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 kNØ25100 GPaØ100/50300 mmσr​ = ?

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

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 100 GPaL = 300 mm
σr = MPa
2.Easy
Ø 25 mm2 mP = 10 kN

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

P = 10 kNd = 25 mm
σ = MPa
3.Medium
50 kNØ30120 GPaØ80/60800 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 GPa). Both are 800 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 800 mm
δ = mm
4.Medium
Ø 16 mmCopper0.5 mP = 50 kN

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

P = 50 kNd = 16 mmL = 0.5 mE = 117 GPa
ε = µε
5.Hard
Ø 25 mmCopper2 mØ 16 mmBrass1.5 mP = 35 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 = 35 kNsegment 1: Ø25 mm, 2 m, copper (E = 117 GPa)segment 2: Ø16 mm, 1.5 m, brass (E = 100 GPa)
σmax = MPa
6.Hard
P = ?Ø40100 GPaØ80/60600 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 60 mm, E = 100 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 200 MPatube: Ø80/Ø60 mm, E = 100 GPa, σallow = 70 MPa
Pmax = kN

Answer key

  1. 1. σr = 14.55 MPa
  2. 2. σ = 20.37 MPa
  3. 3. δ = 0.0987 mm
  4. 4. ε = 2125 µε
  5. 5. σmax = 174.1 MPa
  6. 6. Pmax = 329.9 kN

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