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
200 kNØ20110 GPaØ120/50400 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 50 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: Ø20 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 110 GPaL = 400 mm
σr = MPa
2.Easy
Ø 10 mm0.5 mP = 105 kN

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

P = 105 kNd = 10 mm
σ = MPa
3.Medium
250 kNØ25110 GPaØ100/70600 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 70 mm, E = 110 GPa). Both are 600 mm long and are compressed together between rigid plates by 250 kN. Find the shortening δ.

P = 250 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 110 GPaL = 600 mm
δ = mm
4.Medium
50 kNØ25120 GPaØ120/50400 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 50 mm, E = 120 GPa). Both are 400 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 120 GPaL = 400 mm
δ = mm
5.Hard
100 kN12300 mm200 mmØ20Ø40σ2​ = ?

A steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) and a segment made of bronze (diameter 40 mm, length 200 mm, E = 110 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, Ø20 mm, 300 mm, E = 200 GPasegment 2: bronze, Ø40 mm, 200 mm, E = 110 GPaP = 100 kN
σ2 = MPa
6.Hard
Ø 25 mmAluminium1 mØ 20 mmCopper1.5 mP = 35 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 = 35 kNsegment 1: Ø25 mm, 1 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 1.5 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σr = 36.67 MPa
  2. 2. σ = 1337 MPa
  3. 3. δ = 0.2784 mm
  4. 4. δ = 0.0164 mm
  5. 5. σ2 = 61.07 MPa
  6. 6. σmax = 111.4 MPa

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