Question

Strain energy of any member may be defined as work done to

• A. deformation
• B. pressure
• C. moment
• D. Force

Hint:

Strain energy is equal to the area under the load-deformation curve.
For a linear elastic material, $U = \frac{1}{2} \times \text{Load} \times \text{Deformation}$.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the definition of strain energy stored in a structural member in terms of the work done on it.

Step 2: Detailed Explanation:

• Concept of Strain Energy:
When an external force acts on an elastic body, the body undergoes deformation.
During this deformation, the applied force does work on the body.
According to the conservation of energy, this work done is stored internally within the material of the body as potential energy, which is called elastic strain energy ($U$).

• Mathematical Definition:
For a uniaxial bar subjected to a gradually applied tensile load $P$ causing a deformation $\delta$: \[ U = \int P \cdot d\delta \] Under linear elastic conditions: \[ U = \frac{1}{2} P \cdot \delta \]
• Therefore, strain energy is directly defined as the work done by external forces to deform the material.

Step 3: Final Answer:
The strain energy of a member is defined as the work done to cause deformation.