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 = 35 kN

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

P = 35 kNd = 25 mm
σ = MPa
2.Easy
150 kNØ20120 GPaØ100/70500 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 GPa). Both are 500 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 120 GPaL = 500 mm
σr = MPa
3.Medium
Ø 30 mmBrass0.5 mP = 95 kN

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

P = 95 kNd = 30 mmL = 0.5 mE = 100 GPa
ε = µε
4.Medium
50 kNØ3070 GPaØ80/50600 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 50 mm, E = 70 GPa). Both are 600 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 70 GPaL = 600 mm
δ = mm
5.Hard
Ø 35 mmCopper2 mØ 20 mmAluminium1.5 mP = 70 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 = 70 kNsegment 1: Ø35 mm, 2 m, copper (E = 117 GPa)segment 2: Ø20 mm, 1.5 m, aluminium (E = 70 GPa)
σmax = MPa
6.Hard
40 kN12500 mm300 mmØ20Ø40σ2​ = ?

A steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) and a segment made of brass (diameter 40 mm, length 300 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, Ø20 mm, 500 mm, E = 200 GPasegment 2: brass, Ø40 mm, 300 mm, E = 100 GPaP = 40 kN
σ2 = MPa

Answer key

  1. 1. σ = 71.3 MPa
  2. 2. σr = 55.2 MPa
  3. 3. ε = 1344 µε
  4. 4. δ = 0.08432 mm
  5. 5. σmax = 222.8 MPa
  6. 6. σ2 = 24.49 MPa

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