Short Answer:

Shear stress is the type of stress that acts tangentially to the surface of a material when two equal and opposite forces are applied parallel to each other. These forces try to slide one layer of the material over another. It is measured as the force per unit area acting parallel to the surface.

In simple words, shear stress is the internal resistance developed when a material is subjected to forces that cause one part of it to move or slide over another. It plays a key role in the design of shafts, rivets, bolts, and beams where tangential forces act.

Detailed Explanation:

Shear Stress

Definition and Meaning:
When a material is subjected to two equal and opposite forces that act along the surface or parallel to each other, these forces create a tendency for one layer of the material to slide over another. The internal resistance offered by the material to oppose this sliding motion is called shear stress.

Mathematically, shear stress (τ) is defined as:

Where:

• τ = Shear stress (N/m² or Pascal)
• F = Tangential or shear force (N)
• A = Area of the surface under shear (m²)

Shear stress is different from normal stresses like tensile or compressive stress because it acts parallel to the surface rather than perpendicular to it. It tends to distort or change the shape of a material without significantly altering its volume.

Explanation of Shear Stress

When a tangential force is applied on the surface of a body while keeping the opposite face fixed, the body tends to deform by sliding or shearing. The layers of the material get displaced relative to each other. However, the material resists this deformation by developing internal resisting forces, known as shear stresses.

If the force is small, the deformation will be temporary and disappear when the force is removed. But if the shear stress exceeds the material’s elastic limit, permanent deformation or failure can occur.

Example:

• When you cut paper with scissors, the blades apply shear force, and the material fails due to shear stress.
• The pin in a riveted joint or bolt connecting two plates experiences shear stress when the plates are pulled apart.
• A shaft rotating under torque experiences shear stress throughout its cross-section.

Types of Shear Stress

Shear stress can occur in different forms depending on how the forces are applied. The main types are explained below:

1. Direct Shear Stress

Direct shear stress occurs when the tangential force acts directly along the plane of contact between two surfaces.
Example:

• A rivet connecting two plates under tension experiences direct shear stress along the section where the plates meet.
• A pin or bolt subjected to transverse loads also develops direct shear stress.

2. Torsional Shear Stress

Torsional shear stress is produced when a circular shaft or bar is twisted by applying torque or a twisting moment. The material particles in the outer surface experience maximum shear stress, while those near the center experience minimum shear stress.
Example:

• The shaft of a motor or propeller under twisting load develops torsional shear stress.
• Drive shafts, crankshafts, and axles are designed based on torsional shear stress.

Formula and Units of Shear Stress

The general formula for shear stress is:

In the case of torsion, it can be expressed as:

Where:

• τ = Shear stress
• T = Torque applied
• r = Radius of the shaft
• J = Polar moment of inertia

Units:
In SI system: Pascal (Pa) or N/m²
In practical use: MPa (Mega Pascal)

Shear Strain and Modulus of Rigidity

When shear stress acts on a body, it causes shear strain, which is the angular deformation produced between two perpendicular planes.

The ratio of shear stress to shear strain is called the modulus of rigidity (G) or shear modulus.

This property helps engineers determine how resistant a material is to shape distortion under shear forces. Materials like steel and brass have high modulus of rigidity, meaning they resist shear deformation strongly.

Examples of Shear Stress in Engineering

1. Riveted Joints:
   The rivets holding two plates together experience shear stress when the plates are subjected to tensile forces.
2. Bolted Connections:
   Bolts connecting machine parts resist shearing forces acting along the joint plane.
3. Beams and Shafts:
   • Beams under transverse loads develop shear stress at every cross-section.
   • Shafts under torque experience torsional shear stress throughout their material.
4. Scissors and Punching Machines:
   When scissors cut paper or a punch cuts a hole, the material fails under high shear stress.
5. Fluids:
   In fluid mechanics, the resistance to flow between layers of fluid is also expressed as shear stress.

Factors Affecting Shear Stress

1. Magnitude of Applied Force:
   Greater tangential force leads to higher shear stress.
2. Area of Contact:
   Smaller area results in higher shear stress for the same load.
3. Material Properties:
   Materials with high shear strength, such as steel, can resist larger shear stresses compared to weaker materials like aluminum.
4. Type of Loading:
   Static, dynamic, or impact loads affect shear stress differently.
5. Temperature and Fatigue:
   Repeated or cyclic loads, as well as high temperatures, can reduce shear strength over time.

Importance of Shear Stress in Engineering

Shear stress is a vital concept in mechanical and civil engineering because it helps in analyzing and designing parts that must resist sliding or twisting forces.

• It ensures safety and stability in joints, fasteners, beams, and shafts.
• It helps in selecting suitable materials that can resist shear failure.
• It assists in determining the shear strength and rigidity of materials during testing and design.
• It allows engineers to calculate the maximum safe load that a structure or component can handle.

Without proper understanding of shear stress, structures could fail by sliding, twisting, or shearing apart under load.

Conclusion:

Shear stress is the internal resistance developed in a material when subjected to tangential or sliding forces acting parallel to its surface. It causes deformation by sliding one layer of material over another. The magnitude of shear stress depends on the applied force and the cross-sectional area resisting it. It plays a crucial role in the analysis and design of mechanical components such as shafts, rivets, bolts, and beams. Understanding shear stress helps engineers ensure the strength, safety, and reliability of mechanical and structural systems.