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 mm2 mP = 105 kN

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

P = 105 kNd = 12 mm
σ = MPa
2.Easy
150 kNØ20110 GPaØ100/60400 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 60 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 110 GPaL = 400 mm
σr = MPa
3.Medium
P = ?12500 mm200 mmØ40Ø30δ = 0.2 mm

A bar is made of a steel segment (diameter 40 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 30 mm, length 200 mm, E = 110 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.2 mm in total.

segment 1: steel, Ø40 mm, 500 mm, E = 200 GPasegment 2: bronze, Ø30 mm, 200 mm, E = 110 GPaδ = 0.2 mm
P = kN
4.Medium
Ø 12 mmCopper0.5 mP = 40 kN

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

P = 40 kNd = 12 mmL = 0.5 mE = 117 GPa
ε = µε
5.Hard
Ø 40 mmCopper0.5 mØ 16 mmCopper1 mP = 75 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 = 75 kNsegment 1: Ø40 mm, 0.5 m, copper (E = 117 GPa)segment 2: Ø16 mm, 1 m, copper (E = 117 GPa)
σmax = MPa
6.Hard
80 kN12600 mm300 mmØ30Ø30σ2​ = ?

A steel segment (diameter 30 mm, length 600 mm, E = 200 GPa) and a segment made of brass (diameter 30 mm, length 300 mm, E = 100 GPa) are joined end to end and fixed between two rigid walls. An axial load of 80 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø30 mm, 600 mm, E = 200 GPasegment 2: brass, Ø30 mm, 300 mm, E = 100 GPaP = 80 kN
σ2 = MPa

Answer key

  1. 1. σ = 928.4 MPa
  2. 2. σr = 48.72 MPa
  3. 3. P = 43.84 kN
  4. 4. ε = 3023 µε
  5. 5. σmax = 373 MPa
  6. 6. σ2 = 56.59 MPa

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