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
300 kNØ4070 GPaØ120/70400 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 400 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 70 GPaL = 400 mm
σr = MPa
2.Easy
300 kNØ25120 GPaØ80/60500 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 GPa). Both are 500 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 500 mm
σr = MPa
3.Medium
Ø 10 mmAluminium1 mP = 35 kN

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

P = 35 kNd = 10 mmL = 1 mE = 70 GPa
δ = mm
4.Medium
P = ?12600 mm200 mmØ20Ø50δ = 0.25 mm

A bar is made of a steel segment (diameter 20 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 50 mm, length 200 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.25 mm in total.

segment 1: steel, Ø20 mm, 600 mm, E = 200 GPasegment 2: aluminium, Ø50 mm, 200 mm, E = 70 GPaδ = 0.25 mm
P = kN
5.Hard
Ø 40 mmSteel1 mØ 12 mmBrass1.5 mP = 55 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 = 55 kNsegment 1: Ø40 mm, 1 m, steel (E = 200 GPa)segment 2: Ø12 mm, 1.5 m, brass (E = 100 GPa)
σmax = MPa
6.Hard
20 kN12500 mm200 mmØ40Ø50σ2​ = ?

A steel segment (diameter 40 mm, length 500 mm, E = 200 GPa) and a segment made of bronze (diameter 50 mm, length 200 mm, E = 110 GPa) are joined end to end and fixed between two rigid walls. An axial load of 20 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø40 mm, 500 mm, E = 200 GPasegment 2: bronze, Ø50 mm, 200 mm, E = 110 GPaP = 20 kN
σ2 = MPa

Answer key

  1. 1. σr = 77.56 MPa
  2. 2. σr = 165.7 MPa
  3. 3. δ = 6.366 mm
  4. 4. P = 22.72 kN
  5. 5. σmax = 486.3 MPa
  6. 6. σ2 = 6.951 MPa

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