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 10 mm1.5 mP = 60 kN

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

P = 60 kNd = 10 mm
σ = MPa
2.Easy
50 kNØ25100 GPaØ120/60800 mmσr​ = ?

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 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 100 GPaL = 800 mm
σr = MPa
3.Medium
P = ?12300 mm500 mmØ25Ø30δ = 0.25 mm

A bar is made of a steel segment (diameter 25 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 30 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, Ø25 mm, 300 mm, E = 200 GPasegment 2: bronze, Ø30 mm, 500 mm, E = 110 GPaδ = 0.25 mm
P = kN
4.Medium
P = ?12600 mm400 mmØ40Ø30δ = 0.25 mm

A bar is made of a steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 30 mm, length 400 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, 600 mm, E = 200 GPasegment 2: bronze, Ø30 mm, 400 mm, E = 110 GPaδ = 0.25 mm
P = kN
5.Hard
Ø 40 mmSteel1 mØ 16 mmBrass1.5 mP = 80 kN

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

P = 80 kNsegment 1: Ø40 mm, 1 m, steel (E = 200 GPa)segment 2: Ø16 mm, 1.5 m, brass (E = 100 GPa)
δ = mm
6.Hard
Ø 30 mmAluminium2 mØ 20 mmSteel1.5 mP = 65 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 = 65 kNsegment 1: Ø30 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 1.5 m, steel (E = 200 GPa)
σmax = MPa

Answer key

  1. 1. σ = 763.9 MPa
  2. 2. σr = 10.57 MPa
  3. 3. P = 26.35 kN
  4. 4. P = 33.19 kN
  5. 5. δ = 6.287 mm
  6. 6. σmax = 206.9 MPa

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