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
300 kNØ40110 GPaØ100/70500 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 70 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 110 GPaL = 500 mm
σr = MPa
2.Easy
80 kNØ25120 GPaØ100/70400 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 GPa). Both are 400 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: Ø100/Ø70 mm, E = 120 GPaL = 400 mm
σr = MPa
3.Medium
200 kNØ40110 GPaØ80/60400 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 200 kN. Find the shortening δ.

P = 200 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 400 mm
δ = mm
4.Medium
Ø 25 mmCopper3 mP = 85 kN

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

P = 85 kNd = 25 mmL = 3 mE = 117 GPa
ε = µε
5.Hard
100 kN12600 mm400 mmØ25Ø50σ2​ = ?

A steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) and a segment made of brass (diameter 50 mm, length 400 mm, E = 100 GPa) are joined end to end and fixed between two rigid walls. An axial load of 100 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: brass, Ø50 mm, 400 mm, E = 100 GPaP = 100 kN
σ2 = MPa
6.Hard
Ø 35 mmBrass1.5 mØ 20 mmCopper2 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: Ø35 mm, 1.5 m, brass (E = 100 GPa)segment 2: Ø20 mm, 2 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σr = 86.71 MPa
  2. 2. σr = 27.64 MPa
  3. 3. δ = 0.1622 mm
  4. 4. ε = 1480 µε
  5. 5. σ2 = 38.2 MPa
  6. 6. σmax = 31.83 MPa

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