Question

Problem 6.7: For a bronze alloy, the stress at which plastic deformation begins is 275 MPa (40,000 psi), and the modulus of elasticity is 115 GPa (16.7 ×106psi).(a)What is the maximum load that may be applied to a specimen with a cross-sectional area of 325 mm2(0.5 in.2) without plastic deformation?(b)If the original specimen length is 115 mm (4.5 in.), what is the maximum length to which it may be stretched without causing plastic deformation?

Answer 1

a) P = 20000 lbf

b) ΔL = 0.01 in

Step-by-step explanation:

a) We apply the following formula

σ = P / A ⇒ P = σ*A ⇒ P = (40000 PSI)*(0.5 in²) = 20000 lbf

b) We use the equation of Hook's Law:

ΔL = (P*L) / (A*E)

⇒ ΔL = (20000 lbf *4.5 in) / (0.5 in² * 16.7 ×10∧6 PSI) = 0.01 in