Calculation Method for the Lateral Deflection of Timber Modular Buildings

Abstract

In the Netherlands, there is a significant housing demand. The Dutch government aims to construct 100,000 houses per year, which presents an enormous challenge. To address this demand and simultaneously tackle the challenge of creating a more sustainable construction industry, timber modular construction emerges as a potential solution. Compared to traditional construction methods, timber modular buildings offer several advantages: lower weight, more sustainable, faster construction, reduced waste, greater efficiency, and higher quality. Currently, most modular components can be prefabricated off-site, except for the stability system. Traditionally, this system involves a concrete core
or a steel frame. To eliminate their need, self-supporting modules can be applied, making the building purely modular and more sustainable. Within self-supporting modules, stability is a critical aspect. While incorporating stability elements along the longitudinal side of the module poses no issue, the main challenge lies in the limited available length for stability walls in the transverse direction. Also, the shear wall located in the module conflicts with the preferred open floor area. The design of the module, and in particular the shear wall, has a significant influence on the transverse deflection. Calculating the deflection is crucial to fulfil the requirements for maximum displacements. Therefore, the
main research question of this thesis is: Is it possible to predict the lateral deflection in the transverse direction of multi-storey timber modular buildings with a calculation method based on proposed equations?. The goal of this thesis is to propose a calculation method that can be used in the design phase, which will give insight in the effect of design choices on the lateral deflection of multi-storey modular buildings.

The approach to answer the main research question consists of several steps. The first step was a literature study that was conducted on modular construction, lateral stability and deformations of modular buildings. Knowledge on the structural design of timber modules and cross-laminated timber was obtained. Also, the deformation mechanisms of multi-storey modular buildings were investigated. The second step was analysing the deformation of individual modules. A general module design and four configurations were established and the numerical modelling method was investigated and validated.
Hereafter, the equations to calculate the deformation of individual modules in the transverse direction were proposed for the four module configurations. Based on the numerical model, the equations for the horizontal displacement and rotation were established. Additionally, the formulas were extended to incorporate various design options like connection design, shear wall thickness and shear wall position. The proposed equations were integrated in a calculation method that predicts the lateral deflection of multi-storey modular buildings in transverse direction. Hereby only the deformation of the modules was taken into account and not those from the inter-module connections. The cumulative effect due to rotation of lower modules is added to the individual module displacement to find the total deflection.

The results showed that the proposed equations accurately calculate the deformation of the individual modules. With differences below 10%, the formulas are able to calculate the horizontal displacement and rotation for various designs. The calculation method was validated with two examples. Example 1 was a four-storey, four-span building where at the top a maximum error of 8.7% was found. Example 2 was an eight-storey, eight-span building where the proposed calculation method resulted in a maximum error of 9.5%, which was on the lowest storey. At the top, a difference of 2.6% was found. Both
errors were lower than 10% and at the safe side, meaning that the calculation method provides accurate and safe results. A case study was performed to verify the practical applicability of the method. The lateral deflection results showed significant differences (45%), which can be assigned to limitations of the calculation method. These limitations ensure the method is not suited for detailed calculations that are necessary in later design phases. For these detailed calculations, a (parametric) finite element model
would be more suited. However, the calculation method offers a solution for early design stages, as it provides quick and easy insight into effects of certain design choices on the building’s lateral deflection.