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 = 45 kNd = 20 mm

σ = MPa

2.Easy

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 50 mm, E = 120 GPa). Both are 800 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σ_r in the rod.

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 120 GPaL = 800 mm

σ_r = MPa

3.Medium

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

P = 75 kNd = 16 mmL = 1.5 mE = 70 GPa

ε = µε

4.Medium

Find the elongation δ of the aluminium bar under the axial load.

P = 95 kNd = 10 mmL = 1 mE = 70 GPa

δ = mm

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 = 115 kNsegment 1: Ø30 mm, 1.5 m, copper (E = 117 GPa)segment 2: Ø20 mm, 0.5 m, aluminium (E = 70 GPa)

σ_max = MPa

6.Hard

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 70 mm, E = 110 GPa, allowable stress 100 MPa). They are compressed together between rigid plates. Find the largest load P_max.

rod: Ø30 mm, E = 200 GPa, σ_allow = 120 MPatube: Ø100/Ø70 mm, E = 110 GPa, σ_allow = 100 MPa

P_max = kN

Answer key

1. σ = 143.2 MPa
2. σ_r = 8.199 MPa
3. ε = 5329 µε
4. δ = 17.28 mm
5. σ_max = 366.1 MPa
6. P_max = 349.2 kN

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