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 = 75 kN

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

P = 75 kNd = 12 mm
σ = MPa
2.Easy
150 kNØ20120 GPaØ120/60600 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 60 mm, E = 120 GPa). Both are 600 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 120 GPaL = 600 mm
σr = MPa
3.Medium
Ø 20 mmSteel1.5 mP = 110 kN

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

P = 110 kNd = 20 mmL = 1.5 mE = 200 GPa
δ = mm
4.Medium
Ø 10 mmCopper2.5 mP = 40 kN

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

P = 40 kNd = 10 mmL = 2.5 mE = 117 GPa
ε = µε
5.Hard
60 kN12300 mm300 mmØ40Ø30σ2​ = ?

A steel segment (diameter 40 mm, length 300 mm, E = 200 GPa) and a segment made of bronze (diameter 30 mm, length 300 mm, E = 110 GPa) are joined end to end and fixed between two rigid walls. An axial load of 60 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø40 mm, 300 mm, E = 200 GPasegment 2: bronze, Ø30 mm, 300 mm, E = 110 GPaP = 60 kN
σ2 = MPa
6.Hard
20 kN12300 mm400 mmØ25Ø60σ2​ = ?

A steel segment (diameter 25 mm, length 300 mm, E = 200 GPa) and a segment made of bronze (diameter 60 mm, length 400 mm, E = 110 GPa) are joined end to end and fixed between two rigid walls. An axial load of 20 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø25 mm, 300 mm, E = 200 GPasegment 2: bronze, Ø60 mm, 400 mm, E = 110 GPaP = 20 kN
σ2 = MPa

Answer key

  1. 1. σ = 663.1 MPa
  2. 2. σr = 27.76 MPa
  3. 3. δ = 2.626 mm
  4. 4. ε = 4353 µε
  5. 5. σ2 = 20.06 MPa
  6. 6. σ2 = 4.978 MPa

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