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 = 65 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 100 mm, inner diameter 50 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σ_r in the rod.

P = 250 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 300 mm

σ_r = MPa

3.Medium

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa). Both are 600 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 600 mm

δ = mm

4.Medium

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

P = 120 kNd = 16 mmL = 2 mE = 100 GPa

ε = µε

5.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 = 40 kNsegment 1: Ø30 mm, 1 m, copper (E = 117 GPa)segment 2: Ø12 mm, 1 m, copper (E = 117 GPa)

σ_max = MPa

6.Hard

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

P = 25 kNsegment 1: Ø35 mm, 1.5 m, brass (E = 100 GPa)segment 2: Ø12 mm, 1.5 m, copper (E = 117 GPa)

δ = mm

Answer key

1. σ = 132.4 MPa
2. σ_r = 55.6 MPa
3. δ = 0.03801 mm
4. ε = 5968 µε
5. σ_max = 353.7 MPa
6. δ = 3.224 mm

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