Question

If a horizontal load applied to the bar AC causes point A to be displaced to the right by an amount A L, determine the normal strain in the wire AB. Originally, theta = 45 degree.

Answer 1

Concepts and reason

This problem is based on the concept of the linear strain.

Linear Strain: The linear is ratio of the change in length to initial length. The Linear strain is the unitless parameter. The linear strain is also defined as the change in length per unit initial length.

First of all, calculate the value of the length of the wire. Use the Pythagoras theorem in order to calculate the value of the stretched length of the wire. Use the expression for the linear strain to calculate the value of the normal strain in the wire.

Fundamentals

Linear stress is expressed as,

Here, is final length after straining and is the initial length of the member.

Draw the arrangement of the wire and bar in stretched condition.

Use Pythagoras theorem to calculate the length of the wire AB.

Here, is length of the wire.

Use Pythagoras theorem to calculate the stretched length of the wire AB.

Neglect because the length is very small.

Write the expression for the normal strain in the wire.

Here, is strain in the wire.

Substitute for and for .

Ans:

The normal strain in the length is .