Short Answer:
Strain energy due to axial load is the energy stored in a body when it is subjected to an axial force, either in tension or compression. When a load is applied along the axis of a material, it causes deformation, and this deformation results in internal energy being stored in the material.
This energy is recoverable when the load is removed, meaning the body returns to its original shape if the material remains within the elastic limit. The strain energy helps in understanding how much energy the material can absorb without permanent deformation or failure under axial loading conditions.
Detailed Explanation:
Strain Energy Due to Axial Load
When an external axial load acts on a body, it produces deformation in the form of elongation or contraction, depending on whether the load is tensile or compressive. The work done by the applied force during this deformation is stored within the body as potential energy. This stored energy is known as strain energy. It represents the internal resistance offered by the material to the applied load.
If the material behaves elastically, it follows Hooke’s Law, which means that the stress is directly proportional to the strain up to the elastic limit. Within this region, when the external load is removed, the stored strain energy is released, and the material regains its original shape and size.
Let us consider a bar of length , cross-sectional area , and subjected to an axial load . Due to the applied load, the bar elongates by a small amount . The strain energy stored in the bar is equal to the work done by the load during this elongation.
Derivation of Strain Energy Formula
If the load on the bar increases gradually from zero to , then the load-extension curve is a straight line (as per Hooke’s Law). The work done by the load is equal to the area under this load-extension curve, which is a triangle. Hence,
Now, from the definition of strain,
and stress,
Using Hooke’s Law,
where is the Young’s modulus of the material.
Substituting the values, we get:
Now substituting the value of in the equation for :
This is the total strain energy stored in the bar due to the applied axial load .
If we want to find the strain energy per unit volume, then dividing both sides by the volume , we get:
where is the stress in the material.
Thus, strain energy per unit volume (also called strain energy density) due to an axial load is:
Importance of Strain Energy
Strain energy plays an important role in understanding the behavior of materials under different loading conditions. It helps engineers to design structures and components that can safely absorb and release energy without failure.
For example, in bridges, machines, and building structures, members are subjected to different types of loads. By knowing how much strain energy a member can store, engineers can ensure that the structure remains safe and durable under working conditions.
If the energy stored exceeds the material’s capacity, it may cause permanent deformation or even fracture. Therefore, knowledge of strain energy is essential for preventing failure and ensuring safety in mechanical and civil structures.
Applications
- Design of Springs: Strain energy helps in calculating the energy stored in springs and determining their stiffness and resilience.
- Impact and Shock Loading: It helps to determine how much energy a material can absorb during sudden impacts.
- Failure Prediction: Helps to predict failure points when the energy stored exceeds the elastic limit.
- Energy Methods in Mechanics: Used to find deflections in beams and other members using strain energy principles.
Conclusion
Strain energy due to axial load is the energy stored within a body when it is stretched or compressed along its axis under the influence of an axial force. It depends on the applied load, length, cross-sectional area, and material property (Young’s modulus). Within the elastic limit, this energy is completely recoverable. Understanding strain energy is crucial for designing components that can withstand stresses safely and avoid structural failures.