Page History

...

Performing the three-dimensional analysis results in tip deflections in agreement with theory including the shear deformation but does not render normal stresses at the wall given by simple beam theory.  Below are the hand calculations from (one-dimensional) Euler-Bernoulli beam theory and the predictions for the normal stress at the fixed wall obtained from a fully three-dimensional analysis that includes Poisson effects from the dimensions in the cross section. Recall, from calculation in the Pre-Analysis section, the normal stress at the wall due to bending deformation alone is 854.9 psi whereas that predicted by the FEA analysis is nearly double at 1715 psi.

Image Removed 

                                                                         Image Added                     

The Euler-Bernoulli theory predicts normal stresses in the absence of out=of=plane stresses (which are presumed negligibly small. Here the out-of-plane ZZ component of stress is predicted to be approximately 810 psi, i.e on the order of normal stresses due to bending alone. These substantial out-of-plane stresses result in Poisson effects on the normal wall stress, increasing its value substantially. 

...