Once again, the answers:
1a. 0.492"
1b. No. Actual stress exceeds allowable.
2. 2.55"
3a. 8197 psi
3b. 0.00027
3c. 0.037"
1a. Elongation = PL/AE; you're given maximum elongation, force (P), length (L) and modulus of elasticity (E). Solve for area (A). Make sure your units are consistent: all lengths in inches, areas in square inches, forces in pounds, E in psi. Once you find A, use the equation for the area of a circle; solve it for diameter.
b. Stress = P/A. Use the area you found in part a. I get 27,368 psi, which exceeds the allowable of 13,600.
2. Again, stress = P/A. You're given the force and the allowable stress. Solve for A, then find the diameter. By the way, this is a very slender column (assuming it's solid, and not a tube), and would have to be extremely short for compressive stress, rather than buckling, to control.
3a. Stress = P/A
b. Strain = stress/E. Both of these have units of psi, so there are no units on strain. It's a unit change in length (inch per inch).
c. Elongation can be expressed several ways. Since strain is a unit change in length, total change in length = strain x length. Since strain = stress/E, elongation can also be written as (stress x L)/E. Since stress = P/A, elongation can also be written as ((P/A)/E) x L, or PL/AE as stated in 1a.
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