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 30 mm2 mP = 110 kN

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

P = 110 kNd = 30 mm
σ = MPa
2.Easy
80 kNØ40100 GPaØ100/50600 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 50 mm, E = 100 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: Ø40 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 100 GPaL = 600 mm
σr = MPa
3.Medium
150 kNØ40120 GPaØ80/60800 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 GPa). Both are 800 mm long and are compressed together between rigid plates by 150 kN. Find the shortening δ.

P = 150 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 800 mm
δ = mm
4.Medium
Ø 20 mmAluminium3 mP = 55 kN

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

P = 55 kNd = 20 mmL = 3 mE = 70 GPa
ε = µε
5.Hard
Ø 35 mmBrass1 mØ 20 mmSteel0.5 mP = 90 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 = 90 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
40 kN12600 mm500 mmØ40Ø40σ2​ = ?

A steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) and a segment made of brass (diameter 40 mm, length 500 mm, E = 100 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, Ø40 mm, 600 mm, E = 200 GPasegment 2: brass, Ø40 mm, 500 mm, E = 100 GPaP = 40 kN
σ2 = MPa

Answer key

  1. 1. σ = 155.6 MPa
  2. 2. σr = 19.04 MPa
  3. 3. δ = 0.2329 mm
  4. 4. ε = 2501 µε
  5. 5. σmax = 286.5 MPa
  6. 6. σ2 = 11.94 MPa

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