What is Stress and Strain?
Stress and strain describe how a material responds to an applied load: stress is the internal force per unit area, and strain is the resulting fractional deformation. Together they define a material's strength, stiffness and the stress-strain curve engineers use to select materials.
Stress is force per unit cross-sectional area, σ = F/A (in Pa or MPa), and strain is the change in length divided by original length, ε = ΔL/L (dimensionless).
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Step-by-step worked examples
A steel rod with a cross-sectional area of 500 mm² carries an axial force of 50,000 N. Find the normal stress.
σ = F / A σ = 50000 / 500 = 100 N/mm² σ = 100 MPa
A 2 m rod stretches by 4 mm under load. Find the strain.
ε = ΔL / L ΔL = 0.004 m, L = 2 m ε = 0.004 / 2 = 0.002 (0.2%)
A bolt with a cross-sectional area of 200 mm² must not exceed a stress of 150 MPa. Find the maximum allowable force.
σ = F / A → F = σ × A F = 150 N/mm² × 200 mm² F = 30000 N = 30 kN
Flashcards
Quick quiz
Q1.A force of 50,000 N acts on a 500 mm² cross-section. What is the stress?
Q2.What is the unit of strain?
Q3.On a stress-strain curve, what happens at the yield point?
Q4.Young's modulus is defined as:
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Common mistakes
Confusing stress (force per area) with force itself. — Correct: Stress accounts for the area the force is spread over — the same force on a smaller area produces higher stress.
Treating strain as having units like meters or newtons. — Correct: Strain is dimensionless — it's a ratio, ΔL/L, so both lengths must use the same unit and cancel out.
Assuming a material stays elastic no matter how much force is applied. — Correct: Beyond the yield point, deformation becomes permanent (plastic); beyond the ultimate stress, fracture occurs.
Mixing area units, e.g. using mm² with force in kN without converting. — Correct: Keep units consistent: N with mm² gives stress directly in MPa; always convert before dividing.
FAQ
What is stress and strain?
Stress (σ = F/A) is internal force per unit area; strain (ε = ΔL/L) is the fractional deformation a material undergoes under that stress.
What is the stress and strain formula?
Stress: σ = F/A (Pa). Strain: ε = ΔL/L (dimensionless). Young's modulus links them elastically: E = σ/ε.
What are some stress and strain examples?
A steel cable under tension, a bridge girder under bending, a bolt torqued into a joint, and a rubber band being stretched.
How do you calculate stress and strain?
Divide the applied axial force by the cross-sectional area for stress, and divide the length change by the original length for strain.