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 kNØ25100 GPaØ100/50400 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 50 mm, E = 100 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: Ø25 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 100 GPaL = 400 mm
σr = MPa
2.Easy
200 kNØ30110 GPaØ120/70500 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 70 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 110 GPaL = 500 mm
σr = MPa
3.Medium
Ø 20 mmAluminium2 mP = 75 kN

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

P = 75 kNd = 20 mmL = 2 mE = 70 GPa
δ = mm
4.Medium
Ø 30 mmCopper2 mP = 120 kN

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

P = 120 kNd = 30 mmL = 2 mE = 117 GPa
ε = µε
5.Hard
60 kN12400 mm200 mmØ40Ø60σ2​ = ?

A steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) and a segment made of copper (diameter 60 mm, length 200 mm, E = 120 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, 400 mm, E = 200 GPasegment 2: copper, Ø60 mm, 200 mm, E = 120 GPaP = 60 kN
σ2 = MPa
6.Hard
Ø 25 mmBrass1 mØ 20 mmCopper1.5 mP = 10 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 = 10 kNsegment 1: Ø25 mm, 1 m, brass (E = 100 GPa)segment 2: Ø20 mm, 1.5 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σr = 58.21 MPa
  2. 2. σr = 41.58 MPa
  3. 3. δ = 6.821 mm
  4. 4. ε = 1451 µε
  5. 5. σ2 = 15.49 MPa
  6. 6. σmax = 31.83 MPa

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