Question

A 29-mm-diameter copper rod is 1.1 m long with a yield strength of 73 MPa. Determine the axial force necessary to cause the diameter of the rod to reduce by 0.01 percent, assuming elastic deformation. Check that the elastic deformation assumption is valid by comparing the axial stress to the yield strength. The axial force necessary to cause the diameter of the rod to reduce by 0.01 percent is ____kN.

Answer 1

32.96 MPa

Step-by-step explanation:

The Poisson ratio of copper is:

μ = 0.355

The Young's modulus of copper is:

E = 117 GPa

The equation for reduction of diameter of a rod is:

D = D0 * (1 - μ*σ/E)

Rearranging:

D = D0 - D0*μ*σ/E

D0*μ*σ/E = D0 - D

D0*μ*σ = E*(D0 - D)

σ = E*(D0 - D) / (D0*μ)

If the diameter is reduced by 0.01 percent

D = 0.9999*D0

σ = E*(D0 - 0.9999*D0) / (D0*μ)

σ = E*(0.0001*D0) / (D0*μ)

σ = 0.0001*E / μ

σ = 0.0001*117*10^9 / 0.355 = 32.96 MPa

This value is below the yield strength, therefore it is valid.