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 mm1.5 mP = 10 kN

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

P = 10 kNd = 16 mm
σ = MPa
2.Easy
250 kNØ4070 GPaØ80/50500 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 50 mm, E = 70 GPa). Both are 500 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 70 GPaL = 500 mm
σr = MPa
3.Medium
Ø 25 mmAluminium1.5 mP = 110 kN

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

P = 110 kNd = 25 mmL = 1.5 mE = 70 GPa
δ = mm
4.Medium
P = ?12300 mm400 mmØ40Ø60δ = 0.2 mm

A bar is made of a steel segment (diameter 40 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 60 mm, length 400 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, Ø40 mm, 300 mm, E = 200 GPasegment 2: copper, Ø60 mm, 400 mm, E = 120 GPaδ = 0.2 mm
P = kN
5.Hard
Ø 30 mmAluminium1 mØ 16 mmCopper2 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: Ø30 mm, 1 m, aluminium (E = 70 GPa)segment 2: Ø16 mm, 2 m, copper (E = 117 GPa)
δ = mm
6.Hard
40 kN12300 mm400 mmØ20Ø60σ2​ = ?

A steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) and a segment made of brass (diameter 60 mm, length 400 mm, E = 100 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, Ø20 mm, 300 mm, E = 200 GPasegment 2: brass, Ø60 mm, 400 mm, E = 100 GPaP = 40 kN
σ2 = MPa

Answer key

  1. 1. σ = 49.74 MPa
  2. 2. σr = 107.4 MPa
  3. 3. δ = 4.802 mm
  4. 4. P = 84.3 kN
  5. 5. δ = 7.892 mm
  6. 6. σ2 = 10.91 MPa

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