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 25 mm0.5 mP = 65 kN

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

P = 65 kNd = 25 mm
σ = MPa
2.Easy
100 kNØ20120 GPaØ120/70400 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 70 mm, E = 120 GPa). Both are 400 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 120 GPaL = 400 mm
σr = MPa
3.Medium
Ø 20 mmAluminium3 mP = 20 kN

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

P = 20 kNd = 20 mmL = 3 mE = 70 GPa
ε = µε
4.Medium
300 kNØ30120 GPaØ80/60300 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 GPa). Both are 300 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 300 mm
δ = mm
5.Hard
Ø 25 mmCopper1.5 mØ 20 mmAluminium0.5 mP = 45 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 45 kNsegment 1: Ø25 mm, 1.5 m, copper (E = 117 GPa)segment 2: Ø20 mm, 0.5 m, aluminium (E = 70 GPa)
δ = mm
6.Hard
50 kN12400 mm200 mmØ30Ø40σ2​ = ?

A steel segment (diameter 30 mm, length 400 mm, E = 200 GPa) and a segment made of bronze (diameter 40 mm, length 200 mm, E = 110 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, Ø30 mm, 400 mm, E = 200 GPasegment 2: bronze, Ø40 mm, 200 mm, E = 110 GPaP = 50 kN
σ2 = MPa

Answer key

  1. 1. σ = 132.4 MPa
  2. 2. σr = 20.87 MPa
  3. 3. ε = 909.5 µε
  4. 4. δ = 0.2221 mm
  5. 5. δ = 2.198 mm
  6. 6. σ2 = 26.33 MPa

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