Short Answer:

Normal and tangential stresses are two main types of stresses that act on a material when external forces are applied. Normal stress acts perpendicular to the surface and is responsible for either stretching (tensile) or compressing (compressive) the material.

On the other hand, tangential stress acts parallel to the surface and is responsible for the deformation due to sliding between layers of the material. These stresses together describe the complete state of stress on any plane within a material under load.

Detailed Explanation:

Normal and Tangential Stresses

When a body or material is subjected to external forces, internal stresses are developed to resist the deformation. These internal stresses can be divided into two major components based on the direction of the applied load with respect to the surface — normal stress and tangential stress.

Both types of stresses play a significant role in the analysis and design of mechanical and structural components. Understanding them helps engineers determine the strength, safety, and deformation behavior of materials under different loading conditions.

Normal Stress

Definition:
Normal stress is the stress that acts perpendicular (at a right angle) to the surface or cross-section of a material. It is denoted by the symbol σ (sigma) and is calculated as the force acting per unit area in the perpendicular direction.

Where,

•  = Normal stress
•  = Normal force acting perpendicular to the area
•  = Cross-sectional area

Normal stress can be of two types:

1. Tensile Stress: When the external force tends to stretch or elongate the material, the normal stress is tensile.
2. Compressive Stress: When the external force tends to compress or shorten the material, the normal stress is compressive.

Examples of Normal Stress:

• A rod or wire under tension experiences tensile stress.
• A column under axial compression experiences compressive stress.

Normal stress affects the length of the material and is mainly responsible for axial deformation (change in length).

Tangential Stress

Definition:
Tangential stress, also known as shear stress, acts parallel to the surface or cross-section of a material. It is denoted by the symbol τ (tau) and represents the intensity of internal resisting force developed per unit area due to tangential or sliding action.

Where,

•  = Tangential (or shear) stress
•  = Force acting tangentially to the surface
•  = Area on which the force acts

Tangential stress is responsible for angular distortion or change in shape of a material, without much change in volume.

Examples of Tangential Stress:

• The twisting of a shaft under torque produces tangential (shear) stress.
• Scissors cutting paper apply tangential stresses along the blades.
• Rivets or bolts under transverse load experience tangential stresses.

Relation Between Normal and Tangential Stresses

In most practical applications, a body is not subjected to only one type of stress. Often, both normal and tangential stresses act simultaneously on different planes within the material.

For example, in a beam under bending and shear load:

• The top and bottom fibers experience normal stress due to bending.
• The middle part experiences tangential stress due to shear force.

At a certain point inside the body, stresses can act in different directions, forming a two-dimensional (2D) stress system with both normal and tangential components. The combination of these stresses determines the state of stress and helps in identifying principal stresses, maximum shear stress, and possible failure planes.

Behavior of Material Under Normal and Tangential Stresses

1. Under Normal Stress:
   • The material either elongates (tension) or shortens (compression).
   • The deformation occurs along the direction of the applied force.
   • The cross-sectional area may change slightly due to Poisson’s effect.
2. Under Tangential Stress:
   • The material tends to deform by sliding of layers over each other.
   • There is no change in volume, only change in shape (angular deformation).
   • The magnitude of deformation depends on the shear modulus of the material.

Units and Measurement

Both normal and tangential stresses are measured in the same units because both represent force per unit area.

Common units used:

• Pascal (Pa)
• Newton per square meter (N/m²)
• Megapascal (MPa) for engineering materials

1 MPa =  N/m²

Applications in Engineering

Understanding normal and tangential stresses is essential in designing mechanical and structural systems, as both stresses contribute to failure modes.

1. Normal Stress Applications:
   • Design of bridges, beams, columns, and pressure vessels.
   • Tensile testing of materials to find yield strength and ultimate strength.
   • Analysis of axial loads in structural members.
2. Tangential Stress Applications:
   • Design of shafts under torque.
   • Calculation of shear stress in bolts, pins, and rivets.
   • Determining the safety of beams against shear failure.

Importance in Mechanics of Materials

Both stresses are essential for understanding how a material behaves under different loading conditions. Engineers must analyze them to ensure that the maximum stress does not exceed the material’s strength limit, thus preventing failure.

For example:

• If the normal stress exceeds the tensile strength, the material may break.
• If the tangential stress exceeds the shear strength, the material may fail by sliding or distortion.

Hence, in mechanical design, it is important to evaluate both stresses to ensure safety, durability, and performance.

Conclusion

Normal and tangential stresses are fundamental in stress analysis. Normal stress acts perpendicular to a surface, causing elongation or compression, while tangential stress acts parallel to the surface, causing shear deformation. Together, they define how materials respond under various loading conditions. A clear understanding of these stresses helps engineers design strong and reliable mechanical systems that can safely withstand the applied loads.