Stress and strain describe how solid materials respond when forces try to stretch, compress, bend, or shear them. Engineers use these ideas to predict whether beams, bolts, cables, and machine parts will safely carry loads. A loaded rectangular metal bar pulled in tension is a simple model for understanding how force spreads through an area and causes measurable deformation.
These quantities matter because structures can look rigid while still changing shape under load.
Key Facts
- Normal stress: σ = F/A, where F is axial force and A is cross-sectional area.
- Normal strain: ε = ΔL/L0, where ΔL is change in length and L0 is original length.
- In the linear elastic range, Hooke's law for tension is σ = Eε.
- Shear stress: τ = F/A for a force applied parallel to the surface area.
- Shear strain: γ = Δx/h, where Δx is sideways displacement and h is the height of the sheared layer.
- Stress has units of pascals, 1 Pa = 1 N/m^2, while strain is dimensionless.
Vocabulary
- Stress
- Stress is internal force per unit area inside a material caused by an external load.
- Strain
- Strain is the relative deformation of a material compared with its original size.
- Young's modulus
- Young's modulus is a material property that measures stiffness in tension or compression.
- Shear stress
- Shear stress is stress caused by forces that act parallel to a surface and tend to slide layers past each other.
- Elastic deformation
- Elastic deformation is a temporary shape change that disappears when the load is removed.
Common Mistakes to Avoid
- Using total force instead of force per area for stress is wrong because a larger cross-section spreads the same load and lowers the stress.
- Giving strain units like meters is wrong because strain is a ratio of two lengths and has no units.
- Applying σ = Eε beyond the elastic range is wrong because many materials stop behaving linearly after yielding.
- Confusing normal stress with shear stress is wrong because normal stress acts perpendicular to an area, while shear stress acts parallel to it.
Practice Questions
- 1 A steel bar is pulled by a tension force of 12,000 N. Its rectangular cross-section is 20 mm by 30 mm. Find the normal stress in MPa.
- 2 A 2.0 m aluminum bar stretches by 1.4 mm under load. Find the normal strain, then use E = 70 GPa to find the stress.
- 3 Two bars have the same length and carry the same tensile force, but one has twice the cross-sectional area of the other. Explain which bar has greater stress and how that affects its expected strain if both are made of the same material.