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
100 kNØ25100 GPaØ80/50300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 50 mm, E = 100 GPa). Both are 300 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 100 GPaL = 300 mm
σr = MPa
2.Easy
80 kNØ3070 GPaØ80/50300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 50 mm, E = 70 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: Ø80/Ø50 mm, E = 70 GPaL = 300 mm
σr = MPa
3.Medium
Ø 16 mmCopper2 mP = 10 kN

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

P = 10 kNd = 16 mmL = 2 mE = 117 GPa
ε = µε
4.Medium
100 kNØ20110 GPaØ80/60300 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 100 kN. Find the shortening δ.

P = 100 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 300 mm
δ = mm
5.Hard
Ø 35 mmCopper1.5 mØ 16 mmCopper0.5 mP = 60 kN

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

P = 60 kNsegment 1: Ø35 mm, 1.5 m, copper (E = 117 GPa)segment 2: Ø16 mm, 0.5 m, copper (E = 117 GPa)
δ = mm
6.Hard
P = ?Ø30120 GPaØ120/60600 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 60 mm, E = 120 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 150 MPatube: Ø120/Ø60 mm, E = 120 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σr = 49.45 MPa
  2. 2. σr = 44.97 MPa
  3. 3. ε = 425.1 µε
  4. 4. δ = 0.09845 mm
  5. 5. δ = 2.075 mm
  6. 6. Pmax = 772.8 kN

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