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ProcediaEngineering

Procedia Engineering 00 (2011) 000–000

www.elsevier.com/locate/procedia

The Twelfth East Asia-Pacific Conference on Structural Engineering and Construction

Stiffness and Strength Of Perforated Steel Plate Shear Wall

Ricky Chana, Faris Albermanib and S. Kitipornchaic

aSchool of Civil, Environmental and Chemical Engineering, RMIT University, Australia bDepartment of Civil Engineering, University of Queensland, Australia

cDepartment of Building & Construction, City University of Hong Kong, Hong Kong

Abstract

Steel Plate Shear Walls (SPSW) have been used as a lateral-load-resisting system in buildings. With formation of tension fields, unstiffened SPSW possesses good ductility and high energy dissipating capability under cyclic loading. However, large demand is induced to the frame members from panel yielding. For typical frame configurations, very thin panels are often required to limit such demand but sometimes result in construction difficulties. This paper attempts to reduce such demand by introducing perforations to thicker panels. The effect on stiffness and strength is investigated through nonlinear finite element technique. Based on results described in this paper a simple linear reduction function is proposed.

© 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of [name organizer]

Keywords: Steel Plate Shear Wall, perforation.

*Corresponding author: E-mail address: ricky.chan@rmit.edu.au

1877–7058 © 2011 Published by Elsevier Ltd.doi:10.1016/j.proeng.2011.07.086

Procedia Engineering 14 (2011) 675–679

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1. Introduction

For decades steel plate shear walls (SPSW) has been used as a form of lateral-load resisting system in tall buildings. Traditionally the in-fill panels are heavily stiffened to prevent elastic shear buckling. SPSW provides high lateral stiffness and offers an alternative solution to more massive reinforced-concrete walls. SPSW also provides saving in gross footage and facilitates fast construction. Generally the panels are installed after construction of the structural frame and most of the dead load has occurred to reduce compressive stresses in panels. Because of high slenderness, unstiffened panels buckle in shear in a relatively small lateral drift. Extensive research efforts into the post-buckled strength and ductility, with particular concern in earthquake resistance of the system, have been undertaken and led to its first codification in the Canada in 1994. It was later introduced to the US in 2005 (AISC 2005). Thorburn et al. (1983) and Timler et al. (1983) pioneered the analytical methods to estimate the post-buckled capacity. The thin plate is substituted by a series of strips inclined at an angle determined by principle of least work. Numerous researches followed and significant works include experimental and analytical investigations in the US (Elgaaly et al, 1993); testing of multi-storey SPSW (Driver et al, 1998) and development of plastic analysis (Berman et al, 2003). More recently, SPSW utilizing a light-gauge infill, reduced beam sections and perforated panels have been investigated (Berman et al 2005, Vian et al 2009).

In order to provide proper anchorage to tension field action, the Canadian steel design code CAN/CSA-S16-01 specifies minimum column stiffness index,

5.22

7.0 4 ≤=c

sh LI

whω (1)

where hs is the story height, w is the panel thickness, L is bay width and Ic is second moment of area of the column. A stiffness requirement is also present for the top beam for similar rationale which requires an iterative solution. To satisfy these limits, very thin panels are often required. Such high slenderness may lead to computational difficulties and/or difficulties in fabrication and construction. In a retrofit situation, the use of hot-rolled infill panels (typically 5mm minimum) would require significant reinforcement of the existing frame members due to large demand induced from yielding of panel. This paper attempts to alleviate this problem by introducing perforations onto the panel. It reduces the effective in-plane stiffness and thus reduces demand on its surrounding frame members. Perforations at the same time may enhance architectural flexibilities by allowing services such as conduits and pipes to pass through. The effect on strength and stiffness of SPSW with regular perforation pattern is presented in this paper.

2. Method of study

The shear panel configuration in this study is shown in Figure 1. Canadian sections W310 x 118 and W530 x 82 were selected for columns and beams respectively. A regular pattern of perforations of diameter cd was formed at 1 meter centers. Ratio of perforation can be expressed by diac Sd / where

diaS is the width of imaginary diagonal strips shown. Web stiffener plates in columns were included for full beam-column continuity. Young’s modulus E was taken to be 200GPa with 1% post-yield stiffness. Yield stress of all elements was assumed to be 250MPa. Panel thickness of 5mm and 10mm (ωh= 2.97 and 3.53 respectively); and dc/Sdia ranged from 0 to 0.35 were selected for investigation. It should be noted that stiffness index in Eqn (1) was not satisfied for the selected thicknesses. Nonlinear finite

Ricky Chan et al. / Procedia Engineering 14 (2011) 675–679 677 Author name / Procedia Engineering 00 (2011) 000–000 3

element analysis with ABAQUS version 6.8 was carried out. All structural elements were modeled by the four-node doubly-curved shell elements with reduced integration (element S4R). The column base-plates were fully fixed, while the top flange of the top beam was restrained from out-of-plane movement. Analysis was carried out in two steps. In the first step elastic mode-shapes were obtained by linear perturbation analysis. Nonlinear force-displacement analysis was carried out in the second step. To initiate buckling and development of tension field action, geometric imperfection was defined by a linear modal superposition of the first five modes, with out-of-plane displacement at 10mm in the first mode and varied linearly to 1mm in the fifth mode. A top drift of 2.5% (88mm) was applied monotonically to the top flange of the top beam.

1000

1000

3528

1000 1000 1000

4314

dc

W530 x 82

W530 x 82

W31

0x

118

Sdia

3000

4000

Figure 1: Perforated SPSW

3. Results and Discussions

Buckled modeshapes and stress patterns at 1.4% drift for two selected models are shown in Figure 2. Perforations reduced eigenvalues but did not change the buckled shapes significantly. When cd was small, yielding of panel was limited to a middle diagonal strip. The remaining panel area was less effective. The boundary frames were too flexible to create a uniform tension field throughout the panel area. As

cd increased, yielding spread more uniformly. Furthermore, less deformation was observed in the top beam, indicating demand on the top beam was reduced.

(a) 5=w mm and 200=cd mm (b) 5=w mm and 500=cd mm Figure 2: Fundamental modeshape and stress pattern at 1.4% top drift

Load versus displacement plots for w=5mm are shown in Figure 3(a). Similar behaviors were obtained for w=10mm. Perforations reduced both stiffness and strengths, similar to effect of reducing panel thickness in solid panel SPSW. Normalized yield strengths and stiffness are related to perforation ratio in Figure

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3(b). As a distinct yield was not observed, yield strength was defined by the intersection of the load-displacement curve with a line parallel to the initial slope of the curve and which intercepts the abscissa at 0.2% drift. Interestingly both strength and stiffness were reduced in a similar manner. To approximate effect of perforation, a linear reduction function is proposed herein. Vyp is the yield strength of perforated SPSW and Vy is that of a solid panel. Similarly Kp and Ko is stiffness for perforated and solid panel respectively. α is a linear reduction coefficient. For the present SPSW configuration, α=1.0 safely predicts the strength and stiffness.

ydia

cyp V

S

dV ⎟⎟

⎠

⎞⎜⎜⎝

⎛−= α1 and 01 K

S

dK

dia

cp ⎟⎟

⎠

⎞⎜⎜⎝

⎛−= α (2)

Figure 3: Load vs displacement (w=5mm) (left) and Normalized strength and stiffness (right)

4. Conclusion

Results of a nonlinear finite element investigation of perforated SPSW are presented in this paper. Geometric imperfection and material nonlinearity was considered. Results demonstrated that under monotonic loading perforations reduce strength and stiffness of the system. In particular, perforations on panel promote more uniform stress on panels and reduce deformation demand on surrounding frame elements. The effect on strength and stiffness is quantified and a simple linear reduction function is proposed.

Acknowledgement

The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. 9041352 (CityU 115208)]. The authors are grateful for this financial support.

References

[1] American Institute of Steel Construction (AISC), 2005, Seismic Provisions for Structural Steel Buildings [2] Berman, J. W., and Bruneau, M., “Plastic Analysis and Design of Steel Plate Shear Walls”, Journal of Structural Engineering,

ASCE, Vol. 129, No. 11, 2003, pp1448-1456. [3] Berman, J.W., and Bruneau, M., “Experimental Investigation of Light-Gauge Steel Plate Shear Walls”, Journal of Structural

Engineering, Vol. 131, No. 2, February 2005, 2005, pp. 259-267

Ricky Chan et al. / Procedia Engineering 14 (2011) 675–679 679 Author name / Procedia Engineering 00 (2011) 000–000 5

[4] CAN/CSA-S16, Limit States Design of Steel Structures, Canadian Standards Association, 2001 [5] Driver, R.G., Kulak, G.L., Kennedy, D.J.L., and Elwi, A.E. (1998), “Cyclic Test of Four-Story Steel Plate Shear Wall”,

Journal of Structural Engineering, ASCE, Vol.124, No. 2, Feb. 1998, pp 112-130. [6] Elgaaly, M., Caccese, V., and Du, C., “Postbuckling Behavior of Steel-Plate Shear Walls Under Cyclic Loads”, Journal of

Structural Engineering, ASCE, Vol. 119, No. 2, Feb. 1993, 1993, pp. 588-605. [7] Thorburn, L.J., Kulak, G.L., and Montgomery, C.J. , "Analysis of Steel Plate Shear Walls", Structural Engineering Report

No. 107, Department of Civil Engineering, University of Alberta, Edmonton, Alberta, Canada, 1983. [8] Timler, P.A. and Kulak, G.L. , "Experimental Study of Steel Plate Shear Walls", Structural Engineering Report No. 114,

Department of Civil Engineering, University of Alberta, Edmonton, Alberta, Canada, 1983. [9] Vian, D., Bruneau, M. and Purba, R. , “Special Perforated Steel Plate Shear Walls with Reduced Beam Section Anchor

Beams. II: Analysis and Design Recommendations”, J. Struct. Engrg. Volume 135, Issue 3, 2009, pp. 221-228