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 20 mm1 mP = 45 kN

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

P = 45 kNd = 20 mm
σ = MPa
2.Easy
50 kNØ25110 GPaØ100/50600 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa). Both are 600 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: Ø100/Ø50 mm, E = 110 GPaL = 600 mm
σr = MPa
3.Medium
80 kNØ20100 GPaØ80/60800 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 60 mm, E = 100 GPa). Both are 800 mm long and are compressed together between rigid plates by 80 kN. Find the shortening δ.

P = 80 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 100 GPaL = 800 mm
δ = mm
4.Medium
Ø 10 mmSteel2.5 mP = 55 kN

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

P = 55 kNd = 10 mmL = 2.5 mE = 200 GPa
ε = µε
5.Hard
Ø 35 mmCopper0.5 mØ 16 mmSteel1 mP = 70 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 = 70 kNsegment 1: Ø35 mm, 0.5 m, copper (E = 117 GPa)segment 2: Ø16 mm, 1 m, steel (E = 200 GPa)
σmax = MPa
6.Hard
P = ?Ø2070 GPaØ100/50400 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 250 MPatube: Ø100/Ø50 mm, E = 70 GPa, σallow = 60 MPa
Pmax = kN

Answer key

  1. 1. σ = 143.2 MPa
  2. 2. σr = 13.4 MPa
  3. 3. δ = 0.2264 mm
  4. 4. ε = 3501 µε
  5. 5. σmax = 348.2 MPa
  6. 6. Pmax = 407.3 kN

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