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
200 kNØ30110 GPaØ120/60400 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 60 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 110 GPaL = 400 mm
σr = MPa
2.Easy
150 kNØ3070 GPaØ80/50400 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 50 mm, E = 70 GPa). Both are 400 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 70 GPaL = 400 mm
σr = MPa
3.Medium
300 kNØ30110 GPaØ100/70500 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 70 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 110 GPaL = 500 mm
δ = mm
4.Medium
50 kNØ20110 GPaØ80/60500 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 500 mm
δ = mm
5.Hard
100 kN12400 mm500 mmØ30Ø50σ2​ = ?

A steel segment (diameter 30 mm, length 400 mm, E = 200 GPa) and a segment made of copper (diameter 50 mm, length 500 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 100 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø30 mm, 400 mm, E = 200 GPasegment 2: copper, Ø50 mm, 500 mm, E = 120 GPaP = 100 kN
σ2 = MPa
6.Hard
Ø 35 mmCopper2 mØ 12 mmCopper0.5 mP = 110 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 = 110 kNsegment 1: Ø35 mm, 2 m, copper (E = 117 GPa)segment 2: Ø12 mm, 0.5 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σr = 37.23 MPa
  2. 2. σr = 84.32 MPa
  3. 3. δ = 0.2577 mm
  4. 4. δ = 0.08204 mm
  5. 5. σ2 = 29.1 MPa
  6. 6. σmax = 972.6 MPa

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