Short Answer:

Stress is the internal resistance developed per unit area within a material when it is subjected to an external force. It is the measure of the intensity of internal forces acting within a body to resist deformation.

In simple words, when an external force acts on a body, the particles of the body try to resist this force by developing internal opposing forces. The ratio of this internal resisting force to the area on which it acts is called stress. It is usually expressed in units of N/m² or Pascal (Pa).

Detailed Explanation:

Stress

In engineering mechanics and strength of materials, the concept of stress is extremely important for analyzing how materials behave under different types of forces. Every material, whether it is steel, wood, or concrete, has the ability to resist external loads up to a certain limit. When an external force acts on a body, it tends to deform it — either by stretching, compressing, or twisting it. To resist this deformation, internal forces develop within the body.

The internal force per unit area that resists deformation is known as stress. Stress ensures that the body remains in equilibrium under the action of external forces. It is a measure of the intensity of the internal forces acting on a material’s cross-section.

Mathematically,

where,

•  = Stress (N/m² or Pascal, Pa)
•  = Applied or internal resisting force (N)
•  = Area over which the force acts (m²)

Units of Stress

1. SI Unit:
   The SI unit of stress is N/m² or Pascal (Pa).
   1 Pascal = 1 Newton per square meter.
2. Other Common Units:
   • kPa (kilo Pascal) = 10³ Pa
   • MPa (Mega Pascal) = 10⁶ Pa
   • GPa (Giga Pascal) = 10⁹ Pa

Explanation of Stress Formation

When a body is subjected to external forces, the particles inside the body experience a tendency to move or deform. To resist this tendency, the internal particles of the body develop opposing forces. These internal forces are distributed throughout the material’s cross-section. The ratio of this internal force to the cross-sectional area is the stress.

For example:
If a steel rod of cross-sectional area 500 mm² is subjected to a tensile load of 10,000 N, then the stress on the rod is:

This means the internal resistance developed within the rod is 20 N/mm².

Types of Stress

Stress can be classified based on the type of force acting on the body and the nature of deformation it produces. The main types are:

1. Tensile Stress:
   • Occurs when the external forces tend to stretch or elongate the material.
   • The internal resisting force acts opposite to the applied load.
   • Example: A steel wire being pulled from both ends.

where  is the tensile load and  is the area.

1. Compressive Stress:
   • Occurs when the external forces tend to compress or shorten the material.
   • The internal force developed resists compression.
   • Example: A column supporting a building load.

1. Shear Stress:
   • Occurs when the external forces act tangentially or parallel to the surface, causing layers of the material to slide over each other.
   • Example: Riveted joints, bolts, or shafts under torsion.

where  = shear stress.

1. Bending Stress:
   • Develops when a beam or structural member is subjected to bending loads.
   • It varies linearly across the cross-section, being tensile on one side and compressive on the other.
2. Torsional Stress:
   • Produced when a circular shaft or member is twisted by an applied torque.
   • The shear stress varies from zero at the center to maximum at the surface.

Each type of stress affects materials differently and must be considered during design to prevent failure.

Stress-Strain Relationship

When a material is loaded, it undergoes deformation. The amount of deformation per unit original length is known as strain, denoted by . The relationship between stress (σ) and strain (ε) in the elastic range of materials is linear, according to Hooke’s Law, which states that:

where  = Modulus of Elasticity or Young’s Modulus.

This relationship holds true only within the elastic limit, beyond which the material experiences permanent deformation.

Graphical Representation

If a graph of stress versus strain is plotted, the curve initially shows a straight line (elastic region) and then bends (plastic region). The slope of the linear portion represents the modulus of elasticity (E), indicating the stiffness of the material.

In the elastic region:

• The material returns to its original shape when the load is removed.
  In the plastic region:
• The material undergoes permanent deformation and may eventually fracture.

Importance of Stress in Engineering

1. Structural Safety:
   Stress analysis helps ensure that materials do not fail under applied loads.
2. Material Selection:
   Helps in selecting materials with sufficient strength and elasticity for specific applications.
3. Design Optimization:
   Engineers design machine parts such as shafts, beams, and columns to withstand specific stresses without failure.
4. Predicting Failure:
   By comparing induced stress with material strength, failure points can be predicted.
5. Performance Improvement:
   Stress study assists in improving designs by minimizing excess weight and material use.

Example in Real Life

• Tensile Stress: In a crane cable lifting a load.
• Compressive Stress: In a bridge pillar under heavy weight.
• Shear Stress: In scissors cutting paper or rivet joints holding plates.
• Torsional Stress: In the axle of a rotating vehicle wheel.

These examples show that stress acts in almost every mechanical or structural component.

Conclusion

In conclusion, stress is the internal resistance developed per unit area within a material when subjected to external forces. It represents the material’s ability to resist deformation and failure under different loading conditions. Stress is the foundation of strength analysis in mechanical and structural engineering, helping engineers design safe, reliable, and efficient components. By understanding stress and its types, materials can be utilized effectively within their strength limits to ensure stability and safety.