, " S Y - " , F6 . A , 5 X , "T O L F AC TOR ■ F 8.6 ) 3 WRITE (6,315 ) I,CO DE(I),X(I),YU),AREA(I),IXY(I),IYXCI) 215 CONTINUE INPUT ACTING LOADS G NUMBER OF LOAD LEVELS REQUIRED. LEGEND» AAP(J )■ ACTUAL AXIAL LOAC AMY J } - ACTU AL MOMENT A3 OUT Y - A X I S AhX(J i ■ ACTUAL MOMENT ABOUT X-AXIS M- NUMBCP. OF LOAD LE V E LS TO F A IL U R E STRMAX-MAX.COMP.STRAIN SUSTAINED BY CONCRETE,EX. 0.0035 C1,C2 G C3 DEFINE CONCRETE STRESS STRAIN CURVE Gl,G| G £3 r DfcFIN£ _ GROUT,STRESS STRAIN CURVE. ___ WHERE I «■ITRE! S- Cl*STRAlN- C2* (STRAIN )++Z (FOR CONCRETE) I TP. I 1*STRAIN - G2*(STRAIN)**2 (FOR GROUT) ‘ RAIN LEVEL AT WHICH CONCBEIi BECO bL... - j . F A l N LEV EL AT WHICH GROUT BECOMES . INES S RAlN _ LEVEL______AT WHICH ... . .STEEL ______BECOMES PLA ^L|RAJjCE IN CONVERGENCE OF ACTIONS) EX. RE AD(5,*) STRMAX,C1,C2,C3,SY,TOL,Gl,G2,G3,STRSK gJP.jK-JNHANCEMENT FACTOR DUE TO CONFINEMENT. R E A D ( 5 , * ) AAP(J) , A MY(J ),AMX(J) 11 CONTINUE DO 10 00 J« 1, M A«DR-D. . fc8iJC_ * WRITE(6,300) STRMAX,Cl,C2,C3,SY,TOL WP.I TE ( 6, 3 ° 1 ) G 1 , G 2 , G 3 , S T R S K VPITEl6,33Qi AAP(J),AMY(J),AMX( J) CALCULATE STRAINS IN ALL ELEMENTS OF SECTION TRAIN IN THEN CALCULATE RELEVANT TANGENT MODULUS) ET( NT MODI CALCULATE PEDUCCD MODULUS) £*(!)■ "REDUCEO" MODULUS 1S ffrf? k iU - TA!.m02 «£{I)#CT I ).IR DO 34 I-l.N SUHK-SMMKM CTl I )*( (T (IJ*T(IJA A REA (H I*IXr M 2. 1 *M3.2 )-(M 2.2 )*M3.1>) )/DET (M l,2l*K(3.1))-(M l.l)*M 3.2>) )/DET . K(1.2 ) } - j < < 1 » 3 ) LATE Sti. h-MATRlX k HFRE 1 -3 „ P.IX IS STIFFNESS MATRIX FOR CALCULATING ACTIONS. IIMS-O. 0 50 I - l . M 50 i w & u ,•1»M siiis-suii5Mcem*( xm*x(n*AREAm)MET(i>*iYxm)) 52 U h n : - ms DO 5 A I - l . N S1IMS-SUMS*(ER(IJ* itffS LA?EMLOADS f r o m p r o p o s e d STRAINS I.E.A.BGC LEGEND» CAP(J)- CALCULATED AXIAL LOAD OF SECTION AT LOAO LEVEL- "4 "* $ $ 1 CALCULATED BENDICG MOMENT ABOUT Y-AXIS AT 1 CALCULATED-- _. 8CN0IHG______MOMENT_____ ABOUT____ X-AXIS "AXIS AtAT LOAD l I v I l . - ...... CMX(J)« ir(3»l)*A)+{S(3»2)*D)+(S<3.3)*CI ALPHA. P, ETA G GANA CALCULATES THE DISCREPENCY 3ETVEEN ACTING LOADS ANO CA L C U LA T E D L O A D S. ALPIIA«CAP(J)—AAP(J ) APPIIA-AOS( ALPHA) A p t A-ABS( p CT a ) A B G A -A D S i GAMA) DEFINE ALLOWED ERRORS IN LOADS AS AALPHA.ABETA.AGAMA AALPHA-AB s TTOL*AAP(J))*TOL A8ETA-ABSIT0L*AMY( J) ) a*T3L AGAHA-ABS(TOL*AMX(4)[♦ TIL TF(ABPHA.LE.AALPHA),0 TO 100 GO TO 50D 500 [F (^ T A j L E . A B E T A , GO TO 501 - 501 [ P u B G A . L C . A G A M A ) GO TO 502 100 ONTINUE ALCO l a TE AMOUNT OF M O D IF IC A T IO N TO BE DONE TO A . B S C • :M--UlK(3»li*ALPHA)*(IK(3.2)*BETA)MlK(3,3)*GAMA)> A-A^AM ' " . ‘ * C-CKH IvrwoUu £ q I C O - I C O + I _ fro \ 11 0 0 FORMAT ( 5X» NO. OF ITERATIONS-".110) GO TO 15 502 WRITE(6#36D) A.E.C.ICO WRITE(6.340) IUUUO. B i p l i f i ? 090®’I.E(!) 503 CONTINUE WRITE(6.3 ?0 ) GO TO 10 00 504 WRITE(6,11 DO) ICO WPI Tt1 6.380 ) 1000 CONTINUE STOP End 383 S u b r o u t i n e re-cnm,SS^fJxc!;Tr;i'5?^,/,:ffi:t5^8i-f67t,S./ S i r w i i s w ^ - I T . * ,B»CnN6IM,L»LI?T25#DD. /•v^AVr SUBROUTINE TANMOD (E> ET»CR#i:OOE,Cl.C2#C3>SY»S1»G2#S3#STRSK) STRSHX IS MAX STRESS LEVEL FOR UNCONFINED CONCRETE. ITI§&°ISIB Of P C55SAieMiSTae$:96RSS6ir,fo ‘ COHFIN6H6HT, EQUATION OF CGHCRETE CONFINED BY RECTILINEAR TIES. STRESS- -S2*STRAlN*STRAlN ♦ S1*$TRAIN *53 ABOVE EOUATION IS VALID BEYOND BOX OF STRSHX SLOPE$TRSMX AT• STRSK*5TRSMXTC1*C3)-{C2*(C3*C3>) IS ISSJMED Yo 8E ZERO. STRN0Q-(C1-SQRT((Cl*Cl)-(A,*C2*0.8*STRSMX))j/<2.*CZ> f2 -((STRSK-O.O^STRSMXRSMX )fi ((STRSK*C31-STRN801**2.) S3-(o!fi*rYRSMX)*c:CS2*STRN8O*STRN0O)-(S1-STRN8O) iK3-STPSK*Cr If (Icooe.E:iq . o ) g o t o 2000 50 TO 2100 2000 IF (E.LE.CK3) GO TO 2D05 ET-0 . 0 0 0 0 0 1 FP»STRSMX**TRSK/E 50 TO 2500 2005 I F ( E . L Ll .S.STPNBO) T P N 8 0 ) GU TO 2010 rT-SI- ( 2 , ) [ P ■ S 1 - (S2 * E ) ♦ ( S 3 / E ) 50 TO 2500 2010 GO TO 2020 *£ ) tnmmth10 rnTO 2020 :R-0. T-0 £ 2100 50?crt0ii??Po. TO 2200 1) CO TO 2 1 05 2105 F(E.LE.SY) GO TO 2 1 1 D R-200.*Sv'/[T » 0 . 000001 y'.n U TO I U <-2500 JV 1/ 2110 IF(r.LT.-rY)GP TO !12D CT.2p°. GOr p. ■ TO2 0 02500. 2120 ET-O,000001 'M EP..-200,*SY/E GO TO 2500 2200 IFfC.LE.G?) GO TO 2213 FT.0,0000001 fR-T[G3*C.1 )-(G3*G3*G2) ) / E 5n TQ 2500 2210 IF (E.LT.O.) GU TC 2220 ET- Gl -(2•* 02* E) EP.« G1-(G2*E) 30 TO 2500 2220 |R«g. 2500 v END 3*4 (b) Input file for computer programme 2 a Number of elements <_) a | ■ 2 0 0 0 O • , (.1 , •:.) ■JT <_) a ? y 5 a 200 0 1 o- . »o , 0 O . ,75. 2000 ,0 ,0 . 0 , 6 5 • 2000 7 i•- i , o ,0 , 5 5 . 1598 ,0 ,0 . o ,45. 2000 . o ,0 Elements in section described *T ITT as follows; 7 ■ 2000 ■!I I 2000 () o x-coordinate (mm), y-coordinate (mm), O . , 15 2000•,0• o O . . r-.. n . area (mm2), 0 * , -■•c5 - , 2000 - moment of inertia about x & y axes o - . 15..2000 o . assumed to be zero in this case, code of element e.g. 0=concrete 0 • . —25•.2000 *» . 1 o 0 • , —35■,2000 . (‘.1 & l = s t e e l . o . , -4 5 .,2 0 0 0 •) - , I.J • . -55 ■ . 1598 o . , —1-5 . , 200'.. O o . , -75•.2000 O . , o t;j . •4* o • . -85. , 2:000 o • 1 --95 . , 2000 <’) - , 0 - 4 5 .,4 5 .,2 0 1 0 • • i..) 4 5 . , 4 5 . ,201• o * 70 . -45 . , - 4 5 . , 2 0 1 ,o . , , 1 45 . ,-4 5 .,2 0 1 • 70 • , (■) a 1 19 Number of case loadings ^ 0 • 004,38 . 9 , l 0 4 0 ' , 0). 0)0' 1 7 , 0 • 0)0) 14.0). 0)00001 ,0). , 0 • , 0 . ,1.14 1070,0.0 1070 , , 400< 107 0 , a 0 0 0 ' Various loadings; 1070 , , 12000 axial load(kN) 1070,i . 11< O O 0 moment about y-axis(kN-mm) 1070,0,20000 moment about x-axis(kN-mm) 1 0 7 0 ,0 . 2400C 10)70) , O', 28 Oh, 1 0>7 0), 0), 320)0)0' 10>70>, 0), 360)0)0' 10)70), 0 ,40)0)0)0) 10)70), 0), 4 1 000 1070,( 41 Tf.c (,i 10)70), 0>., 4 2 Ox 0) 10)70)', 0 ,4 2 2 ' 0> 10)70), 0,4240)0) 1 0 7 0 ,( , 4260)0) 10)70), 0), 4280)0) 1 0)70-', 0) a 430)0)0) * The ten values are the following; 4: maximum concrete strain, modulus of elasticity of concrete(E), first coefficient in equation of parabola 1 in figure ‘5.1, peak strain of concrete i.e. £ in figure g.l, yield strain of steel reinforcement, maximum ^ error accepted to end iteration, three values for defining properties of the grout (not used in this case), and confinement factor.