Chapter 1, Problem 1.7.6P

A circular aluminum tube of length L = 600 mm is loaded in compression by forces P (see figure). The outside and inside diameters are d₂= 75 mm and d₁= 63 mm, respectively. A strain gage is placed on the outside of the lube to measure normal strains in the longitudinal direction. Assume that E = 73 GPa and Poissons ratio is v = 0.33.

(a) IF the compressive stress in the tube is 57 MPa, what is the load P?

(b) If the measured strain is e = 78 J X 10-6, what is the shortening & of the tube? What is the percent change in its cross-sectional area? What is the volume change of the tube?

(c) If the tube has a constant outer diameter of d₂= 75 mm along its entire length L but now has increased inner diameter d₃with a normal stress of 70 MPa over the middle third (see figure, part b) while the rest or the lube remains at normal stress of 57 MPa, what is the diameter d₃?