Shear stiffness of cross laminated timber diaphragms - A study of the influence of connection and member stiffness

Abstract: Since ancient times, buildings have been constructed with the use of timber and during the modern era, new types of timber products have been developed. Today, more constructions, especially residential buildings are being built with timber as the main load-bearing material. By utilizing timber in buildings, the amount of greenhouse gases emitted in production decreases compared to other common materials. The increase in timber buildings is partly due to the implementation of Cross Laminated Timber (CLT) during the late 20th century. The composition of CLT with crosswise glued boards minimizes the orthotropic behaviour of timber and has a high load-bearing capacity compared to its low self-weight. It is a strong and stiff material useful in diaphragms both in floor- and wall constructions for stabilizing against lateral forces. Due to the crosswise composition, the stiffness varies depending on load direction and fibre orientation with the highest stiffness and strength being in the longitudinal direction of the element. Floor- and wall segments in buildings consisting of CLT-panels are comprised of several panels, connected with each other. The performance of the structure is therefore dependent on the parameters in the connection as well as the element itself. When utilizing CLT as a floor structure, there are several types of connections which could be applied. For the purpose of stabilizing against lateral forces, butt joints, lap joints and spline connections are the most common used today. They differ in appearance, stiffness and strength but, all of them fasten elements with the use of screws. The connection has to handle forces in between elements due to in-plane bending and shear deformation of the floor diaphragm. In this work, analytical and numerical modeling and calculations are performed. The shear stiffness for the different types of connections studied is determined, which includes assumptions of inclination angle, screw type, length and diameter of the screw. Subsequent calculations are made by making use of a finite element structural software, RFEM. The model, containing seven interconnected CLT panels is created in the software with the panels used being modeled according to the plate theory of MindlinReissner. Loads are introduced followed by implementing the laminate add-on in the software, which is crucial as it gives the opportunity to analyze materials composed of layers with different properties. Two behaviours are studied, each with the variation of element stiffness and connection shear stiffness through spring constants. Initially, the displacements are analysed for a simply supported structure. Then, additional supports are modeled while studying the effects of force distribution from the same parameters as the previous study. Extracting results indicates a higher shear stiffness for equal number of screws is achieved for implementing butt joints with inclined screws in both the vertical and horizontal plane. The same stiffness can be obtained for the other connections, if more screws are installed per metre. I Displacements in the lateral direction of the floor are affected more by the variation of the shear stiffness in the connections compared to the variation of CLT panel stiffness. A decreasing connection stiffness results in a exponentially increasing displacement. However, the results indicate that after a certain limit in stiffness for both parameters, no major variation of displacement takes place. To reduce the magnitude of displacements, a shear stiffness of at least 4 N/mm2 is recommended whilst not having having a reduction factor for the in-plane shear stiffness of the panel ks, which is smaller than 0.3-0-4. From the results, the distribution of reaction forces depending on the amount of supports is a bit more unclear. However, more supports have a positive effect since it results in distributing the load more evenly with less load on a single support. The parameter contributing to the most even distribution is the shear stiffness in the connection. A higher shear stiffness means less variation of the amount of force that is distributed on the supports. However, more supports tend to have a larger difference between maximum and minimum values when varying the stiffness parameters compared to when varying the reduction factor for the in-plane shear stiffness of the panel ks. A high element stiffness in a CLT panel combined with low shear stiffness in the connection between panels, results in more concentrated loads on the middle supports. Different connections require different amount of screws per metre to reach a sufficient stiffness which in this project was set as 4 N/mm2 for the shear stiffness and not reduce the stiffness of the CLT panel by more than 60-70% corresponding to a reduction factor, ks for the CLT panel, that is equal or higher than a factor of 0.3-0.4 to obtain small lateral displacement in the floor. The shear stiffness in the connection affects the displacement more than the element stiffness and the distribution of forces for 4 or less supports are more affected by the shear stiffness as the difference is larger when varying the shear stiffness in the connections.