TABLE OF CONTENTS The Computer program VABS implements the cross-sectional analysis methodology described in Chapter 4. VABS is able to calculate cross-sectional stiffness constants, with transverse shear and Vlasov refinements, for initially twisted and curved beams with arbitrary geometry and material properties. The material in this chapter is intended to provide two types of examples: a) comparisons with solutions from elasticity theory and b) comparisons with accepted engineering results, three-dimensional finite-element results, and experimental data. When appropriate, we also include comparisons with results from the asymptotic formulae for cross-sectional constants derived for thin-walled beams in Chapter 6.
In the analytical validations we use the VAM as implemented in VABS analytically on problems for which analytical solutions are feasible (other than the thin-walled cases treated in the previous chapter). [Note: this section quotes extensively from Yu and Hodges (2004, 2005), with permission from the American Society of Mechanical Engineers and the American Helicopter Society, respectively.] In the first of these we examine prismatic, homogeneous, isotropic beams using both classical and generalized Timoshenko analyses. Examples include elliptic and rectangular cross-sections. These are modeled analytically with transverse shear refinement using the VAM to show that the solution is identical to that obtained from the theory of elasticity. The shear center locations calculated by VABS for various cross-sections are calculated and compared with published results. Comparisons with other composite beam theories are also included where appropriate.
To apply the VAM analytically in the same manner as we have applied it in...
