Area under the stress-strain curve upto the __________ is referred to as the modulus of resilience.

ANS:C - proportional limit

The proportional limit is a point on the stress-strain curve of a material where the relationship between stress and strain becomes linear and proportional. At stresses below the proportional limit, the material behaves elastically, meaning that when the stress is removed, the material returns to its original shape without any permanent deformation. In this region, the strain experienced by the material is directly proportional to the stress applied to it, according to Hooke's Law. Mathematically, Hooke's Law can be expressed as: σ=E⋅ϵ Where:

• σ (sigma) is the stress applied to the material,
• E (E) is the modulus of elasticity or Young's modulus of the material, and
• ϵ (epsilon) is the strain experienced by the material.

The proportional limit is the highest stress at which this linear relationship between stress and strain exists. Beyond the proportional limit, the material begins to exhibit nonlinear behavior, and the stress-strain curve deviates from linearity. At higher stresses, the material may experience plastic deformation, where it undergoes permanent changes in shape even after the stress is removed. In engineering applications, the proportional limit is an important consideration because it represents the maximum stress level at which a material can be loaded without experiencing permanent deformation. It helps engineers determine the safe operating conditions for materials and ensures that structures and components remain within their elastic deformation range to avoid failure.