A Higher‐Order Composite Beam Theory for Closed‐Form Analysis of Beams with Box and I Cross‐Section

Abstract

AbstractFor many cases of beam structures such as composite beams with box or I cross‐sections, shear forces can not be neglected and it is necessary to take shear deformation into account. Therefore, a higher‐order theory for composite beams is developed. The cross‐section of the beams can be divided into webs and flanges, both are assumed to have different symmetric layups with balanced angles. The axial displacement representation is chosen to be of second‐order for the flanges and of third‐order for the webs. There is no transverse contraction allowed. All parts of a cross‐section are assumed to have the same deflection in vertical direction. The geometric coupling of the flanges and webs is ensured by corresponding constraints. Based on the introduced kinematic representation, the principle of minimum potential energy is used to derive the respective differential equations. These governing equations are solved in a completely closed‐form analytical manner. This way, a closed‐form description of the whole beam behavior is achieved. In particular, all resultant local in‐plane stresses can be obtained directly. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)