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
50 kNØ40110 GPaØ80/60300 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 300 mm
σr = MPa
2.Easy
Ø 12 mm0.5 mP = 115 kN

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

P = 115 kNd = 12 mm
σ = MPa
3.Medium
Ø 20 mmCopper2 mP = 65 kN

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

P = 65 kNd = 20 mmL = 2 mE = 117 GPa
δ = mm
4.Medium
P = ?12300 mm500 mmØ40Ø60δ = 0.25 mm

A bar is made of a steel segment (diameter 40 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 60 mm, length 500 mm, E = 110 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.25 mm in total.

segment 1: steel, Ø40 mm, 300 mm, E = 200 GPasegment 2: bronze, Ø60 mm, 500 mm, E = 110 GPaδ = 0.25 mm
P = kN
5.Hard
80 kN12500 mm500 mmØ20Ø40σ2​ = ?

A steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) and a segment made of aluminium (diameter 40 mm, length 500 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 80 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: aluminium, Ø40 mm, 500 mm, E = 70 GPaP = 80 kN
σ2 = MPa
6.Hard
Ø 30 mmCopper2 mØ 16 mmBrass1.5 mP = 95 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 95 kNsegment 1: Ø30 mm, 2 m, copper (E = 117 GPa)segment 2: Ø16 mm, 1.5 m, brass (E = 100 GPa)
δ = mm

Answer key

  1. 1. σr = 20.27 MPa
  2. 2. σ = 1017 MPa
  3. 3. δ = 3.537 mm
  4. 4. P = 89.24 kN
  5. 5. σ2 = 37.14 MPa
  6. 6. δ = 9.385 mm

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