*Step 2.*** Elongation/Force Relationship. **
To solve for the elongation, break the bar into lengths (segments) over which all the values (force, area and modulus) are constant.
The top such segment, AB, has length *a*, area A_{1}, modulus E_{1}, and internal force P_{AB} = –W (compression). The change in length of AB is:
Since AB is in compression, it shortens: **D***a*<0. Therefore, Point B moves up. Taking each of the other lengths with constant force, area and modulus:
Here, segments BC, CD and DE are all in tension, so each get longer.
*Step 3.*** Compatibility. **
The total elongation or deflection D_{total} is:
The displacement of any point (upward or downward) depends on the extension (compression) of the bar segments above it. |