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 = 85 kNd = 30 mm

σ = MPa

2.Easy

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 50 mm, E = 120 GPa). Both are 800 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σ_r in the rod.

P = 100 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 120 GPaL = 800 mm

σ_r = MPa

3.Medium

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

P = 35 kNd = 16 mmL = 3 mE = 117 GPa

ε = µε

4.Medium

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

P = 10 kNd = 16 mmL = 2.5 mE = 200 GPa

ε = µε

5.Hard

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa, allowable stress 100 MPa). They are compressed together between rigid plates. Find the largest load P_max.

rod: Ø20 mm, E = 200 GPa, σ_allow = 160 MPatube: Ø100/Ø50 mm, E = 110 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 largest normal stress σ_max in the bar.

P = 25 kNsegment 1: Ø30 mm, 1 m, steel (E = 200 GPa)segment 2: Ø20 mm, 0.5 m, steel (E = 200 GPa)

σ_max = MPa

Answer key

1. σ = 120.3 MPa
2. σ_r = 39.3 MPa
3. ε = 1488 µε
4. ε = 248.7 µε
5. P_max = 568.6 kN
6. σ_max = 79.58 MPa

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