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 12 mm2 mP = 60 kN

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

P = 60 kNd = 12 mm
σ = MPa
2.Easy
150 kNØ2570 GPaØ80/60800 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 60 mm, E = 70 GPa). Both are 800 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 70 GPaL = 800 mm
σr = MPa
3.Medium
Ø 30 mmAluminium3 mP = 75 kN

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

P = 75 kNd = 30 mmL = 3 mE = 70 GPa
ε = µε
4.Medium
100 kNØ30110 GPaØ80/60400 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 100 kN. Find the shortening δ.

P = 100 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 400 mm
δ = mm
5.Hard
Ø 35 mmCopper1 mØ 12 mmBrass1 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, copper (E = 117 GPa)segment 2: Ø12 mm, 1 m, brass (E = 100 GPa)
σmax = MPa
6.Hard
60 kN12400 mm400 mmØ40Ø30σ2​ = ?

A steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) and a segment made of aluminium (diameter 30 mm, length 400 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 60 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø40 mm, 400 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 400 mm, E = 70 GPaP = 60 kN
σ2 = MPa

Answer key

  1. 1. σ = 530.5 MPa
  2. 2. σr = 119 MPa
  3. 3. ε = 1516 µε
  4. 4. δ = 0.1044 mm
  5. 5. σmax = 795.8 MPa
  6. 6. σ2 = 13.96 MPa

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