Question:

Relation between strain and displacement

Lincoln: 3 days ago

Consider a vertical prismatic bar fixed at top end, it elongates due to its self weight. Stress and strain at top are non zero and the two are related by hooke's law, but the vertical displacement of top end is zero because it is fixed. How is this possible that strain is non zero but displacement is zero?

Answer:
Everleigh: 3 days ago

Perhaps an analogy will help. Consider a simpler example of a block attached to a horizontal ideal spring on a frictionless surface. The spring is attached to the wall. When the block is displaced, how can there be nonzero stress and strain in the spring (by Hooke's Law) if the fixed end doesn't move?

Strain is a measure of how stretched an object gets. You really need the displacement of two points on an object to calculate the strain (for instance, the knowledge that one end is fixed, and the displacement of another point on the object); the displacement of one point doesn't really tell you anything.