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Experimental seismic study on shear walls with fully-connected and beam-only-connected web plates
Journal of Constructional Steel Research 141 (2018) 204–215
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Journal of Constructional Steel Research
Experimental seismic study on shear walls with fully-connected and beam-only-connected web plates B. Shekastehband a,⁎, A.A. Azaraxsh a, H. Showkati b a b
Department of Civil Engineering, Urmia University of Technology, Urmia, Iran Department of Civil Engineering, University of Urmia, Urmia, Iran
a r t i c l e
i n f o
Article history: Received 30 December 2016 Received in revised form 23 October 2017 Accepted 12 November 2017 Available online xxxx Keywords: Steel plate shear walls (SPSW) Steel shear walls connected to frame beams only (SSW-BO) Cyclic loading Hysteresis Dissipated energy Ductility
a b s t r a c t Typically, in conventional steel plate shear walls (SPSWs), web plates are connected to both beams and columns; however, steel shear walls connected to beams only (SSW-BOs) with the idea of reducing surrounding columns demands and alleviating web plate damage was proposed since the mid-2000s. This paper presents an experimental investigation on seismic behavior of steel plate shear walls comprising SPSWs and SSW-BOs. Cyclic loading tests were performed on four 1:6 scaled one-story specimens with two plate thickness and two different web plate boundary conditions. The observed predominant failure modes include i: plate tearing at the corners, ii: slippage along connection zone of web plates, and iii: plate-to-frame connection bearing. Using frame connection for plates increases the energy dissipation, shear strength and elastic stiffness by up to 150%, 200% and 110% on average, respectively compared to those of beams-only connected walls. Experimental results indicate that the SSW-BO systems reached a ductility ratio of 7.3 on average, almost 1.5 times the value for SPSWs. It is demonstrated further that with an increase in the slenderness ratio (height to thickness), the strength, stiffness and energy absorbed by the SPSW and SSW-BO systems show a decreasing trend being less stiff for SSW-BO panels. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Steel plate shear walls (SPSWs) have been in use as the primary lateral load-resisting system of buildings in high seismic areas for a long time [1,2]. These systems have specific advantages in terms of ductility, stiffness and shear strength that merit their consideration for use as a load bearing system in different structures whole over the world [3,4]. In a conventional SPSW (Fig. 1(a)), the web plates connected to the surrounding beams and columns, buckle in shear at low lateral loads and develop a diagonal tension field that induces sever stresses on the surrounding frame members, as shown in Fig. 1(b). In addition, using of web plates with minimum available thickness larger than required for resisting specified lateral loads may also result in excessive design forces to the horizontal and vertical boundary elements (HBEs and VBEs), thus increasing their size. As a result, there exists an obstacle concerning VBEs high demand that may impede further widespread acceptance of this system. To prevent plastic hinges in the columns and thus to prevent collapse of the structure, strong columns with large sections must be used [6]. Attempts at mitigating column demands were recently addressed by the use of (i) light-gauge, cold-formed steel plates [7], (ii) low-yield steel [8,9], (iii) coupling beams to alleviate overturning forces [2,10],
⁎ Corresponding author. E-mail address: [email protected] (B. Shekastehband).
https://doi.org/10.1016/j.jcsr.2017.11.013 0143-974X/© 2017 Elsevier Ltd. All rights reserved.
(iv) perforations layout covering the entire web plate in a specified regular pattern [11] and (v) web plates connected to the beams only [12,13]. The presumed benefits of alleviating column demands gained from the use of beam-only-connected web plates must be weighed against possible drawbacks associated with their reduced shear strength and mitigated energy absorption compared with fully-connected web plates. The web plates are not connected to frame columns, large stresses due to tension field, developing plastic hinges in the columns are avoided (Fig. 2). Limited performed experimental studies on SSW-BO illustrated that these systems have considerable shear strength and can be used to separate the shear walls from the main columns and therefore, reduce the dimension of columns [14,15]. It was recognized that the frame has the capability of developing a tension field in the wall plate, so that the wall plate yields before the frame [14]. A comparative experimental study was conducted in this research to investigate the structural performance of SPSW and SSW-BO systems. Four wall specimen configurations were tested under cyclic loading and the results are presented as follows.
2. Analytical shear load-displacement of SPSW and SSW-BO Considering the web plate of width L, height H and thickness t, the nominal lateral strength of a SPSW, Vnf, using the kinematic method of
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(a)
(b)
Fig. 1. Conventional SPSW: (a) fully-connected web plate; (b) stresses on boundary elements [5].
plastic analysis is obtained as presented in the AISC Seismic Provisions [16]: V nf ¼ 0:42F y tL sin2α
ð1Þ
where Fy and α are yield strength and angle of inclination of tension field from the vertical. The elastic shear displacement, Ue, neglecting buckling shear strength is obtained as [16]: Ue ¼
2F y H E sin2α
ð2Þ
where, E is modulus of elasticity. Using Eqs. (1) and (2), the elastic stiffness of SPSW is calculated as follows: Kf ¼
0:21LtE H
ð3Þ
The nominal lateral strength for SSW-BO, Vnb, can be assessed as [17]: V nb ¼ 0:42F y tLPTF sin2θ
where the inclination angle, α, was replaced with that of a SSW-BO partial tension field, θ, and the total fully-connected web plate length, L, with the partial tension field length, LPTF. The rest of the web plate outside of the partial tension field does not contribute to the plate's lateral force resistance. In Eq. (4), the partial tension field length along the beams, and partial tension field inclination are given as [17]:
LPTF ¼ L−H tanðθÞ
ð5Þ
θ ¼ 0:5 tan−1 ðL=H Þ
ð6Þ
V2
V1
(a)
ð4Þ
(b)
Fig. 2. SSW-BO: (a) beam-only connected web plate; (b) stresses on boundary elements.
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Considering both the shear and bending deformations of the web plate, the theoretical elastic stiffness proportional to the lateral displacement is obtained as [12]: Kb ¼
Et 1=ðL=HÞ3 þ 2ð1 þ ν Þ:k=ðL=H Þ
Pin
Web plate
Stiffening boxes in SSW-BO
ð7Þ
Bolt
3. Test procedure 3.1. General
2 UNP 12 An actual view of the experimental set-up is illustrated in Fig. 3. Experimental models were scaled as 1:6 one-story SPSW and SSW-BO, with hinge type connections in boundaries at four corners (Fig. 4). The slenderness ratio (plate height to thickness ratio) was considered as variables in these specimens. For this purpose, two thicknesses of 0.5 and 1.25 mm were selected for the plates. Each test was performed under fully reversed cyclic quasi-static loading in the elastic and inelastic response zones of the specimens in compliance with the SAC [18] test protocol by means of an actuator of 100 kN capacity. A lateral restrain system was used to prevent out of plane deformations of the testing frame (Fig. 3). An A-framed superstructure was used for supporting the actuator. Table 1 provides the detailed geometry and slenderness ratios of the specimens. The frames measured 620 mm wide and high between HBEs and VBEs centerlines, while the depth/width of the web plates in SPSW and SSW-BO were equal to 500/500 mm and 500/ 460 mm, respectively. The boundary elements of the frame were similar and consisted of the standard profile double section UNP120. Two 20 × 30 × 2 mm box sections of 460 mm height located at a distance of 20 mm from the surrounding beams were used for stiffening the free edges and preventing more out of plane deformations of infill plates due to shear buckling. It should be noted that the out-of-plane deformation along the free edge produces large curvature demands at the edge of the bolted infill plate-to-beam connection which may in turn cause tearing of infill plate [17]. The edges of the web plates in SPSW and SSW-BO were clamped between frame elements and beams-only respectively by the means of two rows of high tensile 10 mm bolts. To connect the vertical edges of the web plate to stiffening boxes in SSWBO, high strength bolts with a diameter of 5 mm were used. The systems were established and connected by means of 8 high tensile bolts on the rigid base of the laboratory. To determine the stress–strain curves of the web plates and boundary element materials, four tensile coupon tests were performed on two
Fig. 4. Details of the experimental specimens.
web plate thicknesses according to the ASTM A370-05 [18]. A summary of the coupon test results is presented in Table 2.
3.2. Measuring devices In order to measure the load during the tests, a load cell located between hydraulic jack and loading point was used. The hydraulic jack was connected to the top of the specimens through a U-shape pin joint system. Slotted hole on the joint system perpendicular to the line of applied force provides a load path to transfer the force horizontally (Fig. 5). LVDT displacement transducers were attached on desired points of the specimens to measure the relative displacements within the accuracy of 0.001 mm (Fig. 3). The strain gauges were attached to the corners and center of the web plates (Fig. 3). Locations of the strain gauges were determined at probable plastic zones in the elements based on the preliminary numerical analysis results. Note that the gauge series of YF/Y is post-yield foil/wire gauge, which features a special plastic carrier base of withstanding extreme elongation without creeping or cracking. All data were recorded and processed by means
Fig. 3. Lateral restrain system of the steel shear wall specimens in the laboratory.
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Table 1 Specification of specimens. Specimen
Plate thickness t (mm)
Primary columns & beams
Stiffening boxes
Slenderness ratio H/t
SSW-BO-1 SSW-BO-2 SPSW-1 SPSW-2
0.5 1.25 0.5 1.25
2UNP120 2UNP120 2UNP120 2UNP120
2 box (20 × 30 × 2 mm) 2 box (20 × 30 × 2 mm) – –
1000 400 1000 400
Table 2 Material properties of steel used in the test. Steel material
Elastic modulus (GPa)
Yield stress (MPa)
Yield strain (%)
Ultimate stress (MPa)
Ultimate strain (%)
Rupture strain (%)
Web plate (thickness = 0.5 mm) Web plate (thickness = 1.25 mm) UNP120 & Box 20 × 30 × 2 mm
200 200 200
138.15 182 240
0.11 0.09 0.12
280.80 328 360
27 27 20
37 40 20
of a KYOWA type digital data logger, a scanner and a software named UCAM-20PC, Japan. 3.3. Cyclic loading program The lateral quasi-static loading was applied to the top of upper beam in accordance with SAC protocol [20]. Fig. 6 shows the cyclic
displacement-control loading history of the specimens. In this graph, the loading began with very small values of the overall drift and increased gradually up to a drift of 5%. No vertical load was applied to the specimens. 3.4. Test process Prior to the tests, the signals emanating from the strain-gauges, LVDT transducers and the load cell were initialized to zero. It should be noted that a trial run was conducted before testing main specimens to evaluate the efficiency of the test rig. Note the actuator moving throughout the tests was always at a rate of 0.5 mm/s. During the tests, displacements as well as local strains were recorded at short and regular intervals to have a well detection and evaluation of the buckling phenomenon. 4. Observations and discussions 4.1. General observations The specimens were failed in a progression of tears at the plate corners, wave buckling, bearing failure of the plate and bolts in connections and knot type local buckling at the plate corners. The evolution of failure of SPSW and SSW-BO specimens is illustrated as follows:
Fig. 5. Pin connection of actuator to top of the specimen [19].
1. In the SPSW specimens consisting of web plates with the thickness of 0.5 mm and 1.25 mm, formation of tension field line and buckling
Fig. 6. Loading protocol based on SAC [20].
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SPSW-2;
(a)
0.75 % Drift
(b)
Fig. 7. Tension field buckles in SPSWs: (a) SPSW-1; (b) SPSW-2.
Fig. 8. Tension field buckles in SSW-BOs: (a) SSW-BO-1; (b) SSW-BO-2.
wave were evident in the last cycle of 0.375% and 0.75% drift level, respectively (Fig. 7). However, as shown in Fig. 8, in the SSW-BO counterparts, buckling waves could be distinguished in the last cycle of around 0.5% and 1.0% drift, respectively. In the whole specimens, as the test progressed, audible buckling sounds coming from the alternating tension field orientation during reversed loading cycles began and the magnitude of the buckling waves grew remarkably. 2. In excess 2% drift, due to development of tension field yielding and buckling waves in the load excursions, the residual out of plane deformation remaining like knot was formed in the SSW-BO specimens (Fig. 9). This type of deformation was not observed in the SPSW specimens. 3. In the SPSW specimens, a number of relatively large buckle waves, at least four at N1.5% drift, were formed. However, SSW-BO specimens, due to developing partial tension field action, have less buckling waves than SPSW counterparts. As shown in Fig. 10, eight waves were developed in the SPSW-1, while only three waves were seen in the SSW-BO-1 in 3% drift.
Fig. 9. Forming knot due to residual out of plane deformation in the SSW-BO systems.
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SPSW-1;
3 % Drift
209
SSW-BO-1;
3 % Drift
1 2 3
4 5
6
7
8
1
(a)
3
2
(b)
Fig. 10. Tension field developed in steel shear walls: (a) SPSW-1; (b) SSW-BO-1.
SSW-BO-1;
4 % Drift
SSW-BO-2;
(a)
(b) Fig. 11. Tear in the plate bottom corners: (a) SSW-BO-1; (b) SSW-BO-2.
(a)
(b) Fig. 12. Failure modes of SSW-BOs: (a) SSW-BO-1; (b) SSW-BO-2.
4 % Drift
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SPSW-1;
3 % Drift
(a)
SPSW-1;
5 % Drift
(b)
Fig. 13. Tears in the plate bottom corners of SPSW-1: (a) at 3% drift; (b) at 5% drift.
4. In the SSW-BO specimens, slippage along connection zone of web plate to bottom HBE at corners at 3% drift level was accompanied with local tears appeared adjacent to the corners of web plates at drift value of 4%. When the drift ratio reached 4%, because of the growing of stress concentration, small tear along HBEs were developed in the plate bottom corners as shown in Fig. 11. Continued large displacement cycling (5% drift) finally caused progression of tearing in plate bottom west corner as well as yielding and slippage in the plate bottom east corner implying bearing failure of the plate and bolts in connections (Fig. 12). 5. A small tear at the bottom west corner of the web plate of SPSW-1 was initiated in 2% drift by the low cycle fatigue as the web plate buckled cyclically with load reversals. By increasing the lateral movement (drift N 4%) a local tear was also initiated at the bottom east corner of the web plate (Fig. 13). The web plate tears continued to propagate more severely as the test proceeded. In the last excursion of drift 3%, fracture of the steel plate was occurred between adjacent bolts along a row at the bottom and right of the wall. These fractures grew with each cycle of loading, eventually fracturing through the entire length of the bottom edge of the web plate at 5% drift, as shown in Fig. 14. This was accompanied by in-plane slippage of web plate at the connections in last cycles of 4% drift and therefore, a main kink as well as out-of-plane deformation was formed at the middle of panel at the end of test (Fig. 15). The SPSW-2 was only loaded up to 4% drift in both directions because of the capacity
limitation of the load cell. Therefore, no signs of web plate tearing at drifts slightly b 4% was observed in the specimen. In larger drifts (N 2%) two small kinks appeared in the right half of the middle panel, as shown in Fig. 16. 6. The SSW-BO with 0.5 mm thick panel experienced no tearing and plate fracturing in cycles prior to 3% drift; however, in the SPSW counterpart, tearing was initiated in 2% drift. Therefore, SSW-BO specimens illustrated a delay and reduction of web plate tearing compared with the SPSW specimens. Full-connection in comparison with the beam-only connection causes increased strain demands in the web plate under cyclic lateral loadings. In both SSSW-BO and SPSW specimens, a number of local minor tears took place near the corners of thinner panel by the material low cycle fatigue resulting from severe cyclic distortion of the web plates. The more number of web plate tearing in SSW-BO specimens can be attributed to the out-of-plane web plate deformation along the unrestrained edge of the corners that are not present in conventional SPSW web plates connected continuously along all edges. 7. Average inclination angle of tension fields for all the specimens through measuring the inclination of the buckled waves is presented in Table 3. As the extent of web plate bearing fracture increases with increasing drift demands, as does the scatter in the measured angle of inclination in the SPSW-1, that can be attributed to the increased slippage preventing the full formation of tension field (Fig. 17).
Fig. 14. Failure mode of SPSW-1.
Fig. 15. A main kink and out-of-plane deformation at the middle of web plate in SPSW-1.
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Small kinks
Fig. 16. Deformed shape at the end of test in SPSW-2. Fig. 17. Inclination of the tension field in the specimens.
4.2. Hysteretic behavior of the specimens The hysteresis lateral load-top displacement responses with backbone curves for all specimens obtained from the tests are presented in Fig. 18. All specimens exhibited stable hysteretic behavior until the end of the loading program, with some pinching of hysteresis loops that are consistent with the features observed in other tests on SPSW and SSW-BO systems [15,19]. Specimens of 0.5-mm panels, i.e. SPSW1 and SSW-BO-1, yielded at 0.5% and 0.75% drift, respectively (Table 4). The specimen with 1.25-mm-thick panels, SPSW-2 and SSW-BO-2, yielded at approximately 0.75% and 1.00% drift. Fig. 19 compares the back-bone of the hysteresis curve for the whole specimens. The lateral resistance capacity of SSW-BO specimens was about 25% of SPSWs, indicating that the lateral resistance is much reduced by isolating the web plate from boundary columns. Moreover, the pinch effect of the hysteretic loops of SPSWs was less than that of SSW-BO, demonstrating that full connecting of web plate to boundary frame may increase the overall wall stability resulting in increased energydissipation of the system. All specimens exhibited stable behavior up to cycles of 4% drift, at which point the strength deteriorated. The ultimate displacement of the fully-connected specimen with 1.25 mm thick, i.e. SPSW-2, was 4% drift, owing to the limitation of the load cell capacity. The contribution of the web plate connection to the shear capacity increases with lateral displacement. Thus, as given in Table 4, the difference between SSW-BO-1 and SPSW-1 (as well as SSW-BO-2 and SPSW2) in terms of yield resistance was 22% (16%), but ultimate capacity decreased by 32.45% and 4.3% in fully-connected and beam-only connected, respectively. The difference in the hysteretic behavior between fully-connected and beam-only connected web plate specimens can be explained through the 28th cycle for specimens SSW-BO-1 and SPSW-1, as shown in Fig. 20. The tensile half-cycles of hysteresis loops can be categorized into three classes of behavior: 1- From point a to point b, the specimen exhibits a plateau in the loaddeflection curve. This region represents the main contribution of the surrounding frame to the stiffness. Therefore, due to pin connections of the boundary elements, the hysteresis loop appears with zero slope upon development of the tension field. 2- After point b, the web plate resists lateral load through the development of tension field action, and stiffness increases as the plate
Table 3 Measured tension field inclination of the specimens. Specimen Inclination angle
SSW-BO-1 28
SSW-BO-2 28
SPSW-1 42.5
SPSW-2 40.5
deforms. When compared to the beam-only connected web plates with partial tension field action, the fully-connected ones due to the development of tension field action show an increase in resistance and stiffness. Strength ratio of point b to point a is 3.5 and 1.7 for SPSW and SSW-BO, respectively. For this reason, as illustrated in Table 4, the maximum strength to yield strength of the fully-connected web plate is much more than that of beam-only connected one. 3- After point c, the plate deforms plastically in tension and the stiffness decreases. At this stage, SSW-BO specimen experiences more plastic deformation than that of SPSW one for the same lateral strength. Therefore, the pinching effect resulted due to the accumulated diagonal plastic stretch of the web plate, was more visible in the SSW-BO compared to the SPSW. Comparison of the loops corresponding to same drift demonstrated that the shear strength decreased slightly in next loops because of residual strains and plastic deformations caused by first cycle. In SPSW-1 at 4% drift, propagation of plate fracture along the bolts led to a considerable drop in strength and stiffness of the loop. It is worthy of mention that strength of the specimens was not affected by web plate tearing and its propagation. However, fracture occurred in the web plate between the connections resulted in reduced panel strength at larger drifts. Unloading strengths of the specimens are also given in Table 4. It can be seen that the residual strengths of SPSW specimens are about 354% of SSW-BOs, illustrating that the web plate residual strength is a function of tension field action in the web plates as they deform during unloading. 4.3. Strength and stiffness Elastic stiffness, ultimate strength and ductility of the all specimens based on experimental hysteresis curves are presented in Table 5. In addition, the shear strength and stiffness of the specimens obtained from the theoretical equations are also listed in Table 5. The two last columns of Table 5 represent ratio of the stiffness and shear strength from the two experimental and theoretical methods. Strength of the SPSW and SSW-BO specimens tend to decrease as much as roughly 25% and 44%, respectively as the slenderness ratio of the web plate increases from H/t = 400 to 1000. The strength of the specimen with the beam-only connected web plate of 0.5 mm and 1.25 mm thickness was about 37% and 64% of that with the fully-connected one, respectively. It can be seen that the elastic stiffness of the SPSWs was larger than that of the SSW-BO specimens; where, the lower difference is 59% in the specimen SPSW-1, and the higher one is about 70% in SPSW-2. As can be seen in Table 5, the analytical stiffness of SPSWs (Eq. (3)) was much overestimated which can be attributed to slippage in bolted connections
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(a)
(b) 40000
Hysteretic 30000
Applied force (N)
Back-bone 20000 10000 0 -10000 -20000 -30000 -40000 -40
-20
0
20
40
Displacement (mm)
(d)
(c)
Fig. 18. Force-displacement hysteretic curve and back-bone curves of the specimens: (a) SPSW-1, (b) SPSW-2, (c) SSW-BO-1, (d) SSW-BO-2.
Table 4 Comparison of the yield strength, maximum strength, ultimate strength and unloading strength of experimental specimens. Specimen
Yield drift (%)
Yield strength, Py (kN)
Py. rel. (kN)/(kN)
Max. strength, Pmax (kN)
Pmax. rel. (kN)/(kN)
Ultimate strength (kN)
Strength degradation (%)
Unloading strength, Pres. (kN)
Pres. rel. (kN/kN)
SSW-BO-1 SPSW-1 SSW-BO-2 SPSW-2
0.5 0.75 0.75 1
7.74 9.480 22.812 26.240
1.00 1.22 1.00 1.16
11.48 45.838 31.32 71.258
1.00 3.99 1 2.28
10.99 30.962 25.010 –
4.27 32.45 20.15 –
3.20 11.32 8.77 –
1.00 3.54
and geometric imperfections of the experimental specimens. However, the significant differences between experimental and theoretical stiffness of SSW-BOs stem primarily as a result of the rather assumptions
and simplifications made in obtaining Eq. (7) in which the SSW-BO was idealized as a beam fixed at both two bottoms. Therefore, designers are cautioned that Eqs. (3) and (7) overestimate the initial stiffness of
Fig. 19. Back-bone of lateral force versus top displacement curves.
Fig. 20. Behavior at the 28th cycle for SSW-BO-1 and SPSW-1 specimens.
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Table 5 Comparison of the experimental and theoretical results of the specimens. Specimen
Elastic stiffness
Experimental K. rel.
(kN/mm) SSW-BO-1 SSW-BO-2 SPSW-1 SPSW-2 a b
2.38 4.13 4.69 9.05
1.00 1.74 1.00 1.93
Theoretical
Max. strength
Ductility
Elastic stiffnessa
Shear strengthb
(kN)
(%)
(kN/mm)
(kN)
11.48 45.838 31.32 71.258
7.8 6.7 5.43 3.92
21.39 53.47 21.00 52.50
5.21 17.14 14.51 47.76
Stiffness ratio (theo./exp)
Strength ratio (theo./exp)
8.99 12.94 4.47 5.52
0.45 0.37 0.46 0.67
Calculated using Eqs. (3) and (7). Calculated using Eqs. (1) and (4).
SPSWs and SSW-BOs by as much as roughly 5 times and 10 times, respectively more than experimental values. The Eqs. (1) and (4) estimated the nominal shear strength of the experimental specimens more conservatively. Degradation which defined as the ratio of the secant stiffness and the elastic stiffness versus drift ratio is calculated and presented in Fig. 21, illustrating that the stiffness degradation is more intensive at the early stage of the loadings especially for SSW-BO specimens. Increasing the web plate thickness from 0.5 mm to 1.25 mm decreased the stiffness degradation of the SPSW and SSW-BO at 2% drift by −78% and 24%, respectively. The discrepancy between secant stiffness of the SPSWs and SSW-BO decreased at larger drifts (N3%). As can be seen in Table 5, the maximum strength of SSW-BO-2 with thicker web plate and larger yield strength is comparable to that of SPSW-1 having thinner web plate and smaller yield strength.
4.4. Dissipated energy and ductility Fig. 22 shows the cumulative energy dissipation versus drift for specimens with similar displacement histories. The energy dissipation was calculated for each cycle of loading by summing the area under hysteretic curve created. It is observed that the energy dissipation in the SSW-BO-1 and SSW-BO-2 specimens at 3% drift is less as much as 68% and 52% than the energy dissipated by SPSW-1 and SPSW-2 counterparts, respectively. This behavior is expected because in the SSW-BO specimens, only a portion of the web plate is yielding and contributing the energy dissipation. Another observation from Fig. 22 is the trend of SSW-BO and SPSW specimens with the web plate thickness of 1.25 mm to dissipate more energy by 58% and 133%, respectively, compared to the counterparts with 0.5 mm thickness web plate. Ductility factor, provided in Table 5, is defined as the ratio of maximum drift and yielding drift of the specimens: μ¼
Δu Δy
ð8Þ
where μ is the displacement ductility factor, Δu the maximum displacement and Δy the yield displacement. For evaluating the yield displacement Δy (Fig. 23), a method recommended in ECCS [21] was adopted which is based on the tangent of the 10% slope of the elastic stiffness. In that sense, ductility factors of the specimens were given in Table 2, indicating more ductile behavior for SSW-BO specimens than for SPSW specimens. By increasing the web plate thickness from 0.5 mm to 1.25 mm, the ductility ratio of SSW-BO and SPSW specimens decreased 14% and 28%, respectively. 4.5. Strain results
Fig. 21. Stiffness degradation at different drift ratios for specimens.
Recorded strains versus lateral displacements are presented in Fig. 24(a) and (b) for SSW-BO-1 and SPSW-1, respectively. These specimens are taken for example to illustrate the recorded strains. The
Fig. 22. Cumulative energy dissipation versus drift ratio.
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5. Conclusions
Fig. 23. Determination of yielding displacement Δy [21].
strains increased from practically zero in the first displacement step to 0.08 and 0.1, for St.G0-SSW-BO-1 and St.G2-SSW-BO-1, respectively, when the specimens were cycled up to 5% drift amplitude. In SPSW-1, the corner strains vary in the positive or negative strain directions depending on the upward or downward out-of-plane buckling mode, respectively. However, the maximum absolute magnitude of strains in SPSW specimen is b0.03.
This paper describes an experimental work related to the tests of four 1:6 scale steel shear walls with beam-only connected and fully-connected web plates under cyclic loading. Based on the tests, the following conclusions are given. SPSW and SSW-BO specimens possess good ductility and energy dissipation capacity. Compared to SSW-BOs, it is shown that SPSWs contribute significantly to the overall strength, stiffness, and energy dissipation capacity of the structural system and the structural system performed as intended. The yielding strength and maximum strength of SPSWs are approximately 1.2 times and 3.0 times of SSW-BOs respectively; the elastic stiffness of SPSWs are 2.1 times of SSW-BOs; the ductility of SPSWs are 0.65 times of SSW-BOs. The cumulative energy dissipation of SPSWs is 2.50 times of SSW-BOs. The results show that increasing the web plate thickness and yield stress in SSW-BO specimens result in similar shear strength and energy dissipation to thinner web plates in SPSW specimens. The observed degradation of the shear capacity in the SPSW with a 0.5 mm thickness was caused by a growth of the existing tears, and fracture of the steel plate occurred between adjacent bolts along a row at the bottom and right of the wall. However, the strength degradation of SSW-BO was much smaller than that of SPSW specimen. For SSW-BO systems, the orientation of the tension field remained approximately at 28°, regardless of web plate thickness. There is a fluctuation in the inclination of tension field of SPSW systems after 2% drift. However, the orientation of the tension field reached approximately at 40° in the SPSWs. The ultimate shear strength of the experimental specimens using theoretical model was estimated more conservatively. Contrary to the theoretical model containing perfect geometry and ideal connections, the experimental specimens experienced low initial stiffness due to developing slippage along the bolt connections of infill plate to surrounding elements and presence of initial imperfections. These differences were further accentuated due to simplifications made in obtaining theoretical equations. Acknowledgments The authors wish to express their gratitude to the thin-walled structural research laboratory of Urmia University. Special thanks go to the laboratory technician; Mr. Azimzadeh for his valuable contribution. References
Fig. 24. Strains versus lateral displacement: (a) SSW-BO-1; (b) SPSW-1.
[1] I.F. Seilie, J.D. Hooper, Steel plate shear walls: practical design and construction, Mod. Steel Constr. 45 (4) (2005) 37–43. [2] R. Sabelli, M. Bruneau, Design Guide 20: Steel Plate Shear Walls, American Institute of Steel Construction, Chicago, IL, 2007. [3] R.G. Driver, G.L. Kulak, D.L. Kennedy, A.E. Elwi, Cyclic test of four-story steel plate shear wall, J. Struct. Eng. 124 (1998) 112–120. [4] A. Astaneh-Asl, Seismic behavior and design of steel shear walls, Steel TIPS Report, Structural Steel Educational Council, Moraga, CA, 2001www.aisc.org. [5] K.A. Bhowmick, R.G. Driver, Y.G. Gilbert, Application of indirect capacity design principles for seismic design of steel-plate shear walls, J. Struct. Eng. 137 (2011) 521–530. [6] S. Sabouri-Ghomi, M. Ventura, M. Kharrazi, Shear analysis and design of ductile steel plate walls, J. Struct. Eng. ASCE 131 (6) (2005) 878–889. [7] J. Berman, M. Bruneau, Experimental investigation of light-gauge steel plate shear walls, J. Struct. Eng. ASCE 131 (2) (2005) 259–267. [8] D. Vian, M. Bruneau, R. Purba, Special perforated steel plate shear walls with reduced beam section anchor beams II: analysis and design recommendations, J. Struct. Eng. ASCE 135 (3) (2009) 221–228. [9] D. Vian, M. Bruneau, K.C. Tsai, Y.C. Lin, Special perforated steel plate shear walls with reduced beam section anchor beams I: experimental investigation, J. Struct. Eng. ASCE 135 (3) (2009) 211–220. [10] D. Borello, L. Fahnestock, Seismic design and analysis of steel plate shear walls with coupling, J. Struct. Eng. 139 (2013) 1263–1273. [11] R. Purba, M. Bruneau, Finite-element investigation and design recommendations for perforated steel plate shear walls, J. Struct. Eng. 135 (11) (2009) 1367–1376. [12] L. Guo, Q. Rong, X. Ma, S. Zhang, Behavior of steel plate shear wall connected to frame beams only, Int. J. Steel Struct. 11 (4) (2011) 467–479.
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Contents lists available at ScienceDirect
Journal of Constructional Steel Research
Experimental seismic study on shear walls with fully-connected and beam-only-connected web plates B. Shekastehband a,⁎, A.A. Azaraxsh a, H. Showkati b a b
Department of Civil Engineering, Urmia University of Technology, Urmia, Iran Department of Civil Engineering, University of Urmia, Urmia, Iran
a r t i c l e
i n f o
Article history: Received 30 December 2016 Received in revised form 23 October 2017 Accepted 12 November 2017 Available online xxxx Keywords: Steel plate shear walls (SPSW) Steel shear walls connected to frame beams only (SSW-BO) Cyclic loading Hysteresis Dissipated energy Ductility
a b s t r a c t Typically, in conventional steel plate shear walls (SPSWs), web plates are connected to both beams and columns; however, steel shear walls connected to beams only (SSW-BOs) with the idea of reducing surrounding columns demands and alleviating web plate damage was proposed since the mid-2000s. This paper presents an experimental investigation on seismic behavior of steel plate shear walls comprising SPSWs and SSW-BOs. Cyclic loading tests were performed on four 1:6 scaled one-story specimens with two plate thickness and two different web plate boundary conditions. The observed predominant failure modes include i: plate tearing at the corners, ii: slippage along connection zone of web plates, and iii: plate-to-frame connection bearing. Using frame connection for plates increases the energy dissipation, shear strength and elastic stiffness by up to 150%, 200% and 110% on average, respectively compared to those of beams-only connected walls. Experimental results indicate that the SSW-BO systems reached a ductility ratio of 7.3 on average, almost 1.5 times the value for SPSWs. It is demonstrated further that with an increase in the slenderness ratio (height to thickness), the strength, stiffness and energy absorbed by the SPSW and SSW-BO systems show a decreasing trend being less stiff for SSW-BO panels. © 2017 Elsevier Ltd. All rights reserved.
1. Introduction Steel plate shear walls (SPSWs) have been in use as the primary lateral load-resisting system of buildings in high seismic areas for a long time [1,2]. These systems have specific advantages in terms of ductility, stiffness and shear strength that merit their consideration for use as a load bearing system in different structures whole over the world [3,4]. In a conventional SPSW (Fig. 1(a)), the web plates connected to the surrounding beams and columns, buckle in shear at low lateral loads and develop a diagonal tension field that induces sever stresses on the surrounding frame members, as shown in Fig. 1(b). In addition, using of web plates with minimum available thickness larger than required for resisting specified lateral loads may also result in excessive design forces to the horizontal and vertical boundary elements (HBEs and VBEs), thus increasing their size. As a result, there exists an obstacle concerning VBEs high demand that may impede further widespread acceptance of this system. To prevent plastic hinges in the columns and thus to prevent collapse of the structure, strong columns with large sections must be used [6]. Attempts at mitigating column demands were recently addressed by the use of (i) light-gauge, cold-formed steel plates [7], (ii) low-yield steel [8,9], (iii) coupling beams to alleviate overturning forces [2,10],
⁎ Corresponding author. E-mail address: [email protected] (B. Shekastehband).
https://doi.org/10.1016/j.jcsr.2017.11.013 0143-974X/© 2017 Elsevier Ltd. All rights reserved.
(iv) perforations layout covering the entire web plate in a specified regular pattern [11] and (v) web plates connected to the beams only [12,13]. The presumed benefits of alleviating column demands gained from the use of beam-only-connected web plates must be weighed against possible drawbacks associated with their reduced shear strength and mitigated energy absorption compared with fully-connected web plates. The web plates are not connected to frame columns, large stresses due to tension field, developing plastic hinges in the columns are avoided (Fig. 2). Limited performed experimental studies on SSW-BO illustrated that these systems have considerable shear strength and can be used to separate the shear walls from the main columns and therefore, reduce the dimension of columns [14,15]. It was recognized that the frame has the capability of developing a tension field in the wall plate, so that the wall plate yields before the frame [14]. A comparative experimental study was conducted in this research to investigate the structural performance of SPSW and SSW-BO systems. Four wall specimen configurations were tested under cyclic loading and the results are presented as follows.
2. Analytical shear load-displacement of SPSW and SSW-BO Considering the web plate of width L, height H and thickness t, the nominal lateral strength of a SPSW, Vnf, using the kinematic method of
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(a)
(b)
Fig. 1. Conventional SPSW: (a) fully-connected web plate; (b) stresses on boundary elements [5].
plastic analysis is obtained as presented in the AISC Seismic Provisions [16]: V nf ¼ 0:42F y tL sin2α
ð1Þ
where Fy and α are yield strength and angle of inclination of tension field from the vertical. The elastic shear displacement, Ue, neglecting buckling shear strength is obtained as [16]: Ue ¼
2F y H E sin2α
ð2Þ
where, E is modulus of elasticity. Using Eqs. (1) and (2), the elastic stiffness of SPSW is calculated as follows: Kf ¼
0:21LtE H
ð3Þ
The nominal lateral strength for SSW-BO, Vnb, can be assessed as [17]: V nb ¼ 0:42F y tLPTF sin2θ
where the inclination angle, α, was replaced with that of a SSW-BO partial tension field, θ, and the total fully-connected web plate length, L, with the partial tension field length, LPTF. The rest of the web plate outside of the partial tension field does not contribute to the plate's lateral force resistance. In Eq. (4), the partial tension field length along the beams, and partial tension field inclination are given as [17]:
LPTF ¼ L−H tanðθÞ
ð5Þ
θ ¼ 0:5 tan−1 ðL=H Þ
ð6Þ
V2
V1
(a)
ð4Þ
(b)
Fig. 2. SSW-BO: (a) beam-only connected web plate; (b) stresses on boundary elements.
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Considering both the shear and bending deformations of the web plate, the theoretical elastic stiffness proportional to the lateral displacement is obtained as [12]: Kb ¼
Et 1=ðL=HÞ3 þ 2ð1 þ ν Þ:k=ðL=H Þ
Pin
Web plate
Stiffening boxes in SSW-BO
ð7Þ
Bolt
3. Test procedure 3.1. General
2 UNP 12 An actual view of the experimental set-up is illustrated in Fig. 3. Experimental models were scaled as 1:6 one-story SPSW and SSW-BO, with hinge type connections in boundaries at four corners (Fig. 4). The slenderness ratio (plate height to thickness ratio) was considered as variables in these specimens. For this purpose, two thicknesses of 0.5 and 1.25 mm were selected for the plates. Each test was performed under fully reversed cyclic quasi-static loading in the elastic and inelastic response zones of the specimens in compliance with the SAC [18] test protocol by means of an actuator of 100 kN capacity. A lateral restrain system was used to prevent out of plane deformations of the testing frame (Fig. 3). An A-framed superstructure was used for supporting the actuator. Table 1 provides the detailed geometry and slenderness ratios of the specimens. The frames measured 620 mm wide and high between HBEs and VBEs centerlines, while the depth/width of the web plates in SPSW and SSW-BO were equal to 500/500 mm and 500/ 460 mm, respectively. The boundary elements of the frame were similar and consisted of the standard profile double section UNP120. Two 20 × 30 × 2 mm box sections of 460 mm height located at a distance of 20 mm from the surrounding beams were used for stiffening the free edges and preventing more out of plane deformations of infill plates due to shear buckling. It should be noted that the out-of-plane deformation along the free edge produces large curvature demands at the edge of the bolted infill plate-to-beam connection which may in turn cause tearing of infill plate [17]. The edges of the web plates in SPSW and SSW-BO were clamped between frame elements and beams-only respectively by the means of two rows of high tensile 10 mm bolts. To connect the vertical edges of the web plate to stiffening boxes in SSWBO, high strength bolts with a diameter of 5 mm were used. The systems were established and connected by means of 8 high tensile bolts on the rigid base of the laboratory. To determine the stress–strain curves of the web plates and boundary element materials, four tensile coupon tests were performed on two
Fig. 4. Details of the experimental specimens.
web plate thicknesses according to the ASTM A370-05 [18]. A summary of the coupon test results is presented in Table 2.
3.2. Measuring devices In order to measure the load during the tests, a load cell located between hydraulic jack and loading point was used. The hydraulic jack was connected to the top of the specimens through a U-shape pin joint system. Slotted hole on the joint system perpendicular to the line of applied force provides a load path to transfer the force horizontally (Fig. 5). LVDT displacement transducers were attached on desired points of the specimens to measure the relative displacements within the accuracy of 0.001 mm (Fig. 3). The strain gauges were attached to the corners and center of the web plates (Fig. 3). Locations of the strain gauges were determined at probable plastic zones in the elements based on the preliminary numerical analysis results. Note that the gauge series of YF/Y is post-yield foil/wire gauge, which features a special plastic carrier base of withstanding extreme elongation without creeping or cracking. All data were recorded and processed by means
Fig. 3. Lateral restrain system of the steel shear wall specimens in the laboratory.
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Table 1 Specification of specimens. Specimen
Plate thickness t (mm)
Primary columns & beams
Stiffening boxes
Slenderness ratio H/t
SSW-BO-1 SSW-BO-2 SPSW-1 SPSW-2
0.5 1.25 0.5 1.25
2UNP120 2UNP120 2UNP120 2UNP120
2 box (20 × 30 × 2 mm) 2 box (20 × 30 × 2 mm) – –
1000 400 1000 400
Table 2 Material properties of steel used in the test. Steel material
Elastic modulus (GPa)
Yield stress (MPa)
Yield strain (%)
Ultimate stress (MPa)
Ultimate strain (%)
Rupture strain (%)
Web plate (thickness = 0.5 mm) Web plate (thickness = 1.25 mm) UNP120 & Box 20 × 30 × 2 mm
200 200 200
138.15 182 240
0.11 0.09 0.12
280.80 328 360
27 27 20
37 40 20
of a KYOWA type digital data logger, a scanner and a software named UCAM-20PC, Japan. 3.3. Cyclic loading program The lateral quasi-static loading was applied to the top of upper beam in accordance with SAC protocol [20]. Fig. 6 shows the cyclic
displacement-control loading history of the specimens. In this graph, the loading began with very small values of the overall drift and increased gradually up to a drift of 5%. No vertical load was applied to the specimens. 3.4. Test process Prior to the tests, the signals emanating from the strain-gauges, LVDT transducers and the load cell were initialized to zero. It should be noted that a trial run was conducted before testing main specimens to evaluate the efficiency of the test rig. Note the actuator moving throughout the tests was always at a rate of 0.5 mm/s. During the tests, displacements as well as local strains were recorded at short and regular intervals to have a well detection and evaluation of the buckling phenomenon. 4. Observations and discussions 4.1. General observations The specimens were failed in a progression of tears at the plate corners, wave buckling, bearing failure of the plate and bolts in connections and knot type local buckling at the plate corners. The evolution of failure of SPSW and SSW-BO specimens is illustrated as follows:
Fig. 5. Pin connection of actuator to top of the specimen [19].
1. In the SPSW specimens consisting of web plates with the thickness of 0.5 mm and 1.25 mm, formation of tension field line and buckling
Fig. 6. Loading protocol based on SAC [20].
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SPSW-2;
(a)
0.75 % Drift
(b)
Fig. 7. Tension field buckles in SPSWs: (a) SPSW-1; (b) SPSW-2.
Fig. 8. Tension field buckles in SSW-BOs: (a) SSW-BO-1; (b) SSW-BO-2.
wave were evident in the last cycle of 0.375% and 0.75% drift level, respectively (Fig. 7). However, as shown in Fig. 8, in the SSW-BO counterparts, buckling waves could be distinguished in the last cycle of around 0.5% and 1.0% drift, respectively. In the whole specimens, as the test progressed, audible buckling sounds coming from the alternating tension field orientation during reversed loading cycles began and the magnitude of the buckling waves grew remarkably. 2. In excess 2% drift, due to development of tension field yielding and buckling waves in the load excursions, the residual out of plane deformation remaining like knot was formed in the SSW-BO specimens (Fig. 9). This type of deformation was not observed in the SPSW specimens. 3. In the SPSW specimens, a number of relatively large buckle waves, at least four at N1.5% drift, were formed. However, SSW-BO specimens, due to developing partial tension field action, have less buckling waves than SPSW counterparts. As shown in Fig. 10, eight waves were developed in the SPSW-1, while only three waves were seen in the SSW-BO-1 in 3% drift.
Fig. 9. Forming knot due to residual out of plane deformation in the SSW-BO systems.
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SPSW-1;
3 % Drift
209
SSW-BO-1;
3 % Drift
1 2 3
4 5
6
7
8
1
(a)
3
2
(b)
Fig. 10. Tension field developed in steel shear walls: (a) SPSW-1; (b) SSW-BO-1.
SSW-BO-1;
4 % Drift
SSW-BO-2;
(a)
(b) Fig. 11. Tear in the plate bottom corners: (a) SSW-BO-1; (b) SSW-BO-2.
(a)
(b) Fig. 12. Failure modes of SSW-BOs: (a) SSW-BO-1; (b) SSW-BO-2.
4 % Drift
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SPSW-1;
3 % Drift
(a)
SPSW-1;
5 % Drift
(b)
Fig. 13. Tears in the plate bottom corners of SPSW-1: (a) at 3% drift; (b) at 5% drift.
4. In the SSW-BO specimens, slippage along connection zone of web plate to bottom HBE at corners at 3% drift level was accompanied with local tears appeared adjacent to the corners of web plates at drift value of 4%. When the drift ratio reached 4%, because of the growing of stress concentration, small tear along HBEs were developed in the plate bottom corners as shown in Fig. 11. Continued large displacement cycling (5% drift) finally caused progression of tearing in plate bottom west corner as well as yielding and slippage in the plate bottom east corner implying bearing failure of the plate and bolts in connections (Fig. 12). 5. A small tear at the bottom west corner of the web plate of SPSW-1 was initiated in 2% drift by the low cycle fatigue as the web plate buckled cyclically with load reversals. By increasing the lateral movement (drift N 4%) a local tear was also initiated at the bottom east corner of the web plate (Fig. 13). The web plate tears continued to propagate more severely as the test proceeded. In the last excursion of drift 3%, fracture of the steel plate was occurred between adjacent bolts along a row at the bottom and right of the wall. These fractures grew with each cycle of loading, eventually fracturing through the entire length of the bottom edge of the web plate at 5% drift, as shown in Fig. 14. This was accompanied by in-plane slippage of web plate at the connections in last cycles of 4% drift and therefore, a main kink as well as out-of-plane deformation was formed at the middle of panel at the end of test (Fig. 15). The SPSW-2 was only loaded up to 4% drift in both directions because of the capacity
limitation of the load cell. Therefore, no signs of web plate tearing at drifts slightly b 4% was observed in the specimen. In larger drifts (N 2%) two small kinks appeared in the right half of the middle panel, as shown in Fig. 16. 6. The SSW-BO with 0.5 mm thick panel experienced no tearing and plate fracturing in cycles prior to 3% drift; however, in the SPSW counterpart, tearing was initiated in 2% drift. Therefore, SSW-BO specimens illustrated a delay and reduction of web plate tearing compared with the SPSW specimens. Full-connection in comparison with the beam-only connection causes increased strain demands in the web plate under cyclic lateral loadings. In both SSSW-BO and SPSW specimens, a number of local minor tears took place near the corners of thinner panel by the material low cycle fatigue resulting from severe cyclic distortion of the web plates. The more number of web plate tearing in SSW-BO specimens can be attributed to the out-of-plane web plate deformation along the unrestrained edge of the corners that are not present in conventional SPSW web plates connected continuously along all edges. 7. Average inclination angle of tension fields for all the specimens through measuring the inclination of the buckled waves is presented in Table 3. As the extent of web plate bearing fracture increases with increasing drift demands, as does the scatter in the measured angle of inclination in the SPSW-1, that can be attributed to the increased slippage preventing the full formation of tension field (Fig. 17).
Fig. 14. Failure mode of SPSW-1.
Fig. 15. A main kink and out-of-plane deformation at the middle of web plate in SPSW-1.
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Small kinks
Fig. 16. Deformed shape at the end of test in SPSW-2. Fig. 17. Inclination of the tension field in the specimens.
4.2. Hysteretic behavior of the specimens The hysteresis lateral load-top displacement responses with backbone curves for all specimens obtained from the tests are presented in Fig. 18. All specimens exhibited stable hysteretic behavior until the end of the loading program, with some pinching of hysteresis loops that are consistent with the features observed in other tests on SPSW and SSW-BO systems [15,19]. Specimens of 0.5-mm panels, i.e. SPSW1 and SSW-BO-1, yielded at 0.5% and 0.75% drift, respectively (Table 4). The specimen with 1.25-mm-thick panels, SPSW-2 and SSW-BO-2, yielded at approximately 0.75% and 1.00% drift. Fig. 19 compares the back-bone of the hysteresis curve for the whole specimens. The lateral resistance capacity of SSW-BO specimens was about 25% of SPSWs, indicating that the lateral resistance is much reduced by isolating the web plate from boundary columns. Moreover, the pinch effect of the hysteretic loops of SPSWs was less than that of SSW-BO, demonstrating that full connecting of web plate to boundary frame may increase the overall wall stability resulting in increased energydissipation of the system. All specimens exhibited stable behavior up to cycles of 4% drift, at which point the strength deteriorated. The ultimate displacement of the fully-connected specimen with 1.25 mm thick, i.e. SPSW-2, was 4% drift, owing to the limitation of the load cell capacity. The contribution of the web plate connection to the shear capacity increases with lateral displacement. Thus, as given in Table 4, the difference between SSW-BO-1 and SPSW-1 (as well as SSW-BO-2 and SPSW2) in terms of yield resistance was 22% (16%), but ultimate capacity decreased by 32.45% and 4.3% in fully-connected and beam-only connected, respectively. The difference in the hysteretic behavior between fully-connected and beam-only connected web plate specimens can be explained through the 28th cycle for specimens SSW-BO-1 and SPSW-1, as shown in Fig. 20. The tensile half-cycles of hysteresis loops can be categorized into three classes of behavior: 1- From point a to point b, the specimen exhibits a plateau in the loaddeflection curve. This region represents the main contribution of the surrounding frame to the stiffness. Therefore, due to pin connections of the boundary elements, the hysteresis loop appears with zero slope upon development of the tension field. 2- After point b, the web plate resists lateral load through the development of tension field action, and stiffness increases as the plate
Table 3 Measured tension field inclination of the specimens. Specimen Inclination angle
SSW-BO-1 28
SSW-BO-2 28
SPSW-1 42.5
SPSW-2 40.5
deforms. When compared to the beam-only connected web plates with partial tension field action, the fully-connected ones due to the development of tension field action show an increase in resistance and stiffness. Strength ratio of point b to point a is 3.5 and 1.7 for SPSW and SSW-BO, respectively. For this reason, as illustrated in Table 4, the maximum strength to yield strength of the fully-connected web plate is much more than that of beam-only connected one. 3- After point c, the plate deforms plastically in tension and the stiffness decreases. At this stage, SSW-BO specimen experiences more plastic deformation than that of SPSW one for the same lateral strength. Therefore, the pinching effect resulted due to the accumulated diagonal plastic stretch of the web plate, was more visible in the SSW-BO compared to the SPSW. Comparison of the loops corresponding to same drift demonstrated that the shear strength decreased slightly in next loops because of residual strains and plastic deformations caused by first cycle. In SPSW-1 at 4% drift, propagation of plate fracture along the bolts led to a considerable drop in strength and stiffness of the loop. It is worthy of mention that strength of the specimens was not affected by web plate tearing and its propagation. However, fracture occurred in the web plate between the connections resulted in reduced panel strength at larger drifts. Unloading strengths of the specimens are also given in Table 4. It can be seen that the residual strengths of SPSW specimens are about 354% of SSW-BOs, illustrating that the web plate residual strength is a function of tension field action in the web plates as they deform during unloading. 4.3. Strength and stiffness Elastic stiffness, ultimate strength and ductility of the all specimens based on experimental hysteresis curves are presented in Table 5. In addition, the shear strength and stiffness of the specimens obtained from the theoretical equations are also listed in Table 5. The two last columns of Table 5 represent ratio of the stiffness and shear strength from the two experimental and theoretical methods. Strength of the SPSW and SSW-BO specimens tend to decrease as much as roughly 25% and 44%, respectively as the slenderness ratio of the web plate increases from H/t = 400 to 1000. The strength of the specimen with the beam-only connected web plate of 0.5 mm and 1.25 mm thickness was about 37% and 64% of that with the fully-connected one, respectively. It can be seen that the elastic stiffness of the SPSWs was larger than that of the SSW-BO specimens; where, the lower difference is 59% in the specimen SPSW-1, and the higher one is about 70% in SPSW-2. As can be seen in Table 5, the analytical stiffness of SPSWs (Eq. (3)) was much overestimated which can be attributed to slippage in bolted connections
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(a)
(b) 40000
Hysteretic 30000
Applied force (N)
Back-bone 20000 10000 0 -10000 -20000 -30000 -40000 -40
-20
0
20
40
Displacement (mm)
(d)
(c)
Fig. 18. Force-displacement hysteretic curve and back-bone curves of the specimens: (a) SPSW-1, (b) SPSW-2, (c) SSW-BO-1, (d) SSW-BO-2.
Table 4 Comparison of the yield strength, maximum strength, ultimate strength and unloading strength of experimental specimens. Specimen
Yield drift (%)
Yield strength, Py (kN)
Py. rel. (kN)/(kN)
Max. strength, Pmax (kN)
Pmax. rel. (kN)/(kN)
Ultimate strength (kN)
Strength degradation (%)
Unloading strength, Pres. (kN)
Pres. rel. (kN/kN)
SSW-BO-1 SPSW-1 SSW-BO-2 SPSW-2
0.5 0.75 0.75 1
7.74 9.480 22.812 26.240
1.00 1.22 1.00 1.16
11.48 45.838 31.32 71.258
1.00 3.99 1 2.28
10.99 30.962 25.010 –
4.27 32.45 20.15 –
3.20 11.32 8.77 –
1.00 3.54
and geometric imperfections of the experimental specimens. However, the significant differences between experimental and theoretical stiffness of SSW-BOs stem primarily as a result of the rather assumptions
and simplifications made in obtaining Eq. (7) in which the SSW-BO was idealized as a beam fixed at both two bottoms. Therefore, designers are cautioned that Eqs. (3) and (7) overestimate the initial stiffness of
Fig. 19. Back-bone of lateral force versus top displacement curves.
Fig. 20. Behavior at the 28th cycle for SSW-BO-1 and SPSW-1 specimens.
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Table 5 Comparison of the experimental and theoretical results of the specimens. Specimen
Elastic stiffness
Experimental K. rel.
(kN/mm) SSW-BO-1 SSW-BO-2 SPSW-1 SPSW-2 a b
2.38 4.13 4.69 9.05
1.00 1.74 1.00 1.93
Theoretical
Max. strength
Ductility
Elastic stiffnessa
Shear strengthb
(kN)
(%)
(kN/mm)
(kN)
11.48 45.838 31.32 71.258
7.8 6.7 5.43 3.92
21.39 53.47 21.00 52.50
5.21 17.14 14.51 47.76
Stiffness ratio (theo./exp)
Strength ratio (theo./exp)
8.99 12.94 4.47 5.52
0.45 0.37 0.46 0.67
Calculated using Eqs. (3) and (7). Calculated using Eqs. (1) and (4).
SPSWs and SSW-BOs by as much as roughly 5 times and 10 times, respectively more than experimental values. The Eqs. (1) and (4) estimated the nominal shear strength of the experimental specimens more conservatively. Degradation which defined as the ratio of the secant stiffness and the elastic stiffness versus drift ratio is calculated and presented in Fig. 21, illustrating that the stiffness degradation is more intensive at the early stage of the loadings especially for SSW-BO specimens. Increasing the web plate thickness from 0.5 mm to 1.25 mm decreased the stiffness degradation of the SPSW and SSW-BO at 2% drift by −78% and 24%, respectively. The discrepancy between secant stiffness of the SPSWs and SSW-BO decreased at larger drifts (N3%). As can be seen in Table 5, the maximum strength of SSW-BO-2 with thicker web plate and larger yield strength is comparable to that of SPSW-1 having thinner web plate and smaller yield strength.
4.4. Dissipated energy and ductility Fig. 22 shows the cumulative energy dissipation versus drift for specimens with similar displacement histories. The energy dissipation was calculated for each cycle of loading by summing the area under hysteretic curve created. It is observed that the energy dissipation in the SSW-BO-1 and SSW-BO-2 specimens at 3% drift is less as much as 68% and 52% than the energy dissipated by SPSW-1 and SPSW-2 counterparts, respectively. This behavior is expected because in the SSW-BO specimens, only a portion of the web plate is yielding and contributing the energy dissipation. Another observation from Fig. 22 is the trend of SSW-BO and SPSW specimens with the web plate thickness of 1.25 mm to dissipate more energy by 58% and 133%, respectively, compared to the counterparts with 0.5 mm thickness web plate. Ductility factor, provided in Table 5, is defined as the ratio of maximum drift and yielding drift of the specimens: μ¼
Δu Δy
ð8Þ
where μ is the displacement ductility factor, Δu the maximum displacement and Δy the yield displacement. For evaluating the yield displacement Δy (Fig. 23), a method recommended in ECCS [21] was adopted which is based on the tangent of the 10% slope of the elastic stiffness. In that sense, ductility factors of the specimens were given in Table 2, indicating more ductile behavior for SSW-BO specimens than for SPSW specimens. By increasing the web plate thickness from 0.5 mm to 1.25 mm, the ductility ratio of SSW-BO and SPSW specimens decreased 14% and 28%, respectively. 4.5. Strain results
Fig. 21. Stiffness degradation at different drift ratios for specimens.
Recorded strains versus lateral displacements are presented in Fig. 24(a) and (b) for SSW-BO-1 and SPSW-1, respectively. These specimens are taken for example to illustrate the recorded strains. The
Fig. 22. Cumulative energy dissipation versus drift ratio.
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5. Conclusions
Fig. 23. Determination of yielding displacement Δy [21].
strains increased from practically zero in the first displacement step to 0.08 and 0.1, for St.G0-SSW-BO-1 and St.G2-SSW-BO-1, respectively, when the specimens were cycled up to 5% drift amplitude. In SPSW-1, the corner strains vary in the positive or negative strain directions depending on the upward or downward out-of-plane buckling mode, respectively. However, the maximum absolute magnitude of strains in SPSW specimen is b0.03.
This paper describes an experimental work related to the tests of four 1:6 scale steel shear walls with beam-only connected and fully-connected web plates under cyclic loading. Based on the tests, the following conclusions are given. SPSW and SSW-BO specimens possess good ductility and energy dissipation capacity. Compared to SSW-BOs, it is shown that SPSWs contribute significantly to the overall strength, stiffness, and energy dissipation capacity of the structural system and the structural system performed as intended. The yielding strength and maximum strength of SPSWs are approximately 1.2 times and 3.0 times of SSW-BOs respectively; the elastic stiffness of SPSWs are 2.1 times of SSW-BOs; the ductility of SPSWs are 0.65 times of SSW-BOs. The cumulative energy dissipation of SPSWs is 2.50 times of SSW-BOs. The results show that increasing the web plate thickness and yield stress in SSW-BO specimens result in similar shear strength and energy dissipation to thinner web plates in SPSW specimens. The observed degradation of the shear capacity in the SPSW with a 0.5 mm thickness was caused by a growth of the existing tears, and fracture of the steel plate occurred between adjacent bolts along a row at the bottom and right of the wall. However, the strength degradation of SSW-BO was much smaller than that of SPSW specimen. For SSW-BO systems, the orientation of the tension field remained approximately at 28°, regardless of web plate thickness. There is a fluctuation in the inclination of tension field of SPSW systems after 2% drift. However, the orientation of the tension field reached approximately at 40° in the SPSWs. The ultimate shear strength of the experimental specimens using theoretical model was estimated more conservatively. Contrary to the theoretical model containing perfect geometry and ideal connections, the experimental specimens experienced low initial stiffness due to developing slippage along the bolt connections of infill plate to surrounding elements and presence of initial imperfections. These differences were further accentuated due to simplifications made in obtaining theoretical equations. Acknowledgments The authors wish to express their gratitude to the thin-walled structural research laboratory of Urmia University. Special thanks go to the laboratory technician; Mr. Azimzadeh for his valuable contribution. References
Fig. 24. Strains versus lateral displacement: (a) SSW-BO-1; (b) SPSW-1.
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