NONLINEAR ANALYSIS OF COMPOSITE BEAMS USINGREDDY’S HIGHER ORDER BEAM THEORY

In this study, implicit small deformation kinematics for two-layer composite beams is proposed by using Reddy’s higher order beam theory (RHBT). A displacement-based nonlinear finite element for RHBT composite beams is formulated with the help of the modified minimum potential energy principle, in which the proposed implicit kinematics is incorporated through the Lagrangian multiplier method. This finite element also takes into account the nonlinear properties of each sub-layer and shear connectors. In addition, it can easily be reformulated as Timoshenko or Euler-Bernoulli composite beam finite elements. Subsequently, the quasi-static mechanical behaviour of a two-span continuous composite beams is analyzed using the proposed composite beam finite elements based on RHBT, Timoshenko and Euler-Bernoulli beam theories, aiming to examine the shear effects on static behavior, including the deflection, interfacial slip and cross-sectional stress of the structure. Moreover, the effects of span-to-depth ratio of composite beams on the shear effects have also been explored by parametric analysis. Results show significant shear effects of composite beams with small span-to-depth ratios, in which case the Newmark model is not applicable.