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
80 kNØ25110 GPaØ80/60600 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa). Both are 600 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 600 mm
σr = MPa
2.Easy
Ø 20 mm2 mP = 105 kN

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

P = 105 kNd = 20 mm
σ = MPa
3.Medium
Ø 16 mmAluminium2 mP = 50 kN

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

P = 50 kNd = 16 mmL = 2 mE = 70 GPa
δ = mm
4.Medium
250 kNØ40110 GPaØ100/60400 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 60 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 250 kN. Find the shortening δ.

P = 250 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 110 GPaL = 400 mm
δ = mm
5.Hard
Ø 35 mmBrass1 mØ 20 mmSteel0.5 mP = 80 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 = 80 kNsegment 1: Ø35 mm, 1 m, brass (E = 100 GPa)segment 2: Ø20 mm, 0.5 m, steel (E = 200 GPa)
σmax = MPa
6.Hard
100 kN12600 mm500 mmØ20Ø40σ2​ = ?

A steel segment (diameter 20 mm, length 600 mm, E = 200 GPa) and a segment made of aluminium (diameter 40 mm, length 500 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 100 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: aluminium, Ø40 mm, 500 mm, E = 70 GPaP = 100 kN
σ2 = MPa

Answer key

  1. 1. σr = 47.05 MPa
  2. 2. σ = 334.2 MPa
  3. 3. δ = 7.105 mm
  4. 4. δ = 0.1243 mm
  5. 5. σmax = 254.6 MPa
  6. 6. σ2 = 49.88 MPa

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