Bar AB has length L, constant thickness d, and a width that tapers linearly from 3d at its fixed end (A) to d at its free end (B; see the figure below). The bar is homogeneous with mass density ρ and Young's modulus E. When hung vertically as shown in the figure, the bar stretches under its own weight. No other loads are applied. Assume that the x-axis is oriented downward with x=0 located at the ceiling (A).

Question

Obtain a symbolic expression for N(x) in terms of L, d, g, x, and ρ

Answer 1

An interesting problem.
Would you kindly describe the figure so we can share how the bar was hung?
Is the bar tapering downwards, i.e. thin end at the bottom, and hung at the top (ceiling)?

Answer 2

Also, does N(x) represent the tensile stress at section x?
Assuming the wide end is at A, then the area is given by
a(x)=d²(3-2x/L)
and the tensile stress is given by the weight of material below divided by the area at each section.

Answer 3

i too have the same problem and
unable to paste the url for image

Answer 4

See if you can post by omitting "http://"