6th National Congress on Civil Engineering, April 26-27, 2011, Semnan University, Semnan, Iran

The Behavior of Concrete Frames Retrofitted by Steel Plate Shear Walls in Earthquake

A. Ranjbaran1, A. R. Shokrzadeh2 1- Associate Professor, Department of Civil Engineering, Shiraz University, Shiraz, Iran 2- Msc candidate, Department of Civil Engineering, Shiraz University, Shiraz, Iran

Amir_sh4919@yahoo.com

Abstract Steel plate shear walls have been used more frequently in recent years as the lateral load resisting system in the design and retrofit of high-rise buildings. Expected low cost fabrication, speedy erection, and good energy absorbing potential make the steel plate shear wall system an attractive alternative for the seismic upgrading of existing buildings. A new structural steel lateral load building system, called the steel plate shear wall (SPSW) currently under development in Canada, United States, Japan and other countries is gaining interest for its potential application in the seismic upgrading of buildings. While SPSW system can be easily integrated into existing steel frames, its suitability in concrete frames is still in the development stage. This paper concentrates on analytical studies of steel plate shear walls added to concrete frames. First using the fiber-based finite element analysis we propose an analytical model and verify this model by several experimental results (Numerical modeling has been developed in SeismoStruct). This model has been used to compare the behavior of concrete frames with and without steel shear wall. Then we continue our investigations with a parametric study on the behavior of concrete frames retrofitted by steel plate shear wall. We study the influence of changing in parameters such as concrete and steel plate characteristics, width to height ratio of frame and etc on behavior of such frames. Based on analytical results, some design recommendations for the structural system have been proposed. Keywords: Steel plate shear wall, retrofit, fiber-based finite element analysis, parametric study

1. INTRODUCTION A new structural steel lateral load building system, called the steel plate shear wall (SPSW) – currently under development in Canada, United States, Japan, Taiwan and other countries is gaining interest for its potential application in the seismic upgrading of buildings. Extensive analytical studies on steel plate shear walls in the United States, Canada, Taiwan and other countries have already validated the simple analytical model known as strip model to predict the monotonic behavior of this kind of structural system. [7]. A SPSW element is essentially a thin steel in-fill panel bordered by the wide flange members of the column and beam frame. The system’s lateral resistance is controlled by the post-buckling strength of the thin steel in-fill panels and the integral moment resisting frame. Extensive analytical and experimental investigations have shown that SPSW system exhibits stable hysteretic characteristics and that SPSW system can be a very effective energy absorbing lateral framing system. While SPSW system can be easily integrated into existing steel frames, its suitability in concrete frames is still in the development stage and a few experimental and analytical results are available.

This paper summarized the analytical work on three separate tests. Some of these specimens have elements such as steel brace or steel plate. Computer models were conducted by SeismoStruct. For more confidence verifying of computer simulations were performed by the three experiments. As a result many situations were experienced in simulations and many factures were considered. Computer simulation is the most cost effective way to predict and study buildings subjected to earthquake loading. In this study, models were developed in SeismoStruct to analyze these experimental models in order to correlate future analytical tools and new design methods and in addition to conduct other computer models to experience them. After verifying models parametric studies were performed on them.

2. THE EXPERIMENTS THAT HAVE BEEN USED FOR VALIDATION OF SIMULATIONS 2.1. MAHERI AND GHAFFARZADEH EXPERIMENT. [1], [2]

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Unit frames were modeled using a mid-span panel measuring 4.0 m by 3.0 m from the third floor of a four storey frame with the dimensions of 12.0 m by 12.0 m. Two (The) lateral load resisting systems, namely; moment frames and braced moment frames, were considered. A 2/5 scaled model, measuring 1.76 m by 1.36 m, was found satisfactory. The gravity forces acting on the models were also scaled down by a factor of (2/5)2. This factor was chosen to keep the stresses in the scaled model similar to the full-scale panel. The dimensions of the beams and columns were chosen to be 140 mm by 160 mm. Reinforcement details for the RC frames are shown in Figure 1.

The frames were tested using the setup presented in Figure 2. The lateral load–drift hysteresis for the frames F1, FX1 and FX2 are (is) shown in Figure 3.

Figure 1. Detailing of the Figure 2. Setup for cyclic Figure 3. Detail of applied load moment frames testing of model frames 2.2. LUBELL EXPERIMENTS. [3] Lubell conducted experiments on two one-story steel plate shear wall specimens (SPSW1 and SPSW2), depicted in Figures 4(a, b).

In all specimens, the beams were connected to the columns using moment-resisting connections. The top beam of specimen SPSW2 consisted of two S75*8 sections, one on top of the other, with the sections fully welded along the adjacent flange tips. It was found during the fabrication of SPSW1 that out-of-plane deformations in the infill plate, with maximum of 26 mm measured at the centre of panel, occurred due to welding distortion. The deformations were corrected in specimen SPSW2 such that the maximum out-of-plane deformation was less than 5 mm. (a) (b)

Figure 4. One-story test specimens (Lubell 1997): (a) SPSW1; and (b) SPSW2 2.4. MAHERI AND SAHEBI EXPERIMENT. [4], [5] They conducted an experiment on a concrete square frame with steel bracing .The frame was tested using the setup presented in Figure 5.

An actuator was used to apply an incremental diagonal load. The dimensions of the beams and columns were chosen to be 100 mm by 100 mm.

Figure 5. Test set up and concrete frame geometry

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3. MODELING APPROACH 3.1. MATHEMATICAL TOOL The finite element analysis program SeismoStruct is utilized to run all analysis. SeismoStruct is able to predict the large displacement behavior of space frames under static or dynamic loading, take into account both geometric nonlinearities and material inelasticity. SeismoStruct accepts static load (either forces or displacements) as well as dynamic (accelerations) actions and has the ability to perform eigenvalues, nonlinear static pushover (conventional and adaptive), nonlinear static time history analysis, nonlinear dynamic analysis and incremental dynamic analysis. 3.2. MODELING OF MEMBERS Structural members have been discretized by using a beam-column model based on distributed plasticity-

fiber element approach. The model takes into account geometrical nonlinearity and material inelasticity. Sources of geometrical nonlinearity considered are both local (beam-column effect) and global (large displacement/rotation effects). Material inelasticity is explicitly represented through the employment of fiber modeling approach with allow for the accurate estimation of structural damage distribution, the spread of material inelasticity across the section area and along the member length. In the fiber model the Sectional stress-strain state or beam-column elements are obtained through the integration of the nonlinear uniaxial stress-strain response of individual fibers in with the section has been subdivided, see figure 6.

Figure 6. Fiber plasticity discretization in a reinforced concrete section 3.3. MATERIAL Material properties were obtained from articles or direct communication with experiment’s researchers.

The concrete is modeled by employing a uniaxial constant confinement concrete model based on the constitutive relationship proposed by Mander et al.(1988) and later modified by Martinez-Rueda and Elnashai (1997) for reasons of numerical stability under larger displacement analysis.

Longitudinal reinforcement steel has been account by using a uniaxial steel model initially formulated by Menegotto and Pinto (1973) and later enhanced by Filippou et al. (1983) with the introduction of new isotropic hardening rules. It utilizes a damage modulus to represent more accurately the unloading stiffness. It is employment is advised to modeling reinforced concrete structures, particularly those subjected to complex loading histories, where significant load reversals might occur. 4. VALIDATION OF MODEL To validate the accuracy of the model, the FE analysis results are compared with the test results of maheri and ghaffarzadeh. [1], [2], Lubell. [3] and Maheri and Sahebi. [4], [5]. Comparisons have been made for some results of tests that are shown in section 2, such as pushover and Hysteresis curves. The comparison results are shown in Figures 7–10. It can be seen that the numerical results have good agreement with the test results. The model can accurately simulate the initial stiffness. For the plastic part of the some curves, the modeling result is slightly higher. This is because the concrete tension model ignores the loss of concrete strength after the concrete reaches the ultimate tensile stress. After cracking, the concrete still contributes to

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the moment capacity of the section. However, the difference between the modeling results and the test results are slight.

Figure 7. (a) Pushover curves for seismostruct model and maheri , sahebi braced specimen. [4], [5] ; (b) Simulation of Maheri and Sahebi experiment

Figure 8. (a) Detail of applied load

; (b) Hysteresis curve of computer simulation and Envelope of hysteresis curve for Maheri and Ghaffarzadeh test. [1], [2]

Figure 9. (a) Equation of Thorburn. [7] for angle of strips; (b) Use of Thorburn strip model for simulation of

Lubell experiment. [3]

Figure 10. (a) Pushover curves for seismostruct model and Lubell first specimen (SPSW1) . [3] ; (b) Pushover curves for seismostruct model and Lubell second specimen (SPSW2) . [3]

5. PARAMETRIC STUDIES OF CONCRETE FRAMES RETROFITTED BY SPSW To better understand the structural behavior of the frames, it is important to investigate the frames with systematic parametric studies. Only one variable was changed at one group so as to assess its effect clearly. They are considered to be the most influential factors for the frames.

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5.1. EFFECT OF THICKNESS OF THE STEEL PLATE Seven plate thicknesses 0.1 mm, 0.4 mm, 0.7 mm, 1 mm, 1.3 mm, 1.6 mm, 1.9 mm were modeled respectively.

The modeling results are shown in figures 11(a, b, c). When the thickness increased, the capacity and the initial stiffness of the retrofitted frame have been increased distinctly.

Analysis results obviously have been shown that the effect of plate thickness in increasing of the capacity and initial stiffness has a descending procedure.

Figure 11. Analytical results (a) Pushover results of FE models for different plate thicknesses; (b) Effect of plate thickness on capacity; (c) Effect of plate thickness on initial stiffness

5.2. EFFECT OF REINFORCEMENTS AND STEEL PLATE YIELD STRESS The comparison results were shown in Figure 12(a, b, c). Fourteen computer models were conducted, and it can be seen that there is not any difference in the initial stiffness. This is because that the stiffness of the materials was not changed.

Figure 12(c), Shows the comparison of change in capacity for these parameters. As shown the influence of the plate yield stress is greater than influence of the reinforcement yield stress.

Figure 12. Analytical results (a) Pushover results for different reinforcement yield stress; (b) Pushover results for

different plate yield stress; (c) influence of the plate and reinforcements yield stress on capacity Sensitivity of capacity to variation of the steel plate yield stress is good reason for studies are done on

low yield stress plates (LYP). These plates may have 96 MPa yield strength [6]. In some cases the design plate thickness is very thin. Such hot rolled thin plates don’t exist in steel

markets, and one solution for this problem is low yield strength plate usage. In Figure 13 (a), two pushover curves compare in a graph, one of them is the pushover curve of retrofitted frame with normal hot rolled steel plate and the other is the pushover curve of the frame retrofitted by LYP, thicknesses are same in two curves of the graph. Figure 13 (b) is same as Figure 13(a) but with one change, in the Figure 13(b) the thickness of low yield strength plate multiply by 2.

Figure 13. Analytical results (a) Pushover results for the frames retrofitted by LYP and normal steel plate with same thicknesses; (b) Pushover results for the frames retrofitted by LYP and normal steel plate

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5.3. EFFECT OF DIFFERENT MAGNITUDE OF ELASTIC MODULUS OF THE REINFORCEMENTS AND STEEL PLATE

Figure 14 (a), Shows the influence of the plate elastic modulus is greater than influence of the reinforcement module of elasticity on initial stiffness.

Figure 14. (a) Effect of plate and reinforcement module of elasticity on capacity; (b) Effect of plate and reinforcement module of elasticity on initial stiffness

5.4. COMPARATIVE STUDY ON CONCRETE FRAMES WITH AND WITHOUT SPSW AND INFLUENCE OF SOME PARAMETERS 5.4.1. EFFECT OF COMPRESSIVE STRENGTH OF CONCRETE Two frames were considered, one with SPSW and the other without it. In order to better study on the effect of this parameter, nine compressive strengths were chosen for each frame. The analysis results are shown in figures 15 (a, b, c). In Figure 15 (c), influence of compressive strength on two models is compared. As shown increment of capacity by increasing of fc has a descending procedure. The initial stiffness didn’t have change.

In the figure 15 (c) can be observed that the compressive strength of the concrete is more effective on retrofitted frame. The reason for this is shown in figure 16. It can be seen that the retrofitted frame subjected to a lateral loading, tension field of the plate pulled the columns inside of the frame. So in retrofitted case greater moments develop in the cross sections of the column, thus for this frame fc has more effectiveness.

Figure 15. Analytical results (a) Pushover curves of different compressive strength (retrofitted concrete frame); (b) Pushover curves of different compressive strength (not retrofitted concrete frame); (c) influence of

compressive strength changes on capacity in two conditions. (Condition 1: with SPSW and condition 2: without SPSW).

5.4.2. EFFECT OF WIDTH TO HEIGHT RATIO (L/H) OF THE FRAME ON CHARACTERISTICS OF THE RETROFITTED AND NOT RETROFITTED FRAMES In order to investigate the effect of the different width to height ratio (L/H) on each frame, twelve models have been built with different width to height ratios as shown in figures 16 (a, b). However, as shown in figure 19, existence of the plate has more influence on the frames with more L/H. the reason of this discusses here. In retrofitted frames as the L/H decrease further, effect of plate existence on increasing of capacity

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decrease. The reason for this is that as the L/H of the retrofitted frame decrease the length of the columns increase respectively, so tension field of steel plate pull the columns and decrease the capacity. So, however plate existence has incremental effect on capacity but this effect decrease by decreasing of the L/H.

Figure 16. Analytical results (a) deformed shape of different width to height ratios (retrofitted concrete frame); (b) deformed shape of different width to height ratios (not retrofitted concrete frame)

Figure 17. Analytical results (simulation of single frame) (a) Pushover curves of different width to height ratios (retrofitted concrete frame); (b) Pushover curves of different width to height ratios (not retrofitted concrete

frame); (c) influence of width to height ratio changes on capacity in two conditions. (Condition 1: with SPSW and condition 2: without SPSW).

Figure 18. Effect of plate existence on capacity versus width to height ratio

Figure 19. Analytical results for rigid beam condition (simulation of inter story frame) (a) influence of width to height ratio changes on capacity in two conditions. (Condition 1: with SPSW and condition 2: without SPSW); (b)

Effect of plate existence on capacity versus width to height ratio

6. Conclusions It can be concluded that the proposed FE modeling can accurately represent many of the main features of the behavior of concrete frames retrofitted by SPSWs. It offers a reliable and very cost-effective alternative to

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laboratory testing as a way of generating results. To better understand the behavior of SPSW, a series of analyses either using simple strip model were developed to analyze Lubell tests on two one-story SPSWs. The adequacy of the strip model using tension-only strips was found accurate to predict the nonlinear behavior of SPSW, as demonstrated by the experimental results. The pushover curves were shown to be equally well predicted by a monotonic pushover analysis using a FE model, when comparing to the experimental results.

In this study, models were developed in SeismoStruct to analyze experimental models in order to correlate future analytical tools and new design methods and in addition to conduct other computer simulations to experience them. Different variables have been studied on their influence on the structural behavior of the frames. Below the findings are summarized:

1. This system is very sensitive to yield stress of the steel plate so; many studies can perform in this

field in future. Studying on low yield strength plates (LYP) is an important case of this field. 2. By using of LYPs in frames we can use thicker plates, so some problems in construction and

welding procedure can be solved. 3. Analytical and experimental studies show maximum tension occurs in corners, so the connection of

the plate to frame’s corners must be performed carefully. 4. For retrofitting purposes, placement of steel plates in frames with greater width to height ratio leads

to more increment in initial stiffness and capacity. On the other hand in greater ratios columns experience lower moments. Greater ratios are suitable except in frames that there is no retrofitted frame in story above them (such as upper story of the buildings). In such frames in greater width to height ratio, beam pulls down and greater moments act on it.

References

1. Ghaffarzadeh, H. and Maheri, M. R. (2006) "Capacity interaction between the steel bracing and concrete frame", Proc. 7th Int. Congress on Civil Engineering, Tehran, Iran

2. Ghaffarzadeh, H., Maheri, M. R. Nehdi A. (2006), "Applicability of the Uniform Force Method in design of steel brace-RC frame connections" Submitted for publication to the Journal of Engineering Structures.

3. Lubell, A. S., 1997, "Performance of unstiffened steel plate shear walls under cyclic quasi- static loading", M. A. Sc. Thesis, Department of Civil Engineering, University of British Columbia, Vancouver, BC, Canada.

4. M.R. Maheri and A. Sahebi, "Use of steel bracing in reinforced concrete frames. " Eng Struct 19 12 (1997), pp. 1018–1024.

5. M.R. Maheri and A. Sahebi, "Experimental investigation on the use of steel bracing in reinforced concrete frames. " In: Proceedings of the Second International Conference on Seismic and Earthquake Engineering, Iran 1 (1995), pp. 775–784

6. Shun-Tyan Chen, Van Jeng, Sheng-Jin Chen, Cheng-Cheng Chen. (2001) "Seismic Assessment and Strengthening Method of Existing RC Buildings in Response to Code Revision", Earthquake Engineering and Engineering Seismology Volume 3, pp. 67–77

7. Thorburn,L.J., Kulak, G.L., and Montgomery, C.J., 1983, “Analysis of Steel Plate Shear Walls” Structural Engineering Report No.107, Department of Civil Engineering, University of Alberta, Edmonton, Canada.