Stress and Strain | Mechanical Properties of Solids | Don't Memorise

A beam in mechanical engineering is a long structural element made of materials like wood, steel, or concrete. When a downward force is applied to the surface area of such a beam, it experiences stress—a state where atoms are compressed closer than their natural spacing. This compression generates interatomic and intermolecular forces that resist deformation if the material remains within its elastic limits.

Stress is the force applied per unit cross-sectional area, mathematically expressed as F/A. Increasing the applied force while keeping the area constant results in higher stress because a larger numerator increases the ratio. Conversely, increasing surface area with constant force decreases stress since a larger denominator reduces this ratio.

Stress is defined as force per unit area. The SI unit for force is Newton (N), and the SI unit for area is square meters (m²). Therefore, the SI unit of stress becomes Newton per meter squared (N/m²).

Strain is defined as the change in dimensions of an object per unit of its original dimensions when subjected to stress. When a material experiences stress, it undergoes deformation, altering one or more of its physical measurements. The extent of this dimensional change quantifies strain.

Strain measures the deformation of a material when force is applied, expressed as the change in length (ΔL) divided by its original length (L). This ratio quantifies how much an object stretches or compresses relative to its initial size. It provides insight into how materials respond under stress and varies depending on their composition.

Strain can be expressed as the change in area or volume due to deformation. For instance, when a sponge ball is compressed, its strain is calculated by dividing the change in volume (Delta V) by its original volume (V). Similarly, stretching a thin rubber sheet equally from opposite sides alters its area; here, strain equals the change in area (Delta A) divided by the initial area (A). These examples illustrate how deformation impacts material dimensions.