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 GPaØ120/50400 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 50 mm, E = 100 GPa). Both are 400 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: Ø120/Ø50 mm, E = 100 GPaL = 400 mm
σr = MPa
2.Easy
250 kNØ25110 GPaØ100/60300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 60 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 110 GPaL = 300 mm
σr = MPa
3.Medium
Ø 20 mmBrass3 mP = 15 kN

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

P = 15 kNd = 20 mmL = 3 mE = 100 GPa
δ = mm
4.Medium
Ø 10 mmBrass1 mP = 20 kN

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

P = 20 kNd = 10 mmL = 1 mE = 100 GPa
ε = µε
5.Hard
P = ?Ø30100 GPaØ100/60600 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 60 mm, E = 100 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 150 MPatube: Ø100/Ø60 mm, E = 100 GPa, σallow = 80 MPa
Pmax = kN
6.Hard
Ø 30 mmAluminium0.5 mØ 20 mmBrass0.5 mP = 25 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 = 25 kNsegment 1: Ø30 mm, 0.5 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 0.5 m, brass (E = 100 GPa)
σmax = MPa

Answer key

  1. 1. σr = 9.682 MPa
  2. 2. σr = 76.79 MPa
  3. 3. δ = 1.432 mm
  4. 4. ε = 2546 µε
  5. 5. Pmax = 483 kN
  6. 6. σmax = 79.58 MPa

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