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 steel rod (diameter 25 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 80 kN. Find the compressive stress σ_r in the rod.

P = 80 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 300 mm

σ_r = MPa

2.Easy

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

P = 115 kNd = 16 mm

σ = MPa

3.Medium

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

P = 50 kNd = 30 mmL = 2.5 mE = 200 GPa

δ = mm

4.Medium

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

P = 55 kNd = 30 mmL = 2.5 mE = 70 GPa

ε = µε

5.Hard

A steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) and a segment made of bronze (diameter 60 mm, length 400 mm, E = 110 GPa) are joined end to end and fixed between two rigid walls. An axial load of 100 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ₂ in segment 2.

segment 1: steel, Ø20 mm, 300 mm, E = 200 GPasegment 2: bronze, Ø60 mm, 400 mm, E = 110 GPaP = 100 kN

σ₂ = MPa

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 = 70 kNsegment 1: Ø25 mm, 2 m, copper (E = 117 GPa)segment 2: Ø16 mm, 1 m, aluminium (E = 70 GPa)

σ_max = MPa

Answer key

1. σ_r = 21.44 MPa
2. σ = 572 MPa
3. δ = 0.8842 mm
4. ε = 1112 µε
5. σ₂ = 27.86 MPa
6. σ_max = 348.2 MPa

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