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
150 kNØ25110 GPaØ80/50300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 50 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 110 GPaL = 300 mm
σr = MPa
2.Easy
Ø 25 mm1 mP = 50 kN

A solid round bar carries an axial tensile load P. Find the normal stress σ in the bar.

P = 50 kNd = 25 mm
σ = MPa
3.Medium
50 kNØ2570 GPaØ80/60300 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 60 mm, E = 70 GPa). Both are 300 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 70 GPaL = 300 mm
δ = mm
4.Medium
Ø 12 mmCopper1 mP = 50 kN

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

P = 50 kNd = 12 mmL = 1 mE = 117 GPa
ε = µε
5.Hard
P = ?Ø40120 GPaØ120/60600 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 60 mm, E = 120 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 150 MPatube: Ø120/Ø60 mm, E = 120 GPa, σallow = 80 MPa
Pmax = kN
6.Hard
Ø 30 mmAluminium2 mØ 20 mmBrass0.5 mP = 35 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the largest normal stress σmax in the bar.

P = 35 kNsegment 1: Ø30 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 0.5 m, brass (E = 100 GPa)
σmax = MPa

Answer key

  1. 1. σr = 68.95 MPa
  2. 2. σ = 101.9 MPa
  3. 3. δ = 0.0595 mm
  4. 4. ε = 3779 µε
  5. 5. Pmax = 846.1 kN
  6. 6. σmax = 111.4 MPa

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