ABSTRACT

The straight beam represented by engineering beam theory has been used as an example throughout this work. This theory takes into account the effects of extension, bending, and shear deformation. The local and global forms of the straight beam equations were derived in Chapters 1 and 2, respectively. It is the intention here to present rather complete equations for straight beams. The derivations are based on the reduction of three-dimensional elasticity equations to the appropriate beam theory. The governing equations can be integrated and solved, using the displacement method, to find the displacements, including rotations, and the corresponding forces (stress resultants) along the member. Furthermore, analyses are presented for the cross-sectional properties needed for the study of beams. Also, analytical expressions for the distribution of normal and shear stresses on the cross-section are discussed. Computational methods for calculating cross-sectional properties and stress distributions for arbitrary cross-sectional shapes are presented.