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 16 mm2 mP = 65 kN

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

P = 65 kNd = 16 mm
σ = MPa
2.Easy
200 kNØ25110 GPaØ120/70400 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 70 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: Ø25 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 110 GPaL = 400 mm
σr = MPa
3.Medium
P = ?12300 mm300 mmØ20Ø60δ = 0.5 mm

A bar is made of a steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 60 mm, length 300 mm, E = 110 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.5 mm in total.

segment 1: steel, Ø20 mm, 300 mm, E = 200 GPasegment 2: bronze, Ø60 mm, 300 mm, E = 110 GPaδ = 0.5 mm
P = kN
4.Medium
Ø 12 mmSteel0.5 mP = 110 kN

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

P = 110 kNd = 12 mmL = 0.5 mE = 200 GPa
δ = mm
5.Hard
40 kN12300 mm200 mmØ25Ø60σ2​ = ?

A steel segment (diameter 25 mm, length 300 mm, E = 200 GPa) and a segment made of copper (diameter 60 mm, length 200 mm, E = 120 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, Ø25 mm, 300 mm, E = 200 GPasegment 2: copper, Ø60 mm, 200 mm, E = 120 GPaP = 40 kN
σ2 = MPa
6.Hard
Ø 25 mmCopper1 mØ 12 mmBrass1 mP = 75 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 75 kNsegment 1: Ø25 mm, 1 m, copper (E = 117 GPa)segment 2: Ø12 mm, 1 m, brass (E = 100 GPa)
δ = mm

Answer key

  1. 1. σ = 323.3 MPa
  2. 2. σr = 43.53 MPa
  3. 3. P = 87.12 kN
  4. 4. δ = 2.432 mm
  5. 5. σ2 = 11.86 MPa
  6. 6. δ = 7.937 mm

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