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
250 kNØ40100 GPaØ100/70500 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 70 mm, E = 100 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/Ø70 mm, E = 100 GPaL = 500 mm
σr = MPa
2.Easy
80 kNØ25100 GPaØ80/60500 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 60 mm, E = 100 GPa). Both are 500 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 100 GPaL = 500 mm
σr = MPa
3.Medium
Ø 10 mmSteel2.5 mP = 65 kN

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

P = 65 kNd = 10 mmL = 2.5 mE = 200 GPa
ε = µε
4.Medium
Ø 16 mmBrass2 mP = 105 kN

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

P = 105 kNd = 16 mmL = 2 mE = 100 GPa
δ = mm
5.Hard
60 kN12300 mm400 mmØ40Ø30σ2​ = ?

A steel segment (diameter 40 mm, length 300 mm, E = 200 GPa) and a segment made of aluminium (diameter 30 mm, length 400 mm, E = 70 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: aluminium, Ø30 mm, 400 mm, E = 70 GPaP = 60 kN
σ2 = MPa
6.Hard
Ø 30 mmBrass0.5 mØ 16 mmSteel0.5 mP = 60 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 = 60 kNsegment 1: Ø30 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø16 mm, 0.5 m, steel (E = 200 GPa)
σmax = MPa

Answer key

  1. 1. σr = 76.7 MPa
  2. 2. σr = 50.3 MPa
  3. 3. ε = 4138 µε
  4. 4. δ = 10.44 mm
  5. 5. σ2 = 10.92 MPa
  6. 6. σmax = 298.4 MPa

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