Short Answer:

Stress is the internal resisting force developed in a material when an external force or load is applied to it. It represents how much force is acting inside the material per unit area. The formula for stress is given as Stress (σ) = Force (F) / Area (A).

In simple words, stress shows the intensity of internal force within a body that resists deformation. It helps engineers to know how strong a material is and how much load it can bear without failure. Stress is usually measured in pascal (Pa) or newton per square meter (N/m²).

Detailed Explanation :

Stress

Stress is a fundamental concept in Mechanics of Materials and plays an important role in the design and analysis of machine parts and structures. When a material or component is subjected to an external force, it experiences an internal resistance to oppose the applied load. This internal resistance per unit area is known as stress. It helps in determining whether a material can safely carry the applied load without deforming or breaking.

Mathematically, stress (σ) is expressed as:

where,
σ = Stress (N/m² or Pascal),
F = Applied force (Newton),
A = Cross-sectional area (m²).

This relationship shows that stress depends on both the magnitude of the applied force and the area over which the force acts. If the area is small and the force is large, the stress will be high. Therefore, the same force acting on a smaller area causes more stress compared to a larger area.

Types of Stress

There are mainly three basic types of stress based on the direction of the applied force:

1. Tensile Stress:
   Tensile stress occurs when a body is subjected to a force that tends to stretch it or increase its length. For example, when a rod is pulled from both ends, the internal resisting force developed within the rod is tensile stress. It acts opposite to the applied load to resist elongation.
2. Compressive Stress:
   Compressive stress occurs when a body is subjected to a force that tends to shorten it or decrease its length. For example, when a column is pressed or pushed from both ends, the internal resistance developed is compressive stress. It acts to resist shortening or crushing of the material.
3. Shear Stress:
   Shear stress occurs when a force acts parallel or tangential to the surface of a material. It tends to cause one layer of the material to slide over the adjacent layer. For example, in bolts, rivets, and pins, shear stress is commonly developed when forces act across their cross-sectional area.

Each type of stress affects the material in a different way and must be analyzed carefully while designing any mechanical part.

Normal and Shear Stress

Stress can also be classified based on its direction with respect to the surface:

• Normal Stress: It acts perpendicular to the cross-section and can be tensile or compressive.
• Shear Stress: It acts parallel to the cross-section and tries to slide one surface over another.

Units of Stress

The SI unit of stress is Pascal (Pa) or N/m². In practical applications, larger units like MPa (Mega Pascal) or GPa (Giga Pascal) are used because the values of stress in engineering materials are generally large.

Importance of Stress in Engineering

Stress analysis is very important in mechanical and civil engineering. Every component in a machine or structure, such as beams, shafts, bolts, or frames, experiences different types of stresses under operation. If the stress in a component exceeds the material’s strength, it will lead to failure. Therefore, by calculating the stress, engineers can ensure that the material can safely withstand the applied load.

Understanding stress helps in selecting suitable materials for various applications. For example, materials with high tensile strength are chosen for cables and wires, while materials with high compressive strength are used in columns and supports.

Stress-Strain Relationship

When a material is loaded, it undergoes deformation. The amount of deformation per unit length is called strain. The relationship between stress and strain gives useful information about the behavior of materials under load. For small deformations, stress is directly proportional to strain, which is stated by Hooke’s Law. This proportional relationship is valid up to the elastic limit of the material.

Practical Applications

• Structural Design: Stress analysis is used in bridges, buildings, and dams to ensure they can support loads safely.
• Machine Design: Shafts, gears, springs, and beams are designed based on stress calculations to prevent failure.
• Material Selection: Helps in choosing materials that can resist particular types of stress like tension, compression, or shear.
• Safety and Efficiency: Prevents accidents by ensuring the parts operate within their safe stress limits.

Example:

If a steel rod with a cross-sectional area of 0.01 m² is subjected to a pulling force of 1000 N, the stress developed in the rod is:

This shows how internal resistance develops to balance the external force.

Conclusion:

Stress is the internal resistance developed in a material when external loads act on it. It plays a key role in determining the strength and safety of engineering structures and components. By understanding stress, engineers can design materials and systems that perform effectively under various conditions without failure or permanent deformation.