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 = 60 kNd = 12 mm

σ = MPa

2.Easy

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa). Both are 400 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: Ø100/Ø50 mm, E = 120 GPaL = 400 mm

σ_r = MPa

3.Medium

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

P = 120 kNd = 16 mmL = 1.5 mE = 70 GPa

ε = µε

4.Medium

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

P = 110 kNd = 25 mmL = 2.5 mE = 100 GPa

ε = µε

5.Hard

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load P_max.

rod: Ø30 mm, E = 200 GPa, σ_allow = 120 MPatube: Ø120/Ø50 mm, E = 70 GPa, σ_allow = 70 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 = 55 kNsegment 1: Ø40 mm, 1 m, copper (E = 117 GPa)segment 2: Ø16 mm, 0.5 m, aluminium (E = 70 GPa)

σ_max = MPa

Answer key

1. σ = 530.5 MPa
2. σ_r = 23.58 MPa
3. ε = 8526 µε
4. ε = 2241 µε
5. P_max = 477.4 kN
6. σ_max = 273.5 MPa

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