- Original article
- Open Access
Seismic performance of post and beam timber buildings I: model development and verification
© The Japan Wood Research Society 2011
- Received: 24 March 2011
- Accepted: 31 August 2011
- Published: 17 December 2011
This paper presents a structural model called “PB3D” to perform nonlinear time history analyses of post and beam timber buildings under seismic loads. The model treats the three-dimensional structure as an assembly of roof/floor diaphragms and wall subsystems. The roof/floor diaphragms are modeled by beam elements and diagonal brace elements in order to take into account the in-plane stiffness. The wall system consists of vertical beam elements, for wall posts, as well as nonlinear shear springs to consider the contribution of diagonal wall bracing members or sheathing panels. The hysteretic characteristics of the shear springs are represented by a simplified, mechanics-based model named a “pseudo-nail”. Standard finite element procedure is used to construct the system’s equation of motion, which is solved by Newmark’s integration. The model was verified against shake test results of a three-story post and beam building subjected to strong ground motions scaled to the 1995 Kobe earthquake. Model predictions agreed very well with the test results in terms of base shear forces and inter-story drift responses. This model provides a robust and efficient tool to study the seismic behavior of post and beam timber buildings.
- Seismic performance
- Timber buildings
- Nonlinear analysis
- Post and beam construction
The 1995 Hyogo-ken Nanbu (Kobe) earthquake raised a lot of concerns about the seismic safety of traditional post and beam (P&B) timber construction in Japan. The poor performance of the severely damaged P&B houses can be attributed to some structural design issues such as heavy tile roofs, weak first stories, irregular shear wall layout, and inadequate provision of inter-story and foundation anchorage. Poor maintenance was also a culprit . Since the Kobe earthquake, a lot of efforts have been directed to study the seismic behavior of the P&B buildings and the Building Standard Law (BSL) in Japan has also been upgraded. Similar to the wood-frame construction in North America, P&B timber buildings in Japan are also box-type structures consisting of two-dimensional horizontal and vertical assemblies such as walls, floors, ceilings and roofs. Nail fasteners are also extensively used to attach sheathing panels to timber frames. However, the timber frames of the P&B buildings are usually constructed by members with relatively large cross sections, for example, 105 mm × 105 mm for wall posts and 105 mm × 210 mm for floor/roof beams. A special feature of the P&B construction is the extensive use of traditional mortise-and-tenon joinery reinforced by metal hardware. Thus, it is very challenging to develop detailed finite element (FE) models to simulate the seismic response of such complicated building systems.
Performance-based seismic design of wood buildings requires reliable and efficient numerical models to perform nonlinear time history analyses. Compared with the state-of-art numerical models for steel or concrete structures, very limited numerical models have been developed to study wood structures. A simple model to study the seismic responses of a wood building might be a multidegree-of-freedom (MDOF) model in which each floor or roof is lumped into a structural mass point and nonlinear shear springs are used to connect floors and roof. Only horizontal degrees of freedom (DOF) are considered. The characteristics of each shear spring are calibrated by the total contribution of the shear walls at each story. Agawa and Miyazawa  used such a MDOF model to study existing residential buildings in Japan. Although MDOF models are very computationally efficient for nonlinear time history analyses, they are highly simplified and cannot consider torsional effects and vertical effects in the buildings. Researchers also developed models which are able to consider the hysteresis of individual shear walls. Folz and Filiatrault  reported a benchmark modeling study of a two-story building tested in the CUREE-Caltech wood-frame project. Blind predictions with the assumption of rigid roof/roof diaphragms were reported. One of models was built in the RUAUMOKO program  and two were built in DRAIN-2DX and DRAIN-3D program . Recently, van de Lindt et al.  reported a model called SAPWood to perform time history analyses of wood-frame buildings. In this model, the assumption of rigid floor/roof diaphragms was also used. The model consists of nonlinear shear springs for shear walls and non-symmetric linear springs to provide vertical restraints for the buildings. The assumption of rigid roof/floor diaphragms can greatly simplify the analyses since only three DOFs (two translational and one rotational) need to be considered for each floor or roof. The model accuracy greatly relies on the level of the accuracy of shear wall hystereses implemented into the building model.
Detailed FE models have also been developed to model wood buildings. He et al.  developed a sophisticated model called LightFrame3D for wood-frame buildings. In this model, a wood-frame building was modeled as an assembly of generic super-elements consisting of framing elements, panel elements and nail connection lines. Nakagawa and Ohta [8, 9] and Nakagawa et al.  developed a model to simulate the collapsing process of traditional Japanese wood houses under severe ground shaking using the extended distinct element method since the authors believe that it is difficult to simulate such an ultimate failure process using common finite element methods. This model provides a very insightful tool to study the relationship between seismic intensity and collapse limit of timber buildings. Commercial structural analysis software has also been used to model wood buildings, although most of them might have limited ability to represent the hysteretic characteristics of wood connections/walls, such as strength/stiffness degradation and pinching effect. Masalam et al.  developed a dynamic model in SAP2000 for a three-story wood-frame building tested in the CUREE-Caltech wood-frame project. Collins et al.  developed a static model in ANSYS for a one-story wood-frame building. Lam et al.  also developed a static model in ANSYS for a one-story P&B building. Xu and Dolan  developed a dynamic FE model in ABAQUS to study the seismic behavior of a two-story wood-frame building in which the modified Bouc-Wen-Barber-Wen (BWBN) model was integrated to represent the hystereses of shear walls.
Typically, detailed FE models are very computational intensive to perform nonlinear time history analyses of complicated wood systems although they are more comprehensive and more accurate to predict structural responses. Therefore, they may not be suitable for seismic reliability evaluations which require a robust and efficient computer model to run a large number of simulations, considering the uncertainties in ground motions and structural capacity. In this study, a computer model called “PB3D” is developed to model the seismic behavior of the P&B timber buildings. This model aims to capture the global characteristics in the seismic response of the buildings with reasonable accuracy and computational efficiency by incorporating simplified structural component models for the roof/floor diaphragms and shear walls. For model verification purpose, shake table test results of a full-scale three-story building, excited by strong ground motions, were used.
Observations from past earthquake experiences and shake table tests show that when wood buildings are excited by strong ground motions, roof and floor diaphragms usually do not experience high nonlinearity. Severe structural damage and most of the input energy dissipation take place in the wall systems. Therefore, in the “PB3D” model, roof/floor components are modeled by linear elastic 3D beam and truss elements. The roof and floor beams with large cross sections are modeled by the beam elements with each node having three translational DOFs and three rotational DOFs. Other components such as joists/rafters, sheathing panels and nail connections are condensed and simply modeled by diagonal truss elements with each node having three translational DOFs. The connections between the beam elements and the truss elements are simply assumed to be rigid. The cross sections of truss elements are calibrated to match the in-plane stiffness of the floor/roof diaphragms in actual buildings. The element stiffness matrices can then be calculated and assembled into a global system stiffness matrix.
Formulation of system equation
In the “PB3D” model, for computation efficiency, the stiffness matrices for the linear elastic elements are established in a pre-process procedure. Thus, during iterations, only the stiffness matrices of the nonlinear elements need to be updated for each time step. Newton–Raphson iterations are used to solve for the incremental nodal displacement vector. Both energy and force convergence criteria are used to assure a converged solution.
“Pseudo-nail” model parameters in three-story building
0.91 m X-brace + OSB + GWB
0.91 m X-brace + GWB
0.91 m Doubl. GWB
1.82 m Doubl. GWB
0.91 m OSB + GWB
1.82 m OSB + GWB
Q 0 (kN/mm)
Q 1 (kN/mm2)
D max (mm)
In this study, the building model did not consider the contributions from exterior wall claddings (FMQ5MIV siding panels manufactured by AT-WALL) to the building lateral resistance because these claddings were simply hanging on the exterior walls by metal clips and it is believed that their contributions to the shear wall resistance are very small compared with those from the OSB sheathings, cross braces and GWBs. It should be noted that the building model also did not consider the contributions from the walls with openings. One reason is that this building had a limited number of walls with window/door openings. For example, using the opening reduction factor K o stipulated by the guideline from Seismic Evaluation and Retrofit for Wood Houses by Japan Building Disaster Prevention Association , the calculated effective length of walls with openings in the first story was 3.185 m along the x direction and 4.55 m along the y direction, approximately 4.4 and 5.8% of the total effective length of full-height walls with OSB sheathing, cross braces, and GWBs along the corresponding direction in the first story. Therefore, the lateral resistance of this building was mainly governed by the full-height shear walls. Of course, the model predictions of the seismic response of this building would be more accurate should the actual shear resistances of these walls with openings be available and considered by the model as well. In other situations, if a building has significant amount of walls with openings or the wall finishing materials have significant contributions to shear wall resistance, the seismic simulations should take into account their influence on the seismic response of the entire building.
Model predicted peak inter-story drifts versus test results
Shake table test
Peak inter-story drift (mm)
150% Kobe JMA
200% Kobe JMA
This paper presents a computer model called “PB3D” to simulate the seismic response of post and beam wood buildings commonly used in Japan. The roof/floor diaphragms are modeled by beam elements and truss elements considering the in-plane stiffness of diaphragms. The shear walls are modeled by vertical beam elements as wall posts and nonlinear shear springs. The hysteresis of the nonlinear shear springs is represented by a mechanics-based algorithm called a “pseudo-nail” model which can be calibrated by shear wall test results or detailed wall models. Model predictions of a full-scale three-story building were compared against the shake table test results. The predictions agreed very well with the test results, especially in terms of the base shear forces and the first story inter-story drift responses. The torsional effect was also captured very well by the model.
For seismic reliability analysis of timber buildings, a major computational demand is to establish a seismic response database, considering different seismic events and structural characteristics. The “PB3D” model presented in this paper provides a robust and efficient tool to estimate the seismic response of the post and beam timber buildings, facilitating the development of reliability-based assessment of the seismic safety of such building systems.
Research grant from Natural Sciences and Engineering Research Council (NSERC) of Canada and Coast Forest Products Association of British Columbia is greatly acknowledged. The collaboration of Mr. Minoru Okabe from the Centre for Better Living of Japan is also acknowledged for providing the technical information on shear walls.
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