This thesis studies the behaviour of diaphragms in multi-storey timber buildings by providing methods for the estimation of the diaphragm force demand, developing an Equivalent Truss Method for the analysis of timber diaphragms, and experimentally investigating the effects of displacement incompatibilities between the diaphragm and the lateral load resisting system and developing methods for their mitigation. The need to better understand the behaviour of diaphragms in timber buildings was highlighted by the recent 2010-2011 Canterbury Earthquake series, where a number of diaphragms in traditional concrete buildings performed poorly, compromising the lateral load resistance of the structure. Although shortcomings in the estimation of force demand, and in the analysis and design of concrete floor diaphragms have already been partially addressed by other researchers, the behaviour of diaphragms in modern multi-storey timber buildings in general, and in low damage Pres-Lam buildings (consisting of post-tensioned timber members) in particular is still unknown. The recent demand of mid-rise commercial timber buildings of ten storeys and beyond has further highlighted the lack of appropriate methods to analyse timber diaphragms with irregular floor geometries and large spans made of both light timber framing and massive timber panels. Due to the lower stiffness of timber lateral load resisting systems, compared with traditional construction materials, and the addition of in-plane flexible diaphragms, the effect of higher modes on the global dynamic behaviour of a structure becomes more critical. The results from a parametric non-linear time-history analysis on a series of timber frame and wall structures showed increased storey shear and moment demands even for four storey structures when compared to simplistic equivalent static analysis. This effect could successfully be predicted with methods available in literature. The presence of diaphragm flexibility increased diaphragm inter-storey drifts and the peak diaphragm demand in stiff wall structures, but had less influence on the storey shears and moments. Diaphragm force demands proved to be significantly higher than the forces derived from equivalent static analysis, leading to potentially unsafe designs. It is suggested to design all diaphragms for the same peak demand; a simplified approach to estimate these diaphragm forces is proposed for both frame and wall structures. Modern architecture often requires complex floor geometries with long spans leading to stress concentrations, high force demands and potentially large deformations in the diaphragms. There is a lack of guidance and regulation regarding the analysis and design of timber diaphragms and a practical alternative to the simplistic equivalent deep beam analysis or costly finite element modelling is required. An Equivalent Truss Method for the analysis of both light timber framed and massive timber diaphragms is proposed, based on analytical formulations and verified against finite element models. With this method the panel unit shear forces (shear flow) and therefore the fastener demand, chord forces and reaction forces can be evaluated. Because the panel stiffness and fastener stiffness are accounted for, diaphragm deflection, torsional effects and transfer forces can also be assessed. The proposed analysis method is intuitive and can be used with basic analysis software. If required, it can easily be adapted for the use with diaphragms working in the non-linear range. Damage to floor diaphragms resulting from displacement incompatibilities due to frame elongation or out-of plane deformation of walls can compromise the transfer of inertial forces to the lateral load resisting system as well as the stability of other structural elements. Two post-tensioned timber frame structures under quasi-static cyclic and dynamic load, respectively, were tested with different diaphragm panel layouts and connections investigating their ability to accommodate frame elongations. Additionally, a post-tensioned timber wall was loaded under horizontal cyclic loads through two pairs of collector beams. Several different connection details between the wall and the beams were tested, and no damage to the collector beams or connections was observed in any of the tests. To evaluate the increased strength and stiffness due to the wall-beam interaction an analytical procedure is presented. Finally, a timber staircase core was tested under bi-directional loading. Different connection details were used to study the effect of displacement incompatibilities between the orthogonal collector beams. These experiments showed that floor damage due to displacement incompatibilities can be prevented, even with high levels of lateral drift, by the flexibility of well-designed connections and the flexibility of the timber elements. It can be concluded that the flexibility of timber members and the flexibility of their connections play a major role in the behaviour of timber buildings in general and of diaphragms specifically under seismic loads. The increased flexibility enhances higher mode effects and alters the diaphragm force demand. Simple methods are provided to account for this effect on the storey shear, moment and drift demands as well as the diaphragm force demands. The analysis of light timber framing and massive timber diaphragms can be successfully analysed with an Equivalent Truss Method, which is calibrated by accounting for the panel shear and fastener stiffnesses. Finally, displacement incompatibilities in frame and wall structures can be accommodated by the flexibilities of the diaphragm panels and relative connections. A design recommendations chapter summarizes all findings and allows a designer to estimate diaphragm forces, to analyse the force path in timber diaphragms and to detail the connections to allow for displacement incompatibilities in multi-storey timber buildings.
According to TS 1170.5, designing a building to satisfy code-prescribed criteria (e.g., drift limit, member safety, P-Δ stability) at the ultimate limit state and relying on the inherent margins within the design code would lead to an acceptable mean annual frequency of collapse (λ꜀) in the range of 10−⁴ to 10−⁵. Modern performance objectives, such as λ꜀ and expected annual loss (EAL), are not explicitly considered. Although buckling-restrained braced frame (BRBF) buildings were widely adopted as lateral load-resisting systems for office and car park buildings in the Christchurch rebuild following the Canterbury earthquakes in New Zealand, there are currently no official guidelines for their design. The primary focus of this study is to develop a risk-targeted design framework for BRBF buildings that can achieve the performance objectives desired by stakeholders. To this extent, key factors influencing λ꜀ and EAL of BRBF buildings are identified. These factors include gusset plate design, number of storeys, design drift limit, BRBF beam-column connection, brace configuration, brace angle, brace material grade, and analysis method (equivalent lateral force vs. modal response spectrum). A novel 3D BRBF modelling approach capable of simulating out-of-plane buckling failure of buckling-restrained brace (BRB) gusset plates is developed. Prior experimental studies on sub-assemblies conducted elsewhere have demonstrated that gusset plates and end zones may buckle out of plane prematurely, before BRBs reach their maximum axial compression load carrying capacity. Current 2D BRBF macro models, typically used in research, cannot simulate this failure mode. A conventional 2D BRBF model underestimates the λ꜀ of a case-study 4-storey super-X configured steel BRBF building (designed according to NZS-3404) by a factor of two compared to the estimate from the proposed 3D model. These findings suggest that the current NZS-3404 gusset plate design method may undersize gusset plates and that using a 2D BRBF model in this case can significantly underestimate λ꜀. Three improved alternative gusset plate design methods that are easy to implement in practice are identified from the literature. Gusset plates in two case-study 4-storey steel BRBF buildings with super-X and diagonal configurations are designed using both the NZS-3404 method and alternative methods. All three alternative design methods are found to be conservative, resulting in an almost three-fold lower λ꜀ for both case-study BRBF buildings compared to those designed using the NZS-3404 method. Analysis results indicate that (i) bidirectional interaction has no significant effect on gusset plate buckling and (ii) mid-span gusset plates are more susceptible to buckling than corner gusset plates. A framework for seismic loss assessment using incremental dynamic analysis (IDA), called loss-oriented hazard-consistent incremental dynamic analysis (LOHC-IDA), is developed. IDA can be conducted with a generic record set, eliminating the arduous site-specific record selection required to conduct multiple stripe analysis (MSA). Traditional IDA, however, is limited in producing hazard-consistent estimates of engineering demand parameters (EDPs), which LOHC-IDA overcomes. LOHC-IDA improves upon existing methods by: (i) incorporating correlations among engineering demand parameters across intensity levels and (ii) using peak ground acceleration (PGA) to predict peak floor acceleration (PFA). For two case-study steel BRBF buildings, LOHC-IDA estimates the EAL and loss distributions conditioned on the intensity level that closely match the MSA results, with an average absolute error of 5%. The influence of factors beyond gusset plate design on the λ꜀ and EAL of 26 case-study steel BRBF buildings (designed in accordance with TS 1170.5) is examined. Hazard-consistent λ꜀ and EAL for these buildings are estimated using the FEMA P-58 loss and risk assessment framework. Among the 26 case-study buildings, 23 satisfy the maximum code-specified λ꜀ limit of 10−⁴. The EAL, normalised by the total building replacement cost, is highest for 2-storey BRBFs (0.22% on average), followed by 4-storey BRBFs (0.16% on average) and 8-storey BRBFs (0.11% on average). Reducing the design drift limit has the most significant effect on lowering λ꜀ (all BRBF designs were drift governed), followed by transitioning from pinned to moment-resisting beam-column connections, reducing the brace angle, and increasing brace strength. BRBF buildings designed using the equivalent lateral force method, on average, have a lower λ꜀ compared to those designed using the modal response spectrum method. Diagonally configured BRBFs exhibit the lowest λ꜀, followed by super- X and chevron configured BRBFs. Most design variables, apart from drift limit and beam-column connection, have limited influence on EAL. A simple method for EDP-targeted design of steel BRBF buildings is proposed. For this purpose, linear regression and CatBoost machine learning models are developed to predict steel BRBF building EDPs using peak storey drift ratio (PSDR) and PFA estimates from the 26 case-study buildings at intensity levels ranging from 80% to 0.5% probability of exceedance in 50 years. The R²ₐₔⱼ of these models is around 0.98, while the average prediction error is less than 10%. Fundamental period (T₁), total building height (Hₜ), and pseudospectral acceleration at T₁, denoted as Sₐ(T₁), are selected as the features to predict PSDR, while T₁, Hₜ, and PGA are the features selected to predict PFA. The EDP-targeted design has three steps: (i) for a given Hₜ value, the PSDR prediction model is used to identify a suitable T₁ that can achieve a desired PSDR target at the design intensity, (ii) a force-based design is then conducted iteratively to achieve the target T₁ by using an appropriate ductility factor and design drift limit, and (iii) based on the T₁ in the final design iteration, the PFA demand estimated by the PFA prediction models is used as a conservative input for the design of acceleration-sensitive non-structural elements. An equation to predict λ꜀ at the design stage is proposed for collapse risk-targeted seismic design of buildings. This equation comprises three principal components: reserve building strength, a proxy for effective structural stiffness, and reserve building deformation capacity. This equation is calibrated for the collapse risk-targeted design of BRBF buildings in New Zealand using results from 26 case-study BRBF buildings. The validity of this equation is demonstrated with three design verification examples designed to specific λ꜀ targets. Considering λ꜀ from hazard-consistent incremental dynamic analysis as the benchmark, the mean absolute percentage error in the design-stage prediction of λ꜀ of the verification buildings is approximately 10%.
