A cylinder is fabricated from steel that has a stress strain

A cylinder is fabricated from steel that has a stress strain diagram shown to the right. The yield strength is 42 ksi and the slope of the initial linear portion is of the stress-strain curve (modulus of elasticity) is 30 times 10^3 ksi. The original length of the cylinder is exactly 4.0 ft. A load is applied that exceeds the yield stress, then the load is removed and the length of the cylinder is measured to be 4.0 ft. and 0.15 inches. If the cross-sectional area of the cylinder is 1.0 in^2, what load was applied to achieve the described deformation and what was the cylinder\'s final length under load?

Solution

strain = 0.15 / 4 * 12   = 0.003125

from the stress strain curve we find that for strain = 0.003125   stress = 42 ksi   (approx)

load = stress * area

load    = 42 * 1   = 42 kips

final length   = 48.15 in