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
50 kNØ2070 GPaØ120/50800 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa). Both are 800 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 70 GPaL = 800 mm
σr = MPa
2.Easy
80 kNØ30120 GPaØ100/60300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 60 mm, E = 120 GPa). Both are 300 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 120 GPaL = 300 mm
σr = MPa
3.Medium
Ø 30 mmSteel2 mP = 100 kN

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

P = 100 kNd = 30 mmL = 2 mE = 200 GPa
ε = µε
4.Medium
P = ?12500 mm400 mmØ25Ø40δ = 0.4 mm

A bar is made of a steel segment (diameter 25 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 40 mm, length 400 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.4 mm in total.

segment 1: steel, Ø25 mm, 500 mm, E = 200 GPasegment 2: brass, Ø40 mm, 400 mm, E = 100 GPaδ = 0.4 mm
P = kN
5.Hard
Ø 25 mmCopper2 mØ 12 mmAluminium1.5 mP = 105 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 = 105 kNsegment 1: Ø25 mm, 2 m, copper (E = 117 GPa)segment 2: Ø12 mm, 1.5 m, aluminium (E = 70 GPa)
σmax = MPa
6.Hard
Ø 30 mmAluminium1.5 mØ 12 mmSteel1 mP = 80 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 80 kNsegment 1: Ø30 mm, 1.5 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 1 m, steel (E = 200 GPa)
δ = mm

Answer key

  1. 1. σr = 13.95 MPa
  2. 2. σr = 21.49 MPa
  3. 3. ε = 707.4 µε
  4. 4. P = 48.33 kN
  5. 5. σmax = 928.4 MPa
  6. 6. δ = 5.962 mm

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