Load-sharing mechanism in timber-steel hybrid shear wall systems

Abstract

The lateral performance of timber-steel hybrid shear wall systems with regard to the interaction between the steel frame and the infill wood shear wall was investigated in this paper. A numerical model for the timber-steel hybrid shear wall system was developed and verified against test results. Design parameters, such as the lateral infill-to-frame stiffness ratio and the arrangements of wood-steel bolted connections were studied using the numerical model. Some design recommendations were also proposed based on the parametric analysis. In the hybrid shear wall system, the infill wood wall was found to resist a major part of the lateral load within relatively small wall drifts, and then the steel frame provided more lateral resistance. Under seismic loads, the infill wood wall could significantly reduce the inter-story drift of the hybrid system, and a complementary effect between the infill wood wall and the steel frame was observed through different lateral load resisting mechanisms, which provided robustness to the hybrid shear wall systems.

Keywords

timer-steel hybrid / shear wall / load sharing mechanism / seismic performance / parametric analysis

Introduction

The majority of low-rise residences in North America are built with wood. However, with the increasing urban density, attempts have been made to develop multi-story timber / timber-hybrid buildings. Hybridization of wood with other materials can be an alternative, since hybridization can combine respective benefits of different materials. Feasibility analysis and prototype tests have been conducted by researchers to study the performance of multi-story timber hybrid buildings recently. In a research project on timber-based hybrid buildings in Japan [ 1], a series of shaking table tests were conducted to study the lateral load sharing effect between timber frame and reinforced concrete shear core. The results showed the connections between wood and concrete had a significant influence on the lateral performance of the hybrid system. A full-scale six-story wood-frame apartment building was designed in accordance with the performance-based philosophy and was subjected to a series of earthquakes on the E-Defense shaking table within the NEESWood Project [ 2, 3]. The building performed excellently with little damage, even following a maximum credible earthquake with a return period of 2500 years. Within the NEWBuilds research network in Canada, Meleki et al. [ 4] studied the possible differential movements between wood and concrete in a six-story timber-concrete hybrid building, and suggested that proper connections between the timber framing and the concrete shear wall should be adopted. Zhou et al. [ 5] studied the lateral performance of a multi-story light wood frame building with a reinforced masonry core. It was found that the masonry core reduced the lateral drift of the structure and the base shear distribution between wood and masonry was affected by their relative stiffness. Dickof et al. [ 6] introduced a wood-steel hybrid seismic force resisting system which is composed of steel frame and infill cross laminated timber (CLT) panels. Static pushover analysis was conducted to determine the overstrength and ductility factors for the hybrid system, and the effectiveness of the infill panels under earthquakes was studied through dynamic analysis.

A multi-story timber-steel hybrid building system was proposed by He et al. [ 7]. It is composed of steel moment-resisting frames, timber-steel hybrid diaphragms and light wood frame shear walls. The light wood frame shear walls are considered as infill walls in the steel moment-resisting frames, forming a timber-steel hybrid shear wall system to resist lateral loads. The understanding of the wall-frame interaction between the wood infill wall and the steel frame is crucial, as it provides fundamental knowledge for the establishment of theoretical analysis model and design methodology for such timber-steel hybrid structures.

The lateral performance of the steel moment-resisting frame infilled with other materials such as concrete or masonry has been investigated [ 8- 10], and several computer models were also proposed [ 11]. However, these studies mainly focused on the failure mechanism and computer modeling of the concrete or masonry infill walls, which were significantly different from wood shear walls. Therefore, the performance of the timber-steel hybrid shear wall systems must be studied before practical application. For the computer modeling of timber-steel hybrid shear walls, a suitable representation for the infill wood shear wall is a key issue. Researchers have proposed a number of numerical models for wood shear walls [ 12- 15]. However, most of these models were developed within specific software packages. To model the behavior of wood shear walls in a more versatile way, Xu and Dolan [ 16] modified the Bouc-Wen-Barer-Wen hysteresis model to represent wood shear walls and embedded the model in a commercially available software package ABAQUS through a user-defined element. An oriented spring pair model was also implemented in ABAQUS by Judd and Fonseca [ 17] to model nail connections in wood diaphragms and shear walls. These two models are both phenomenon-based, which means the loading and unloading paths of the model under hysteretic loads need to be defined explicitly. In this study, a user-defined element, which was developed based on a mechanical wood shear wall model proposed by Gu and Lam [ 18], was implemented in ABAQUS to model the infill wood shear walls. The model was verified by reversed cyclic test results and used in a parametric analysis to study the infill-frame interaction in the hybrid system. Reversed cyclic analysis and dynamic analysis were conducted, and the effectiveness of the infill wood shear wall on enhancing the strength and stiffness of the hybrid system under seismic loads was evaluated.

Method of study

Parameter studies

Figure 1 shows a typical timber-steel hybrid shear wall system in this study. The steel moment frame and the infill wood shear wall served as subsystems in the hybrid system to resist lateral loads together. In this paper, a single-story one-bay timber-steel hybrid shear wall system was studied. The parametric analysis included two wall lengths L (3.6 and 7.2 m), three wall heights H (i.e., 2.4, 3.6, and 4.8 m) and two infill sheathing configurations (i.e., single-, double-sheathed) as shown in Fig. 2. Hot-rolled members H-350 × 175 × 7 × 11 and H-300 × 300 × 12 × 12 were used as beams and columns of the steel frame. The steel beam-column connections were assumed as rigid, semi-rigid and hinged respectively in the parametric analysis. Pushover and reversed cyclic analysis were conducted on 16 hybrid shear walls with various configurations. Figure 3 shows the reversed cyclic loading protocol. The displacement control scheme consisted of fully reversed cycles at drift ratios of 0.3%, 0.6%, 0.9%, 1.2%, 1.5%, 1.8%, 2.1%, 2.4%, 2.7% and 3.0%. To compare the influence of the different parameters on the performance of the hybrid shear walls, each parameter was studied while holding the other parameters constant. Dynamic time-history analysis was also conducted to investigate the effectiveness of the infill wall under seismic loads.

Material propertiees

Mild carbon structural steel Q235B, conforming to Chinese Standard GB 50017-2003, was used for the steel frame members. The strain-stress relationship of the steel was determined through tensile coupon test (as shown in Fig. 4) and served as input for the numerical modeling. For the infill wood shear walls, kiln dried No. 2 and better grade Spruce-Pine-Fir (SPF) 38 mm × 140 mm dimension lumber was used for the framing members. Performance rated 19/32 (APA panel grade) OSB panels, 1220 mm × 2440 mm in plane size and 14.7 mm in thickness, were used as the sheathing materials. The panels were attached to the framing members with 82-mm-long × 3.8-mm-diameter spiral nails spaced at 150 mm on panel edges and 300 mm in field.

Numerical model

A nonlinear finite element (FE) model (Fig. 5) was developed using ABAQUS software package by Li et al. [ 19] to study the lateral performance of the hybrid wall systems. In the model, the steel frame members were represented by 4-node bilinear plane stress elements (S4R) and the infill wall was represented by a user-defined nonlinear spring element which was implemented as a subroutine called UEL in ABAQUS. The load-drift characteristics of the infill walls were fully addressed by the nonlinear springs. To define the nonlinear spring, the pseudo nail wall model as shown in Fig. 6 was adopted. Because the behavior of a wood shear wall is mostly governed by the behavior of nail connections, the hysteretic response from a wall and that from a nail connection show great similarities in characteristics as strength and stiffness degradation as well as the pinching effect, except that the loads and deformations are of different magnitudes. Thus, the wood shear wall could be modeled by an analog depicted by a nail interacting with surrounding wood embedment medium. The load-displacement relationship of the nail connection could be determined through the HYST algorithm [ 20, 21]. However, to model the shear wall behavior, the required parameters in the HYST algorithm must be calibrated base on the load-drift curve of a wood shear wall. Once calibrated for this purpose, the algorithm represents the wall as a “pseudo nail” wall model. The pseudo nail wall model was proved to be computationally efficient and capable of modeling the behavior of wood shear walls under both static and dynamic loads. Furthermore, this model can adapt to any loading protocols calibrated implying an extrapolation from the protocol used for the fitting. The details of the pseudo nail wall model have been discussed elsewhere [ 18]. Using the pseudo nail wall model, Li and Lam [ 22] studied the asymmetric behavior of diagonal-braced walls, and Li et al. [ 23] studied the seismic reliability of diagonal-braced walls and structural-panel-sheathed walls.

In this study, the infill wood shear walls were modeled first by the WALL2D software (developed by Li et al. [ 24]). The hysteresis obtained from WALL2D were used to calibrate a “pseudo nail” shear wall model, which was only used to represent the hysteresis behavior of the wood shear wall in a simplified manner. The pair of pseudo nail springs was first connected to a wood portal frame as shown in Fig. 5. The beam-column joints and the column base joints of the portal frame were defined as pined connected. Thus, this wood portal frame had no lateral resistance. The wood beam was connected to the steel beam via bolted connections. The displacement of the nodes within the wood beam can be extrapolated by the deformation of the pseudo nail springs, and the displacement of the nodes were further used to calculate the shear force in each bolted connection. Detailed information for modeling the wood-steel connections was introduced by Li et al. [ 19].

Boundary conditions

Displacement-control loading was applied to the top of the wall, as shown in Fig. 2. The column base joint was modeled as fully rigid through restraining the degree-of-freedoms of bottom nodes of the steel column. The out-of-plane displacements of the hybrid shear wall were also restrained.

Model verification

The results from the reversed cyclic tests for timer-steel hybrid shear wall systems with a height-to-width ratio of 1.0, as presented in He et al. [ 7], were used to verify the FE model. Figure 7 shows a good agreement of load-displacement hysteresis of the hybrid shear wall system between the model prediction and the test results.

Analysis and discussions

The lateral performance of the timber-steel hybrid shear wall showed an integrated effect of the steel frame and the infill wood shear wall. The relative lateral infill-to-frame stiffness ratio has a major influence on the performance of the hybrid systems. In this study, the elastic stiffness of the wood shear wall was defined as the scant stiffness when the applied load reached 40% of the maximum load resisted by the specimen according to ASTM E2126 [ 25]. For the steel frame, the same definition was adopted. Thus, the lateral stiffness ratio (R) is defined as Eq. (1):

(1) R=k_{infill}/k_{bf},

where k_{infill}=\mathrm{0.4}{P}_{infill}/{\mathrm{\Delta }}_{infill} and k_{bf}=\mathrm{0.4}{P}_{bf}/{\mathrm{\Delta }}_{bf} , P_{infill} (kN) is the peak load resisted by the infill wood shear wall on its envelope; and {\mathrm{\Delta }}_{infill} (mm) is the drift of the infill wood shear wall at \mathrm{0.4}{P}_{infill} ; P_{bf} (kN) is the peak load resisted by the bare steel frame on its envelope; and {\mathrm{\Delta }}_{bf} (mm) is the drift of the bare steel frame at \mathrm{0.4}{P}_{bf} .

Pushover analysis was conducted on the 16 hybrid shear walls in compliance with ASTM E2126 [ 25]. Their lateral load resisting parameters are listed in Table 1.

General behavior

The lateral stiffness-drift curves were used to measure the general behavior of the infill wood shear walls when resisting lateral loads. As examples, the stiffness-drift curves of the hybrid walls No.5, 6, 9 and 10 are shown in Fig. 8. As the wall deformation increases, these curves can be approximately divided into three stages:

Stage 1: Small lateral load was applied on the hybrid shear wall system in this initial stage. In comparison with the bare steel frames, the infill walls considerably improved the lateral stiffness of the hybrid system. Initially, the infill wall experienced almost linear elastic shear deformations and carried most of the lateral load. With the increase of load, the nail connections on the edge of the sheathings began to behave nonlinear. The lateral load carried by the infill wall decreased as a result of the infill wall’s stiffness degradation, which led to a significant loss of the lateral stiffness of the hybrid wall system. It was also observed that, the hybrid system would experience a quicker loss of stiffness if a stiffer infill wall was used. However, the steel frame behaved elastically with a low stress level in this stage.

Stage 2: As the test proceeded, more damage occurred in the infill wood shear wall, which resulted in the further decrease of the relative lateral infill-to-frame stiffness ratio. More lateral force was carried by the steel frame. As the steel members still behaved almost elastically, the lateral stiffness of the hybrid system in this stage was governed by the behavior of steel frame. Therefore, the curves flattened till the yielding of the frame members. After the occurrence of the first yield points in the steel frame members at a drift ratio of 0.6% - 0.8%, the infill walls became less effective.

Stage 3: In the third stage, the steel frame response became nonlinear and the structure dissipated significant amount of energy. Failures of nail connections spread out in the infill wall and plastic hinges also formed in the steel frame members. All stiffness-drift curves began to converge to that of the bare frame, and the steel frame carried most of the lateral loads when the drift ratio exceeded 2%.

Relative lateral infill to frame stiffness

It was noted that the initial lateral stiffness and ultimate capacities of the hybrid shear walls increased when stronger infill walls were used. As shown in Table 1, the infill wall with R vaule of 2.68 brought 230% increase to the lateral stiffness of the bare steel frame. However, the infill wall with R value of 0.23 only brought 16% increase to the lateral stiffness of the bare steel frame. With double-sheathed infill walls, the ductility of the hybrid shear wall increased significantly by 33% - 47%. The effectiveness of the infill wall was directly related to the relative lateral infill-to-frame stiffness ratio. The percentage of the shear force resisted by the infill wall under P_design and P_peak with different R values was also obtained from the numerical analysis, as shown in Fig. 9. The infill wood shear walls resisted more shear force at the design load level P_design. The percentage of the shear force resisted by the infill wall under the ultimate load level P_peak decreased due to the degradation of the infill wall’s stiffness at large drift ratios. The infill wall could not make much contribution in increasing the lateral stiffness and load carrying capacity of the hybrid shear wall when the R value was smaller than 0.5. However, the infill wall had a considerable effect on the hybrid shear wall when the R value was between 0.5 and 2, which was in the scope of most practical situations. The trend of the curves also indicated the effectiveness of the infill wall would be similar if the R value was larger than 3.

Figure 10 shows the percentage of shear force carried by the infill wood shear walls at different drift ratios. As examples, four wall analysis (wall No.3, 9, 10 and 16), with R between 0.5 and 3.0 were illustrated. The infill wall carried a considerable portion of the lateral load within small drift ratios. Thereafter, the contribution from the infill walls decreased, and the curves start to flatten until they become almost horizontal beyond the drift ratio of 1.5%. Higher lateral load capacities were expected for hybrid systems with stronger infill walls with lager R values. A measure of the energy dissipated by each subsystem was obtained by evaluating the area of their respective hysteretic loops from the reversed cyclic analysis. Figure 11 shows the percentages of energy dissipated by the infill walls at different drift ratios. The hysteretic energy dissipated by the steel frame was small within the drift ratio of 0.5%, and beyond that, the energy dissipation was mainly provided by the steel frame. Obvious differences were observed among the curves with different R values, and the infill wall dissipated more energy in the hybrid system with larger R values. The infill wall with R value of 2.68 dissipated about 110% -150% more energy than that with R value of 0.54 when the drift ratio exceeded 1.0%. For walls No.10 and 16, the infill walls dissipated about 40% and 50%, respectively, of the total energy at the drift ratio of 2%, which was generally considered as the drift ratio corresponding to the life safety performance level. However, for walls No. 3 and 9 with smaller R values, less than 30% of the total energy was dissipated by the infill walls at the drift ratio of 2%. Therefore, in terms of energy dissipation, it seems that the R value should be no less than 1.0 to make the infill walls more effective.

Spacing of bolted connections between wood and steel

The bolted connections between wood and steel were important, as they transferred the shear force from the steel frame to the infill wall. Figure 12 shows the monotonic test results of the steel-wood connection, which was used as the input for the multilinear spring element in the FE model. Good ductility was observed in the tests. The lateral performance of timber-steel hybrid shear walls with different connection spacing was investigated using the FE models. Wall No.10, with the bolted connection spacing of 360 mm to connect the top plate of the infill wall to the steel beam, was used as the reference wall. Other bolt spacing, such as 720, 1440 and 2880 mm were also studied. As displacement-control loading was applied on the steel frames, the magnitudes of the shear force in the steel frames were quite similar among these cases. Therefore, changes in the bolted connection spacing mainly led to different infill wall behavior. Figure 13 shows the shear force resisted by the infill wall with different bolted connection spacing. The shear force resisted by the infill wall dropped obviously as the connection spacing increased, which also led to lower lateral load capacity of the hybrid system. The lateral load resisted by the infill wall dropped suddenly after the failure of bolted connections, which were observed in cases with larger bolt spacing (1440 and 2880 mm). The results indicated the effectiveness of the infill wall was closely related to the connections between wood and steel. To ensure the effectiveness of the infill wall, the connections must be capable of transferring the shear force equal to the ultimate load capacity of the infill wall.

Rotational stiffness of steel frame joints

The lateral load resisting capacity of the hybrid systems with semi-rigid and hinged steel beam-column joints were also studied. The semi-rigid joint stiffness was estimated using a simplified design equation introduced by Steenhuis et al. [ 26] based on Eurocode 3 EN 1993-1-8:

(2) S_{j,ini}={\displaystyle \frac{E{z}^{\mathrm{2}}{t}_{\mathrm{f}}}{k_x}},

where E = Young’s modulus of steel (N/mm²); z = lever arm, in this particular sample case, which was assumed as bolted extended end-plate joint, equals to the distance from the center of the compression flange to the bolt row in tension (mm); t_f = steel column flange thickness (mm); k_x = coefficient dependent on the layout of the joint, for bolted extended end-plate joint, equals to 13.0.

The value of the semi-rigid joint stiffness applied in the parametric studies was calculated as 2.33 × 10¹⁰ N·mm/rad, and in addition, the hinged joint (with S_j,ini = 0) was also studied. The hybrid walls’ height was 3.6 m and double-sheathed infill walls were used. The load-displacement curves of the hybrid systems with different steel frame joint stiffness are shown in Fig. 14. It is shown that the application of stiffer steel frame joints resulted in larger initial stiffness and ultimate load carrying capacity of the hybrid system. However, the infill wall was more effective in the hybrid systems with weaker steel frame joints. The percentage of shear force carried by the infill wall increased about 40% when hinged joints instead of rigid joint were used.

Aspect ratio of the wall

It was noted that the aspect ratio of the wall had significant influence on the performance of the hybrid shear walls. As listed in Table 1, for the 4.8 m high walls, the ultimate lateral load capacities were approximately 20% - 27% lower than those of the 3.6 m high walls. The stiffness of the 4.8 m high walls was about 34% - 48% lower than that of the 3.6 m high walls. Similar results could be obtained from the comparison between the 3.6 m high walls and the 2.4 m high walls. For the higher walls, the same lateral load will lead to bigger overturning moments and uplifting forces than the lower walls. Therefore, lower load-carrying capacity and lower shear wall stiffness were obtained. The lateral stiffness of the bare steel frame remained almost unchanged with different wall lengths. However, the lateral stiffness of the infill wood shear wall increased in proportion to its length, which resulted in the change of the relative lateral infill-to-frame stiffness ratio (R). In this manner, wall length had an obvious influence on the behaviors of the hybrid shear walls. The infill wall will carry more lateral load and dissipate more energy in the hybrid system with larger infill wall lengths.

Dynamic analysis

The infill walls were quite effective in resisting lateral loads under pushover and cyclic loads. In this study, dynamic time-history analysis was also conducted to investigate the seismic response of the timber-steel hybrid shear walls, as well as the effectiveness of the infill walls under earthquakes. The validity of the pseudo nail wall model in dynamic analysis was confirmed by previous studies [ 18, 22, 23], and the viscous damping ratio of 2% was assumed in this FE model since most of the energy was dissipated by the non-recoverable nonlinear deformations in the hybrid system. It was assumed the annual arrival rate of earthquakes is 0.2, and the peak ground acceleration (PGA) at the site has a mean value of 0.25 g, with the coefficient of variation (COV) of 0.55 and following a lognormal distribution. Therefore, this site was characterized by a PGA = 0.77 g with a return period of 475 years, and a PGA = 0.43 g for a return period of 50 years. The structural applied mass was assumed as 4000 kg/m. Three earthquake records as listed in Table 2 were scaled to these peak ground accelerations, and served as the input ground motions for the dynamic time-history analysis. However, the earthquake ground motion records could be selected according to a specific site and scaled to the design spectra. The sample earthquake ground motion records used in this section were aimed to illustrate the effectiveness of the infill wall in a more common way.

Hybrid shear wall No.10 and its corresponding bare steel frame were used in the case study. Figure 15 shows the response from the analysis under the El Centro record. The peak drift of the hybrid shear wall under the earthquake with a return period of 50 years was 7.96mm, while that of the bare steel frame was 26.50 mm. Similarly, the peak drift of the hybrid system under the earthquake with a return period of 475 years was 23.35 mm, while that of the bare steel frame was 45.67mm. Compared with the bare steel frame, the infill wall showed a significant contribution on reducing the drift of the hybrid system under seismic load. The results of the dynamic analysis are summarized in Table 3. It was noted when the infill wood shear walls were used, the peak drift was reduced by 70% - 85% under earthquakes with a return period of 50 years; and the peak drift was reduced by 49% - 67% under earthquakes with a return period of 475 years. Figure 16 shows the percentage of base shear resisted by the steel frame obtained from the dynamic analysis under the El Centro record. The base shear in the steel frame decreased significantly when an infill wall was used, which indicated the infill wall resisted a noticeable part of the base shear in the hybrid system. However, the strength / stiffness degradation of the infill walls under large drift ratios made them less effective in resisting lateral loads, which explained why the infill walls were more active in smaller earthquakes. Different lateral load resisting mechanisms in the hybrid system were observed through the dynamic analysis. The infill wall resisted most of the base shear in small earthquakes, and brought an obvious increase to the lateral stiffness of the hybrid system, which largely reduced the drift. This helps a lot for the hybrid systems to reduce the amount of non-structural damage and satisfy the serviceability performance criteria in minor earthquakes. In major earthquakes, the infill wall was able to carry a certain part of the base shear, and at the same time, dissipated a lot of energy through nonlinear deformations. This was ideal as the steel frame and the infill wall showed a complementary effect and provided robustness to the hybrid system.

Conclusions

The timber-steel hybrid shear wall system provides a viable alternative solution to serve as the lateral load resisting system in multi-story timber hybrid buildings. To investigate the load resisting mechanism of such hybrid shear wall systems, FE modeling was used to study the infill-frame interactions in the hybrid shear walls with various structural configurations.

The results showed the effectiveness of the infill wall was directly related to the lateral infill-to-frame stiffness ratio R. It was found that the infill wall had a considerable effect on the hybrid shear wall when R was larger than 0.5. However, in terms of energy dissipation, it was found that the R value should be no less than 1.0 in order to make the infill walls structurally more effective. To ensure the effectiveness of the infill wall, the steel-wood connections must be strong enough to transfer the shear force between the wood infill wall and the steel frame. The infill wall played a more important role in the hybrid systems with relatively weaker steel frame joints, and the wall height and length both had a significant effect on the performance of the hybrid shear wall systems. The initial stiffness and the lateral load carrying capacity decreased when the wall height increased for a given wall length, and the infill wall carried more lateral loads and dissipated more energy in the hybrid systems with larger wall lengths.

Different lateral load resisting mechanisms were observed in the dynamic time-history analysis. The infill wall resisted most of the base shear in minor earthquakes. In major earthquakes, the infill wall was able to carry a significant part of the base shear, and at the same time, dissipated a lot of energy through nonlinear deformations. The steel and the wood subsystems showed a complementary hybrid effect and provided robustness to the hybrid shear wall system.

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