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 25 mm2 mP = 90 kN

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

P = 90 kNd = 25 mm
σ = MPa
2.Easy
100 kNØ4070 GPaØ100/50400 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 GPa). Both are 400 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 400 mm
σr = MPa
3.Medium
Ø 25 mmAluminium1 mP = 110 kN

Find the axial strain ε in the aluminium bar, in microstrain (µε = 10⁻⁶).

P = 110 kNd = 25 mmL = 1 mE = 70 GPa
ε = µε
4.Medium
150 kNØ20100 GPaØ100/60500 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 60 mm, E = 100 GPa). Both are 500 mm long and are compressed together between rigid plates by 150 kN. Find the shortening δ.

P = 150 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 100 GPaL = 500 mm
δ = mm
5.Hard
50 kN12400 mm300 mmØ20Ø30σ2​ = ?

A steel segment (diameter 20 mm, length 400 mm, E = 200 GPa) and a segment made of copper (diameter 30 mm, length 300 mm, E = 120 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, Ø20 mm, 400 mm, E = 200 GPasegment 2: copper, Ø30 mm, 300 mm, E = 120 GPaP = 50 kN
σ2 = MPa
6.Hard
Ø 40 mmAluminium1 mØ 12 mmAluminium2 mP = 110 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 = 110 kNsegment 1: Ø40 mm, 1 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 2 m, aluminium (E = 70 GPa)
σmax = MPa

Answer key

  1. 1. σ = 183.3 MPa
  2. 2. σr = 30.14 MPa
  3. 3. ε = 3201 µε
  4. 4. δ = 0.1326 mm
  5. 5. σ2 = 45.47 MPa
  6. 6. σmax = 972.6 MPa

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