Question

Due to the operational conditions and temperature gradient, a 95 mm diameter, 1.75 m long steel rod within a machine assembly is subjected to a combination of tensile loading of 190 N and thermal loading which imposes a longitudinal force of 244 N. The total loading results in an even distribution of forces on the body of the rod causing it to change its dimensions by increasing 0.45 mm in length at both ends and decreasing by 0.0135 mm at the diameter.

Determine the following:

a) Total normal stress which the rod is subjected to.

b) Total axial strain which the rod is subjected to.

c) Total lateral strain which the rod is subjected to.

d) What is the total length of the rod due to the effects of the combined loading?

e) What is the new diameter of the rod due to the effects of the combined loading?

f) What was the percentage total elongation of the rod?

g) What was the percentage total reduction in the cross-sectional area of the rod?

h) Poisson’s Ratio, v, may be determined by dividing the negative value of the lateral strain by the axial strain. What is Poisson’s Ratio for the rod material? Is this an acceptable amount for the rod?

i) The Shear Modulus, G, of a material may be determined by the following equation: G = E/ 2(1 + ν), where E is the Modulus of Elasticity, and ν, is Poisson’s Ratio. If the Modulus of Elasticity for the rod material is E = 210 GPa, what is the value of the Shear Modulus?

Answer 1