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
200 kNØ4070 GPaØ120/60800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 60 mm, E = 70 GPa). Both are 800 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 70 GPaL = 800 mm
σr = MPa
2.Easy
Ø 20 mm2 mP = 100 kN

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

P = 100 kNd = 20 mm
σ = MPa
3.Medium
Ø 30 mmAluminium2.5 mP = 110 kN

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

P = 110 kNd = 30 mmL = 2.5 mE = 70 GPa
ε = µε
4.Medium
Ø 25 mmBrass1.5 mP = 70 kN

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

P = 70 kNd = 25 mmL = 1.5 mE = 100 GPa
δ = mm
5.Hard
P = ?Ø25120 GPaØ100/50800 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 250 MPatube: Ø100/Ø50 mm, E = 120 GPa, σallow = 70 MPa
Pmax = kN
6.Hard
P = ?Ø20110 GPaØ100/70800 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 70 mm, E = 110 GPa, allowable stress 100 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 150 MPatube: Ø100/Ø70 mm, E = 110 GPa, σallow = 100 MPa
Pmax = kN

Answer key

  1. 1. σr = 47.33 MPa
  2. 2. σ = 318.3 MPa
  3. 3. ε = 2223 µε
  4. 4. δ = 2.139 mm
  5. 5. Pmax = 469.6 kN
  6. 6. Pmax = 377.6 kN

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