Axial stress & strain worksheet with answers

Free printable Axial stress & strain worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A solid round bar carries an axial tensile load P. Find the normal stress σ in the bar.

P = 55 kNd = 25 mm

σ = MPa

2.Easy

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 50 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σ_r in the rod.

P = 50 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 110 GPaL = 500 mm

σ_r = MPa

3.Medium

Find the axial strain ε in the steel bar, in microstrain (µε = 10⁻⁶).

P = 105 kNd = 12 mmL = 2 mE = 200 GPa

ε = µε

4.Medium

Find the axial strain ε in the copper bar, in microstrain (µε = 10⁻⁶).

P = 50 kNd = 12 mmL = 0.5 mE = 117 GPa

ε = µε

5.Hard

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 GPa, allowable stress 100 MPa). They are compressed together between rigid plates. Find the largest load P_max.

rod: Ø40 mm, E = 200 GPa, σ_allow = 120 MPatube: Ø100/Ø70 mm, E = 120 GPa, σ_allow = 100 MPa

P_max = kN

6.Hard

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 70 kNsegment 1: Ø30 mm, 0.5 m, aluminium (E = 70 GPa)segment 2: Ø16 mm, 2 m, steel (E = 200 GPa)

δ = mm

Answer key

1. σ = 112 MPa
2. σ_r = 7.816 MPa
3. ε = 4642 µε
4. ε = 3779 µε
5. P_max = 439.2 kN
6. δ = 4.189 mm

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