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finalsolutions - AE 221 Spring 2004 FINAL EXAM Solutions...

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1 AE 221 – Spring 2004 – FINAL EXAM Solutions 1. (i) Components s xy and s xz are tractions components on the lateral surfaces of the bar and must therefore be zero there. So their variation with the height of the bar cannot be as significant (since they have to start and end at zero) as that for the s xx component which is not constrained to any particular value on the lateral surfaces (since it is not a traction component). Shear stresses may become important if the web section is thin (can lead to buckling) or if the beam is short or the Poisson’s ratio of the material high (in which case the E-B assumptions are increasingly inaccurate). (ii) In torsion of a closed section the shear flow is constant around the cross-section. This is not the case for the shear flow introduced by the shear during bending. (iii) A virtual displacement is an imaginary displacement (in the mind of the analyst) that is used to compute the virtual work done over actual forces. Virtual displacements take no time to occur, do not affect the (real) forces of the material and must be consistent with all geometric constraints of the problem.
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