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
Ø 12 mm1.5 mP = 50 kN

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

P = 50 kNd = 12 mm
σ = MPa
2.Easy
200 kNØ2570 GPaØ120/70300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 70 mm, E = 70 GPa). Both are 300 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 70 GPaL = 300 mm
σr = MPa
3.Medium
150 kNØ2070 GPaØ100/50500 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 GPa). Both are 500 mm long and are compressed together between rigid plates by 150 kN. Find the shortening δ.

P = 150 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 500 mm
δ = mm
4.Medium
Ø 16 mmSteel1 mP = 90 kN

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

P = 90 kNd = 16 mmL = 1 mE = 200 GPa
ε = µε
5.Hard
P = ?Ø2570 GPaØ80/60600 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 160 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: Ø25 mm, E = 200 GPa, σallow = 160 MPatube: Ø80/Ø60 mm, E = 70 GPa, σallow = 70 MPa
Pmax = kN
6.Hard
Ø 25 mmAluminium1.5 mØ 12 mmSteel0.5 mP = 75 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 = 75 kNsegment 1: Ø25 mm, 1.5 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 0.5 m, steel (E = 200 GPa)
σmax = MPa

Answer key

  1. 1. σ = 442.1 MPa
  2. 2. σr = 64.47 MPa
  3. 3. δ = 0.1578 mm
  4. 4. ε = 2238 µε
  5. 5. Pmax = 201.7 kN
  6. 6. σmax = 663.1 MPa

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