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 = 120 kN

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

P = 120 kNd = 12 mm
σ = MPa
2.Easy
250 kNØ30120 GPaØ120/70300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 70 mm, E = 120 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: Ø30 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 120 GPaL = 300 mm
σr = MPa
3.Medium
P = ?12600 mm400 mmØ25Ø40δ = 0.5 mm

A bar is made of a steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 40 mm, length 400 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.5 mm in total.

segment 1: steel, Ø25 mm, 600 mm, E = 200 GPasegment 2: aluminium, Ø40 mm, 400 mm, E = 70 GPaδ = 0.5 mm
P = kN
4.Medium
Ø 16 mmSteel3 mP = 10 kN

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

P = 10 kNd = 16 mmL = 3 mE = 200 GPa
ε = µε
5.Hard
Ø 35 mmCopper1.5 mØ 12 mmCopper0.5 mP = 50 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 = 50 kNsegment 1: Ø35 mm, 1.5 m, copper (E = 117 GPa)segment 2: Ø12 mm, 0.5 m, copper (E = 117 GPa)
σmax = MPa
6.Hard
20 kN12600 mm400 mmØ20Ø40σ2​ = ?

A steel segment (diameter 20 mm, length 600 mm, E = 200 GPa) and a segment made of bronze (diameter 40 mm, length 400 mm, E = 110 GPa) are joined end to end and fixed between two rigid walls. An axial load of 20 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø20 mm, 600 mm, E = 200 GPasegment 2: bronze, Ø40 mm, 400 mm, E = 110 GPaP = 20 kN
σ2 = MPa

Answer key

  1. 1. σ = 1061 MPa
  2. 2. σr = 48.23 MPa
  3. 3. P = 46.91 kN
  4. 4. ε = 248.7 µε
  5. 5. σmax = 442.1 MPa
  6. 6. σ2 = 12.21 MPa

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