The rigid beam shown is supported by three cylindrical posts which rest on a rigid base: a 20 mm dia. brass post at B
(E =100 GPa and syld = 600 MPa) and two 75 mm dia. aluminum posts at A and C (E=70 GPa and syld = 20 MPa). All three posts are initially of equal length and free of residual plastic strain.
a. Sketch to scale, on the same graph, axial compressive stress-strain curves for both post types. Extend the curves out to the point where both post types have yielded.
b. If the beam is loaded until, for each load, P = 100 kN and then unloaded to P = 0 kN, on which post or posts will the beam finally rest?
c. After this load cycle, what will be the residual plastic strain (if any) be in each post?
d. What load P would be required to cause all three posts reach their yield point?
e. Consider the posts in their initial unyielded state. If P = 50kN, for what temperature change T would the gap between the brass post and rigid beam equal 10mm?