Cross laminated timber (CLT), as a structural plate-like timber product, has been established as a load bearing product for walls, floor and roof elements. In a bending situation due to the transverse shear flexibility of the crossing layers, the warping of the cross section follows a zigzag pattern which should be considered in the calculation model. The Refined Zigzag Theory (RZT) can fulfill this requirement in a very simple and efficient way. The RZT, founded in 2007 by A. Tessler (NASA Langley Research Center), M. Di Sciuva and M. Gherlone (Politecnico Torino) is a very robust and accurate analysis tool, which can handle the typical zigag warping of the cross section by introducing only one additional kinematic degree of freedom in case of plane beams and two more in case of biaxial bending of plates. Thus, the RZT-kinematics is able to reflect the specific and local stress behaviour near concentrated loads in combination with a warping constraint, while most other theories do not. A comparison is made with different methods of calculation, as the modified Gamma-method, the Shear Analogy method (SA) and the First Order Shear Deformation Theory (FSDT). For a test example of a two-span continuous beam, an error estimation concerning the maximum bending stress is presented depending on the slenderness L/h and the width of contact area at the intermediate support. A stability investigation shows that FSDT provides sufficiently accurate results if the ratio of bending and shear stiffness is in a range as stated in the test example. It is shown that by a simple modification in the determination of the zigzag function, the scope can be extended to beams with arbitrary non-rectangular cross section. This generalization step considerably improves the possibilities for the application of RZT. Furthermore, beam structures with interlayer slip can easily be treated. So the RZT is very well suited to analyze all kinds, of shear-elastic structural element like CLT-plate, timber-concrete composite structure or doweled beam in an accurate and unified way.
We model the dynamic behavior of laminated curved beams on the assumption that the different layers of such structures are perfectly bonded at the interface and can show different flexural rotations from one another. We formulate a mechanical theory and a finite element model accounting for bending, shear, warping and extensional deformation modes, as well as radial, tangential and rotary inertias. The main novelty of the proposed theory consists of a generalization of layer-wise displacement approaches available in literature to the dynamics of beams with finite curvature. The work includes some numerical results related to the free vibration of laminated arches and showing different support conditions and aspect ratios to establish comparisons with different theories in the literature. We observe that an accurate mechanical modeling of curved laminated beams is crucial for correct estimation of the eigenfrequencies and eigenmodes of such structures within a 1D framework.
The paper examines the behaviour of structural timber members subjected to axial compression or combined axial compression and bending. Based on experimental and numerical investigations, the accuracy of the existing approach in Eurocode 5 for the design of timber members subjected to axial compression or combined axial compression and bending is assessed and modifications are suggested. By means of extensive experimental investigations, a data base was created for the validation of calculation models and for the assessment of design concepts. In order to assess the behaviour of timber members subjected to axial compression or combined axial compression and bending, strain-based calculation models were developed.
The investigations indicate that the existing approach of Eurocode 5 based on 2nd order analysis can lead to an overestimation of the load-bearing capacity. Hence, a modified design approach was developed which agrees with the results of the Monte Carlo simulations very well and thus ensures a safe and economical design of timber members subjected to compression or combined compression and bending.
Using bonded fibre-reinforced polymer (FRP) laminates for strengthening wooden structural members has been shown to be an effective and economical method. In this paper, properties of suitable FRP materials, adhesives and two ways of strengthening beams exposed to bending moment are presented. Passive or slack reinforcement is one way of strengthening. The most effective way of such a strengthening was to place reinforcement laminates on both tension and compression side of the beam. However, the FRP material is only partially utilised. The second way is to apply pre-stressing in FRP materials prior to bonding to tension side of flexural members and this way was showed to provide the most effective utilisation of these materials. The state of the art of such a strengthening and various methods are discussed. Increasing the load-bearing capacity, introducing a pre-cambering effect and thus improving serviceability which often governs the design and reducing the amount of needed FRP reinforcement are some of the main advantages. A recent development on how to avoid the requirement for anchoring the laminates at the end of the beams to avoid premature debonding is shown and the advantage of such a system is described.
Cross Laminated Timber (CLT) at in-plane beam loading conditions present a very complex stress state and many failure modes need to be considered in design. The work presented here aims at finding improvements of a specific analytical model for stress analysis and strength verification that has been suggested in literature and which is also suggested as a basis for design equations for the next version of Eurocode 5. Although the model has appealing properties it suffers from some drawbacks related to the assumed distributions of internal forces which, based on comparison to finite element analysis, appear to be inaccurate. The main focus in this paper is on model predictions regarding the distribution and magnitude of internal forces acting in the crossing areas between longitudinal and transversal laminations. The proposed modified model assumptions regarding the distribution of lamination shear forces, which in turn influence the forces acting in the crossing areas, are suggested to be taken into account in design of CLT beams.
The 2009 edition of CSA Standard O86, Engineering Design in Wood (CSA 2009), provides an equation for determining the deflection of shear walls. It is important to note that this equation only works for a single-storey shear wall with load applied at the top of the wall. While the equation captures the shear and flexural deformations of the shear wall, it does not account for moment at the top of the wall and the cumulative effect due to rotation at the bottom of the wall, which would be expected in a multi-storey structure.
In this fact sheet, a mechanics-based method for calculating deflection of a multi-storey wood-based shear wall is presented.
Connections consisting of axially loaded connectors embedded in timber elements can be a strong and competitive alternative to dowel-type connections. Such connections combine high capacity and stiffness. However, especially in the case of screwed-in threaded rods, the up-to date theoretical models and available experimental results are limited. In this paper, a general theoretical model that predicts the withdrawal capacity and stiffness of connections with axially loaded connectors is presented. The model is validated with an experimental study of withdrawal of threaded rods from glulam elements.
In this paper a proposal for the computation of stresses into orthotropic panels (e.g. CLT wall elements) caused by concentrated local load introduction in plane is derived on the basis of linear elastic mechanics. In practice the concept of effective width is often applied for the approximate determination of stresses. On the basis of the elastic solution in this contribution a proposal for the determination of the effective width is submitted. In addition a proposal for the stability verifications by means of the effective width is given..