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 20 mm1 mP = 80 kN

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

P = 80 kNd = 20 mm
σ = MPa
2.Easy
250 kNØ2570 GPaØ100/70600 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 70 mm, E = 70 GPa). Both are 600 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 70 GPaL = 600 mm
σr = MPa
3.Medium
P = ?12300 mm400 mmØ30Ø60δ = 0.3 mm

A bar is made of a steel segment (diameter 30 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 60 mm, length 400 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.3 mm in total.

segment 1: steel, Ø30 mm, 300 mm, E = 200 GPasegment 2: aluminium, Ø60 mm, 400 mm, E = 70 GPaδ = 0.3 mm
P = kN
4.Medium
Ø 10 mmBrass1 mP = 55 kN

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

P = 55 kNd = 10 mmL = 1 mE = 100 GPa
δ = mm
5.Hard
Ø 40 mmAluminium1 mØ 20 mmBrass1.5 mP = 40 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 = 40 kNsegment 1: Ø40 mm, 1 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 1.5 m, brass (E = 100 GPa)
σmax = MPa
6.Hard
50 kN12500 mm400 mmØ30Ø30σ2​ = ?

A steel segment (diameter 30 mm, length 500 mm, E = 200 GPa) and a segment made of aluminium (diameter 30 mm, length 400 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 50 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø30 mm, 500 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 400 mm, E = 70 GPaP = 50 kN
σ2 = MPa

Answer key

  1. 1. σ = 254.6 MPa
  2. 2. σr = 132.1 MPa
  3. 3. P = 72.41 kN
  4. 4. δ = 7.003 mm
  5. 5. σmax = 127.3 MPa
  6. 6. σ2 = 21.53 MPa

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