Rod 500mm

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Allowable Stress problem help please?

A wrought steel rod 500mm long is subjected to a tensile load of 75kN. The allowable tensile stress is 150MPa, and the allowable elongation is not to exceed 0.25mm. Select the diameter of the rod to the nearest mm. The modulus of elasticity is 210 GPa.


Best Answer...


So, this problem is basically asking you to solve two problems and decide which one governs.

1st Problem - Make sure the rod does not yield (Transition from an elastic state to a plastic state)
From your Mechanics of Materials Class:
Sigma = P/A
-Sigma = Allowable Stress
-P = Applied Longitudinal Load
-A = Cross Sectional Area

Solve for the Cross Sectional Area

2nd Problem - Make sure the rod does not deform more than 0.25mm.
Also from your Mechanics of Materials Class:
Delta = PL/EA
-Delta = Allowable Deformation (Elongation)
-P = Applied Longitudinal Load
-L = Length of Rod
-E = Elastic Modulus
-A = Cross Sectional Area

Again, Solve for the Cross Sectional Area

Whichever area is bigger from the two solutions is the one that governs. Make sure that all your units match-up when solving this problem. Good luck.