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 mm2 mP = 90 kN

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

P = 90 kNd = 25 mm
σ = MPa
2.Easy
80 kNØ40100 GPaØ100/60500 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 60 mm, E = 100 GPa). Both are 500 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/Ø60 mm, E = 100 GPaL = 500 mm
σr = MPa
3.Medium
Ø 30 mmBrass1 mP = 105 kN

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

P = 105 kNd = 30 mmL = 1 mE = 100 GPa
δ = mm
4.Medium
P = ?12400 mm200 mmØ30Ø50δ = 0.2 mm

A bar is made of a steel segment (diameter 30 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 50 mm, length 200 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.2 mm in total.

segment 1: steel, Ø30 mm, 400 mm, E = 200 GPasegment 2: aluminium, Ø50 mm, 200 mm, E = 70 GPaδ = 0.2 mm
P = kN
5.Hard
Ø 35 mmCopper2 mØ 12 mmSteel0.5 mP = 25 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 = 25 kNsegment 1: Ø35 mm, 2 m, copper (E = 117 GPa)segment 2: Ø12 mm, 0.5 m, steel (E = 200 GPa)
σmax = MPa
6.Hard
100 kN12600 mm300 mmØ25Ø30σ2​ = ?

A steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) and a segment made of aluminium (diameter 30 mm, length 300 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, Ø25 mm, 600 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 300 mm, E = 70 GPaP = 100 kN
σ2 = MPa

Answer key

  1. 1. σ = 183.3 MPa
  2. 2. σr = 21.22 MPa
  3. 3. δ = 1.485 mm
  4. 4. P = 46.68 kN
  5. 5. σmax = 221 MPa
  6. 6. σ2 = 71.02 MPa

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