NUMERICAL ANALYSIS OF AN EXISTING RC FRAME BY USING 3D ELEMENTS

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1 Journal of Earthquake and Tsunami, Vol. 5, No. 1 (2011) c World Scientific Publishing Company DOI: /S NUMERICAL ANALYSIS OF AN EXISTING RC FRAME BY USING 3D ELEMENTS J.QIAN,G.ZHAO,T.LEIandX.LU State Key Laboratory of Disaster Reduction in Civil Engineering Tongji University, 1239 Siping Road Shanghai , P. R. China Accepted 8 September 2010 In view of the fact that there are no suitable 1D elements that may adequately predict brittle shear failure, a refined finite element (FE) model using full 3D elements has been established for a existing frame structure. Numerical computation is performed to study the seismic damage and failure patterns of existing buildings. Emphases are focused on shear failure of beams and columns and additional stiffness effects of slabs and brick walls. The simulation results agree well with the in situ test and the general damage pattern observed in the 2008 Sichuan earthquake. Keywords: Reinforced concrete; frame structure; shear failure; in situ test. 1. Introduction The observation of damage caused by the 2008 Sichuan earthquake clearly indicates that most structures built after 1990 were resistant to the earthquake while those designed based on older version design codes were damaged seriously and even collapsed completely [Wang, 2008]. In view of the fact that a large number of old buildings are still widely used upon in towns and villages all over China, there is an urgent demand, technically and practically as well, regarding seismic assessment and strengthening to those existing old buildings for improvement in seismic safety and further reduction of casualties and financial losses due to possible earthquakes in the future. Existing old structures are usually weak in seismic safety viewpoint due to their material property degeneration and outdated design standards as well. In fact, undesired structural performance, such as brittle shear failure of RC columns, torsional effects, and weak-story mechanisms, has been quite often observed in postearthquake damage investigation in Sichuan. For a deeper understanding on damage mechanism, close observation of failure pattern, and its evolution, Zhu et al. [1981] and Li and Zhang [1986] carried out in situ damage test on 10 masonry and framed light-weight panel buildings. Corte et al. [2006, 2008] performed a full-scale series test on a real RC building including masonry infill panels and FRP strengthening. More recently, Lei et al. [2009] completed an in situ pushover test on a real 47

2 48 J. Qian et al. three-story reinforced concrete frame building. It is found that brittle shear failure of RC columns is essential in the final collapse of the structure. In this paper, We put forth relevant mechanisms that are necessary for the development of computational model for that tested structure. In view of the fact that there are no suitable one-dimensional (1D) elements that may adequately predict brittle shear failure, a refined finite element (FE) model using full 3D elements was proposed. Numerical simulation on structural response to lateral forces is presented and compared to the in situ test. 2. The Structural Details of the Building The original building was a three-story factory workshop built in 1983 as shown in Fig. 1. Due to the limitation of the in situ test condition, only a small portion was taken as the test object, shown in Fig. 2. The portion to be simulated was Fig. 1. view. (a) Photographs of the original building: (a) South elevation view and (b) East elevation (b) J H G F E Test Part D C B A Fig. 2. Layout of the structure for test and simulation.

3 Numerical Analysis of an Existing RC Frame by Using 3D Elements 49 P1/P3/P5 P2/P4/P6 L (Trapezoid) P6 P4 P2 11xyKB xyKB L L L5 Structural plane layout D L1 C 1xyKB xyKB xyKB L5 L7 1 B A D C B Section 1-1 A ± L1 Ends 6@ @ L5 Ends 8@ L1 Midspan @ @ L5 Midspan Fig. 3. Geometry and details of the steel reinforcement in beams and columns. 4 25/4 22/4 22 6@100/ /4 22/4 22 Z1-1/Z1-2/Z @ L7-1

4 50 J. Qian et al. a single span, single bay frame cut from the original building with a rectangular plan layout about m and three stories having heights equal to 4.84, 4.18, and 4.18 m for the first, second, and third story, respectively. The stories are sustained by RC columns having a cross section of mm, mm, and mm at the first, second, and third story, respectively. Outside the internal frame, there was an attached external masonry wall system. Floors were made of 120-mm-thick precast concrete slabs. Both the essential geometry and the main steel-reinforcement details of the simulated structure are shown in Fig FE Computational Model 3.1. FE modeling by ANSYS An FE model for the tested frame was established for post-test simulation purposes by using ANSYS package, in which concrete beams and columns were modeled by the 3D element SOLID65. An equivalent concrete model was applied to brick (a) (b) (c) (d) (e) (f) Fig. 4. The computational model for the test frame: (a) bare frame, (b) steel bars, (c) full view of the model, (d) detailed steel bars in beam L1, (e) details for joint 3-B, and (f) steel rebar in joint 3-B.

5 Numerical Analysis of an Existing RC Frame by Using 3D Elements 51 Table 1. Material properties used in computation. Concrete Longitudinal rebar Transverse stirrups Property C18 HRB335 HPB235 Density (kg/m 3 ) 2,500 7,800 7,800 Young s modulus (MPa) 26, , ,000 Strength (MPa) 22.7 Yielding stress (MPa) Ultimate stress (MPa) masonry by using the same SOLID65 element. Based on the observations of the test, there was no obvious damage to floor slab, thus floors were assumed to be in elasticity and SHELL143 element was adopted in simulation. Longitudinal rebars and transverse stirrups were modeled by using the 1D truss element LINK8. Figure 4 shows the FE computational model in detail Material properties In computation, the skeleton curve recommended by Code GB was adopted for concrete. An equivalent concrete model was applied to brick masonry with a skeleton curve proposed by Liu et al. [2008]. All material properties used in computation take the mean value measured in the test and are listed in Table Numerical Results 4.1. Results of modal analysis The first three vibration modes are computed and modal frequencies are listed in Table 2. They are compared with those measured in the test. Modal shapes for the first three modes are shown in Fig Results of pushover analysis A static nonlinear analysis (pushover) was carried out using the established FE model. The loading pattern used in pushover computation followed the similar way as that in the test. In view of the fact that the tested frame was a lowrise one with a regular layout both in its plan and elevation, the conventional inverted triangular acceleration distribution in lateral was adopted, which could be written as A6:A5:A4:A3:A2:A1 = 1:1:0.69:0.69:0.38:0.38. Seismic loads were Table 2. Comparison of modal frequencies (in Hz). Modal No FE results Test measured Error (%)

6 52 J. Qian et al. (a) (b) (c) Fig. 5. Vibration modal shapes: (a) the first mode, (b) the second mode, and (c) the third mode.

7 Numerical Analysis of an Existing RC Frame by Using 3D Elements Base shear (kn) Point P5 test Point P5 simulation Base shear (kn) Point P6 test Point P6 simulation Displacement (mm) Displacement (mm) (a) (b) Fig. 6. Base shear displacement curves and comparison. assumed to be proportional to the mass distribution. Thus, the applied load at each loading point, P1 P6, would be the product of the acceleration coefficient A1 A6 multiplied by the represented concentrated mass M1 M6 at each loading point. The relative mass distribution factor for the tested frame was calculated as M6:M5:M4:M3:M2:M1 = :308.36:554.69:432.06:600.84: The final lateral loading ratio at each load point P1 P6 was determined as P6:P5:P4:P3:P2:P1 = 1:0.723:0.898:0.699:0.535: Figure 6 shows base shear displacement curves at loading points P5 and P6, respectively. Numerical results agree well with those measured values in the uprising loading stage. However, divergence appears in simulating post-ultimate behavior of the test frame. It can be seen from Fig. 7 that the structure has underwent an obvious torsional deformation due to the participation of the perimeter walls. Figure 8 shows the Fig. 7. Deformed shape of the test frame at the ultimate loading step.

8 54 J. Qian et al. Fig. 8. (a) Stress distributions in bottom column 3-B compared to failure pattern in the test. (b) Mises stress distribution in bottom column 3-B at the ultimate loading step. It agrees qualitatively with the failure pattern observed in the test. Numerical results indicate that maximum stress may reach a value of 3.27 MPa, which is far beyond the possible strength stress of the equivalent material property, and inclined and horizontal cracks may appear on wall at the corner and between windows. This is confirmed by observation in the test shown in Fig. 9. Fig. 9. Stress distributions in perimeter walls compared to failure pattern in the test.

9 Numerical Analysis of an Existing RC Frame by Using 3D Elements Conclusions Basically, the FE model established using full 3D element provides a good prediction in structural responses in the uprising loading stage. For the test frame structure, numerical results show that columns at the bottom story were weak to lateral loads, and there were no significant damage in other structural members such as beams and floor slabs, although structural failure appeared in a clear pattern of brittle shear damage and this might cause the danger of inevitably collapse during a serious earthquake. However, divergence appears in simulating post-ultimate behavior of the structure, which signifies the fact that more efforts should be dedicated to material model of concrete in softening. Acknowledgments The financial support of the National Basic Research Program of China (973 Program) under the grant no. 2007CB is gratefully acknowledged. References Corte, G. D., Barecchia, E. and Mazzolani, F. M. [2006] Seismic upgrading of RC buildings by FRP: Full-scale tests of a real structure, J. Mater. Civil Eng. 18(5), Corte, G. D., Fiorino, L. and Mazzolani, F. M. [2008] Lateral-loading tests on a RC building including masonry infill panels with and without FRP strengthening, J. Mater. Civil Eng. 20(6), Lei, T., Lu, X. L., Qian, J. et al. [2009] In situ pushover test of an existing reinforced concrete frame, J. Build. Struct. 30(5), Li, G. Q. and Zhang, D. S. [1986] Destructive test study of framed light-weight panel buildings Type 79, Shijiazhuang, J. Wuhan Univ. Technol. 8(2), Liu, G. Q., Shi, C. X. and Liu, Y. B. [2008] Analyses of the elastic modulus values of masonry, J. Hunan Univ. (Nat. Sci.) 35(4), Ministry of Construction of China [2002a] Technical Specification for Concrete Structures of Tall Building JGJ (Beijing, China Architecture & Building Press, China). Ministry of Construction of China [2002b] Code for Design of Concrete Structures GB (Beijing, China Architecture & Building Press, China). Wang, Y. Y. [2008] Lessons learnt from building damages in the Wenchuan earthquakeseismic concept design of buildings, J. Build. Struct. 29(4), Zhu, B. L., Jiang, Z. X. and Wu, M. S. [1981] Seismic analysis of a five-story concrete block masonry building, J. Tongji Univ. (Nat. Sci.) 9(4), 7 14.