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 120 mm, inner diameter 50 mm, E = 110 GPa). Both are 800 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σ_r in the rod.

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 110 GPaL = 800 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 = 60 kNd = 20 mm

σ = MPa

3.Medium

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

P = 60 kNd = 12 mmL = 3 mE = 100 GPa

ε = µε

4.Medium

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

P = 70 kNd = 10 mmL = 0.5 mE = 70 GPa

ε = µε

5.Hard

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 100 kNsegment 1: Ø25 mm, 1.5 m, steel (E = 200 GPa)segment 2: Ø12 mm, 2 m, copper (E = 117 GPa)

δ = mm

6.Hard

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 60 mm, E = 100 GPa, allowable stress 50 MPa). They are compressed together between rigid plates. Find the largest load P_max.

rod: Ø30 mm, E = 200 GPa, σ_allow = 200 MPatube: Ø80/Ø60 mm, E = 100 GPa, σ_allow = 50 MPa

P_max = kN

Answer key

1. σ_r = 8.879 MPa
2. σ = 191 MPa
3. ε = 5305 µε
4. ε = 12732 µε
5. δ = 16.64 mm
6. P_max = 180.6 kN

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