Direct stress and elongation

  • #1

Main Question or Discussion Point

A prismatic bar AB of length L, cross-sectional area A ,modulus of elasticity E ,and weight W hangs vertically under its own weight
a>derive a formula for the downward displacement d(c) of point C which is located at a distance l from the lower end of the bar

The answer is W(L^2-l^2)/(2EA)

how do we get it?

Thanks for any hints or answers!
 

Answers and Replies

  • #2
Well, so delta = PL/EA


So P varies along the y direction...P = W*y/L, right?

and if we're doing incremental displacement changes, the L is your dy

d delta = integral W*y/LEA * dx

so you integrate from your l to L. Shouldn't your answer also have an L term in the denominator?
 

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