Buckling and yielding behavior of unstiffened slender, moderate,and stocky low yield point steel plates

Tadeh Zirakian a,n, Jian Zhang b

a Department of Civil Engineering & Environmental Science, Loyola Marymount University, Los Angeles, CA 90045-2659, USAb Department of Civil and Environmental Engineering, University of California, Los Angeles, CA 90095-1593, USA

a r t i c l e i n f o

Article history:Received 24 November 2013Received in revised form25 November 2014Accepted 25 November 2014Available online 24 December 2014

Keywords:PlatesBucklingYieldingLow yield point steelSteel plate shear walls

a b s t r a c t

Steel plates may be classified as slender, moderate, and stocky based on their distinctive behaviorcharacterized by geometrical buckling and material yielding. Slender plates undergo elastic buckling firstand then yield in the post-buckling stage, while stocky plates yield first and then undergo inelasticbuckling. Moderate plates, on the other hand, buckle and yield simultaneously. The development of lowyield point (LYP) steel enables the application of steel plates with improved buckling and energyabsorption capacities as lateral force-resisting and energy dissipating elements in structures. On thisbasis, buckling and yielding behavior of LYP steel plates with various support and loading conditions isstudied in this paper from the point of view of their application in steel plate shear wall (SPSW) systems.The limiting thicknesses of standalone plates corresponding to concurrent geometrical buckling andmaterial yielding are determined theoretically and verified through detailed numerical simulations.Effects of using LYP steel and plate aspect ratio parameter on the required limiting plate thickness as aneffective parameter in seismic design of SPSW systems are investigated as well. In addition to the studieson the performance of plates with two and four restrained edges and also applicability of someextrapolation techniques for predicting the critical buckling load of moderate plates, detailed studies areperformed on determination of the limiting plate thickness in code-designed SPSW systems. Based onthe findings of this study, some practical recommendations are provided for efficient seismic design ofSPSW systems with LYP steel infill plates.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Thin-walled structures in the form of plates are widely used inmany fields of engineering. Plates of various shapes are used inarchitectural structures, hydraulic structures, pavements, contain-ers, airplanes, missiles, ships, instruments, machine parts, etc.Plate girders, frame bracing as well as steel plate shear wall(SPSW) systems are examples of plated structural elements usedin civil engineering.

Structural stability and performance of plates are characterizedby geometrical buckling and material yielding, which are twoindependent phenomena that may interact with each other [14].Based on the material and geometrical properties, material yield-ing may occur either before or after or even at the same time asbuckling [3].

Elastic instability of thin plates has been extensively studied and well documented in standard textbooks, e.g. Timoshenko and

Gere [22]. In contrast, the stability of thick plates has been morechallenging and relatively less documented because of the complex-ities involved. Inoue [15] and Wang et al. [25] reported two exemplarystudies on plastic buckling of plates and summarized the previousrespective research work. Additionally, Alinia and his co-researchershave recently performed and reported systematic studies, e.g. [3,4]and Gheitasi and Alinia [14], on the structural behavior and character-istics of plates. In all, the research work in cases of both thin and thickplates has by and large resulted in a sufficient knowledge base to allowfor structural application of these elements.

According to Gheitasi and Alinia [14], steel plates may bedivided into slender, moderate, and stocky categories based ontheir slenderness parameter as well as buckling and yieldingbehavior. Slender plates undergo elastic buckling and then yieldin the post-buckling stage. These type of plates have low bucklingcapacity but large post-buckling reserve. Stocky plates, on theother hand, yield first and then undergo inelastic buckling andhave some post-yield reserve, while moderate plates undergosimultaneous geometrical buckling and material yielding andneither have post-buckling nor post-yield reserves [14].

From the point of view of their application in SPSW systemsand also by considering their buckling and yielding behavior, thin

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Thin-Walled Structures

http://dx.doi.org/10.1016/j.tws.2014.11.0220263-8231/& 2014 Elsevier Ltd. All rights reserved.

n Corresponding author.E-mail addresses: Tadeh.Zirakian@lmu.edu (T. Zirakian),

zhangj@ucla.edu (J. Zhang).

Thin-Walled Structures 88 (2015) 105118

www.sciencedirect.com/science/journal/02638231www.elsevier.com/locate/twshttp://dx.doi.org/10.1016/j.tws.2014.11.022http://dx.doi.org/10.1016/j.tws.2014.11.022http://dx.doi.org/10.1016/j.tws.2014.11.022http://crossmark.crossref.org/dialog/?doi=10.1016/j.tws.2014.11.022&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.tws.2014.11.022&domain=pdfhttp://crossmark.crossref.org/dialog/?doi=10.1016/j.tws.2014.11.022&domain=pdfmailto:Tadeh.Zirakian@lmu.edumailto:zhangj@ucla.eduhttp://dx.doi.org/10.1016/j.tws.2014.11.022

and thick plates offer essentially disparate structural and econom-ical characteristics. Thin plates are economically viable compo-nents; however, they possess relatively low buckling strength andweak energy absorption as well as serviceability characteristics.Thick plates, on the other hand, have comparatively higherbuckling as well as energy dissipation capacities and improvedserviceability characteristics, while economically are considered tobe disadvantageous. Nowadays, use of low yield point (LYP) steelplates with extremely low yield strength, high ductility andelongation properties makes it possible to balance betweenstructural and economical demands and consequently designSPSW systems with high buckling and energy dissipation capa-cities and also improved serviceability characteristics. LYP steelplates may indeed undergo early material yielding followed byinelastic geometrical buckling with economical plate thickness.Such efficient lateral force-resisting and energy dissipating ele-ments have been demonstrated to be quite favorable based ontheir superior characteristics and performance (e.g. [9,10], Lashgari[16], and Mistakidis [19]).

In order for efficient design and application of LYP steel plates,it is important to determine the limiting thickness correspondingto simultaneous geometrical buckling and material yielding. Infact, this is believed to consequently serve as an effective para-meter in seismic design of SPSW systems with LYP steel infillplates as the primary lateral force-resisting and energy dissipatingcomponents. On this basis, the limiting plate thicknesses of LYPsteel plates with various support and loading conditions aredetermined theoretically in this paper, which is in turn followedby numerical verification of the theoretical predictions. In addi-tion, advantages of use of LYP steel as compared to the conven-tional steel are also demonstrated along with other case studies.Ultimately, the limiting plate thicknesses in SPSW systems aredetermined and the accuracy of the results is verified via detailednumerical simulations.

2. Theoretical prediction of the limiting plate thickness

Theoretical determination of the limiting thicknesses of simplysupported and clamped plates subjected to shear and/or compres-sive loads is discussed in this section. As mentioned before,limiting thickness corresponds to concurrent geometrical bucklingand material yielding of steel plates. Fig. 1 shows flat plates underpure shear, pure and uniform compression as well as combinationof the two in-plane loadings, where l and h are the respectivelength and height of the plates.

The critical stress of rectangular plates under the action ofshearing stresses uniformly distributed along the edges (Fig. 1(a))

is given by [22]

cr ks2E

121v2 tpb

21

where E and v are Youngs modulus and Poissons ratio, respec-tively, tp is the plate thickness, and ks is the elastic shear bucklingcoefficient which is ks 5:344:0=a=b2 for simply supported andks 8:985:6=a=b2 for clamped support conditions. It is notedthat a maxl;h and b minl;h.

The critical stress of rectangular plates uniformly compressedin one direction (Fig. 1(b)) is similarly expressed by

cr kc2E

121v2 tpl

2: 2

kc in Eq. (2) can be determined from the figures and tablespresented in stability books for various support conditions,e.g. Timoshenko and Gere [22] and Brush and Almroth [8]. How-ever, for simply supported plates kc ml=hh=ml2 may alsobe applied, in which m is the wavelength parameter.

Chen et al. [11] developed a concise formula (Eq. (3)) for thecritical buckling stresses of simply supported rectangular platesunder combined biaxial compression and shear, as shown in Fig. 2.

xxxx;cr

yy

yy;cr

cr

1:0 3

In the above interaction equation, 1, 2,

1; 1ra=br

ffiffiffi2

p

a=b 1 =cr 2

; a=b4

ffiffiffi2

p

8