Refinements of Classical Beam Theory for Beams with a Large Aspect Ratio of Their Cross-Sections

Abstract

In order to obtain a required stiffness ratio between compliant and stiff directions, beams with a large ratio of width to depth are needed. For the simulation of multibody dynamic systems, mostly the Bernoulli–Euler assumptions are made. Some known but mostly neglected effects for beams with a rectangular crosssection, leaf springs, are considered here. The effect of shear stiffness, as in Timoshenko’s beam theory, is important for beams that are short in comparison to their width. For beams under torsion, the effect of constrained warping can become important. The constrained anticlastic bending for large deflections is a non-linear effect. Clamping is never perfect and the support stiffness or restrained transverse contraction needs to be considered. Residual stresses have a marked influence if they exceed the buckling load, which can easily occur if the aspect ratio is large.