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 = 55 kNd = 25 mm

σ = MPa

2.Easy

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 70 mm, E = 70 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 = 70 GPaL = 600 mm

σ_r = MPa

3.Medium

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

P = 80 kNd = 30 mmL = 3 mE = 70 GPa

δ = mm

4.Medium

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

P = 120 kNd = 12 mmL = 1.5 mE = 70 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 100 mm, inner diameter 60 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: Ø100/Ø60 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 total elongation δ.

P = 50 kNsegment 1: Ø40 mm, 2 m, steel (E = 200 GPa)segment 2: Ø12 mm, 1 m, copper (E = 117 GPa)

δ = mm

Answer key

1. σ = 112 MPa
2. σ_r = 52.83 MPa
3. δ = 4.85 mm
4. ε = 15158 µε
5. P_max = 295.9 kN
6. δ = 4.176 mm

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