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 16 mm2 mP = 20 kN

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

P = 20 kNd = 16 mm
σ = MPa
2.Easy
100 kNØ40100 GPaØ100/60800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 60 mm, E = 100 GPa). Both are 800 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 100 GPaL = 800 mm
σr = MPa
3.Medium
Ø 20 mmAluminium2 mP = 115 kN

Find the elongation δ of the aluminium bar under the axial load.

P = 115 kNd = 20 mmL = 2 mE = 70 GPa
δ = mm
4.Medium
Ø 12 mmCopper0.5 mP = 100 kN

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

P = 100 kNd = 12 mmL = 0.5 mE = 117 GPa
ε = µε
5.Hard
P = ?Ø20120 GPaØ120/70300 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 70 mm, E = 120 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 250 MPatube: Ø120/Ø70 mm, E = 120 GPa, σallow = 70 MPa
Pmax = kN
6.Hard
P = ?Ø30110 GPaØ100/70600 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 70 mm, E = 110 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 120 MPatube: Ø100/Ø70 mm, E = 110 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σ = 99.47 MPa
  2. 2. σr = 26.53 MPa
  3. 3. δ = 10.46 mm
  4. 4. ε = 7557 µε
  5. 5. Pmax = 558.9 kN
  6. 6. Pmax = 349.2 kN

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