Young's Modulus?

Question

A steel bar 20 feet long and of rectangular cross-section 2.0 by 1.0 incesh supports a load of 4000lb. How much is the bar streched. Youngs modulus for steel is 2.9x10^7 lb/in^2

Answer 1

First, the steel bar weight:

W= rho ∙ vol

=0.283lb/in³∙20ft∙12in/ft∙2in∙1in = 136lb

This is relatively small compared to load, so can be neglected.



E = σ / ε = (F/A)/(ΔL/L)

rearranging,

ΔL = (F∙L)/(A∙E)

= 0.017 inches

Where A = area (2 x 1 in)

L = length = 20ft * 12in/ft

F = force = 4000 lb