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 kNØ40100 GPaØ80/60500 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 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: Ø80/Ø60 mm, E = 100 GPaL = 500 mm
σr = MPa
2.Easy
Ø 12 mm1.5 mP = 95 kN

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

P = 95 kNd = 12 mm
σ = MPa
3.Medium
P = ?12600 mm500 mmØ20Ø50δ = 0.25 mm

A bar is made of a steel segment (diameter 20 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 50 mm, length 500 mm, E = 120 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.25 mm in total.

segment 1: steel, Ø20 mm, 600 mm, E = 200 GPasegment 2: copper, Ø50 mm, 500 mm, E = 120 GPaδ = 0.25 mm
P = kN
4.Medium
150 kNØ25100 GPaØ120/60800 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 60 mm, E = 100 GPa). Both are 800 mm long and are compressed together between rigid plates by 150 kN. Find the shortening δ.

P = 150 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 100 GPaL = 800 mm
δ = mm
5.Hard
Ø 30 mmSteel0.5 mØ 16 mmBrass1 mP = 110 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 = 110 kNsegment 1: Ø30 mm, 0.5 m, steel (E = 200 GPa)segment 2: Ø16 mm, 1 m, brass (E = 100 GPa)
σmax = MPa
6.Hard
Ø 35 mmCopper2 mØ 16 mmSteel2 mP = 100 kN

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

P = 100 kNsegment 1: Ø35 mm, 2 m, copper (E = 117 GPa)segment 2: Ø16 mm, 2 m, steel (E = 200 GPa)
δ = mm

Answer key

  1. 1. σr = 33.95 MPa
  2. 2. σ = 840 MPa
  3. 3. P = 21.42 kN
  4. 4. δ = 0.1268 mm
  5. 5. σmax = 547.1 MPa
  6. 6. δ = 6.75 mm

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