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 25 mm2 mP = 30 kN

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

P = 30 kNd = 25 mm
σ = MPa
2.Easy
50 kNØ40110 GPaØ120/50800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 50 mm, E = 110 GPa). Both are 800 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 110 GPaL = 800 mm
σr = MPa
3.Medium
50 kNØ20100 GPaØ100/60500 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 60 mm, E = 100 GPa). Both are 500 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 100 GPaL = 500 mm
δ = mm
4.Medium
Ø 16 mmBrass1.5 mP = 30 kN

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

P = 30 kNd = 16 mmL = 1.5 mE = 100 GPa
ε = µε
5.Hard
P = ?Ø4070 GPaØ80/50800 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 50 mm, E = 70 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 250 MPatube: Ø80/Ø50 mm, E = 70 GPa, σallow = 60 MPa
Pmax = kN
6.Hard
Ø 40 mmCopper2 mØ 20 mmBrass1 mP = 20 kN

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

P = 20 kNsegment 1: Ø40 mm, 2 m, copper (E = 117 GPa)segment 2: Ø20 mm, 1 m, brass (E = 100 GPa)
δ = mm

Answer key

  1. 1. σ = 61.12 MPa
  2. 2. σr = 7.816 MPa
  3. 3. δ = 0.04421 mm
  4. 4. ε = 1492 µε
  5. 5. Pmax = 399.2 kN
  6. 6. δ = 0.9087 mm

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