Change in Length of Axially Loaded Members


natural length,  L - unstressed, relaxed, or free length

stiffness, k - spring constant; the force required to produce a unit elongation

spring testing


prismatic bars

prismatic bar - structural member having a straight longitudinal axis and constant cross section throughout its length

elongation, δ (+ stretching, - shortening)



bars with prismatic segments

The bar may consist of several prismatic segments, each with different:
  • axial forces
  • dimensions
  • materials
Solution technique
  1. Identify segments (i=1,2,...,n)
  2. Determine internal forces in each segment
  3. Determine change in length of each segment
  4. Sum (+ tension, - shortening)


tapered bars

The bar may have:
  • varying cross-sectional area
  • varying axial force (e.g. centrifugal forces, friction forces, weight of bar in a vertical position)
Solution technique
  1. cut differential element of length dx
  2. balance forces to determine N(x)
  3. determine A(x)
  4. integrate over the length of the bar