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 30 mm1 mP = 60 kN

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

P = 60 kNd = 30 mm
σ = MPa
2.Easy
250 kNØ2570 GPaØ100/50400 mmσr​ = ?

A steel rod (diameter 25 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 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 400 mm
σr = MPa
3.Medium
Ø 30 mmBrass2.5 mP = 110 kN

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

P = 110 kNd = 30 mmL = 2.5 mE = 100 GPa
ε = µε
4.Medium
100 kNØ3070 GPaØ120/60800 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 60 mm, E = 70 GPa). Both are 800 mm long and are compressed together between rigid plates by 100 kN. Find the shortening δ.

P = 100 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 70 GPaL = 800 mm
δ = mm
5.Hard
80 kN12300 mm400 mmØ20Ø30σ2​ = ?

A steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) and a segment made of brass (diameter 30 mm, length 400 mm, E = 100 GPa) are joined end to end and fixed between two rigid walls. An axial load of 80 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, Ø30 mm, 400 mm, E = 100 GPaP = 80 kN
σ2 = MPa
6.Hard
80 kN12600 mm300 mmØ25Ø40σ2​ = ?

A steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) and a segment made of aluminium (diameter 40 mm, length 300 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 80 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø25 mm, 600 mm, E = 200 GPasegment 2: aluminium, Ø40 mm, 300 mm, E = 70 GPaP = 80 kN
σ2 = MPa

Answer key

  1. 1. σ = 84.88 MPa
  2. 2. σr = 97.94 MPa
  3. 3. ε = 1556 µε
  4. 4. δ = 0.1088 mm
  5. 5. σ2 = 51.79 MPa
  6. 6. σ2 = 40.86 MPa

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