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
Ø 10 mm2 mP = 70 kN

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

P = 70 kNd = 10 mm
σ = MPa
2.Easy
100 kNØ30110 GPaØ120/70300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 70 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 110 GPaL = 300 mm
σr = MPa
3.Medium
80 kNØ30110 GPaØ80/50400 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 50 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 80 kN. Find the shortening δ.

P = 80 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 110 GPaL = 400 mm
δ = mm
4.Medium
P = ?12500 mm200 mmØ20Ø60δ = 0.2 mm

A bar is made of a steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 60 mm, length 200 mm, E = 120 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.2 mm in total.

segment 1: steel, Ø20 mm, 500 mm, E = 200 GPasegment 2: copper, Ø60 mm, 200 mm, E = 120 GPaδ = 0.2 mm
P = kN
5.Hard
Ø 40 mmAluminium2 mØ 20 mmSteel1 mP = 65 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 = 65 kNsegment 1: Ø40 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 1 m, steel (E = 200 GPa)
σmax = MPa
6.Hard
100 kN12300 mm200 mmØ40Ø40σ2​ = ?

A steel segment (diameter 40 mm, length 300 mm, E = 200 GPa) and a segment made of copper (diameter 40 mm, length 200 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, Ø40 mm, 300 mm, E = 200 GPasegment 2: copper, Ø40 mm, 200 mm, E = 120 GPaP = 100 kN
σ2 = MPa

Answer key

  1. 1. σ = 891.3 MPa
  2. 2. σr = 20.79 MPa
  3. 3. δ = 0.0669 mm
  4. 4. P = 23.4 kN
  5. 5. σmax = 206.9 MPa
  6. 6. σ2 = 37.69 MPa

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