The bar has two contributions to elongation — one from its own self-weight, and one

from the applied axial load P.

1. Elongation due to self-weight (W):

Self-weight acts as a distributed load, with the internal force varying from 0 at the bottom

to W at the top. Since the internal force isn't constant along the length, we integrate:

This gives the well-known result: elongation due to self-weight is half of what it would

be if the entire weight acted as a point load

2. Elongation due to applied load P:

    P acts as a point load at the bottom, so the entire bar experiences constant internal force

    P throughout its length:

3. Total elongation: