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
150 kNØ30120 GPaØ120/60800 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 60 mm, E = 120 GPa). Both are 800 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 120 GPaL = 800 mm
σr = MPa
2.Easy
Ø 10 mm0.5 mP = 75 kN

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

P = 75 kNd = 10 mm
σ = MPa
3.Medium
Ø 12 mmBrass1 mP = 25 kN

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

P = 25 kNd = 12 mmL = 1 mE = 100 GPa
ε = µε
4.Medium
P = ?12400 mm200 mmØ30Ø30δ = 0.4 mm

A bar is made of a steel segment (diameter 30 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 30 mm, length 200 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, Ø30 mm, 400 mm, E = 200 GPasegment 2: brass, Ø30 mm, 200 mm, E = 100 GPaδ = 0.4 mm
P = kN
5.Hard
Ø 35 mmCopper2 mØ 12 mmBrass1.5 mP = 75 kN

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

P = 75 kNsegment 1: Ø35 mm, 2 m, copper (E = 117 GPa)segment 2: Ø12 mm, 1.5 m, brass (E = 100 GPa)
δ = mm
6.Hard
Ø 40 mmCopper1 mØ 16 mmCopper0.5 mP = 25 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 = 25 kNsegment 1: Ø40 mm, 1 m, copper (E = 117 GPa)segment 2: Ø16 mm, 0.5 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σr = 25.88 MPa
  2. 2. σ = 954.9 MPa
  3. 3. ε = 2210 µε
  4. 4. P = 70.69 kN
  5. 5. δ = 11.28 mm
  6. 6. σmax = 124.3 MPa

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