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 = 10 mm

σ = MPa

2.Easy

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 60 mm, E = 100 GPa). Both are 500 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σ_r in the rod.

P = 80 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 100 GPaL = 500 mm

σ_r = MPa

3.Medium

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

P = 25 kNd = 25 mmL = 1 mE = 200 GPa

δ = mm

4.Medium

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

P = 55 kNd = 12 mmL = 2.5 mE = 117 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 = 60 kNsegment 1: Ø30 mm, 2 m, copper (E = 117 GPa)segment 2: Ø16 mm, 1.5 m, brass (E = 100 GPa)

σ_max = MPa

6.Hard

A steel segment (diameter 30 mm, length 300 mm, E = 200 GPa) and a segment made of aluminium (diameter 60 mm, length 300 mm, E = 70 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, Ø30 mm, 300 mm, E = 200 GPasegment 2: aluminium, Ø60 mm, 300 mm, E = 70 GPaP = 100 kN

σ₂ = MPa

Answer key

1. σ = 573 MPa
2. σ_r = 21.22 MPa
3. δ = 0.2546 mm
4. ε = 4156 µε
5. σ_max = 298.4 MPa
6. σ₂ = 20.63 MPa

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