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 100 mm, inner diameter 60 mm, E = 110 GPa). Both are 800 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σ_r in the rod.

P = 250 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø60 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 = 55 kNd = 25 mm

σ = MPa

3.Medium

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

P = 100 kNd = 25 mmL = 1 mE = 200 GPa

δ = mm

4.Medium

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

P = 30 kNd = 16 mmL = 3 mE = 70 GPa

δ = mm

5.Hard

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 70 mm, E = 120 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load P_max.

rod: Ø20 mm, E = 200 GPa, σ_allow = 120 MPatube: Ø120/Ø70 mm, E = 120 GPa, σ_allow = 60 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 = 60 kNsegment 1: Ø40 mm, 1 m, copper (E = 117 GPa)segment 2: Ø12 mm, 2 m, steel (E = 200 GPa)

σ_max = MPa

Answer key

1. σ_r = 76.79 MPa
2. σ = 112 MPa
3. δ = 1.019 mm
4. δ = 6.395 mm
5. P_max = 479.1 kN
6. σ_max = 530.5 MPa

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