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 16 mm1.5 mP = 25 kN

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

P = 25 kNd = 16 mm
σ = MPa
2.Easy
250 kNØ3070 GPaØ100/60400 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 60 mm, E = 70 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: Ø30 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 70 GPaL = 400 mm
σr = MPa
3.Medium
P = ?12400 mm500 mmØ25Ø30δ = 0.3 mm

A bar is made of a steel segment (diameter 25 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 30 mm, length 500 mm, E = 120 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.3 mm in total.

segment 1: steel, Ø25 mm, 400 mm, E = 200 GPasegment 2: copper, Ø30 mm, 500 mm, E = 120 GPaδ = 0.3 mm
P = kN
4.Medium
Ø 30 mmAluminium3 mP = 120 kN

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

P = 120 kNd = 30 mmL = 3 mE = 70 GPa
ε = µε
5.Hard
Ø 30 mmAluminium1.5 mØ 12 mmBrass1 mP = 20 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 = 20 kNsegment 1: Ø30 mm, 1.5 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 1 m, brass (E = 100 GPa)
σmax = MPa
6.Hard
80 kN12300 mm300 mmØ20Ø40σ2​ = ?

A steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) and a segment made of bronze (diameter 40 mm, length 300 mm, E = 110 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, Ø20 mm, 300 mm, E = 200 GPasegment 2: bronze, Ø40 mm, 300 mm, E = 110 GPaP = 80 kN
σ2 = MPa

Answer key

  1. 1. σ = 124.3 MPa
  2. 2. σr = 101.4 MPa
  3. 3. P = 30.09 kN
  4. 4. ε = 2425 µε
  5. 5. σmax = 176.8 MPa
  6. 6. σ2 = 43.77 MPa

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