Influence of grain inclination angle on shear buckling of laminated timber sheathing products

Recent advances in timber production industries have enabled production of new innovative laminated timberproducts having layers with grain inclination angle. This paper is aimed to study influence of grain inclinationangle in the laminated veneer lumber (LVL) and plywood sheathings on their shear buckling loads. Two extremeedge conditions of simply supported and clamped edges are considered. First, an accurate differential quadrature(DQ) computational code is developed using MAPLE programming software to obtain eigen buckling values andtheir corresponding eigen mode shapes. Next, for convenience of engineering calculations, approximate algebraic formulae are presented to predict critical shear buckling loads and mode shapes of LVL and plywood panels having layers with grain inclination angle, with adequate accuracy. Furthermore, finite element (FE) modelling is conducted for several cases using ANSYS software to show validity and accuracy of the predicted results for theproblem. It is shown that the highest shear buckling loads of LVL sheathings is achievable when the inclination angle of about 30\ub0 with respect to the shorter edges is considered for production of LVL panels, whereas the same angle with respect to the long edges of the LVL sheathings results in a relatively lower buckling load. Considering similar inclination angle with respect to any edges of a plywood sheathings will also results in its highest prebuckling capacity. It is also demonstrated that, under optimal design and certain loading circumstances, LVL shows a higher shear buckling capacity compared to a similar plywood sheathing

Lateral-Torsional Buckling of Partially Composite Horizontally Layered or Sandwich-Type Beams under Uniform Moment

International audienc

On the shear buckling of clamped narrow rectangular orthotropic plates

This paper deals with stability analysis of clamped rectangular orthotropic thin plates subjected to uniformly distributed shear load around the edges. Due to the nature of this problem, it is impossible to present mathematically exact analytical solution for the governing differential equations. Consequently, all existing studies in the literature have been performed by means of different numerical approaches. Here, a closed-form approach is presented for simple and fast prediction of the critical buckling load of clamped narrow rectangular orthotropic thin plates. Next, a practical modification factor is proposed to extend the validity of the obtained results for a wide range of plate aspect ratios. To demonstrate the efficiency and reliability of the proposed closed-form formulas, an accurate computational code is developed based on the classical plate theory (CPT) by means of differential quadrature method (DQM) for comparison purposes. Moreover, several finite element (FE) simulations are performed via ANSYS software. It is shown that simplicity, high accuracy, and rapid prediction of the critical load for different values of the plate aspect ratio and for a wide range of effective geometric and mechanical parameters are the main advantages of the proposed closed-form formulas over other existing studies in the literature for the same problem

Lateral-torsional buckling of vertically layered composite beams with interlayer slip under uniform moment

International audienceThe lateral-torsional stability of vertically layered composite beams with interlayer slip is investigated in this paper, based on a variational approach. Vertically layered elements are typically used in timber engineering but also in case of laminated glass elements. Both across-longitudinal or vertical slip due to rotation and longitudinal or horizontal slip due to lateral deflection are discussed. The theoretical framework of the lateral-torsional buckling problem is given, and some engineering closed-form solutions are presented for partially composite beams under uniform bending moment. Simplified kinematical relationships neglecting the axial and vertical displacements of the sub-elements give unrealistic values for the lateral-torsional buckling moment. Refined kinematical assumptions remove this peculiarity and render sound buckling moment results. Inclusion of the horizontal and vertical slips significantly affect the lateral-torsional buckling moment of these vertically laminated elements. A single lateral-torsional buckling formulae is derived, depending on both the horizontal and the vertical connection parameters

Analysis of shear deflections of deep composite box-type of beams using different shear deformation models

The deflection of deep box-type elements due to shear deformations is treated. A closed-form expression for the shear correction factor is derived by using an energy approach. The high accuracy and reliability of the developed procedure is demonstrated by comparing its results with accurate 3-D finite element results and also with the results of the conventional theories of Timoshenko with constant shear coefficient and of Reddy-Bickford applied to this kind of cross-section. A comprehensive and comparative parametric study is presented to investigate the effects of various mechanical properties and geometric dimensions for the different models. Unlike the higher-order shear deformation theories, which are accurate only for beams with rectangular cross-sections, there is a very good agreement between the results of the proposed method and the 3-D FE model. Clearly, the proposed energy method is applicable to more complicated cross-sections, including those with abrupt changes in the geometry, e.g. due to holes

Exact Lévy-type solutions for bending of thick laminated orthotropic plates based on 3-D elasticity and shear deformation theories

Exact solutions for static bending of symmetric laminated orthotropic plates with different Lévy-type boundary conditions are developed. The shear deformation plate theories of Mindlin-Reissner and Reddy as well as the three-dimensional elasticity theory are employed. Using the minimum total potential energy principle, governing equilibrium equations of laminated orthotropic plates and pertaining boundary conditions are derived. Closed-form Lévy-type solutions are obtained for the governing equations of both theories using separation of variables method and different types of classical boundary conditions, namely simply-supported, clamped and free edge, are exactly satisfied. Thereafter, 3-D elasto-static equations for orthotropic materials are solved for bending analysis of laminated plates using two different approaches. First, the method of separation of variables is utilised and an exact closed-from solution is achieved for simply-supported laminated orthotropic plates. Next, a combined Fourier-Differential Quadrature (DQ) approach is employed to present a semi-numerical solution for bending of laminated orthotropic plates with Lévy-type boundary conditions based on the three-dimensional elasticity theory. High accuracy of the presented solutions are proven and comprehensive comparative numerical results are provided and discussed. Presented comparative numerical results can serve as benchmark for investigating the correctness of new solution methods which may be established in the future

Accurate free vibration analysis of thick laminated circular plates with attached rigid core

This paper deals with the free vibration behavior of laminated transversely isotropic circular plates with axisymmetric rigid core attached at the center. The governing equations of motion are obtained based on Mindlin\u27s first-order shear deformation plate theory. Two possible categories of vibration modes related to up-down translation of the core and wobbly rotation of the core about a diameter are studied. Accurate natural frequencies hitherto not reported in the literature are presented for a wide range of thickness-to-radius ratio, inner-to-outer radius ratio, mass and moment of inertia ratios of the core and various boundary conditions at the outer edge of the plate. Numerical results are compared with those of a three-dimensional finite element method (3-D FEM) to demonstrate the high accuracy and reliability of the current analysis

An exact closed-form procedure for free vibration analysis of laminated spherical shell panels based on Sanders theory

This paper deals with closed-form solutions for in-plane and out-of-plane free vibration of moderately thick laminated transversely isotropic spherical shell panels on the basis of Sanders theory without any usage of approximate methods. The governing equations of motion and the boundary conditions are derived using Hamilton\u27s principle. The highly coupled governing equations are recast to some uncoupled equations by introducing four potential functions. Also, some relations were presented for the unknowns of the original set of equations in terms of the unknowns of the uncoupled equations. According to the proposed analytical approach, both Navier and L\ue9vy-type explicit solutions are developed for moderately thick laminated spherical shell panels. The efficiency and high accuracy of the present approach are investigated by comparing some of the present study with the available results in the literature and the results of 3D finite element method. The effects of various shell parameters like shear modulus ratio of transversely isotropic materials and curvature ratio on the natural frequencies are studied. Clearly, the proposed solutions can accurately predict the in-plane and out-of-plane natural frequencies of moderately thick transversely isotropic spherical shell panels