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 mP = 35 kN

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

P = 35 kNd = 16 mm
σ = MPa
2.Easy
200 kNØ20100 GPaØ120/50300 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 50 mm, E = 100 GPa). Both are 300 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 100 GPaL = 300 mm
σr = MPa
3.Medium
Ø 16 mmAluminium3 mP = 50 kN

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

P = 50 kNd = 16 mmL = 3 mE = 70 GPa
ε = µε
4.Medium
50 kNØ2570 GPaØ120/70600 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 70 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: Ø25 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 70 GPaL = 600 mm
δ = mm
5.Hard
100 kN12600 mm300 mmØ40Ø30σ2​ = ?

A steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) and a segment made of brass (diameter 30 mm, length 300 mm, E = 100 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, Ø40 mm, 600 mm, E = 200 GPasegment 2: brass, Ø30 mm, 300 mm, E = 100 GPaP = 100 kN
σ2 = MPa
6.Hard
Ø 40 mmBrass0.5 mØ 12 mmBrass2 mP = 65 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 = 65 kNsegment 1: Ø40 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø12 mm, 2 m, brass (E = 100 GPa)
σmax = MPa

Answer key

  1. 1. σ = 174.1 MPa
  2. 2. σr = 40.1 MPa
  3. 3. ε = 3553 µε
  4. 4. δ = 0.04835 mm
  5. 5. σ2 = 50.93 MPa
  6. 6. σmax = 574.7 MPa

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