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 10 mm1.5 mP = 110 kN

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

P = 110 kNd = 10 mm
σ = MPa
2.Easy
250 kNØ25120 GPaØ100/50400 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa). Both are 400 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/Ø50 mm, E = 120 GPaL = 400 mm
σr = MPa
3.Medium
Ø 20 mmCopper2 mP = 35 kN

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

P = 35 kNd = 20 mmL = 2 mE = 117 GPa
ε = µε
4.Medium
150 kNØ20110 GPaØ80/50400 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 50 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 150 kN. Find the shortening δ.

P = 150 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 110 GPaL = 400 mm
δ = mm
5.Hard
Ø 30 mmAluminium0.5 mØ 20 mmCopper1 mP = 60 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 = 60 kNsegment 1: Ø30 mm, 0.5 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 1 m, copper (E = 117 GPa)
σmax = MPa
6.Hard
P = ?Ø25100 GPaØ100/70800 mm

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

rod: Ø25 mm, E = 200 GPa, σallow = 120 MPatube: Ø100/Ø70 mm, E = 100 GPa, σallow = 50 MPa
Pmax = kN

Answer key

  1. 1. σ = 1401 MPa
  2. 2. σr = 62.11 MPa
  3. 3. ε = 952.2 µε
  4. 4. δ = 0.1501 mm
  5. 5. σmax = 191 MPa
  6. 6. Pmax = 249.4 kN

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