How to Calculate Shearing Stress: Step-by-Step Examples & Tips
Shearing stress is a core concept in Physics, especially relevant to understanding forces in solids, fluids, and engineering structures. It quantifies the internal forces that develop when adjacent layers within a material slide or deform relative to each other under parallel (tangential) forces. Instead of pulling or compressing straight on, shearing stress measures what happens when forces try to make layers move sideways against each other—like sliding a deck of cards or the effect of wind on a building.
When a force is applied parallel to a material’s surface (not perpendicular), it can cause the inner particles or layers of the substance to shift in opposite directions. This stress continues increasing until the material either deforms permanently or breaks. Engineers and scientists use shearing stress to predict whether beams, columns, fluids in pipes, or even daily materials like fabric or paper can withstand certain loads or forces.
Shearing stress isn’t limited to solids. In liquids and gases, such as water moving through a river or oil flowing in a pipe, this type of stress arises because different layers of the fluid move at different speeds. Realizing what shearing stress is helps in designing reliable structures, vehicles, and even hydraulic systems.
Shearing Stress Formula and Symbol Breakdown
The main formula for calculating shearing stress is based on the idea of force per unit area, but applications vary for solids, beams, and fluids. The table below summarizes the main meanings and units:
| Symbol | Meaning | Measured in |
|---|---|---|
| τ | Shear stress | Pa (pascals) or N/m² |
| F | Applied force, parallel to surface | N (newtons) |
| A | Area where force acts | m² |
| V | Internal shear force (beams) | N (newtons) |
| Q | First moment of area (beams) | m³ or mm³ |
| t | Thickness (beams) | m or mm |
| I | Moment of inertia (area) | m⁴ or mm⁴ |
| μ | Dynamic viscosity (fluids) | Pa·s (pascal-seconds) or P (poise) |
| du/dy | Velocity gradient (fluids) | s-1 |
For general shearing stress in any material:
τ = F / A
Where τ is shear stress, F is the force applied parallel to the surface, and A is the cross-sectional area.
In beams or structures subjected to transverse loads:
τ = VQ / (I t)
Where V is the internal shearing force at the section, Q is the first moment of area, I is the moment of inertia, and t is the thickness at the point considered.
For fluids and viscous flow:
τ = μ (du/dy)
Here, μ is viscosity, and du/dy is the velocity gradient perpendicular to the flow direction.
Shearing Stress: Everyday Examples
- Using scissors to cut paper or fabric — the blades apply parallel forces in opposite directions, slicing the material.
- Pushing against a wall with the palm; the wall layers (hypothetically) would want to slide, setting up internal shear stress.
- River water flowing over its bed — different layers of water move at different speeds, shearing the bed and causing erosion.
- Walking — when your foot moves forward on the ground, shear stress is created between your shoe and the surface.
How to Solve Shearing Stress Problems (Step-by-Step)
| Step | What to Do |
|---|---|
| 1 | Identify if the force is parallel to the area. Note the values for F and A, or use V, Q, I, t for beams. |
| 2 | Convert all given values to SI units (N, m2). For mm2, divide by 1,000,000. |
| 3 | Apply the correct formula: τ = F/A (general), τ = VQ/It (beam), or τ = μ (du/dy) (fluid). |
| 4 | Calculate and write the answer with units: N/m² (Pa). |
Shearing Stress of Common Steel Types
| Steel Type | Shear Strength (N/mm2) |
|---|---|
| Low-carbon HR steel | 345 |
| Low carbon C.R. sheet | 276 |
| ASTM A-36 (varies by grade) | Depends on grade |
| 45-50 carbon HR sheet | 552 |
| Spring steel 1074/1095 (hardened) | 1,380 |
| COR-TEN Steel | 379 |
Shear Stress vs. Other Types of Stress
| Type | How Force Acts | Resulting Change |
|---|---|---|
| Shear Stress | Parallel to surface (tangential) | Causes different layers to slide past each other (shape change) |
| Tensile Stress | Perpendicular to surface (pulling apart) | Stretches object / increases length |
| Bending Stress | Perpendicular, but with moment acting | Causes object to bend / flex |
Understanding the difference between these stresses is key to predicting material failure and safe design. For detailed exploration of related concepts, see Stress, Tensile Stress, and Strain in Mechanics.
For practice, consider solving problems where you calculate shearing stress in beams, investigate how fluids create shear at boundaries, or compare materials using their tabulated shear strengths. Mastery of shearing stress not only strengthens your grasp of forces in Physics, but directly helps in topics such as Mechanical Properties of Solids and Mechanical Properties of Fluids.
Continue building your skills with Vedantu’s resources and targeted quizzes. For further reading, see Shearing Stress or advance to Shear Modulus and related topics. An in-depth understanding of shearing stress will make you confident in solving Physics problems and understanding real-world engineering designs.
FAQs on Shearing Stress Explained: Physics Concept, Formula & Applications
1. What is shearing stress?
Shearing stress is the force per unit area acting parallel to a material’s surface. It measures how much a layer of a material slides or deforms under a tangential or shear force. This concept is essential for understanding material deformation in Physics and engineering.
2. What is the formula for shearing stress?
The formula for shearing stress is:
τ = F / A
where:
• τ = Shearing stress
• F = Force applied parallel to the surface (in Newtons, N)
• A = Area over which the force is applied (in m2)
3. What is the SI unit of shearing stress?
The SI unit of shearing stress is the Pascal (Pa), which is equivalent to 1 Newton per metre squared (N/m2).
4. What is an example of shearing stress in daily life?
A common example is when you use scissors to cut paper—the blades apply a shear force parallel to the paper surface, causing the layers to slide and resulting in a cut. Other examples include rubbing your hands together, sliding doors, or a deck of cards shifting past each other.
5. How is shearing stress different from tensile stress?
Shearing stress acts parallel to the material's surface, causing shape changes by sliding layers.
Tensile stress acts perpendicular to the surface, causing an increase in length along the force direction.
Summary Table:
• Shearing: Parallel, shape change
• Tensile: Perpendicular, length change
6. Where is shearing stress maximum in a beam?
In most beams (especially rectangular cross-sections), the maximum shearing stress occurs at the neutral axis—the horizontal line passing through the center, equidistant from the top and bottom surfaces.
7. What is the shearing strain and how is it related to shearing stress?
Shearing strain (γ) is the ratio of the relative displacement (x) between two layers to the distance (h) between them: γ = x / h.
The shearing stress (τ) relates to shearing strain by modulus of rigidity (G): G = τ / γ.
8. What are some key applications of shearing stress in Physics and engineering?
Shearing stress is crucial in:
• Beam and bridge design (to prevent structural failure)
• Analysis of fluids (viscosity, laminar flow)
• Manufacturing processes (cutting, drilling, machining)
• Geology (movement of earth layers and fault lines)
9. Is shearing stress the same as pressure?
No, shearing stress is the force acting parallel to the surface, causing one layer to slide over another. Pressure is the force applied perpendicularly to the surface. They have different directions and effects on materials.
10. How do you calculate shearing stress for a rectangular block if a tangential force is applied?
To calculate shearing stress:
1. Find the applied force (F) parallel to the block’s upper surface.
2. Determine the area (A) of the face receiving the force.
3. Apply the formula: τ = F / A.
Express the answer in N/m2 (Pa).
11. What does the symbol ‘τ’ represent in the context of shearing stress?
In Physics, the Greek letter ‘τ’ (tau) is the standard symbol representing shearing stress. It is commonly used in formulas, equations, and diagrams during calculations.
12. What is the relation between shearing stress and viscosity in fluids?
In fluids, shearing stress (τ) is related to velocity gradient and coefficient of viscosity (η) using the formula:
τ = η (dv/dy)
Here, dv/dy is the rate of change of velocity with distance, and η indicates how resistant the fluid is to flow (viscosity).
