EUROSTEEL 2011, August 31 - September 2, 2011, Budapest, Hungary

A STUDY ON THE BEHAVIOUR OF STEEL PLATE SHEAR WALLS Under Monotonic and Cyclic Loading

Irena Hadzhiyaneva a and Borislav Belev

a

a University of Architecture, Civil Engineering and Geodesy, Sofia, Bulgaria

INTRODUCTION

Steel and composite shear walls have been used in earthquake-resistant design for the last 40 years

in USA, Canada, Japan and other regions of high seismicity. A typical steel plate shear wall

(SPSW) is a vertical cantilever including boundary framing members (columns and beams) and thin

steel plate infill panels. In the earlier applications the shear buckling of the infill panels was

prevented by an orthogonal set of stiffeners. The composite steel plate shear walls have a single- or

double-sided reinforced concrete encasement of the steel infill panels which substitutes the

conventional stiffeners. Alternative approach to obtain yielding in shear of the infill panel prior to

its buckling is that of using low-yield steel. The most recent applications entirely avoid the use of

stiffeners and rely on the post-critical tension-field action of the slender infill panels both for lateral

resistance and stiffness of SPSWs.

The main advantages of the seismic-force-resisting system composed by SPSWs are (1) the high

initial stiffness which is essential for limiting the interstorey drifts, (2) the stable energy dissipation

under cyclic loading in the inelastic range of response, and (3) the reduced self-weight compared to

the conventional reinforced concrete shear walls. The reliability and robustness of this relatively

new structural system have been proven by full-scale testing in several strong earthquakes. The

cases reported by Astaneh-Asl [1] indicated that only minor damage was observed in the post-quake

surveys of these SPSWs. The system has been extensively tested since the 1970s, see Driver et al.

[2]. Design provisions for the SPSW-system have been first included in the National Building Code

of Canada (NBCC) in 1994, and afterwards in the AISC Seismic Provisions 2005 [3]. Eurocode 8,

Part 1 [4] contains design rules for the composite SPSWs only. However, the formula for their

design resistance neglects the contribution of the concrete encasement and only considers the shear

resistance of the steel plate infill panels.

The paper presents the experimental and numerical performance evaluation of two identical scaled

specimens representing single-storey SPSWs tested under monotonic and cyclic loading. A specific

feature of the tested specimens was the use of semi-rigid beam-to-column joints in the boundary

steel frames. The main objectives of the study were to investigate the resistance, ductility and

energy dissipation capacity of the steel plate shear wall models including the influence of the joint

detailing.

1 DESCRIPTION OF THE SPECIMENS AND TEST SET-UP

Two scaled specimens with identical dimensions were fabricated in order to perform a monotonic

unidirectional loading test on the first one (W1) and pseudo-static cyclic loading test under

displacement control on the second specimen (W2). The scale of the specimens is approximately

1:4 (Fig. 1). The boundary frame members (top beam, base beam and columns) have hot-rolled

cross sections of IPE200, IPE270 and HEB120, respectively. The infill panel was designed with 1,5

mm thickness and S235 steel grade, but both the actual thickness and the steel properties deviated

from the design values. The nominal slenderness of the web panel with 600x600 mm clear

dimensions is therefore 600/1,5=400.

Fig. 1. Specimen layout

Due to limitations of the loading system it was decided to use pin connections at the column bases.

The beam-to-column joints were purposely made of semi-rigid and partial-strength type using a

couple of 12 mm thick fin-plates welded to beam web only. The fin plates are connected to the

column flange with full-penetration butt welds. The thin infill panel is not connected directly to the

boundary frame members. Instead, 5 mm thick perimeter steel strips were used as interface

component. The W1 and W2 specimens differ in the welding procedure used for executing the two

fillet welds between the infill plate and perimeter strips. Actually the W2-specimen was fabricated

after W1 was tested and the welding procedure for the thin infill panel was improved in order to

avoid any premature connection failure. The initial visual check of the specimens prior to their

testing revealed that due to the small size of the infill panels and large total length of the fillet

welds, the thin infill plates did not show any sign of initial geometrical imperfections in the form of

out-of-flatness. Instead, they looked like “stretched”, most probably due to residual biaxial tensile

stresses induced by the welding. This kind of hidden “prestressing” was suspected to influence the

initial stiffness and onset of yielding of the specimens. Both specimens were tested in a vertical

plane being oriented as short horizontal cantilevers with the transversal loading applied along the

axis of the top boundary beam (Fig. 2). For the testing protocol (loading history) of W2 it was

decided to follow the general rules of the ECCS procedure [5]. An important parameter in this

procedure is the so-called reference yield displacement yU which is further used for defining the

displacement amplitude of the loading cycles. Preliminary numerical studies indicated that the

recommended bilinear approximation of the nonlinear force-displacement diagram did not produce

a realistic estimate of yU and the onset of significant inelastic response was influenced both by the

tensile yielding of the infill panel at its post-buckling stage and inelastic rotations of the semi-rigid

frame joints. It was concluded that the “yield” displacement yU can be assumed in a rather broad

range (3,0 to 4,5 mm). As the testing program was planned to continue with a more rigid partially-

composite specimen (W3) with concrete-encased infill panel, yU =3,0 mm was assumed in order to

apply a common loading history for the bare-steel (W2) and partially-composite (W3) specimens. In

general, the more detailed study of the test results revealed that a tri-linear approximation with a

lower value of the yield displacement and corresponding yield force is more meaningful than the

bilinear approximation of the force-displacement relationship.

Fig. 2. Test set-up for W1-specimen

2 NUMERICAL MODELLING AND ANALYSIS

2.1 Simplified analysis approach

At the early stages of this research the so-called tension strip model proposed by Thorburn et al. [6]

was used. It represents the diagonal tension field developed after buckling of the slender infill panel

as a series of inclined parallel pin-ended strips (Fig. 3). The number of strips required for realistic

modelling depends upon the panel geometry, but in general 10 equally spaced strips per panel are

sufficient. This approach has been further verified against experimental results [2]. As a design

approach, it is included in the Canadian Steel Design Code [7] and suggested as a suitable analysis

model in the Commentary of [3]. The angle of inclination of the strips α measured from the

vertical was estimated to 44 degrees.

Fig. 3. Simplified plane model Fig. 4. Three-dimensional model

This is essentially a plane frame model which was created in SAP2000 and subjected to static

nonlinear pushover analysis assuming lumped plasticity (N-hinges for the tension strips, M-N

hinges for finite elements representing the beam and columns, and nonlinear rotational springs for

the beam-to-column connections). In order to obtain the strength demand for capacity design of the

boundary framing members and connections, the yield strength of the tension strips was increased

by the overstrength factor ovγ = 1,25. Subsequently, the model was updated to reflect the actual

infill panel thickness and yield strength prior to the testing of each specimen. The beam-to-column

joints were assumed pinned in an auxiliary model used to estimate the contribution of the boundary

frame to the overall strength and stiffness.

2.2 Refined analysis approach

In order to better predict the nonlinear response and assess the accuracy of the simplified approach,

three-dimensional models were created in ANSYS v.10.0 software [8]. All components of the test

specimens were modelled with SHELL181 finite elements (Fig. 4). The models can account for the

complex stress distribution at the frame joints and, in addition, allow for simulating the initial

imperfections of the slender infill panel. The pattern of the initial out-of-plane deformations was

assumed to correspond to the first buckling mode shape, with magnitude equal to 1/200 of the panel

span as recommended by EN 1993-1-5, Annex C [9]. The steel is modelled with bilinear stress-

strain diagram with 1 % slope of the post-yield branch.

2.3 Estimation of the expected yield resistance of the specimens

The expected yield resistance of the specimens without the contribution of the boundary frame was

calculated using an equation based on the design formula of [3]:

αγ 2sin5,0, wcfyovwy tLfV = , (1)

where wt is the thickness of the infill panel and cfL is its clear length between the interior column

flanges. The expected yield resistance including the contribution of the frame was assumed to be

wyey VV ,, 30,1= (2)

For the nominal panel properties ( yf =235MPa and wt =1,5mm), assuming α ≈45o and ovγ =1,25,

eyV , ≈172 kN. For the actual panel properties of W1 ( yf =280MPa, wt = 1,59mm), Eq. (1) and (2)

predict eyV , =173,6 kN, while for W2 ( yf =300MPa, wt =1,68mm) eyV , =196,6 kN.

Based on the results of the numerical analyses, the frame members were designed for the internal

forces corresponding to lateral displacement maxU = 50 mm and base shear force bF = 205 kN,

derived from the static nonlinear solution of the 2D-model with pinned beam-to-column joints.

3 EXPERIMENTAL TESTING OF SPSW-SPECIMENS

3.1 Monotonic test of W1-specimen

The buckling of the infill panel took place at force level of about 40 kN, and initial cracking of the

paint layer – at lateral displacement of 3 mm. However, significant development of plastic

deformations was observed at higher force level of 158,5 kN and lateral displacement of 5,6 mm

(Fig. 5). This point of the force-displacement diagram corresponds to interstorey drift ratio (IDR) of

approximately 0,675 %. A failure of the welded connection between the infill plate and perimeter

strip followed by a rupture of the infill panel in the vicinity of the base beam were noticed at load

level approximately equal to 190 kN. Both phenomena took place at the corner where the tension

field was anchored. Despite of the damages the specimen maintained its resistance up to the peak

load level maxF = 235 kN (IDR ≈ 2,2 %). Afterwards, the test was terminated at force level uF = 219

kN (IDR ≈ 3,3 %) due to the drastic increase of the rupture lengths at the infill plate corner and

signs of out-of-plane buckling of the top beam. The magnitude of residual infill panel buckles was

estimated to 25 mm. The condition of the specimen after the end of testing is shown in Fig. 6. The

orthogonal grid drawn on the infill plate prior to the test has spacing of 50 mm in each direction.

The closer investigation of the strain histories recorded at key locations of the specimen revealed

that the tensile yielding of the infill panel occurred almost simultaneously with the yielding in

bending of the fin-plates connecting the top beam to the columns. Afterwards, the overall stiffness

of the shear wall was severely reduced not only by the plastic deformations but also due to the

ruptures at the bottom corner of the tension field. The maximum measured rotation of the beam-to-

column joint was 1,8 %, which exceeds the limit required by [3], equal to 1 %. The displacement

ductility factor ∆µ and the system overstrength Ω were estimated as follows:

yu UU=∆µ = 27,7 / 5,6 = 4,95 ≈ 5,0 and yu FF=Ω = 235 / 158,5 = 1,48 ≈ 1,5 (3)

0

40

80

120

160

200

240

280

0 0.003 0.006 0.009 0.012 0.015 0.018 0.021 0.024 0.027

Displacement (m)

Lo

ad

ing

(k

N)

Fig. 5. Force-displacement curve for W1 Fig. 6. W1 after test completion

3.2 Cyclic test of W-2 specimen

The buckling of the infill panel and intensive cracking of its paint layer took place at lateral

displacements of 4-4,5 mm, which correspond to IDR ≈ 0,5%. During the load reversals, the process

of stretching of already formed buckles along one of the diagonal directions and formation of new

buckles along the other diagonal direction were accompanied by specific noice. The first rupture in

the infill plate was noticed during the first cycle with displacement amplitude of 12mm (IDR ≈

1,5%). The second rupture in the infill plate was noticed in the other bottom corner at displacement

amplitude of 18 mm (IDR ≈ 2,2 %). During the last cycle with this amplitude, cracking in the welds

between one of the fin plates and column flange began to develop, and this was considered as

indication of overall limit state. Despite of the severe damages the specimen maintained its

resistance up to the load levels maxF = 220 kN and 240 kN in the positive and negative directions,

respectively (Fig. 7). The ultimate IDRs reached during the cyclic testing were +2,2 % and -3,3 %,

respectively. The ductility factors ∆µ and the system overstrengths Ω were estimated as follows:

yu UU=+ ∆µ = 18,2 / 5,1 = 3,6 and yu UU=− ∆µ = 27,8 / 4,4 = 6,3 (4)

yu FF=Ω+ = 235 / 162,2 = 1,47 and yu FF=Ω− = 260 / 140,4 = 1,85 (5)

-280

-240

-200

-160

-120

-80

-40

0

40

80

120

160

200

240

280

-28 -24 -20 -16 -12 -8 -4 0 4 8 12 16 20

Displacement (mm)

Lo

ad

ing

(k

N)

-260

-220

-180

-140

-100

-60

-20

20

60

100

140

180

220

260

-16 -12 -8 -4 0 4 8 12 16

Displacement (mm)

Lo

ad

ing

(kN

)

Fig. 7. Envelope curves for W2 Fig. 8. Hysteretic response of W2

The values used for yU and related yF in Eq. (4)-(5) are the true values taken from the test data, not

from bilinear or trilinear approximating diagrams. The hysteretic response of the specimen is

illustrated in Fig. 8 for the set of three cycles with displacement amplitude 12 mm, where some

pinching of the loops can be seen. It could be explained with the accumulation of residual out-of-

plane panel deformations and semi-rigid behaviour of the frame joints.

4 COMPARISON OF EXPERIMENTAL AND NUMERICAL RESULTS

Fig. 9 and 10 compare the test-obtained force-displacement relationships with the numerical

predictions. In general, the FE-models and static nonlinear analyses can well estimate the ultimate

resistance of the specimens. As a general observation, the numerical models predict larger initial

stiffness. They, however, do not account for the residual welding stresses, which according to the

visual check of the infill panels prior to the testing, create an initial biaxial tension stress field. The

summation of these residual stresses with the stresses induced by the applied loading could result in

delay of the initial buckling, but also in earlier tensile yielding at higher load levels.

0

40

80

120

160

200

240

280

0 4 8 12 16 20 24 28 32 36

Displacement (mm)

Lo

ad

ing

(k

N)

ANSYS MODEL, t=1,5mm

STRIP MODEL, t=1,5mm

TEST- W1

0

40

80

120

160

200

240

280

0 4 8 12 16 20 24 28 32 36

Displacement (mm)

Lo

ad

ing

(k

N)

TEST-W2 STRIP MODEL, t=1,68

Fig. 9. Comparison of results for W1 Fig. 10. Comparison of results for W2

5 CONCLUDING REMARKS AND ACKNOWLEDGMENT

The experimental testing showed that the scaled SPSW-specimens have good ductility and stable

hysteretic behaviour. Potential adverse impact on the ductility might be imposed by the complicated

weld connections of the 1,5 mm thick infill panel and the relatively low yu ff ratio of its material.

The semi-rigid frame joints exhibited adequate rotational capacity and could be considered a

reasonable detailing option for the real design applications if the beams are adequately restrained

against lateral-torsional buckling.

The authors gratefully acknowledge the funding provided by CNIP of UACEG for the experimental

part of this research.

REFERENCES

[1] Astaneh-Asl, Ab., Seismic Behaviour and Design of Steel Shear Walls, Steel Tips, 2001.

[2] Driver R., Kulak G., Kennedy, D, and Elwi, A., Seismic Behaviour of Steel Plate Shear Walls,

Structural Engineering Report 215, Univ. of Alberta, Canada, 1997.

[3] American Institute of Steel Construction, SeismicProvisions for Stuctural Steel Buildings, AISC, 2005.

[4] CEN, EN 1998–1. Eurocode 8: Design of structures for earthquake resistance. Part 1: General rules,

seismic actions and rules for buildings, 2004.

[5] ECCS, Recommended Testing Procedure for Assessing the Behaviour of Structural Steel Elements

Under Cyclic Loads. ECCS Publication No. 45, 1986.

[6] Thorburn, L.J., Kulak, G.L., and Montgomery, C.J., Analysis of Steel Plate Shear Walls, Structural

Engineering Report 107, Univ. of Alberta, Canada, 1983.

[7] Canadian Standards Association, CAN/CSA S16-01, Limit State Design of Steel Structures, 2001.

[8] ANSYS, Theory Reference, SAS IP Inc., 1998.

[9] CEN, EN 1993-1-5. Eurocode 3, Design of steel structures, Part 1-5: Plated structural elements, 2007.