Progressive Collapse Assessment of Multistory Irregular Reinforced Concrete Framed Structures Under Gravity Loads

13TH ARAB STRUCTURAL ENGINEERING CONFERENCE UNIVERSITY OF BLIDA 1

DECEMBER 13-15, 2015 ALGERIA

Mohamed El-Bayomy* and Hamed Salem**

*Assistant Lecturer, Structural Engineering Department, Faculty of Engineering, Cairo University [email protected]

** Prof. of Reinforced Concrete Structures, Faculty of Engineering, Cairo University [email protected]

Abstract: Progressive collapse is a disastrous partial or total collapse which causes a massive number of causalities and injuries. It mainly occurs when a structure loses one or more of its main vertical carrying members such as columns or walls. In this research, the effect of plan structural irregularity on progressive collapse resistance was studied on multistory reinforced concrete framed structure subjected to gravity loads. The studied structure was designed according to the ‘Egyptian code of practice’ (ECP)[1] and the limits of elements' rotation were adopted from the ‘Unified Facilities Criteria’ (UFC)[2] guidelines. All the studied cases satisfied the UFC guidelines requirements for progressive collapse resistance of reinforced concrete structures.

Key words: Progressive Collapse, Irregularity, Catenary action, UFC, AEM, ELS

1. INTRODUCTION Progressive collapse recently became an important point of research due to its catastrophic effect. In 1968, ‘Ronan Point apartment’, a 22-story building experienced partial collapse due to a gas explosion in the eighteenth floor which caused failure to corner load bearing walls[3]. In 1973, ‘Skyline Towers’, a 26-story building in Virginia, collapsed due to early shoring removal from an upper floor[3]. In 2013, ‘Savar building’, an eight-story building in Bangladesh, collapsed after appearance of several cracks in the columns of the ground floor[3]. The building was designed as an office building while it was used as a factory. The effect of machines weights and vibrations has caused the structure collapse. The aim of this research is to assess the effect of column sudden loss in a multistory irregular reinforced concrete framed structure under gravity loads, designed according to the Egyptian code of practice (ECP)[1], on progressive collapse according to the UFC guidelines[2]. Multiple cases of plan irregularity were studied with multiple column removal locations in each case. In the current study, a ten-story structure was modeled with slab and beam system. The Applied Element Method is used in this study with a fully nonlinear dynamic analysis scheme. The AEM is based on discrete crack approach which is capable of tracking the actual behavior of structure up to total collapse. The software used in analysis is ‘Extreme Loading for Structures’ (ELS)[4].

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2. THE APPLIED ELEMENT METHOD (AEM) The AEM is based on dividing the structure virtually into small elements. Each two adjacent elements are connected together at certain contact points which are distributed around the elements' surfaces. Each contact point is represented by one normal and two shear springs, these springs represent the stresses and deformations of a certain volume. The AEM is based on discrete crack approach. This method can track the structural behavior passing through all stages of loading; elastic stage, crack initiation, element separation, partial collapse of structure, and collision with the ground and other structures. The software used in the analysis is ‘Extreme Loading for Structures’ (ELS) which is an analytical tool which uses the Applied Element Method (AEM). The ELS uses an implicit method in numerical integration, which models structural collapse better than explicit solver software. The material models used in ELS are shown in Figure 1[5] and Figure 2[6]. Maekawa compression model is used for concrete modeling under compression as shown in Figure 1-a. For concrete shear springs, linear relation between shear stress and shear strain is assumed until cracking of concrete, then the shear stresses drop suddenly as shown in Figure 1-b. The level of drop depends on aggregate interlocking and friction at crack surface. For reinforcement springs, Figure 2 shows the model, presented by Ristic et al.[6], used in ELS. Several factors affect the calculation of tangent stiffness of reinforcement in this model such as: the strain from reinforcement spring, loading status (loading or unloading), and history of steel spring (which controls Baushinger's effect).

ELS was proved to be capable of performing nonlinear, static and dynamic, analysis of structures subjected to extreme cases of loading through elastic and inelastic stages up to structural collapse including automatic detection of cracks' locations, formation of plastic hinges, and buckling of elements. The ‘ELS’ software was extensively validated [7][8][9][10][11][12][13][14][15][16][17][18] and had shown good agreement with real cases. Several validation cases including static, dynamic, and collapse cases were covered. Therefore, and since the goal of the current study is to assess the capability of multistory reinforced concrete framed structures to resist progressive collapse under gravity loads, it was decided that the AEM is the most suitable numerical tool for such assessment.

(a) Concrete under axial force (b) Concrete undeer shear force

Figure 1: Stresses in concrete springs due to relative displacement[5]

Figure 2: Stresses in steel springs due to relative displacement[6]

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3. CASE STUDY

The current study is an extension to the study by Helmy [21], where the progressive collapse of a regular reinforced concrete multi storey reinforced concrete structures was investigate. In the current study, effect of irregularity is investigated. 3.1 Details of Studied Structure

The studied structure is a ten-story reinforced concrete residential building. The building consists of five bays in each direction, the typical span of each bay is five meters. The ground floor is a public area (uncontrolled area). The height of all stories is three meters. The structure is designed according to the Egyptian code for design and construction of reinforced concrete structures[1]. The Ultimate limits state design method was used for design of the structure members. All members were designed to resist both gravity loads and seismic loads. All columns were assumed fixed to the foundation. Figure 3 shows details of the master case of the studied structure.

(b) Elevation of B1 and B2 (250X500)

(d) Rft. details of B2 (a) Master case plan (All spans = 5m)

Figure 3: Details of the master case of the studied structure

3.2 Earthquake Properties The design of the studied structure was checked against seismic loads using ACI318-08/IBC 2009[19][20] guidelines. The structure was assumed to be located in Cairo, Egypt (earthquake zone III according to the Egyptian code for loads). Therefore the peak ground acceleration was taken 0.15g and the response spectrum used is Type I. The importance factor of the building (γI) equals 1, the damping factor (η) equals 1, and the sub-soil group is assumed to be group (B).

3.3 Material Properties Nonlinear behavior of constituent materials are used in the models. The properties of concrete are shown in Table 1 and the properties of reinforcing steel are shown in Table 2. All the beams are assumed to be carrying masonry walls made of 25 cm width bricks, the density of bricks including plaster is assumed 1.8 t/m3.

3.4 Loads The loads considered in the analysis of all cases were as follows: The own weight of the structural members, the flooring load, the live load, and the masonry walls load. The flooring was assumed 0.15 t/m2 and the live load was assumed 0.3 t/m2. The load combination used in the study of column removal due to gravity loads was (1.2 D.L. + 0.5 L.L.) according to the UFC guidelines for nonlinear dynamic analysis of progressive collapse. The column in

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Table 1: Concrete Properties

Young's Modulus 2213590 t/m2 Compressive Strength 2500 t/m2 Tensile Strength 200 t/m2 Specific Weight 2.5 t/m3

Table 2: Steel Properties

Young's Modulus 20389000 t/m2

2 Yield Strength 36000 t/m Ultimate Strength 52000 t/m2

3.5 Mesh Sensitivity Mesh sensitivity analysis was carried out to obtain the optimum size of mesh to be used for each structural member in our case study, aiming to balance between the results preciseness and the required analysis time. The study was performed on a typical 5 m span building and the case of edge ground column removal was conducted. Four mesh groups were tested and mesh group (3) was chosen as shown in Table 3.

Table 3: Properties of Mesh Group (3)

Number of Mesh Group Beams Columns Slabs Elements 3 29586 16x3x3 12x3x3 14x14x2

3.6 Studied Parameters Four cases were chosen to study plan irregularity, where the typical plan consisting of five bays in each direction, each 5m span, is used as the master plan for each of the four cases. The chosen cases were as follows:

a. Varying the span of the middle bay in one direction only.

b. Varying the span of the external bay in one direction only.

c. Varying the span of the middle bay in both directions.

d. Varying the span of the external bay in both directions.

Where the spans studied in each case were 5m, 7m, and 9m and the removal of ground column was studied in all cases from several locations. Removal of edge and interior columns was studied for case (a). Removal of corner, edge, and interior columns was studied for case (b). Removal of interior column from two locations (1st interior bay and 2nd interior bay) was studied for case (c). Removal of corner and interior columns was studied for case (d).

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4. DISCUSSION OF RESULTS

4.1 Satisffying the UFC Guidelines Requirements

In all the studied cases, the studied structure didn't collapse; and the rotation of beamss, columns, and joints didn't exceed the UFC limits. The factor of safety for rotation was calculated by dividing the UFC limits by the maximum rotation obtained from the numerical model. The maximum beam rotation was 0.748 which is less than the UFC limit (3.6) with a safety factor of 4.8. The maximum column rotation was 0.087 which is less than the UFC limit (0.83) with a safety factor of 9.5. The maximum joint rotation was 0.32 which is less than the UFC limit (1.15) with a safety factor of 3.6. Therefore, the minimum safety factor obtained in all the cases was 3.6. In other words, the studied structural irregularities for the studied case showed conservative design against progressive collapse with a minimum safety factor of 3.6. Figure 4 shows a sample of analysis results for case (a) with interior column removal.

(a) Strain distribution after interior column removal in case (a)

(b) Beam rotation history after interior column removal in case (a)

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(d) Joint rotation history after interior column removal in case (a)

Figure 4: Sample of analysis results for interior column removal, case (a) (Middle bay changes from 5m to 7m and 9m (left to right respectively))

4.2 Comparison of Results

Figure 5 shows a comparison between the deflection values of the element just above the removed column. Figure 6 shows a comparison between the maximum beam rotation values for each case; Figure 7 shows a comparison between the maximum column rotation values for each case; and Figure 8 shows a comparison between the maximum joint rotation values for each case. The maximum value of deflection just above the removed column; the maximum beam rotation value; the maximum column rotation values and the maximum joint rotation values are affected by the difference in adjacent spans for different studied cases as shown in Table 4.

For case (a), the change in adjacent spans in the case of interior column removal almost didn't affect the value of deflection. That could be explained that the increase in the span is compensated by the increase in beams' cross sections as well as the slab reinforcement. (In other words, the increase in the catenary action). For the case of edge column removal, the value of deflection was nearly the same for adjacent bays spanning 5m and 7m. When increasing the adjacent span difference to 80% (case of bay span of 9 m), the deflection decreased by 11%.

For case (b), the change in adjacent spans in the case of interior column removal almost had no effect on the value of deflection, due to reasons mentioned above (increase in the catenary action). For the edge column removal case, increasing the adjacent spans difference to 40% (7 m case) lead to increasing the deflection by 35.6%, while increasing the span difference to 80% (9 m case) lead to increasing the deflection by 61%. As for the corner column removal case, increasing the adjacent spans difference to 40% lead to increasing the deflection by 30.6%, while increasing the span difference to 80% lead to increasing the deflection by 54.6%. This could be explained by the fact that the Vierendeel action, formed up by the beams above the removed column and beams in upper floors, is decreased by increasing the span and lower stiffness is achieved.

For case (c), the change in adjacent spans in the case of interior column removal from location (A) almost has no effect on the value of deflection, due to the reasons mentioned above. For the case of interior column removal from location (B), increasing the span difference to 40% and 80% lead to decreasing the deflection by 26.9% and 47.8%, respectively. This may be explained by the fact that the increase in catenary action, due to the increase in slab thickness, reinforcement, and beams' cross sections in both directions, had higher contribution on the deflection than increasing the span.

For case (d), increasing the adjacent spans differences, in case of interior column removal, to 40% and 80% lead to decreasing the deflection by 6% and 35%, respectively. This may be explained by the fact that the increase is in catenary action, due to the increase in slab thickness; reinforcement; and beams' cross sections in both directions, had higher contribution on the deflection than increasing the span. As for the case of corner column removal, increasing the adjacent spans difference to 40% and 80% lead to increasing the deflection by 45.4% and 79.4% respectively. This is explained by the fact that the Vierendeel effect is decreased dramatically, in both directions, by increasing the span of the exterior bays.

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Figure 5: Deflection values of an element just Figure 6: Maximum beam rotation values above the removed coluumn

Figure 7: Maximum column rotation values Figure 8: Maximum joint rotation values

Table 4: Effect of location of removed column on deflection, beam rotation, column rotation, and joint rotation

Removed Case Deflection Beam rotation Column rotation Joint rotation column location Inversely Inversely Directly Inversely a Edge proportional proportional proportional proportional Directly a Interior Not affected Not affected Not affected proportional Directly Directly Directly Directly b Corner proportional proportional proportional proportional Directly Directly Directly Directly b Edge proportional proportional proportional proportional Directly b Interior Not affected Not affected Not affected proportional Directly c Interior (A) Not affected Not affected Not affected proportional Inversely Inversely Inversely Inversely c Interior (B) proportional proportional proportional proportional Directly Directly d Corner Not affected Not affected proportional proportional Inversely Inversely Inversely Inversely d Interior proportional proportional proportional proportional

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5. CONCLUSION

Based on the results obtained from the studied cases, the following points were concluded:

1. All the studied cases, designed according to the ECP, satisfied the UFC guidelines requirements for progressive collapse resistance of reinforced concrete structures with safety factors equal to (4.8), (9.5), and (3.6) for beams, columns, and joints, respectively.

2. The catenary action of slabs has a significant effect in resisting the progressive collapse of the structure in all the studied cases, this effect appears obviously in the double-spanned beams which didn't collapse even when the bending moments exceeded the beams' flexural capacities.

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