Nominal Stress Formula

The question asks to identify what the formula \( \frac{Load}{Original\:cross-sectional\:area} \) represents. This specific formula is a fundamental concept in mechanics of materials and solid mechanics, used to define a particular type of stress.

Stress is generally defined as the force applied per unit area. However, in engineering, we often distinguish between different types of stress based on how the area is measured and how the force is applied.

Let's look at the given formula:

\( \text{Stress} = \frac{Load}{Original\:cross-sectional\:area} \)

Here, 'Load' refers to the applied force on the material, usually acting perpendicular to the cross-sectional area. The key term here is 'Original cross-sectional area'. This means the area is measured before any deformation occurs due to the applied load.

Understanding Nominal Stress

When stress is calculated using the original cross-sectional area of the material sample before the load is applied, it is known as Nominal stress. Nominal stress is also commonly referred to as Engineering stress.

This is in contrast to 'True stress', which is calculated using the instantaneous or current cross-sectional area of the material as it deforms under the load. The instantaneous area changes, especially during tensile testing after the material starts necking, so true stress is different from nominal stress.

Why Other Options Are Not Correct

• True stress: As explained, true stress uses the instantaneous cross-sectional area, not the original area.
• Shear stress: Shear stress occurs when the force is applied parallel to the surface area, causing shearing deformation. The given formula uses a load presumably acting perpendicular to the area (like in tension or compression), defining a normal stress, not a shear stress.
• Bending stress: Bending stress is a type of normal stress that arises in a structural element subjected to bending. It varies across the cross-section (being tensile on one side and compressive on the other in simple bending) and depends on the bending moment and the geometry of the cross-section, not just a simple ratio of total load to original area.

Therefore, the formula \( \frac{Load}{Original\:cross-sectional\:area} \) is the precise definition of Nominal stress (or Engineering stress).