Problem $8$ : SHORT ANSWER

Answer all three of the below short answer questions to receive full credit for this problem.

Answers should be thorough and include neat sketches where appropriate.

a$.)$ Describe and draw failure planes for ductile and brittle materials under a pure axial loading

and a pure torsional loading.

b$.)$ For a rectangular beam cross section, sketch both the stress distribution relative to the

neutral axis for shear stress, and for normal stress due to bending, showing locations of

maximums for each case.

c$.)$ For a column with a non$-$uniform cross$-$section, explain how the moment of inertia in each

direction affects buckling. What might you do to increase the resistance to buckling?