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 kNØ40120 GPaØ120/70800 mmσr​ = ?

A steel rod (diameter 40 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 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 120 GPaL = 800 mm
σr = MPa
2.Easy
50 kNØ30110 GPaØ100/60600 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 60 mm, E = 110 GPa). Both are 600 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 110 GPaL = 600 mm
σr = MPa
3.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
4.Medium
P = ?12300 mm200 mmØ20Ø60δ = 0.4 mm

A bar is made of a steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 60 mm, length 200 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, Ø20 mm, 300 mm, E = 200 GPasegment 2: brass, Ø60 mm, 200 mm, E = 100 GPaδ = 0.4 mm
P = kN
5.Hard
Ø 30 mmBrass1.5 mØ 16 mmAluminium1.5 mP = 115 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 = 115 kNsegment 1: Ø30 mm, 1.5 m, brass (E = 100 GPa)segment 2: Ø16 mm, 1.5 m, aluminium (E = 70 GPa)
σmax = MPa
6.Hard
Ø 40 mmCopper1 mØ 12 mmSteel0.5 mP = 30 kN

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

P = 30 kNsegment 1: Ø40 mm, 1 m, copper (E = 117 GPa)segment 2: Ø12 mm, 0.5 m, steel (E = 200 GPa)
δ = mm

Answer key

  1. 1. σr = 13.95 MPa
  2. 2. σr = 14.4 MPa
  3. 3. ε = 707.4 µε
  4. 4. P = 72.97 kN
  5. 5. σmax = 572 MPa
  6. 6. δ = 0.8672 mm

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