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Q1: In general damped modal analysis is not carried out.
Because modes will be complex. However, it is possible to
find out damped natural frequencies/shapes. But damping
matrix need to be obtained, which is impossible for general
structural components. But modal analysis that is offered in
most of the general purpose FE Codes neglects damping.
Q3 & Q4 : Refer Machine Design by shigley.
Q4: In multi-axial state of stress one cannot know failure
can occur because of which stress (out of 6 stresses). Hence
theories of failure have been developed. When we compare
Von-mises Stress with material strength we are actual using
Distortion energy theory for the design. Which is in very
good agreement with experiments for ductile materials.

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