Question

What happens to the total potential energy of a system if the external work done by applied loads is greater than the increase in internal strain energy?

• A. The total potential energy decreases
• B. The system is in unstable equilibrium
• C. The material has exceeded its yield point
• D. The system reaches a higher energy state

Hint:

According to the Principle of Minimum Potential Energy, stable equilibrium states correspond to a local minimum of the total potential energy function.
Therefore, the potential energy tends to decrease as the system approaches a stable configuration under external loads.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
This question is about the variation of the total potential energy of a structural system during deformation under external loads.

Step 2: Key Formula or Approach:
The total potential energy ($\Pi$) of an elastic system is defined as:
\[ \Pi = U - W \]
where $U$ is the internal strain energy stored in the body, and $W$ is the work done by the external forces.

Step 3: Detailed Explanation:

• When external loads are applied to an elastic body, they perform work $W$ on the system.

• Part of this work is stored as internal strain energy $U$ within the deformed body.

• If the external work done ($W$) is greater than the increase in the internal strain energy ($U$), then the difference ($U - W$) becomes negative.

• Consequently, the total potential energy ($\Pi$) of the system decreases during this process.

Step 4: Final Answer:
The total potential energy decreases when the external work done is greater than the internal strain energy.