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
80 kNØ40110 GPaØ120/50400 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 50 mm, E = 110 GPa). Both are 400 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: Ø120/Ø50 mm, E = 110 GPaL = 400 mm
σr = MPa
2.Easy
Ø 25 mm1.5 mP = 50 kN

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

P = 50 kNd = 25 mm
σ = MPa
3.Medium
50 kNØ20120 GPaØ120/60300 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 60 mm, E = 120 GPa). Both are 300 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 120 GPaL = 300 mm
δ = mm
4.Medium
P = ?12600 mm200 mmØ25Ø50δ = 0.2 mm

A bar is made of a steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 50 mm, length 200 mm, E = 120 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, Ø25 mm, 600 mm, E = 200 GPasegment 2: copper, Ø50 mm, 200 mm, E = 120 GPaδ = 0.2 mm
P = kN
5.Hard
50 kN12500 mm200 mmØ25Ø40σ2​ = ?

A steel segment (diameter 25 mm, length 500 mm, E = 200 GPa) and a segment made of copper (diameter 40 mm, length 200 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 50 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø25 mm, 500 mm, E = 200 GPasegment 2: copper, Ø40 mm, 200 mm, E = 120 GPaP = 50 kN
σ2 = MPa
6.Hard
Ø 35 mmBrass2 mØ 12 mmBrass0.5 mP = 100 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 = 100 kNsegment 1: Ø35 mm, 2 m, brass (E = 100 GPa)segment 2: Ø12 mm, 0.5 m, brass (E = 100 GPa)
σmax = MPa

Answer key

  1. 1. σr = 12.51 MPa
  2. 2. σ = 101.9 MPa
  3. 3. δ = 0.01388 mm
  4. 4. P = 28.73 kN
  5. 5. σ2 = 31.57 MPa
  6. 6. σmax = 884.2 MPa

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