Warping of an I-beam:
When an I-beam is twisted the cross-section of the beam warps; ie. has an out of plane displacement. Shown below are the contours of out of plane displacement -- ignore the word DISPLACEMENT 1 in the legend.
The horizontal shear stress on the cross-section (sig_13) is shown below -- ignore the word STRESS 1 in the legend. Note that these stresses are zero on all vertical surfaces.
The vertical shear stress on the cross-section (sig_23) is shown below -- ignore the word STRESS 2 in the legend. Note that these stresses are zero on all horizontal surfaces.
These figures were made by solving Laplace's Equation for Saint-Venant's warping function using the finite element method.