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
80 kNØ30100 GPaØ100/70800 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 70 mm, E = 100 GPa). Both are 800 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/Ø70 mm, E = 100 GPaL = 800 mm
σr = MPa
2.Easy
Ø 16 mm2 mP = 45 kN

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

P = 45 kNd = 16 mm
σ = MPa
3.Medium
Ø 10 mmBrass2.5 mP = 90 kN

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

P = 90 kNd = 10 mmL = 2.5 mE = 100 GPa
ε = µε
4.Medium
P = ?12300 mm300 mmØ30Ø50δ = 0.4 mm

A bar is made of a steel segment (diameter 30 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 50 mm, length 300 mm, E = 120 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, 300 mm, E = 200 GPasegment 2: copper, Ø50 mm, 300 mm, E = 120 GPaδ = 0.4 mm
P = kN
5.Hard
P = ?Ø3070 GPaØ80/60800 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 60 mm, E = 70 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 200 MPatube: Ø80/Ø60 mm, E = 70 GPa, σallow = 70 MPa
Pmax = kN
6.Hard
Ø 30 mmAluminium0.5 mØ 20 mmCopper2 mP = 95 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 = 95 kNsegment 1: Ø30 mm, 0.5 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 2 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σr = 29.52 MPa
  2. 2. σ = 223.8 MPa
  3. 3. ε = 11459 µε
  4. 4. P = 117.8 kN
  5. 5. Pmax = 295.3 kN
  6. 6. σmax = 302.4 MPa

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