Shearing Stress - Definition, Meaning, Units, Formula, FAQs
Shear stress is a simple concept that explains what happens when a force tries to slide one part of an object over another. Instead of stretching or compressing, the material changes its shape due to a force acting along its surface. You can see this in daily life, like pushing a deck of cards sideways or cutting paper with scissors. It mainly affects the shape of an object without changing its volume.
This Story also Contains
- Shearing Stress
- Shearing Stress in Fluids
- Shearing Strain in Real Life
- Solved Examples on Shearing Stress
In this article, you will learn what shear stress is, how it is defined, and how to calculate it using a simple formula. You will also understand its units, how it works in solids and fluids, and see real-life examples. Along with this, solved problems will help you practice and improve your understanding.
Shearing Stress
Shear stress is defined as the force acting parallel (tangential) to the surface of a material per unit area. It tends to change the shape of the body without changing its volume.
shear stress is given by:
$\tau=\frac{F}{A}$
Where:
- $\tau=$ shear stress
- $F=$ tangential (parallel) force
- $A=$ area of cross-section
- Shear stress is responsible for angular deformation (shear strain).
- Unit: Pascal (Pa) or N/m²
Different Units of Shear Stress
| Unit System | Unit Name | Symbol | Relation |
| SI System | Pascal | Pa |
$(1 , \text{Pa} = 1 , \text{N/m}^2)$ |
| CGS System | dyne per cm² | dyne/cm² |
$(1 , \text{dyne/cm}^2 = 0.1 , \text{Pa})$ |
| Engineering Units | kilopascal | kPa |
$(1 , \text{kPa} = 10^3 , \text{Pa})$ |
| Engineering Units | megapascal | MPa |
$(1 , \text{MPa} = 10^6 , \text{Pa})$ |
| Practical Unit | bar | bar |
$(1 , \text{bar} = 10^5 , \text{Pa})$ |
| Atmospheric Unit | atmosphere | atm |
$(1 , \text{atm} \approx 1.013 \times 10^5 , \text{Pa})$ |
| Imperial System | pounds per sq inch | psi |
$(1 , \text{psi} \approx 6893 , \text{Pa})$ |
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Shearing Stress in Fluids
Shearing stress in fluids is the stress developed when a fluid layer moves relative to another layer. It arises due to the fluid's resistance to flow, known as viscosity.
Shearing stress in a fluid is defined as the tangential force per unit area required to maintain the flow of fluid layers.
$\tau=\eta \frac{d v}{d y}$
Where:
- $\tau=$ shear stress
- $\eta=$ coefficient of viscosity
- $\frac{d v}{d y}=$ velocity gradient
Example : When liquid flows through a pipe, different layers move at different speeds, creating shear stress between them.
Shearing Strain in Real Life
Shearing strain refers to the angular deformation produced when a tangential force acts on a body. It is commonly observed in daily life when objects change shape without a change in volume.
Real-Life Examples
- Sliding of Cards: When a deck of cards is pushed sideways, the layers shift relative to each other, showing shear strain.
- Deformation of Rubber Block: Pressing the top surface sideways while the bottom remains fixed causes angular distortion.
- Cutting with Scissors: The material between the blades experiences shear strain before being cut.
- Flow of Liquids: In fluids, different layers move at different speeds, producing continuous shear strain.
- Earthquakes: Movement of tectonic plates creates shear strain in rocks, leading to fractures.
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Solved Examples on Shearing Stress
Question 1 : A tangential force of 50 N acts on a surface of area $2 \mathrm{~m}^2$. Find the shear stress.
Solution:
$\tau=\frac{F}{A}=\frac{50}{2}=25 \mathrm{~Pa}$
Answer: 25 Pa
Question 2 : A force of 200 N is applied parallel to a surface of area $0.5 \mathrm{~m}^2$. Calculate the shear stress.
Solution:
$\tau=\frac{200}{0.5}=400 \mathrm{~Pa}$
Answer: 400 Pa
Question: 3 Find the shear stress when a force of 1000 N acts on an area of $10 \mathrm{~m}^2$.
Solution:
$\tau=\frac{1000}{10}=100 \mathrm{~Pa}$
Answer: 100 Pa
NCERT Physics Notes:
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Frequently Asked Questions (FAQs)
The unit of the stress is N/m2. It is defined as the internal resisting force per unit area.
Strain is the dimensional less quantity. It is defined as the ratio of the change in dimension to the original dimensions.
Strain is the ratio of two same quantities hence it is dimensionless.
Newton’s law of viscosity gives the relationship between the shear stress and strain rate in fluids.
τ =µ dγ/dt
Where τ is shear stress and dγdt is rate of shear strain and µ is viscosity.
Stress = Internal resisting force/crosssectional area
Strain = Change in dimension after deformation/Original Dimension
The occurrence of shear strain is called shear.
