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 kNØ4070 GPaØ120/70600 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 70 mm, E = 70 GPa). Both are 600 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 70 GPaL = 600 mm
σr = MPa
2.Easy
300 kNØ20120 GPaØ100/70400 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 GPa). Both are 400 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 120 GPaL = 400 mm
σr = MPa
3.Medium
P = ?12400 mm200 mmØ20Ø30δ = 0.4 mm

A bar is made of a steel segment (diameter 20 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 30 mm, length 200 mm, E = 110 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.4 mm in total.

segment 1: steel, Ø20 mm, 400 mm, E = 200 GPasegment 2: bronze, Ø30 mm, 200 mm, E = 110 GPaδ = 0.4 mm
P = kN
4.Medium
Ø 20 mmBrass2 mP = 65 kN

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

P = 65 kNd = 20 mmL = 2 mE = 100 GPa
δ = mm
5.Hard
Ø 35 mmBrass1 mØ 20 mmAluminium1.5 mP = 100 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 = 100 kNsegment 1: Ø35 mm, 1 m, brass (E = 100 GPa)segment 2: Ø20 mm, 1.5 m, aluminium (E = 70 GPa)
σmax = MPa
6.Hard
40 kN12400 mm300 mmØ40Ø60σ2​ = ?

A steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) and a segment made of aluminium (diameter 60 mm, length 300 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 40 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø40 mm, 400 mm, E = 200 GPasegment 2: aluminium, Ø60 mm, 300 mm, E = 70 GPaP = 40 kN
σ2 = MPa

Answer key

  1. 1. σr = 38.78 MPa
  2. 2. σr = 110.4 MPa
  3. 3. P = 44.75 kN
  4. 4. δ = 4.138 mm
  5. 5. σmax = 318.3 MPa
  6. 6. σ2 = 7.246 MPa

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