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 = 25 kNd = 10 mm

σ = MPa

2.Easy

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 70 mm, E = 100 GPa). Both are 600 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σ_r in the rod.

P = 100 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 100 GPaL = 600 mm

σ_r = MPa

3.Medium

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

P = 105 kNd = 25 mmL = 1.5 mE = 200 GPa

ε = µε

4.Medium

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

P = 110 kNd = 25 mmL = 1.5 mE = 100 GPa

δ = mm

5.Hard

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 60 mm, E = 120 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load P_max.

rod: Ø40 mm, E = 200 GPa, σ_allow = 200 MPatube: Ø100/Ø60 mm, E = 120 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 = 115 kNsegment 1: Ø30 mm, 1.5 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 0.5 m, aluminium (E = 70 GPa)

σ_max = MPa

Answer key

1. σ = 318.3 MPa
2. σ_r = 40.1 MPa
3. ε = 1070 µε
4. δ = 3.361 mm
5. P_max = 498.5 kN
6. σ_max = 1017 MPa

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