13th World Conference On Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 3134
NON-LINEAR DYNAMIC BEHAVIOR OF COMBINED SYSTEM ON RC FRAME PRECAST 3D WALL PANELS WITH IRREGULARITIES IN VERTICAL STIFFNESS Mohammad Z. KABIR1 , Omid REZAY FAR2 and M.R.RAHBAR3 Summary The current study investigates the response of combined systems, RC frame pre-cast 3D wall sandwich panels in both linear and non-linear material properties. The seismic behavior of building constructed by 3D panels is studied in details, e.g. ductility evaluation in terms of load-displacement curves, energy loops and its dissipation during applied spectrum and material nonlinearities. The results are compared with regular bending RC frames and complete box type shotcrete sandwich panels system and present the differences of drifts and horizontal load distribution on floors. INTRODUCTION 3-D wall panels are used in construction of exterior and interior bearing and non-load bearing walls and floors of building of all types of construction. This system consists of a welded wire space frame integrated with a polystyrene insulation core. The wall panel is placed in position and wythes of concrete are applied to both sides. Wall panel receives its strength and rigidity by the diagonal cross wires welded to the welded-wire fabric on each side. This combination produces a truss behavior, which provides rigidity and shear terms for full composite behavior, Salmon et al [1]. Speeds in construction, weight lightening and thermal insulation are the marked privileges for building built up with such innovative system.
1
Assistant professor, Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran, Iran ,
[email protected] 2 Ph.D. candidate , Department of Civil and Environmental Engineering, Amirkabir University of Technology, Tehran , Iran ,
[email protected] 3 M. Sc. Structural Eng., Department of R&D , S.A.P. Company, Tehran, Iran ,
[email protected]
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Figure 1. Details of 3D panel One of the most evident limited of such box type system is in parking floor at lower level. Due to vehicle maneuver, some internal walls are replaced by RC frames and the bearing walls are disconnected. So, the gravity and lateral loads are transferred to bottom supported frame. Such non-uniformity in vertical stiffness influences on structural performance under transient dynamic loads under earthquakes. The problem is described as to investigate the seismic behavior of up to five stories building including one parking floor combined with box type 3D system. The study may extend to any combination of 3D bearing wall system and RC frame work. As a background of subject, Moehle [2,3], studied seismic response of four stories RC building. Wood [4] investigates dynamic performance of RC frame with variable stiffness. Lu et al [5] presented the results of the earthquake simulation tests on two of the frames with strength and stiffness irregularities. DYNAMIC ANALYSIS Non-linear Von-Mises and Druger-Prager criterion as two elasto-perfect plastic with bi-linear stressstrain curve are taken in dynamic analysis. The governing equilibrium equation of a finite element system for dynamic response is ••
•
M U + C U + KU = R Where M, C, and K are mass, dampers and stiffness matrices and R is exerted load vectors. ••
•
U , U and U are acceleration, velocity and displacement system, respectively. The ground acceleration is replaced by effective earthquake and is defined as follows. The quasi-static time history method is used for analysis. Ground acceleration record of NAGHAN is adopted, figure 2. The duration of record is totally 21 seconds with the maximum amplitude of 700.8 Gall. The major exerted energy is occurred at the first 10 second. 800 600
Acc. cm/s2
400 200 0
5
10
15
20
25
-200 -400 -600 -800
Figure 2 NAGHAN ground acceleration record
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Both linear and non-linear material models are considered in current study. The analysis is performed in ANSYS environment and two non-linear elements, shell 91 and solid 65, are adopted for concrete at system and component level, respectively. The orthogonal wire meshes are modeled by beam 23. Figure 3 represents the element details.
(a)Shell 91
(b) Solid 65
(c) Beam 23
Figure 3 Numerical models for analysis Material properties of shotcrete and wire meshes are tabulated in table 1. All details are those experimentally measured , [6].
Material
Poisson-ratio
Steel bars Concrete Shotcrete
0.28 0.2 0.15
Table 1 Material properties used in analysis Specific Young Yield stress Gravity Modulus kg/cm2 3 2 T/m kg/cm 7.855 2.06e6 4700 2.4 2.4e5 2.2 1.5e5 -
Tensile strength kg/cm2 30 28
Compression strength kg/cm2 300 180
Also, the stress-strain curves for welded wire meshes are obtained through tensile test based on ASTM and are depicted in figure 4. The final diameter of wires after cold rolling manufacturing is 3.5 mm. There is one stage annealing work have to be done to release the residual stresses.
(a)
(b)
Figure 4 Stress strain curves for (a) welded wire meshes, (b) shear connectors Also, to reduce the executive time of analysis, using of panel symmetry in thickness, only one half of the 3D panel is modeled for shear loading. Figure 5 shows the horizontal displacement of the bearing wall panel subject to shear loading in full and ½ thickness.
3
120
Reaction Force (kN)
100
80 1/2 PANEL PANEL
60
40
20
0 0
1
2
3
4
5
Displacement (mm)
(a) (b) Figure 4. Numerical modeling and load deflection curve for full and ½ thickness of bearing wall panel In dynamic analysis, especially when material behavior is considered as non-linear, the time step sizing in the analysis becomes important and to get more accurate results, ∆t is chosen infinitesimal. In this study, this parameter is taken as identical for all cases and equal 0.005. Table 2 shows the sensitivity analysis to obtain minimum ∆t for all models. Table 2 Sensitivity of Base absorbed shear to the time interval ∆t 0.02 0.01 0.005 0.002 ∆t (sec.) Base absorbed shear (Ton) 1019 753 530 522
0.001 520
Numerical Models To investigate the changes in building stiffness constructed in combination of 3D panels and RC frames, the following figures are 8 types of frames with different panel distribution in spans. All beams and columns cross section are 30 by 30 cm dimensions and have 2.5% steel reinforcement. The frames span length is identical for all models and the top view of each floor is depicted in figure 16.
(5-a) F2S1 (5-b) F2S2 Figure 5 single and double span frames (two stories)
001
002 003 004 005 006 007 Figure 6 Triple span Frame (two stories) F2S3
4
001 002 003 004 Figure 7 Double span frames (three stories) F3S2
001
002 003 004 005 Figure 8 Triple span frames (three stories) F3S3
001
001
001
002
006
002 003 004 005 006 Figure 9 Four span frame (three stories) F3S4
007
002 003 004 Figure 10 Double span frame (four stories) F4S2
005
003 004 005 Figure 11 Triple span frame (four stories) F4S3
006
5
001
002 003 004 005 Figure 12 Four span frames (four stories) F4S4
001
001
001
002 003 004 Figure 13 Double span frames (five stories) F5S2
006
005
002 003 004 005 Figure 14 Triple span frames (five stories) F5S3
002 003 004 005 006 Figure 15 Four span frames (five stories) F5S4
006
007
Figure 16 Floor top view
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All the frames shown in figures 5 to 15 are excited. The brief results are illustrated in table 2 in terms of natural periods. Also, the coefficient α, using UBC formula, T= αΗ 3/4, is calculated. It is seen that for full panel type system and for plane frame work, representing two extreme stiffened and flexible boundaries, the coefficient α is obtained between 0.008 and 0.04. The effect of distribution of 3D shear wall and its density in the first floor on structural period is remarkable.
Full panel
One ductile floor
One ductile floor with 25% panels One ductile floor with 50% panel
Table 2 The variation of structure period with height and length Height (m) 4 8 12 16 Ave. H3/4 Length(m) 6 0.036 0.033 0.022 0.03 3.83 9 0.042 0.034 0.031 0.036 5.2 12 0.063 0.049 0.044 0.052 6.45 15 0.089 0.068 0.058 0.072 7.62 6 0.151 0.171 0.18 0.167 3.83 9 0.21 0.22 0.23 0.22 5.2 12 0.245 0.26 0.26 0.255 6.46 15 0.28 0.287 0.294 0.287 7.62 6 0.033 0.385 0.036 3.83 9 0.0522 0.05 0.05 0.0507 5.2 12 0.077 0.069 0.066 0.0707 6.45 15 0.106 0.092 0.084 0.094 7.62 9 0.04 0.04 0.04 12 0.056 0.056 0.057 15 0.078 0.074 0.079
α 0.008 0.007 0.008 0.009 0.044 0.042 0.04 0.034 0.0094 0.0098 0.011 0.0123 0.0077 0.0088 0.0099
As a case study, consider F3S3 type in figures 8. The flexural frame in case of 001 posses a period which can be calculated by code formula. By adding wall panels at third level, the period is reduced about 12%. When two top floors covered by wall panels, the period decreases to %43. Table 3 represents the change in period by increasing the stiffness. Table 3 Comparison of periods in F3S3 frame type, (a case study) Frame type Natural Period in non-linear analysis Tn Tcode 001 0.383 0.364 002 0.336 003 0.22 004 0.05 005 0.04 006 0.034 0.26 The structural first and second mode shapes are plotted in figure 17 for such specific case. It is seen that the modes have similar trends for 001 and 006 representing full plane frame and box type wall panel, respectively.
7
10
10
8
HIEGHT (m)
7
F3S3001 F3S3002 F3S3003 F3S3004 F3S3005 F3S3006
9 8 7
HIEGHT (m)
9
6 5 4
6 5 F3S3001 F3S3002 F3S3003 F3S3004 F3S3005 F3S3006
3 2 1 0 0.00
4 3 2 1 0
0.20
0.40
0.60
0.80
1.00
1.20
-1.2
-1.0
-0.8
-0.6
NORMALIZED DRIFT
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
NORMALIZED DRIFT
Figure 17 The first and the second mode in F3S3 case In non-linear dynamic analysis, due to the unexpected structure response and sudden changes in structural stiffness, the period is fluctuated and mostly lower than the linear analysis. It is observed that in 002 case of F3S3 frame type, at 0.25 second, the structure changes into plastic mechanism and the period reduces down to %65 of linear analysis. In non-linear analysis, the study of changes in period could represent the changes in stiffness for bearing system. As an example, the variation of period for F5S3 frame type for all possible irregularities stiffness mentioned in figure 14 is sketched in figure 18.
PERIOD (s)
0.7
F5S3001 F5S3002 F5S3004 F5S3005 F5S3006 0.35
0 0
0.5
1
1.5
2
2.5
3
3.5
TIME(s)
Figure 18 The variation of period against time Comparison of Stiffness To estimate of comparative storey stiff nesses, it is assumed that the stiffness of the first soft floor considered as 100, case 001 for all frame types presented previously. Then, the relative stiffness is calculated using both linear and non-linear dynamic analysis. Table 4 shows the results of relative stiffness K. It is revealed that the existing of soft floor at parking lower level induced reduction of relative stiffness for upper levels. However, increasing the percentage of infill 3D wall could increase the relative stiffness in upper stories. As a result of table 5, the stiffness of the first floor over the second floor, (K2/K1) in terms of percentage of surface panel in lower level is plotted in figure 19. This graph is very practical in design criterion for distributing of shear force among building stories. For example, to find the minimum soft floor storey, the panel area should be 57% of total side area of the floor. Another words, in
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panel structures, it is possible by omitting of 43%of 3D wall panels, excluding of opening areas, the design could be processed as regular.
Table 4 Relative stiffness of floors in frames with irregularities in vertical F2S1 F2S2 F3S3
F3S4
F4S3
F4S4
F5S2
RATIO OF STIFNESS OF SOFT FLOOR/OVER FLOOR
F5S4
,001 44 100 48 100 63 52 100 83 67 100 46 48 52 100 47 49 53 100 42 44 45 50 100 47 49 49 53 100
K2 K1 K2 K1 K3 K2 K1 K3 K2 K1 K4 K3 K2 K1 K4 K3 K2 K1 K5 K4 K3 K2 K1 K5 K4 K3 K2 K1
,002 5152 116 1793 113 6848 58 100 9127 59 100 2642 6848 58 100 3993 9127 59 100 782 1431 4108 55 100 2381 4035 9127 59 100
,003 1452 5373 19758 115 4721 24935 114 6870 23374 114 2321 4762 24934 114 3654 6957 23958 114 710 1174 2552 19983 114 2377 4933 5098 23958 114
,004
,005
3939 4830 2946 6167 4226 4453 8375 3382 1829 2963 6166 4227 2917 4502 8379 3384 710 1081 1850 3954 4839 2080 2941 4506 8381 3385
5029 10536 3787 7085 8601 4792 8782 7355 1610 1643 7086 8602 3180 4862 8791 7356 93 1458 2545 5070 10530 2274 3211 4867 8792 7356
,006
4913 8236 13001 5839 9602 10877 2076 2412 8241 13001 4867 7192 10486 14400
2810 4002 5956 9622 10878
,007
7051 10470 14398
3453 4937 7202 10488 14400
145 140 135 130 125 120 115 110 105 100 95 90 85 80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5 0 0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
PERECENTAGE OF SURFACE RATIO OF PANEL
Figure 19 Relative stiffness of the first to the second floor in terms of percentage of 3D shear wall Base shear and structural response Applying the NAGHAN base acceleration record to all models in both linear and non-linear analysis, one can estimate the base shear which could balance the dynamical equilibrium of the structural system. In
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table 5, the relative base shear is presented for all cases in which upper floors are panel type system. However, the stiffness in the first floor varies from purely RC frame, first soft storey (1.S.ST.) as indicated in table 5 to full panel floor. L and N are introduced as linear and non-linear analysis. In linear analysis, for all types of the mentioned building in same table, the absorbed base shear of "001" cases is assumed to be fully 100%, considered as reference value. Then the other combined system is measured compared to it. Table 5 The relative Base shear in linear and non-linear analysis Frame type F2S1 F2S2 F2S3 F3S2 F3S3 F3S4 F4S2 F4S3 F4S4 F5S2 F5S3 F5S4
W(N) 64000 L N 128000 L N 192000 L N 192000 L N 288000 L N 384000 L N 256000 L N 384000 L N 512000 L N 320000 L N 480000 L N 640000 L N
FUL.FRM. 100.00% 54.84% 100.00% 56.32% 100.00% 39.02% 100.00% 28.93% 100.00% 27.20% 100.00% 25.29% 100.00% 24.64% 100.00% 18.70% 100.00% 16.59% 100.00% 22.13% 100.00% 21.60% 100.00%
1.S.ST 256.70% 53.16% 184.68% 57.27% 104.76% 35.32% 93.37% 27.93% 70.54% 21.63% 107.57% 25.04% 84.96% 22.16% 89.22% 18.38% 106.20% 17.78% 180.04% 24.26% 247.93% 20.87% 292.41%
25%P
33%P
50%P
66%P
75%P
190.87% 63.97%
217.67%
252.85%
306.11%
FUL.P. 63.48% 52.07% 72.06% 112.42% 57.55% 76.20% 155.30% 54.13% 58.99% 52.67% 61.58% 57.07% 175.06% 90.30% 154.84% 56.88% 80.62% 56.31% 279.32% 87.25% 321.87% 137.20% 165.70%
20.50%
15.17%
49.08%
50.01%
64.50%
87.91%
76.63% 66.14% 70.90% 60.19%
59.34% 64.70% 174.04% 57.29%
78.94% 63.01%
65.17% 52.31% 71.01% 59.04% 170.84% 42.18%
204.66% 42.04% 273.77% 53.62%
63.61% 57.36%
118.96% 62.40% 149.87% 55.70% 173.50% 56.07%
302.97% 45.89%
203.79% 51.76%
As seen, in linear analysis, e.g. in F2S1, the maximum base shear is occurred in the first soft floor, (1.S.ST). In F2S2 and F2S3 models the situation is similar. In 3 storey frames, F3 type, in short span frame, for 50% of panel covering in first floor, maximum base shear is produced. It is concluded from table 6, as building heightening, in soft floor the maximum base shear is more critical compare to those with stiffer lower floor. In non-linear analysis, it is observed that the base shear is almost similar for both full frame system and the (1.S.St.). As the first floor approaches to get more stiffness by covering of 3D wall panels, the percentage of absorbed base shear force increases. Therefore, it is more logic to rely on non-linear approaches, especially in shotcrete system. As a general conclusion for this part, it is observed that the linear analysis could not be reliable and feasible with real structural performance. Since in shotcrete panels, due to the initial cracks at the early stages of loading, the results for base shear found through linear analysis are not mainly acceptable. In RC frame structures, the absorbed base shear resulted by non-linear analysis is about 20% to 55% of linear analysis. In fact, the non-linear large deformation of structures makes marked reduction in absorbed base
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shear. It is interpreted that for equal deformation in both linear and non-linear analysis, the produced base shear force in non-linear is much lower than linear one.
Excitation of combined stiffness RC frames and 3D walls The F2S2 frame type is subjected to base acceleration of NAGHAN. In plane type RC frame, the maximum base shear is about 73.7 kN and the displacement at the crest is 33.1 mm. The loaddisplacement curve shows considerable energy dissipated. The results indicate that in non-linear analysis, up to 20 kN, the structure behaves linearly and then enter into non-linear portion. At the latter stage, the displacement increases sharply. In combination of 003, soft first floor, the maximum load carrying capacity of structure is 135.1 kN with the maximum drift of 18.9 mm at the top. For this case, up to 25 kN the frame behaves linearly and then gets into non-linear. The area of under envelope load-deflection curve is about 66% of full RC frame. The displacement is more limited. Figure 20 shows the hystersis loops of F2S2 under combination of 001 and 003. 110000
nlin lin over Poly. (over)
FORCE(N)
70000
30000
-0.05
-0.04
-0.03
-0.02
-0.01-10000 0
0.01
0.02
-50000 ROOF DRIFT(m)
(a) F2S2, 001 150000
nlin lin over Poly. (over)
FORCE(N)
100000
50000
0
-0.025
-0.02
-0.015
-0.01
-0.005
0
0.005
0.01
-50000
-100000
ROOF DRIFT (m)
(b) F2S2, 003 Figure 20 The variation of base shear against crest displacement under acceleration record
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In combination No. 004, with 50% panels at first floor, the absorbed shear is obtained at 86.5 kN with top displacement at 2 mm. This structure is mostly behaves linearly. Loading and unloading slope is approximately close to each other. In this model, energy dissipative is quite low. In combination 005, the structure is consisted of fully panels. The maximum absorbed shear force is 147 kN at 2.5 mm crest displacement. The response of structure is almost linear. The load-deflection curves for record acceleration of 004 and 005 combined stiffness are depicted in figure 21. 100000 nli n lin
FORCE(N)
50000
0 -0.0003
-0.0002
-0.0001
0
0.0001
0.0002
0.0003
-50000
-100000 ROOF DRIFT(m)
(a) F2S2 004 180000 120000
nlin lin
FORCE(N)
60000 0 -0.0003
-0.0002
-0.0001
0
0.0001
0.0002
0.0003
-60000 -120000 -180000 ROOF DRIFT(m)
(b) F2S2 005 Figure 21 The variation of base shear against crest displacement under acceleration record It could be shown that in full panel system, the energy dissipation is more than partially panel frames. CONCLUSIONS 1. In suggested building code relation, T=αH3/4, the parameter α could varies between 0.008 for panel type system and 0.04 for combined structures. 2. In ductile frames, the stiffness of the first floor is lower than upper floors. Incorporating panel system could considerably balance the distribution of stiffness. In this study, it is found the optimum percentage of 3D panels side area over the total side area of the floor is about 57%. 3. For more than 50% stiffening with 3D panels, the absorbed shear is approximately to the full panel system. 4. The absorbed base shear in non-linear analysis is 2 to 3 times lower than linear analysis. 5. The ratio of shear to the weight, V/W, is about 0.86 for combined system, 0.7-1.35 in 3D panel system and 0.21-0.87 in frame work structures. This ratio is highly dependent to structure height.
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REFERENCES 1. Salmon, D. C. and Einea A. ” Partially composite sandwich panel deflections”, ASCE, Journal of structural engineering, Vol. 121, No. 4, 1995;778-783 2. Moehle, J.P.” Seismic Analysis of R/C Frame-Wall Structures”, ASCE, Journal of structural Engineering, Vol. 110, No. 11, 1984; 2619-2634 3. Moehle, J.P. “ Seismic response of vertically irregular structures”, ASCE Journal of structural Engineering, Vol. 110, No. 9,1984; 2002-2014
4. Lu, Yong, ”Comparative study of seismic behavior of multistory reinforced concrete framed structures”, ASCE, Vol. 128, No. 2 2002; 169-178 5. Wood Sharon L, "Seismic response of RC frames with irregular profiles”, Journal of Structural Engineering. Vol.118, No. 2,1992, PP 545-566 6.jahanpoor,A.R.,"an estimate of ductility behaviour of 3D wall panels subjected to cyclic shear loads" , M.Sc. dissertation , Amirkabir university of technology ,March 2003
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