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
250 kNØ20120 GPaØ120/70800 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 70 mm, E = 120 GPa). Both are 800 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 120 GPaL = 800 mm
σr = MPa
2.Easy
Ø 20 mm1.5 mP = 90 kN

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

P = 90 kNd = 20 mm
σ = MPa
3.Medium
P = ?12400 mm500 mmØ40Ø40δ = 0.2 mm

A bar is made of a steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 40 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 0.2 mm in total.

segment 1: steel, Ø40 mm, 400 mm, E = 200 GPasegment 2: bronze, Ø40 mm, 500 mm, E = 110 GPaδ = 0.2 mm
P = kN
4.Medium
150 kNØ30120 GPaØ100/50400 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa). Both are 400 mm long and are compressed together between rigid plates by 150 kN. Find the shortening δ.

P = 150 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 120 GPaL = 400 mm
δ = mm
5.Hard
Ø 30 mmAluminium1 mØ 12 mmCopper1.5 mP = 90 kN

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

P = 90 kNsegment 1: Ø30 mm, 1 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 1.5 m, copper (E = 117 GPa)
δ = mm
6.Hard
Ø 30 mmSteel1.5 mØ 12 mmBrass1 mP = 70 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 = 70 kNsegment 1: Ø30 mm, 1.5 m, steel (E = 200 GPa)segment 2: Ø12 mm, 1 m, brass (E = 100 GPa)
σmax = MPa

Answer key

  1. 1. σr = 52.18 MPa
  2. 2. σ = 286.5 MPa
  3. 3. P = 38.4 kN
  4. 4. δ = 0.07074 mm
  5. 5. δ = 12.02 mm
  6. 6. σmax = 618.9 MPa

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