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 = 65 kN

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

P = 65 kNd = 16 mm
σ = MPa
2.Easy
50 kNØ40110 GPaØ120/60300 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 60 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 110 GPaL = 300 mm
σr = MPa
3.Medium
Ø 20 mmAluminium2.5 mP = 95 kN

Find the elongation δ of the aluminium bar under the axial load.

P = 95 kNd = 20 mmL = 2.5 mE = 70 GPa
δ = mm
4.Medium
300 kNØ40120 GPaØ100/70600 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 GPa). Both are 600 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 120 GPaL = 600 mm
δ = mm
5.Hard
Ø 40 mmAluminium2 mØ 12 mmBrass1 mP = 110 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 = 110 kNsegment 1: Ø40 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 1 m, brass (E = 100 GPa)
σmax = MPa
6.Hard
40 kN12400 mm200 mmØ20Ø40σ2​ = ?

A steel segment (diameter 20 mm, length 400 mm, E = 200 GPa) and a segment made of copper (diameter 40 mm, length 200 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 40 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: copper, Ø40 mm, 200 mm, E = 120 GPaP = 40 kN
σ2 = MPa

Answer key

  1. 1. σ = 323.3 MPa
  2. 2. σr = 8.443 MPa
  3. 3. δ = 10.8 mm
  4. 4. δ = 0.2459 mm
  5. 5. σmax = 972.6 MPa
  6. 6. σ2 = 26.34 MPa

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