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.
Due to the increasing environmental awareness, the transition pace to renewable materials has increased, and the use of timber in construction is no exception. However, using timber in high rise building applications comes with structural challenges, e.g dynamic issues originating from timber being lightweight compared to conventional building materials. Some of the structural challenges with timber can be resolved by the implementation of Timber Concrete Composites (TCC), which increases the effective bending stiffness by adding a concrete layer connected to the underlying timber floor. Furthermore, the higher self-weight of concrete contributes to improved dynamic performance.
Despite the fact that the TCC floor is a versatile and quite common structural design solution in Europe, the TCC knowledge in the Swedish construction industry is limited. The main scope of the thesis is to raise this knowledge of TCC by studying the structural behavior and develop applicable design methods. Both analytical design methods and FE-modelling are addressed. The content is limited to TCC floors with a 5-layer Cross-Laminated Timber (CLT) section, with use of notches or screws as shear connectors.
In CLT design, the Gamma method is commonly used and applicable to a CLT layup up to 5 layers. This method can, by a slight modification, be applicable for TCC sections with a 5-layer CLT as well. The concrete layer on top is regarded as an additional longitudinal layer, flexibly connected to the CLT section. The Equivalent gamma method and the Extended gamma method are two modified versions of the conventional Gamma method, valid for TCC floors with 5-layer CLT sections. Each method determines the effective bending stiffness accurately, compared to FE-modelling and laboratory test results. The Extended gamma method has a more solid theoretical base compared to the Equivalent gamma method, and is considered the recommended design method. The simplified methodology of the Equivalent gamma method is theoretically questionable, hence its recommended use is for preliminary calculations only.
The following concluding remarks can be drawn from the analysis of the structural behavior of TCC floors:
- The shear connectors should be concentrated to areas of high shear flow, i.e. close to support, for optimal structural performance.
- An increased ratio of timber in the longitudinal, load-bearing direction of the CLT section increases the effective bending stiffness of the TCC.
- The concrete layer increases the effective bending stiffness due to the high Young's modulus. However, the high density of concrete entails a thin concrete layer thickness to achieve a light-weight and structural efficient TCC system, and the decisive optimisation factor is the ratio of mass-to-effective bending stiffness, m/EI.