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 mm2 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
150 kNØ30100 GPaØ120/50300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 50 mm, E = 100 GPa). Both are 300 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 100 GPaL = 300 mm
σr = MPa
3.Medium
P = ?12300 mm400 mmØ25Ø30δ = 0.4 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 brass (diameter 30 mm, length 400 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.4 mm in total.

segment 1: steel, Ø25 mm, 300 mm, E = 200 GPasegment 2: brass, Ø30 mm, 400 mm, E = 100 GPaδ = 0.4 mm
P = kN
4.Medium
Ø 30 mmBrass1.5 mP = 50 kN

Find the axial strain ε in the brass bar, in microstrain (µε = 10⁻⁶).

P = 50 kNd = 30 mmL = 1.5 mE = 100 GPa
ε = µε
5.Hard
Ø 25 mmSteel1.5 mØ 16 mmBrass1 mP = 30 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 = 30 kNsegment 1: Ø25 mm, 1.5 m, steel (E = 200 GPa)segment 2: Ø16 mm, 1 m, brass (E = 100 GPa)
σmax = MPa
6.Hard
Ø 35 mmCopper0.5 mØ 12 mmCopper1 mP = 60 kN

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

P = 60 kNsegment 1: Ø35 mm, 0.5 m, copper (E = 117 GPa)segment 2: Ø12 mm, 1 m, copper (E = 117 GPa)
δ = mm

Answer key

  1. 1. σ = 763.9 MPa
  2. 2. σr = 27.88 MPa
  3. 3. P = 45.9 kN
  4. 4. ε = 707.4 µε
  5. 5. σmax = 149.2 MPa
  6. 6. δ = 4.801 mm

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