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 = 20 kN

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

P = 20 kNd = 10 mm
σ = MPa
2.Easy
80 kNØ40100 GPaØ100/70500 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 70 mm, E = 100 GPa). Both are 500 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 100 GPaL = 500 mm
σr = MPa
3.Medium
Ø 10 mmAluminium1 mP = 110 kN

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

P = 110 kNd = 10 mmL = 1 mE = 70 GPa
ε = µε
4.Medium
P = ?12600 mm500 mmØ40Ø30δ = 0.5 mm

A bar is made of a steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 30 mm, length 500 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, Ø40 mm, 600 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 500 mm, E = 70 GPaδ = 0.5 mm
P = kN
5.Hard
20 kN12500 mm300 mmØ20Ø60σ2​ = ?

A steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) and a segment made of bronze (diameter 60 mm, length 300 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, 500 mm, E = 200 GPasegment 2: bronze, Ø60 mm, 300 mm, E = 110 GPaP = 20 kN
σ2 = MPa
6.Hard
50 kN12400 mm400 mmØ20Ø60σ2​ = ?

A steel segment (diameter 20 mm, length 400 mm, E = 200 GPa) and a segment made of aluminium (diameter 60 mm, length 400 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 50 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø20 mm, 400 mm, E = 200 GPasegment 2: aluminium, Ø60 mm, 400 mm, E = 70 GPaP = 50 kN
σ2 = MPa

Answer key

  1. 1. σ = 254.6 MPa
  2. 2. σr = 24.54 MPa
  3. 3. ε = 20008 µε
  4. 4. P = 40.02 kN
  5. 5. σ2 = 6.309 MPa
  6. 6. σ2 = 13.42 MPa

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