Mechanical Performance of Mega Steel Frame-Prestressed Composite Bracing Structure
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The Open Civil Engineering Journal, 2014, 8, 23-41 23 Open Access Mechanical Performance of Mega Steel Frame-Prestressed Composite Bracing Structure
Tang Baijian, Shao Jianhua*, Pei Xingzhu and Gu Sheng
Department of Civil Engineering, Jiangsu University of Science and Technology, Zhenjiang, P.R.China 212003
Abstract: The mega structure has been widely studied and applied due to the clear force transferring way, good structural integrity and flexible layout of diverse building functions. Based on the structure of mega truss or mega frame, the research and application of the mega structure with many kinds of bracing structures become a hot topic in recent years. Mega steel frame-prestressed composite bracing structure with a rigid-flexible composite bracing system composed of rigid Λ-shape steel brace and inverted Λ-shape flexible cable is a new kind of mega structure and this composite bracing system is set up in the mega steel frame. By establishing the three-dimensional finite element model and considering the material and geometric nonlinearity, the structural performance under static load in whole process was analyzed and the energy dissipation as well as failure mode under earthquake is also investigated for this new system in this paper. The results indicate that the lateral deformation is mainly decided by horizontal load and the corresponding curve of lateral displacement has the characteristic of flexure mode as a whole, whereas the deflection of mega beam is mainly governed by vertical load and pretension of cables. The internal force equilibrium of composite brace is decided by vertical load and the degree of force unbalance is about 15% when the fluctuation of vertical load is 20%, but the change of anti-symmetric horizontal load has no effect on the internal force equilibrium. The composite braces not only help the mega beam to bear the vertical load but also greatly enhance the lateral stiffness of main structure and so the lateral stiffness of whole system is relatively uniform. Due to the TMD effects of substructure and additional dampers, the seismic energy is mainly dissipated by dampers and substructure and then the main structure is able to maintain elastic. The desired failure mode of MFPCBS under lateral loads is as follows: the web members of mega beam appear to yield at first, and then the braces between mega column limbs, Λ-shape rigid bracing truss, floor beams between mega column limbs and mega column limbs in order. Keywords: Steel structure, mega structure, prestress, composite brace, energy dissipation analysis.
INTRODUCTION Zhang et al. [4] took the building of Tokyo city hall for example and analyzed the wind resisting performance of the The concept of mega structure is derived from the 1960s. mega-sub steel frame control system by means of the Due to many advantages such as the clear force transferring stochastic analysis method. The influence of stiffness ratio way, good structural integrity and the large lateral stiffness, and mass ratio between the main structure and substructure the mega structure has been widely studied and applied since on the control effect was especially studied. the first mega structure of Hancock Center in Chicago is built. Zhao [5] took the building of Shanghai world financial center as an example and studied the simplified model of the In 1990s, the active control of mega substructure under mega structure, especially of the beam-column joints. The earthquake and wind load is investigated by Maria et al. [1, elasto-plastic seismic performance of mega frame structure 2], which is the earliest control research for mega structure was preliminarily researched by applying Pushover analysis from the control view. with the frequently used load mode. In 2004, Zhang [3] studied the space hysteretic behavior Takabatake [6] took Tokyo New City Hall as an example of mega steel column by pseudo-static loading test and and presented the practical method of elasto-plastic analysis modeled it using the theoretical model. This simulation on the mega steel frame through the equivalent model. The achieved some promising results. Zhang’s research will natural period of vibration, elastic response and static elasto- provide a basis for the mega steel column simplified to a plastic analysis for this structure were analyzed and then single column and the large-scale numerical experiments. many satisfactory results were achieved.
Fan et al. [7] completely introduced the three- *Address correspondence to this author at the Department of Civil dimensional finite element fine model, natural vibration Engineering, Jiangsu University of Science and Technology, Zhenjiang, characteristic, response spectrum analysis and seismic time P.R.China 212003; Tel: +86-511-84432200; Fax: +85-511-84402322; history analysis of the Taipei 101 building which is the mega E-mail: [email protected] frame structure with concrete filled steel tubular.
1874-1495/14 2014 Bentham Open 24 The Open Civil Engineering Journal, 2014, Volume 8 Baijian et al.
Kyoung [8] proposed a design method based on the structural stiffness for the mega truss so as to effectively determine the initial size of mega brace. Zhou and Deng et al. [9] theoretically presented the mega frame-brace system and the mega frame- energy dissipation brace system to improve the lateral stiffness and seismic performance of mega frame structure. According to the numerical simulation and comparison of calculated results, the better static and dynamic performances were achieved for these new systems compared to the traditional mega structure. Lian et al. [10] studied the applications of frictional energy dissipation brace in the mega structure. The first author [11] presents a new type of the mega steel frame-prestressed composite bracing structure with a rigid-flexible composite bracing system composed of rigid Λ-shape steel brace and inverted Λ-shape flexible cable. This composite bracing system is set up in the mega steel frame. Fig. (2). Detail drawing of main members The numerical example based on the actual project is adopted in this paper. According to the numerical analysis, the static performance of this new system is researched from of each mega storey, there is mega rigid Λ-shape brace the internal force and deformation view, the seismic having a same section as mega beam, and at the lower part performance is evaluated from the structural energy there is inverted Λ-shape pre-stressed flexible cable (Fig. dissipation and the ultimate state is investigated from the (1a)). On each mega storey, there are 8 crisscross plane desired failure modes. trusses supporting on mega beams in order to suspend substructure. The damper is installed between the tail part of 1. NUMERICAL EXAMPLE the suspended substructure and the main structure. Main member sizes are listed in Table 1. The computing model of the mega frame-prestressed composite bracing structure is shown in Figs. (1 and 2). The In Fig. (1), the points A, D, G, J, M and P are the structure is diagonally symmetrical with square plan of 36 intersections of prestressed cable and lower chord of mega m×36 m (Fig. (1c)). The total height of the 54-storey frame Λ-shape brace, as well as the inside limb of mega column. structure is 216 m above the ground, and the height of each The point C, F, I, L, O and R are the intersections of lower storey is 4 m [6]. There are four same 6 m square lattice chord of mega Λ-shape brace and mega beam. The point B, mega columns at four corners. Each mega column consists of E, H, K, N and Q are the intersections of lower chord of four box section columns through K-shape brace connecting mega beam and outside limb of mega column. together. Mega beams are set to connect mega columns at The diameter and initial prestress of every cable shown in Floor 9, 18, 27, 36, 45 and 54. Each mega beam is a one- Table 1 are determined according to the two principles: storey height space truss including four I-section chords, internal force equilibrium in composite bracings, and non- several vertical and oblique web members. At the upper part failure of prestressed cables at any condition.
(a) Elevation view of main structure (b) Elevation view of main-sub-structure (c) Typical floor plan Fig. (1). Steel mega frame and prestressed composite bracing structure. Mechanical Performance of Mega Steel Frame-Prestressed Composite Bracing Structure The Open Civil Engineering Journal, 2014, Volume 8 25
Table 1. Member size of MFPCBS.
Member Section Shape H/mm B/mm tf/mm tw/mm
Limb of mega column(1st 2nd mega storey) 900 900 60 60
Limb of mega column(3rd 4th mega storey) 口 900 900 36 36
Limb of mega column(5th 6th mega storey) 900 900 20 20
K-shape brace of mega column 200 200 12 8
Horizontal web member of mega column 350 200 11 7
Chord of mega beam 1000 500 30 20
web member of mega beam 300 300 15 12
Chord of plane truss H 400 200 12 8
web member of plane truss 300 300 15 12
Chord of mega Λ-shape brace 1100 600 30 20
Horizontal web member of mega Λ-shape brace 250 250 14 7
vertical web member of mega Λ-shape brace 200 200 12 8
Hanging member(upper part) 250 250 10 10 口 Hanging member(lower part) 250 250 6 6
Beam of substructure H 350 200 11 7
Floor slab of substructure Profiled sheet composite floor 80 mm thickness Floor slab of main structure (C30 concrete covered) 80 mm thickness
inverted Λ-shape cable(1st mega storey) ○ Diameter 344.1mm/ pre-stress 12304 kN
inverted Λ-shape cable(2nd mega storey) ○ Diameter 303.8mm / pre-stress 15942 kN
inverted Λ-shape cable(3rd mega storey) ○ Diameter 287.7mm / pre-stress 15860 kN
inverted Λ-shape cable(4th mega storey) ○ Diameter 235.3mm / pre-stress 10857 kN
inverted Λ-shape cable(5th mega storey) ○ Diameter 178.4mm / pre-stress 6290 kN
inverted Λ-shape cable(6th mega storey) ○ Diameter 142.7mm / pre-stress 4634 kN
Chinese Q345B is adopted in the material of all steel wind load according to equivalence of bottom bending members, whose Young’s modulus is 2.06×105 MPa and the moment. The wind load of 7.38 kN/m is applied on the linear expansion coefficient 1.2×10-5. The tensile strength of outside column limbs of mega columns with the right 5 cables is 1470 MPa, whose Young’s modulus is 1.40×10 direction. MPa and the linear expansion coefficient is 1.59×10-5. 1.1.3. Seismic Load E 1.1. Load The seismic fortification intensity is 8 degree. The classification of design earthquake is group 1, and the site 1.1.1. Vertical Load V classification is class II according to Chinese code. The dead load D and live load L of each mega storey are The damping ratio is 0.02 if the structure is at the 6.0 kN/m2 and 2.5 kN/m2, respectively. The dead load D and 2 elastic stage, while the value will be calculated by the live load L of each substructure storey are 4.5 kN/m and 2.5 following formula [12] at the elasto-plastic stage: kN/m2, respectively. The basic composition of vertical load V is equal to D+0.5L in this example. 1 12.0 .0 02 (1) D 1.1.2. Wind Load H f 2 Provided that the basic wind pressure 0 = 0.45 kN/m . Where: D f is the plasticity ratio of structure [13], and For convenience, the uniformly distributed wind load is Q D sd (2) adopted as a substitution for inverted triangular distribution f dsQ 26 The Open Civil Engineering Journal, 2014, Volume 8 Baijian et al.
Where: counterclockwise shear is positive.
d -the displacement representative value at the elasto- plastic critical state 2. STATIC ANALYSIS 2.1. Under Initial Prestress P s - the displacement representative value at the plastic state 2.1.1. Structural Deformation Qd - the bottom shear force at the elasto-plastic critical state
Qs -the bottom shear force at the plastic state As shown in Fig. (3), the deformation of each mega storey is very similar at the original prestressed state. The The finite element program SAP2000 is used for mega beam is upward convex and the maximum deflection analysis. The column element is adopted to simulate all at midpoint is 12.6 mm which is about 1/2300 of the beam members in mega beams, mega columns and mega bracings. length. The mega column is inward concave. And the The cable element is used for pre-stressed cables, the four- maximum displacement at midpoint is 15.8 mm which is node shell element is applied to model floor plate and the about 1/1100 of the column height. link element is used for damper. The negative temperature method is adopted to apply the prestress [14, 15] and the 2.1.2. Internal Forces of Mega Column material and geometry nonlinearity are considered in the As shown in Fig. (4), the axial force of mega column is calculation. pressure except that column is located at the rigid Λ-shape The sign of internal force is ruled by the followings in brace segment at the top storey and this axial value changes this paper. The pressure for the axial force of mega column suddenly at intersections of mega members. The maximum and mega Λ-shape steel brace is positive, while the tension axial force occurs at the four bottom stories and is 4361 kN, for the axial force of cable is positive. The tension at the which is equal to the vertical component of tension in the outside limb for the moment of mega column is positive and cable. The sign of shear force at the mega column alters at the clockwise shear is positive. The tension at the lower the intersection of rigid Λ-shape brace and prestressed cable, chord for the moment of mega beam is positive and the it can be explained by that the force transferred from the
14 Q 12 P N 10 M K 8 J H
6 Node G E 4 D Deflection/mm 2 B A 0 0 0 1 2 3 4 5 6 -30 -20 -10 0 10 20 30 Mega storey number Horizontal displacement/mm (a) Overall deformation (b) Deflection at midpoint of mega beam (c) Horizontal displacement of mega column Fig. (3). Structural deformation at the prestress state.
5000 2000 10000 1500 4000 7500 1000 5000 3000 500 2500 0 2000 0 9 18 27 36 45 54 -2500 9 18 27 36 45 54 Shear force/kN -500
Axial force/kN 1000 -5000 -1000 Bending moment/kN.m -7500 0 9 18 27 36 45 54 -1500 -10000 Storey number -1000 Storey number -2000 Storey number -12500
(a) Axial force (b) Shear force (c) Bending moment Fig. (4). Internal forces in right-side mega column at the prestress state. Mechanical Performance of Mega Steel Frame-Prestressed Composite Bracing Structure The Open Civil Engineering Journal, 2014, Volume 8 27 cable is shared by the upper and lower part of mega column. 2.2. Under Prestress and Vertical Loads P+V The bending moment diagram of mega column is accordance 2.2.1. Structural Deformation with the overall deformation diagram of mega column at the prestressed state (Fig. (3a)). The maximum negative bending As shown in Fig. (7), the mega column showed slightly moment appears at the intersection of rigid Λ-shape brace inward concave deformation and the mega beam except at and prestressed cable where the maximum concave the top storey showed upward convex deformation under deformation occurs, while the maximum positive bending P+V. Since the prestress value in this example is determined moment occurs at the connection between mega beam and according to internal force equilibrium in composite bracing mega column. under regular service, the above deformation characteristic has generality for mega frame and prestress bracing 2.1.3. Internal Forces of Mega Beam structure, which indicates that the pre-tension in cable can As shown in Fig. (5), the maximum shear force and resist the compression caused by the vertical load and a bending moment all appear at the midpoint of mega beam at small amount of surplus tension in cable is necessary to meet the prestressed state, which is mainly because of the the reduction of tension induced by the following horizontal concentrated forces. The bending moment diagram coincides load. with the deformation of upward convex at the prestressed The deformation diagram of each mega beam in P+V state (Fig. (3a)). condition is similar. Inverted arch appears at Storey 1~5, and 2.1.4. Internal Force of Composite Bracing the maximum deflection is about 7 mm, which is close to the half value at the pure prestress state. Concave deformation The sign of ic represents cable at the i mega storey and appears at both end sections of the mega beam due to vertical ib refers to the rigid brace at the i mega storey in Fig. (6). loads. Inverted arch dose not appear at the top storey because At the pure prestressed state, the internal forces of composite there is not prestressed cables at that storey, but the trend of bracings are in disequilibrium, and the maximum difference deformation is the same as that at the other storey. occurring at bottom storey is nearly 6000 kN. The internal force of cable at each mega storey is tension and the rigid Under P+V condition, there is almost no horizontal braces are compressed except at the top storey, however the displacement of mega column and the maximum drift compression is relatively small. displacement is only about 3 mm. so it can be confirmed that the internal forces of composite bracings are in equilibrium
4000 3000 Storey1 Storey2 Storey3 2000 2000 Storey4 W mid Storey5 0 1000 Storey6 0 5 10 15 20 25 30 35 -2000 W T mid 0 -4000 Storey1 0 5 10 15 20 25 30 35 40 Storey2 Shear force/kN -1000 -6000 Storey3 Storey4
-2000 Beanding moment/kN.m -8000 Storey5 Storey6 -3000 -10000 Axial direction of mega beam/m Axial direction of mega beam/m (a) Shear force (b) Bending moment Fig. (5). Internal forces of mega beam in prestress state. 6000 5000 4000 3000 2000 1000 0 c1 b1 c2 b2 c3 b3 c4 b4 c5 b5 c6 b6 Axial force/kN -1000 -2000 Bracing number
Fig. (6). Internal force of composite bracings at the prestress state. 28 The Open Civil Engineering Journal, 2014, Volume 8 Baijian et al. according to the deformation diagram. The bending moment of mega column at each mega storey changes periodically and it is negative in the rigid 2.2.2. Internal Forces of Mega Column bracing segment except the bottom storey, while it is positive Under P+V condition, the axial force diagram of mega in the prestressed cable segment. The bending moment column in Fig. (8) shows the stepped shape and the threshold diagram shows the stepped shape, which reflects the transfer position is the intersection of the rigid Λ-shape brace and the of the axial force in bilateral limbs of mega column. The prestressed cable. maximum bending moment appears at four bottom stories. The shear force of mega column jumps drastically at The bending moment turns direction at intersection of rigid intersections of mega members and the maximum value brace and mega column, which is accordance with the appearing at Storey 27 is 1321 kN. It should be pointed that deformation inflection point in Fig. (7a). the equilibrium of composite bracings in this example means 2.2.3. Internal Forces of Mega Beam that the total tension of cables is equal to the total axial compression of upper and lower chords in the rigid Λ-shape Comparing Fig. (9) with Fig. (5), the value of maximum brace, and the internal force of web member of rigid brace is shear force and bending moment at the mega beam midpoint not taken into account, which results in jump of the shear under P+V condition is less than that under the pure prestress force at the connection between chords of the rigid brace and condition because the increments of internal forces under mega column. vertical loads is opposite to those caused by prestressing, and
Q 8 Storey1 P Storey2 N 6 Storey3 M 4 Storey4 K Storey5 J 2 Storey6 H W S T mid Node G 0 E 0 5 10 15 20 25 30 35 D Deflection/mm -2 B A -4 0 -6 -30 -20 -10 0 10 20 30 Axial direction of mega beam/m Horizontal displacement/mm (a) Overall deformation (b) Deflection of mega beam (c) Horizontal displacement of mega column Fig. (7). Structural deformation under P+V
120000 1400 12000 100000 1200 9000 80000 1000 800 6000 60000 600 3000 40000
Axial force/kN 400 0 9 18 27 36 45 54 20000 200 -3000 Shear force/kN 0 -6000 0 9 18 27 36 45 54 Beanding moment/kN.m 9 18 27 36 45 54 -200 Storey number -9000 Storey number Storey number (a) Axial force (b) Shear force (c) Bending moment Fig. (8). Internal forces in right-side mega column under P+V.
Storey1 Storey1 9000 Storey2 Storey2 Storey3 15000 Storey3 Storey4 Storey4 Storey5 6000 Storey5 10000 Storey6 Storey6 K=0 3000 K=0 5000 K=∞ W mid K=∞ W mid 0 0 S T 0 5 S 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 -5000 -3000 Shear force/kN -10000 -6000 -15000 Beanding moment/kN.m -9000 Axial direction of mega beam/m -20000 Axial direction of mega beam/m (a) Shear force (b) Bending moment Fig. (9). Internal forces in mega beams under P+V. Mechanical Performance of Mega Steel Frame-Prestressed Composite Bracing Structure The Open Civil Engineering Journal, 2014, Volume 8 29
5000 Q P P 4800 N P+V M P+V+H 4600 K J 4400 H G Node E 4200 D B 4000 A 3800 0
Axial force/kN -30 0 30 60 90 120 150 180 3600 Horizontal displacement/mm c1 b1 c2 b2 c3 b3 c4 b4 c5 b5 c6 b6 Fig. (12). Comparison of lateral displacement of mega column. Bracing number 16
P Fig. (10). Internal forces of composite bracings under P+V. 12 P+V P+V+H it can be seen that the shear force and bending moment are 8 mainly generated by P. The bending moment is positive at each end and is negative at the middle part, which is 4 accordance with the deformation diagram in Fig. (7b). 0 2.2.4. Internal Forces of Composite Bracings Deflection/mm 0 5 10 15 20 25 30 35 Under the P+V loads, the internal forces of composite -4 Axial direction of mega beam/m bracings at each mega storey are in equilibrium and fluctuated around 4400 kN, and the maximum amplitude of Fig. (13). Comparison of vertical displacement of mega beam. difference between the maximum and minimum is 11% for all composite bracings. Since the P+V condition is a high uniform, which is governed by the structural form and the frequency case under the normal service condition, the stiffness ratio of internal members. The displacement equilibrium of internal forces under P+V loads is very characteristic is flexure on the whole, while the bending- important. Comparison between Fig. (10) and Fig. (6) shows shearing deformation characteristic is significant at joint that the force increment of the rigid brace from P to P+V is zones. greater than that of the cable, so the internal forces equilibrium of composite bracing can be achieved. It can be found from Fig. (11b) that in each mega storey the maximum storey drift ratio appears at the storey where the rigid brace and the cable intersect, and then decreases 2.3. Under Prestress, Vertical Loads and Horizontal both from upper direction and from lower direction. At the Loads (P+ V+ H) middle part of structure, the story drift ratio distribution is 2.3.1. Structural Deformation very uniform. At the bottom part, the storey drift varies dramatic in the cable segment, while keeps gentle in the rigid As shown in Fig. (11), the horizontal deformation at the brace segment. At the top part, the variation pattern is top under P+V+H condition is 164.3 mm and the maximum opposite to that at the bottom part. storey drift appearing at Storey 42 is 4.5 mm, which is about Further comparison of structural deformation is made 1/900 of storey height. among three load conditions. From Fig. (12), the horizontal It can be concluded from the displacement curve of main displacement is mainly generated by horizontal load and the structure in Fig. (11a) that the lateral stiffness is relatively effect of prestress and vertical load can be ignored.
54 54 45 45 36 36 27 27 18 18
Storey number 9
Storey number 9 0 0 0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.0000 0.0003 0.0006 0.0009 0.0012 Horizontal displacement/m Storey drift angle (a) Lateral displacement curve (b) Storey drift curve Fig. (11). Lateral displacement and storey drift ratio under P+V+H. 30 The Open Civil Engineering Journal, 2014, Volume 8 Baijian et al.
2100 150000 20000 1800 120000 15000 1500 10000 90000 1200 5000 900 60000 9 18 27 36
Shear force/kN 0 Axial force/kN 600 45 54 30000 -5000 300 Bending moment/kN.m -10000 0 0 9 18 27 36 45 54 9 18 27 36 45 54 -15000 Storey number Storey number Storey number (a) Axial force (b) Shear force (c) Bending moment Fig. (14). Internal forces of right-side mega column under P+V+H.
Storey1 8000 6000 Storey2 Storey3 4000 Storey4 4000 mid Storey5 0 Storey6 0 5W 10T 15 20 25V 30 35 40 2000 -4000 Storey1 SW T mid U V 0 -8000 Storey2 0 5 10 15 20 25 30 35 40 Storey3 Storey4 -12000 Storey5 Shear force/kN -2000 Bending moment/kN.m Storey6 -16000 -4000 Axial direction of mega beam/m Axial direction of mega beam/m (a) Shear force (b) Bending moment Fig. (15). Internal forces in mega beam under P+V+H.
According to Fig. (13), the vertical displacement of mega brace segment. The maximum bending moment appearing at beam is mainly generated by prestress and vertical load and Storey 4 is 17605 kN.m. On the whole, the internal forces of the effect of horizontal load can be ignored. mega column are uniform along the height. 2.3.2. Internal Forces of Mega Column 2.3.3. Internal Forces of Mega Beam The right-side mega column is selected for analysis. The Under P+V+H condition, the axial force diagram of axial force distribution under P+V+H condition is similar to mega column in Fig. (14) shows the stepped shape. that under P+V condition, but the maximum axial force Compared with Fig. (9), the internal forces distribution of increases about 20%. The shear force jump appears at the mega beam under P+V+H condition shown in Fig. (15) is intersections of mega members and the rest stories gradually similar to that under P+V condition, but both the maximum change due to uniform horizontal load. The maximum shear force and bending moment increase. Taking Storey 1 as positive shear force is 1907 kN and appears at the 9th storey. example, the maximum positive shear force increases about The bending moment of mega column turns direction at the 42% from 3318 kN to 4728 kN. The maximum positive intersection of composite bracing and mega column, and it is bending moment appearing at the 1/4 span increases about positive in the cable segment while is negative in the rigid 50% from 4180 kN to 6148 kN. The maximum negative bending moment appearing at the midpoint increases about 10000 60% from 9424 kN.m to 15240 kN.m. The above variation phenomenon of mega beam internal force is decided by the left side 8000 existence of composite brace because the inner forces of right side bilateral braces are no longer equal to each other under horizontal load, so it is different from that in pure mega 6000 frame. 4000 2.3.4. Internal Forces of Composite Bracing As shown in Fig. (16), under P+V+H loads, the axial
Axial force/kN 2000 force diagram of composite bracings shows the stepped shape and the composite bracings at each mega storey are in 0 equilibrium except for Storey 6, where a slight difference is c1 b1 c2 b2 c3 b3 c4 b4 c5 b5 c6 b6 exists. The axial force of left bracings at bottom storey is Bracing number close to zero, which is one general rule so as to save prestress for vertical prestressed structures where the Fig. (16). Internal forces of composite bracings under P+V+H prestressed cables together with other members resist Mechanical Performance of Mega Steel Frame-Prestressed Composite Bracing Structure The Open Civil Engineering Journal, 2014, Volume 8 31
54 54 45 45 P+0.8V+H P+V+H 36 36 P+1.2V+H 27 27 P+0.8V+H 18 P+V+H 18
P+1.2V+H Storey number Storey number 9 9 0 0 0.00 0.03 0.06 0.09 0.12 0.15 0.18 0.0000 0.0003 0.0006 0.0009 0.0012 0.0015 Horizontal displacement/m Storey drift angle Fig. (17). Comparison of lateral displacement and storey drift ratio considering ±20%V.
P+0.8V+H 9 9 P+V+H P+1.2V+H 6 6 P+0.8V+H P+V+H 3 3 P+1.2V+H 0 0 0 1 2 3 4 5 6 0 5 10 15 20 25 30 35 40 -3 Deflection/mm -3 -6 Maximum deflection/mm Mega storey number -6 Axial direction of mega beam/m -9 (a) Comparison of mega beam deflection in 3rd storey (b) Comparison of maximum mega beam deflection Fig. (18). Comparison of mega beam deflection considering ±20%V. 180000 2400 P+0.8V+H 150000 25000 P+0.8V+H 2000 P+V+H P+0.8V+H 120000 P+V+H P+1.2V+H 20000 P+V+H P+1.2V+H 1600 15000 P+1.2V+H 90000 1200 10000 5000 60000 800 0 Axial force/kN 30000 0 9 18 27 36 45 54 400 -5000 Shear force/kN 0 0 -10000
0 9 18 27 36 45 54 Beanding moment/kN.m 0 9 18 27 36 45 54 -15000 Storey number -400 Storey number Storey number (a) Axial force (b) Shear force (c) Bending moment Fig. (19). Comparison of internal forces in right-side mega column considering ±20%V. horizontal load. At the same time, it can be found that the load variation. The maximum deflection at each mega beam axial force of right bracing at bottom storey is nearly one is less than 9 mm that is about 1/3300 mega beam span under time more than the average. three conditions. 2.4. Sensitivity Analysis of Load 2.4.1.2. Internal Forces of Mega Column 2.4.1. Vertical Loads Variation As shown in Fig. (19), internal forces at mega column The vertical loads of D+0.5L in this example that plus fluctuate with the variation of vertical loads, but their and minus 20% of fluctuation are nearly corresponding with distribution characteristics remain unchanged. The variation of vertical loads has an obvious effect on the axial force, “D+L” condition and “D” condition, which means 0.5L accounts for about 20% of the sum of static vertical loads. especially for those columns near the bottom. The shear force in the cable segment changes significantly, but changes 2.4.1.1. Structural Deformation a little in the rigid brace segment. The bending moments of mega columns at the bottom change greatly, but change a Fig. (17) shows that the variation of vertical loads within little at other places. 20% range has almost no effect on the lateral displacement of the structure and storey drift distribution does not alter, 2.4.1.3. Internal Force of Mega Beam however the storey drift value fluctuates slightly. It can be found from Fig. (20) that the internal forces of It can be seen from Fig. (18a) that the variation of mega beams fluctuate with the variation of vertical loads, but vertical loads has a great influence on mega beam deflection. their distribution characteristics remain unchanged. Taking When vertical load decreasing, the upward convex at middle mega beam at storey 1 as example, the shear force under part is more significant, while the deflection at the 1/4 span P+1.2V+H condition is greater than those under P+V+H decreases evidently, and vice versa. So it is confirmed that condition. The shear forces at both ends increase obviously, the location of maximum deflection will change with vertical while increases about 3% on the middle part. Under the 32 The Open Civil Engineering Journal, 2014, Volume 8 Baijian et al.
5000 P+0.8V+H 5000 P+0.8V+H 3000 P+0.8V+H P+V+H 4000 P+V+H 4000 2000 P+V+H P+1.2V+H 3000 P+1.2V+H P+1.2V+H
3000 /kN 1000 2000 2000 1000 1000 0 0 0 5 10 15 20 25 30 35 40 0 0 5 10 15 20 25 30 35 40 -1000 0 5 10 15 20 25 30 35 40 Shear force/kN -1000 -1000 Shear force/kN -2000 Shear force -2000 -2000 -3000 -3000 Axial direction of mega beam/m Axial direction of mega beam/m -3000 Axial direction of mega beam/m (a) Shear force at storey 1 (b) Shear force at storey 3 (c) Shear force at storey 6
9000 8000 6000 8000 P+0.8V+H P+V+H 3000 4000 6000 P+1.2V+H 0 0 -30000 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 4000 -4000 -6000 2000 P+0.8V+H -9000 -8000 P+0.8V+H P+V+H P+V+H 0 -12000 P+1.2V+H 0 5 10 15 20 25 30 35 40 -12000 P+1.2V+H -2000 -15000 Beanding moment/kN.m Beanding moment/kN.m Axial direction of mega beam/m Beanding moment/kN.m Axial direction of mega beam/m -18000 -16000 Axial direction of mega beam/m -4000 (d) Bending moment at storey 1 (e) Bending moment at storey 3 (f) Bending moment at storey 6 Fig. (20). Comparison of inter forces in mega beam considering ±20%V.
left hand under P+0.8V+H 12000 right hand under P+0.8V+H left hand under P+V+H 10000 right hand under P+V+H left hand under P+1.2V+H 8000 right hand under P+1.2V+H 6000 4000 2000
Axial force/kN 0 c1 b1 c2 b2 c3 b3 c4 b4 c5 b5 c6 b6 -2000 Bracing number
Fig. (21). Comparison of internal forces in composite bracing considering ±20%V.
P+0.8V+H, it is on the contrary. Under P+1.2V+H 2.4.2. Horizontal Load Variation condition, the maximum positive bending moment appearing at the 3/4 span is 6662, kNm, which increases by about 8% 2.4.2.1. Structural Deformation compared with that under P+V+H condition. Need to pay It is shown in Fig. (22) that horizontal load variation only attention to the top mega beam, where bending moment has influence on the value of horizontal displacement and increases by about 50% because one part of vertical loads on storey drift ratio, and does not change their distribution the lower mega beam are transferred to the top mega beam pattern. The top horizontal displacement under P+V+0.8H through the composite bracing. condition is about 130.7 mm and deceases about 20.1% 2.4.1.4. Internal Force of Composite Bracing compared with that under P+V+H condition, while the value under P+V+1.2H condition is about 197 mm and increases It can be seen from Fig. (21) that the variation of vertical about 20.1%. So on the whole the lateral displacement and loads leads to the disequilibrium of internal forces at storey drift are proportional to horizontal load due to the composite bracings and the internal force increment at rigid elastic structure. bracing is greater than that at cable, so the vertical load plays a decisive role for internal forces equilibrium of composite As shown in Fig. (23), the effect of horizontal load bracings. Taking the composite bracings at the bottom storey variation within 20% range on mega-beam deflection can be as an example, the degree of disequilibrium is about 13% ignored. under the P+1.2V+H loads and about 15% under the P+0.8V+H loads. Mechanical Performance of Mega Steel Frame-Prestressed Composite Bracing Structure The Open Civil Engineering Journal, 2014, Volume 8 33
54 54 45 45 36 36 27 27 P+V+0.8H 18 P+V+H 18 P+V+1.2H P+V+0.8H Storey number Storey number 9 9 P+V+H P+V+1.2H 0 0 0.00 0.04 0.08 0.12 0.16 0.20 0.0000 0.0003 0.0006 0.0009 0.0012 0.0015 Horizontal displacement/m Storey drift angle Fig. (22). Comparison of lateral displacement and storey drift ratio considering ±20%H. 8 P+V+0.8H P+V+0.8H 8 P+V+H 6 P+V+H 6 P+V+1.2H 4 P+V+1.2H 4 2 2 0 0 0 1 2 3 4 5 6 0 5 10 15 20 25 30 35 40 -2 Deflection/mm -2 Maximum deflection/mm -4 -4 Mega storey number Axial direction of mega beam/m -6 (a) Comparison of mega beam deflection in 3rd storey (b) Comparison of maximum mega beam deflection Fig. (23). Comparison of mega beam deflection considering ±20%H.
150000 2100 P+V+0.8H P+V+0.8H P+V+H 20000 120000 1800 P+V+0.8H P+V+H P+V+1.2H 15000 P+V+H P+V+1.2H 1500 90000 10000 P+H+1.2H 1200 5000 60000 900 0 Axial force/kN Shear force/kN 600 9 18 27 36 45 54 30000 -5000 300 -10000
0 0 Beanding moment/kN.m 0 9 18 27 36 45 54 0 9 18 27 36 45 54 -15000 Storey number Storey number -20000 Storey number (a) Axial force (b) Shear force (c) Bending moment Fig. (24). Comparison of internal forces in right-side mega column considering ±20%H.
2.4.2.2. Internal Forces of Mega Column condition, the upwind cables at the two bottom stories quit work and the rigid brace at storey 1 is slightly tensioned. As shown in Fig. (24), the distribution pattern of internal forces at mega-column doesn’t change, however the values of internal forces especially at the structural bottom change 2.5. Comparison with Mega Frame and Mega Truss obviously due to cumulative effect of horizontal load. The shear force variation of mega columns in the cable segment The numerical model of steel mega frame structure is greater than that in the rigid brace segment and there is a (MFS) can be simply built by deleting all the composite positive relationship between the shear force of mega bracings in the steel mega frame and pre-stressed composite column and horizontal load. brace structure (MFPCBS). The numerical model of steel mega truss structure (MTS) can be built by substituting all 2.4.2.3. Internal Force of Mega Beam the composite bracings of the steel MFPCBS with diagonal Comparison of the shear force and bending moment of truss braces, which has the same section as the rigid Λ-shape the mega beams at storey 1, 3 and 6 as shown in Fig. (25) brace in MFPCBS. Comparison of the three different under different horizontal loads is made. It is obvious that structures is made under the final load condition (for the the internal forces of mega beam change little. MFS and MTS is V+H, and for the MFPCBS P+V+H). 2.4.2.4. Internal Forces of Composite Bracings 2.5.1. Structural Deformation As shown in Fig. (26), the internal forces of composite As shown in Fig. (27), the maximum mega beam bracings are in equilibrium no matter how the anti- deflection in MFPCBS is about 7.2 mm under the final load symmetric horizontal load varies. Under P+V+1.2H condition, which is about 1/5 of that in MTS or MFS. 34 The Open Civil Engineering Journal, 2014, Volume 8 Baijian et al.
6000 5000 P+V+0.8H P+V+0.8H 2000 P+V+0.8H P+V+H 4000 P+V+H P+V+H 4000 1500 P+V+1.2H P+H+1.2H 3000 P+H+1.2H 1000 2000 2000 500 1000 0 0 0 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 -500 0 5 10 15 20 25 30 35 40 Shear force/kN Shear force/kN -1000 Shear force/kN -1000 -2000 -2000 -1500 Axial direction of mega beam/m -3000 Axial direction of mega beam/m -4000 Axial direction of mega beam/m -2000 (a) Shear force at storey 1 (b) Shear force at storey 3 (c) Shear force at storey 6
8000 8000 5000 4000 4000 4000 P+V+0.8H 0 P+V+H 0 5 10 15 20 25 30 35 40 0 3000 -4000 0 5 10 15 20 25 30 35 40 P+V+1.2H -4000 2000 -8000 P+V+0.8H P+V+0.8H 1000 P+V+H -8000 P+V+H
-12000 Beanding moment/kN.m P+V+1.2H P+V+1.2H 0 -16000 -12000 0 5 10 15 20 25 30 35 40
Beanding moment/kN.m -1000 Axial direction of mega beam/m Beanding moment/kN.m -20000 -16000 Axial direction of mega beam/m -2000 Axial direction of mega beam/m (d) Bending moment at storey 1 (e) Bending moment at storey 3 (f) Bending moment at storey 6 Fig. (25). Comparison of internal forces of mega beam considering ±20%H.
Because the composite bracing transfers part of the loads at 2.5.2. Internal Forces of Mega Column the mega beam to the near mega column, the deflection of Under the final load condition, the maximum axial force the mega beam is dramatically reduced and then the at mega column of MFPCBS is greatest among three systems performance of the mega-beam is improved. as shown in Fig. (29a), which can be explained by that the It can be seen from Fig. (28) that the top horizontal composite bracing transfers the load on the mega beam to the displacement of MFPCBS is much smaller than that of MFS mega column and the effect of prestress of cables. and close to that of MTS, which means that the composite As shown in Fig. (29b), the maximum shear force of bracing can not only bear vertical load together with mega mega column of 1907 kN in MFPCBS is reduced by about beam, but also greatly improve the lateral stiffness of the 78% and 43% respectively, compared with that of 9001 kN frame structure. It is important that the maximum storey drift in MFS and of 3359 kN in MTS. So MFPCBS is a highly ratio in MFPCBS is significantly less than that in the other efficient system from the view of bearing shear force. two systems and the fluctuation amplitude of storey drift ratio diagram in MFPCBS is relatively much small, which Fig. (29c) further shows that the maximum bending means that the lateral stiffness distribution of MFPCBS is moment of mega column of 17605kN.m in MFPCBS is more homogeneous. reduced by about 85% and 22% respectively, compared with that of 121145 kN.m in MFS and of 22491 kN.m in MTS. So in the view of bearing bending moment, MFPCBS is a left side under P+V+0.8H highly efficient system. 12000 right side under P+V+0.8H left side under P+V+H 10000 right side under P+V+H 10 left side under P+V+1.2H 8000 right side under P+V+1.2H 0 0 1 2 3 4 5 6 6000 -10 4000 MFPBS -20 MFS 2000 MTS -30
Axial force/kN 0 c1 b1 c2 b2 c3 b3 c4 b4 c5 b5 c6 b6 -40 -2000 Brace number Maximum deflection/mm Mega storey number -50
Fig. (26). Comparison of internal forces in composite bracings Fig. (27). Comparison of maximum deflection of mega beam considering ±20%H. among three systems. Mechanical Performance of Mega Steel Frame-Prestressed Composite Bracing Structure The Open Civil Engineering Journal, 2014, Volume 8 35
54 54 MFPBS MFPBS 45 MFS 45 MFS MTS MTS 36 36
27 27
18 18 Storey number Storey number 9 9
0 0 0.0 0.2 0.4 0.6 0.8 1.0 0.000 0.002 0.004 0.006 0.008 Horizontal displacement/m Storey drift angle Fig. (28). Comparison of lateral displacement and storey drift ratio among three systems.
150000 6000 60000 MFBS 120000 4000 MFS 30000 MTS 2000 90000 0 0 0 9 18 27 36 45 54 9 18 27 36 45 54 -30000 60000 -2000
Axial force/kN -4000 -60000 MFPBS
30000 Shear force/kN MFS MFBS -6000 -90000 MTS
MFS Bending moment/kN.m 0 -8000 -120000 0 9 18 27 36 45 54 MTS Storey number Storey number -10000 Storey number -150000 (a) Axial force (b) Shear force (c) Bending moment Fig. (29). Comparison of internal forces in right-side mega column among three systems.
12000 12000 8000 MFPBS MFPBS MFPBS 9000 MFS 9000 MFS 6000 MFS MTS MTS MTS 6000 6000 4000 3000 3000 2000 0 0 0 0 5 10 15 20 25 30 35 40
0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Shear force/kN Shear force/kN -3000 Shear force/kN -3000 -2000 -6000 -6000 -4000 Axial direction of mega beam/m Axial direction of mega beam/m -9000 -9000 -6000 Axial direction of mega beam/m (a) Shear force at storey 1 (b) Shear force at storey 3 (c) Shear force at storey 6
50000 30000 40000 MFPBS MFPBS MFPBS MFS 40000 MFS 25000 MFS 30000 MTS 30000 MTS MTS 20000 20000 20000 10000 15000 10000 0 10000 0 5 10 15 20 25 30 35 40 0 0 5 10 15 20 25 30 35 40 5000 -10000 -10000
Bending moment/kN.m -20000 0 Bending moment/kN.m -20000 0 5 10 15 20 25 30 35 40
-30000 -30000 Bending moment/kN.m -5000 Axial direction of mega beam/m -40000 -40000 Axial direction of mega beam/m -10000 Axial direction of mega beam/m (d) Bending moment at storey 1 (e) Bending moment at storey 3 (f) Bending moment at storey 6 Fig. (30). Comparison of internal forces in mega beam among three systems.
2.5.3. Internal Forces of Mega Beam 8836 kN in MTS. The maximum bending moment in MFPBS is 15240 kN.m, which is reduced by about 59% and Comparison of internal forces of mega beam at storey 1, 55% respectively, compared with 37148 kN.m in MFS and storey 3 and storey 6 among three systems is shown in Fig. 33576 kN.m in MTS. (30). 3. SEISMIC PERFORMANCE ANALYSIS Compared with the other two systems, the maximum shear forces and bending moment of mega beam in 3.1. Seismic Wave MFPCBS is reduced significantly, which demonstrates that According to the relationship between acceleration mega beam’s performance in MFPCBS is improved. Taking spectrum and velocity spectrum is SSav , the seismic mega beam in storey 1 as example, the maximum shear force influence coefficient curve in Chinese code for seismic of 4682 kN in MFPCBS is reduced by about 60% and 47% design of buildings (GB50011-2010) can be transferred to respectively, compared with that of 11528 kN in MFS and of velocity spectrum, which is taken as the target velocity 36 The Open Civil Engineering Journal, 2014, Volume 8 Baijian et al.
400 400 -2 300 -2 300 200 200 100 100 0 0 -100 -100 -200 -200 -300 -300 Acceleration/cm.s
-400 Acceleration/cm.s -400 0 20 40 60 80 100 0 40 80 120 160 200 Time/s Time/s
(a)ART EL CENTRO wave (b)ART HACHINOHE wave 300 180 -2 200 150 100
0 -1 120 90 -100 Chinese code /cm.s ART EL CENTRO
-200 Sv 60 ART HARCHINOHE -300 30 ART KOBE Acceleration/cm.s -400 0 0 40 80 120 160 200 0 1 2 3 4 5 6 7 Time/s Time/s (c) ART KOBE wave (d) Velocity spectrum fitting Fig. (31). Earthquake waves. Table 2. Parameters of rare artificial earthquake wave.
Artificial Earthquake Phase Characteristics Dt/s Length/s Maximum/Gal Time/Sec
ART EL CENTRO EL CENTRO 1940 NS 0.01 81.92 419.15 2.22
ART HACHINOHE HACHINOHE 1968 EW 0.01 163.84 392.62 17.3
ART KOBE JMA KOBE 1995 NS 0.01 163.84 393.85 5.56 spectrum in this example. Then the phase characteristics of Under ART EL CENTRO earthquake wave, the seismic EL CENTRO 1940 NS, HACHINOHE 1968 EW relationship between additional damping and the top and JMA KOBE 1995 NS are used to form the frequent and displacement of the structure is shown in Fig. (32). It can be rare found that the horizontal vibration displacement of the artificial earthquake waves. The seismic fortification basic intensity is 8 degree, the classification of design earthquake is group 1 and the site soil classification is class II. The 2400000 velocity spectrum of artificial wave is fitted with the target spectrum. The parameters of the rare artificial earthquake 2000000 wave are shown in Table 2. Fig. (31d) shows the design -1 seismic velocity spectrum curve and the velocity spectrum 1600000 curves of ART EL CENTRO, ART HACHINOHE and ART 1200000 KOBE, respectively. A good agreement is found between the design velocity spectrum curve and the velocity spectrum 800000 curve of the artificial earthquake. 400000 3.2. Optimization of Damping Damping/ N.s.m 0 When the relative displacement of main structure and 0.085 0.090 0.095 0.100 0.105 0.110 substructure is large enough, collision is easily appeared Top horizontal displacement/m between them. So the damper is installed to reduce the lateral displacement. Fig. (32). Curve of additional damping and top displacement. Mechanical Performance of Mega Steel Frame-Prestressed Composite Bracing Structure The Open Civil Engineering Journal, 2014, Volume 8 37 structure is not boundlessly reduced with the increase of 3.3.2. Energy Consumption of Main Structure and additional damping, which has an optimal value of about 400 Substructure kN.s/m for ART ELCENTRO earthquake wave. It is hoped that the substructure can consume most energy to protect main structure from being destroyed. Fig. 3.3. Analysis of Energy Dissipation (34) shows plastic deformation energy comparison between 3.3.1. Energy Distribution of Overall Structure main and sub structures under three different earthquake waves. Obviously the plastic deformation energy only exits Fig. (33) is the time history curves of structure kinetic in substructure and main structure keeps elastic state, which energy (potential energy), damping consumption energy and meets expectation. structure plastic deformation energy under three different earthquake waves. The damping consumes about 90% of input energy from earthquake, and the plastic deformation 4. PUSHOVER ANALYSIS energy is very little, which means that most members are still Only the main structure was analyzed with the pushover in elastic stage and that the seismic performance of the analysis method in this paper, and the substructure is used as MFPCBS is excellent. the gravity load representative values in the way of
18000000 15000000 18000000 kinetic energy damping energy 15000000 15000000 plastic deformation energy 12000000 input energy 12000000 12000000 9000000 kinetic energy 9000000 9000000 kinetic energy damping energy damping energy 6000000 plastic deformation energy
Energy/J 6000000 plastic deformation energy 6000000 input energy Energy/J
input energy Energy/J 3000000 3000000 3000000
0 0 0 0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50 Time/s Time/s Time/s (a)ART ELCENTRO (b) ART HACHINOHE (c) ART KOBE Fig. (33). Energy distribution of overall structure.
/% 35 35 30 30 main structure main structure 30 main structure 25 substructure 25 substructure substructure 25 20 20 20 15 15 15 10 10 10 5 5 5 0 0 0 Energy consumption ratio/% Energy consumption ratio 0 1 2 3 4 5 6 0 1 2 3 4 5 6 Energy consumption ratio/% 0 1 2 3 4 5 6 Mega storey number Mega storey number Mega storey number (a) ART EL CENTRO (b) ART HACHINOHE (c) ART KOBE Fig. (34). Energy dissipation in main and sub structures.
(a) Base shear-roof displacement (b) Lateral stiffness-roof displacement Fig. (35). Base shear and lateral stiffness 38 The Open Civil Engineering Journal, 2014, Volume 8 Baijian et al. concentrated force to apply on the mega beam. 4.1. Base Shear and Lateral Stiffness The mega steel frame-prestressed composite bracing The curves of base shear and lateral stiffness varying structure is carried out the pushover analysis by using the with the roof displacement are shown in Fig. (35a and b), finite element analysis software SAP2000. The P-MM respectively. It can be seen from the graph that the different plastic hinge is set at the ends of giant column limb and the horizontal loading patterns have a major influence on the MM plastic hinge is set at the ends of floor beams, giant curves of structural performance. beam chords, plane truss chords and giant Λ-shape steel brace chord. The frame element only bearing axial load Fig. (35a) shows that with the horizontal load increasing, where the P hinge is set at the middle of members is used for the structural system gradually transits from elastic state to the braces between giant column limbs, web members of elasto-plastic state and the curve of base shear and roof giant beam, web members of plane truss and web members displacement varies from a line segment to curve segment of giant Λ-shape steel brace truss. The frame element only with the slope gradually decreasing. Finally, when the bearing tension is used for the pre-stressed cable and the horizontal load increases to a maximum value, this structural axial P hinge is also set at the middle of member. The FEMA system reaches the limit state of destruction because of model is used for all the plastic hinges. forming a lot of plastic hinges in structure. The horizontal maximum load of system obtained from Pushover analysis The vertical load and pre-tension are applied on structure at first so that the static nonlinear analysis will be conducted for the lateral inverse triangular distribution is less than that before carrying out Pushover analysis and the P-△ effect is for the uniform distribution. The former ultimate bearing took into account. The two different lateral load distributions capacity is 38714 kN and the corresponding displacement is of uniform distribution and inverse triangle distribution are 2160 mm. While, the latter is 43007 kN and roof applied in the Pushover analysis for the mega steel frame- displacement is 1585 mm. It is also known from the graph prestressed composite bracing structure [16,17]. that the roof displacement under the inverse triangular distribution is larger than that under the uniform distribution The recommended method in FEMA-273 [18] or ATC-40 when bearing the same horizontal load. [19] used in SAP2000 is adopted to evaluate the seismic performance of members. It can be seen from Fig. (35b) that when the horizontal load gradually increases, the resisting lateral stiffness of
(a) Cables at upper three large layers (b) Cables at lower three large layers Fig. (36). The tension of cables and roof displacement under the horizontal load of inverse triangle distribution.
(a) Cables at upper three large layers (b) Cables at lower three large layers Fig. (37). The tension of cables and roof displacement under the horizontal load of uniform distribution. Mechanical Performance of Mega Steel Frame-Prestressed Composite Bracing Structure The Open Civil Engineering Journal, 2014, Volume 8 39 structure gradually reduces and the lateral stiffness derived reaches 888mm, all the cables with symbol of number “1” from Pushover under the inverse triangular distribution is are out of working and the cables of S6-1 stop working in the less than that under the uniform distribution, the former end last. However, the increased speeds of tension in each elastic lateral rigidity is 27.1 kN/mm and the latter is 38.8 large layer are different for the cables with symbol of kN/ mm. number “2” because the slopes of curve for the tension of cables are different from each other and the increment of 4.2. Prestressed Cable tension for the cables at top large layer is slowest. As a The curve of cable tension in each large layer and whole, the cable quits working sooner and the increased displacement at the top of structure under the horizontal load speed of tension for another cable at the same layer is faster. of inverse triangle distribution is shown in Fig. (36). A The curve of cable tensiossssn in each large layer and symbol of S6-1 represents the cable at left of 6th large layer roof displacement under the horizontal load of uniform and S6-2 represents the cable at right of 6th large layer in distribution is shown in Fig. (37). On the whole, it can be figure. The other symbols are similar to these two meanings. seen from this figure that the change of tension for cables is When the displacement at top is 159 mm, the tensions of similar to that under the horizontal load of inverse triangle cables with symbol of S2-1 begin to reduce the zero at first distribution. But the time is later when the last group of and these cables quit working. When the roof displacement
(a) whole (b) mega beams (c) braces between mega column limbs (d) mega Λ-shape steel bracing truss (e) floor beams between mega column limbs Fig. (38). Plastic hinges under the horizontal load of inverse triangular distribution at the ultimate bearing capacity.
(a) whole (b) giant beams (c) braces between mega column limbs (d) mega Λ-shape steel bracing truss (e) floor beams between mega column limbs Fig. (39). Plastic hinges under the horizontal load of uniform distribution at the ultimate bearing capacity. 40 The Open Civil Engineering Journal, 2014, Volume 8 Baijian et al. cables quit working and the increased speed of tension is model. By studying the static performance of whole loading also slower. process in the view of deformation and internal force, the seismic performance in the view of energy dissipation and 4.3. Failure Mode of Structure [20] the limit state in the view of failure mode, main conclusions (1) The horizontal load of inverse triangular distribution. are obtained as follows. When the horizontal load of inverse triangular distri- The lateral deformation of MFPCBS is mainly caused by bution is up to limit state of 38714 kN, the displacement at horizontal loads and the displacement characteristic is top is 2160 mm and then a lot of plastic hinges occur at the flexure on the whole, while the bending-shearing structure. deformation characteristic is significant at joint zones. With the increase of horizontal load, the destruction of The mega beam deflection is decided by vertical loads this structural system gradually develops from bottom to and prestress. The horizontal loads have influence on upper layer under the horizontal load of inverted triangular maximum shear force and bending moment of mega beam, distribution mode. The yielding order of all members is as but have no effect on its deflection. follows: the web members of giant beam yield at first, and The vertical load variation within 20% range which - then the braces between the giant column limbs, giant Λ obviously affects the deformation and internal forces of shape steel bracing truss and floor beams between the giant mega beam leads to the internal forces of composite bracings column limbs in order. The plastic development occurred at in disequilibrium. The internal force increment of rigid brace the system is quite well when this structure reaches the is greater than that of cable and the degree of disequilibrium ultimate state under the horizontal load. The plastic degree of is about 15%. braces between the giant column limbs, giant beam and giant Λ-shape steel bracing truss is quite large and many plastic The horizontal load variation within 20% range almost hinges are occurred. has no effect on horizontal members. The lateral deformation pattern is unchanged and the horizontal displacement is (2) The horizontal load of uniform distribution approximately proportional to the horizontal loads. The When the horizontal load of uniform distribution is up to internal forces of composite bracings are in equilibrium, limit state of 43007 kN, the displacement at the top of which means that the variation of anti-symmetric horizontal structure is 1585 mm and then many plastic hinges shown in loads has no effect on the equilibrium of composite bracings. the Fig. (39) occur at the structure. Compared with MFS and MTS, the composite bracings With the increase of horizontal load, the destruction of in MFPCBS transfer a considerable part of loads on mega structural system under the horizontal load of uniform beam to mega column, so the deflection and internal force of distribution mode is mainly concentrated at bottom and the mega beam are obviously reduced. The composite bracings middle story. The yielding order of all members is as have also improved the lateral stiffness at the same time. The fluctuation amplitude of storey drift ratio diagram in follows: the web members of giant beam yield at first, and MFPCBS is relatively much small, which means that the - then the braces between the giant column limbs, giant Λ lateral stiffness distribution of MFPCBS is more shape steel bracing truss and floor beams between the giant homogeneous. column limbs in order. MFPCBS under various earthquake waves has excellent Compared with Fig. (38 and 39), when structure reaches seismic performance because of the TMD effect of the horizontal limit state, the number of destroyed storey substructures and the existence of additional dampers. Most under the horizontal load of uniform distribution mode is of energy is dissipated by dampers and substructures, so lower than that under the horizontal load of inverted main structure is able to maintain elastic. triangular distribution mode. At the same time, the different base shear-top displacement curve, horizontal lateral The two different distribution patterns of lateral loads which are the uniform distribution and the inverse triangle stiffness and ultimate bearing capacity are obtained under the distribution do not affect the yielding order and failure mode different horizontal loading mode, but the failure mode of of structure, but the relationship between the base shear force structure is similar. and the top horizontal displacement, the lateral structural The giant Λ-shape steel bracing truss used for the seismic stiffness and the ultimate load are different under the two energy dissipation has a large number of plastic hinges and different distribution patterns. the giant column limb which is the most critical factor for The desired failure mode of MFPCBS under lateral loads the safety of structure begins to form some plastic hinges is as follows: the web members of mega beam appear to after the giant beams and giant Λ-shape steel bracing truss yield at first, and then the braces between mega column have plastic hinges, which conforms to the seismic design limbs, Λ-shape rigid bracing truss, floor beams between philosophy of “strong column and weak beam” and “the first mega column limbs and mega column limbs in order. seismic fortification line destroys at first”. CONFLICT OF INTEREST 5．CONCLUSION The authors confirm that this article content has no Considering nonlinear effects of both material and conflicts of interest. geometry, MFPCBS is studied based on 3-D finite element Mechanical Performance of Mega Steel Frame-Prestressed Composite Bracing Structure The Open Civil Engineering Journal, 2014, Volume 8 41
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Received: October 17, 2012 Revised: December 19, 2013 Accepted: December 20, 2013
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