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Investigation of lateral torsional buckling of timber beams subjected to combined bending and axial compression
Abstract
Due to the increasing demand for long-spanning, material-efficient timber structures, the design of slender components is getting more and more important. While short beams reach the maximum load bearing capacity due to exceeding of the maximum tensile and compressive strength (stress failure), a so-called stability failure usually occurs with slender components. This is characterized by excessive deformations and the resulting additional internal forces (which may exceed the load bearing capacity) due to imperfections and second-order theory effects. For beams of intermediate length there is a transition zone between these two failure modes. For the verification of members subjected to lateral torsional buckling, EN 1995-1-1 provides two design concepts. The first one is the simplified effective length method, the second one is based on second order analysis. However, within these design concepts the material behaviour of timber is considered highly simplified. In this article the material-specific behaviour, in particular the plasticizing under compression and the size effect, is taken into account on the basis of analytical and numerical models. The results are compared to the methods provided by the code.
... For a realistic representation of the load-bearing behaviour of imperfection-sensitive timber members he incorporated plasticising and the size effect according to Weibull [18]. For relative slenderness ratios λrel,m ≤ 1.15 a significant increase of the load-bearing capacity up to 30 % due to these two effects can be observed [12]. So far, the influence of plasticising has only been discussed in relation to the resistance [10] and not concerning its effect on the geometrically nonlinear calculation of the internal forces. ...
... When solving (7) to (9), this results in Equations (10) to (12). By the Macaulay brackets these equations contain 5 different cases, which can be graphically interpreted as different shapes of the plastic region, where gpl represents the plastic regions' lower boundary as shown in Figure 7. zpl,0/1 are the z-coordinates of gpl at y = +/-b/2. ...
... For a more detailed description see [10]. For the stability of the analytical calculations, when κy/z is close to 0, Equations (10) to (12) can be solved separately for each of the 5 cases in order to avoid the corresponding κy/z being in the denominator. Due to their complexity, these transformations are not shown here. ...
The verification of slender timber members at risk of lateral torsional buckling is one of the basic verifications in timber design. However, latest investigations have shown that the design formulas provided in Eurocode 5 for imperfection-sensitive members subjected to combined bending and compression tend to be conservative and more advanced verification methods are needed. Analytical and numerical models are presented that allow for the consideration of the geometrically and materially nonlinear behaviour as well as of the size effect of tensile strength ft,0 for Nx-My-Mz interaction. These models and calculation results increase the understanding of the main influencing parameters of the load-bearing capacity of imperfection-sensitive timber beams and columns and may be the basis of a revision of the current design formulas provided in EN 1995-1-1.
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