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 12 mm0.5 mP = 60 kN

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

P = 60 kNd = 12 mm
σ = MPa
2.Easy
300 kNØ30100 GPaØ100/50800 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 50 mm, E = 100 GPa). Both are 800 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 100 GPaL = 800 mm
σr = MPa
3.Medium
Ø 16 mmBrass2 mP = 40 kN

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

P = 40 kNd = 16 mmL = 2 mE = 100 GPa
δ = mm
4.Medium
Ø 12 mmSteel1.5 mP = 45 kN

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

P = 45 kNd = 12 mmL = 1.5 mE = 200 GPa
ε = µε
5.Hard
P = ?Ø25100 GPaØ120/70400 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 70 mm, E = 100 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 120 MPatube: Ø120/Ø70 mm, E = 100 GPa, σallow = 80 MPa
Pmax = kN
6.Hard
P = ?Ø40110 GPaØ80/50500 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 50 mm, E = 110 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 150 MPatube: Ø80/Ø50 mm, E = 110 GPa, σallow = 70 MPa
Pmax = kN

Answer key

  1. 1. σ = 530.5 MPa
  2. 2. σr = 82.14 MPa
  3. 3. δ = 3.979 mm
  4. 4. ε = 1989 µε
  5. 5. Pmax = 506.6 kN
  6. 6. Pmax = 374.3 kN

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