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 12 mm2 mP = 50 kN

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

P = 50 kNd = 12 mm
σ = MPa
2.Easy
250 kNØ40120 GPaØ100/50500 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 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: Ø100/Ø50 mm, E = 120 GPaL = 500 mm
σr = MPa
3.Medium
Ø 25 mmAluminium2.5 mP = 45 kN

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

P = 45 kNd = 25 mmL = 2.5 mE = 70 GPa
ε = µε
4.Medium
100 kNØ20120 GPaØ100/50500 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa). Both are 500 mm long and are compressed together between rigid plates by 100 kN. Find the shortening δ.

P = 100 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 120 GPaL = 500 mm
δ = mm
5.Hard
80 kN12400 mm400 mmØ40Ø60σ2​ = ?

A steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) and a segment made of aluminium (diameter 60 mm, length 400 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, Ø40 mm, 400 mm, E = 200 GPasegment 2: aluminium, Ø60 mm, 400 mm, E = 70 GPaP = 80 kN
σ2 = MPa
6.Hard
50 kN12400 mm300 mmØ25Ø40σ2​ = ?

A steel segment (diameter 25 mm, length 400 mm, E = 200 GPa) and a segment made of bronze (diameter 40 mm, length 300 mm, E = 110 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, Ø25 mm, 400 mm, E = 200 GPasegment 2: bronze, Ø40 mm, 300 mm, E = 110 GPaP = 50 kN
σ2 = MPa

Answer key

  1. 1. σ = 442.1 MPa
  2. 2. σr = 52.18 MPa
  3. 3. ε = 1310 µε
  4. 4. δ = 0.06496 mm
  5. 5. σ2 = 12.47 MPa
  6. 6. σ2 = 25.96 MPa

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