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 = 10 kNd = 20 mm

σ = MPa

2.Easy

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σ_r in the rod.

P = 150 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 400 mm

σ_r = MPa

3.Medium

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

P = 110 kNd = 12 mmL = 0.5 mE = 117 GPa

δ = mm

4.Medium

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

P = 50 kNd = 20 mmL = 3 mE = 200 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 = 10 kNsegment 1: Ø25 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø16 mm, 1.5 m, aluminium (E = 70 GPa)

σ_max = MPa

6.Hard

A steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) and a segment made of brass (diameter 40 mm, length 300 mm, E = 100 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, Ø40 mm, 400 mm, E = 200 GPasegment 2: brass, Ø40 mm, 300 mm, E = 100 GPaP = 100 kN

σ₂ = MPa

Answer key

1. σ = 31.83 MPa
2. σ_r = 98.45 MPa
3. δ = 4.156 mm
4. ε = 795.8 µε
5. σ_max = 49.74 MPa
6. σ₂ = 31.83 MPa

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