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
100 kNØ20120 GPaØ100/70600 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 GPa). Both are 600 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 120 GPaL = 600 mm
σr = MPa
2.Easy
80 kNØ2570 GPaØ100/60300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 60 mm, E = 70 GPa). Both are 300 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 70 GPaL = 300 mm
σr = MPa
3.Medium
Ø 30 mmSteel2 mP = 45 kN

Find the elongation δ of the steel bar under the axial load.

P = 45 kNd = 30 mmL = 2 mE = 200 GPa
δ = mm
4.Medium
200 kNØ2570 GPaØ100/70600 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 70 mm, E = 70 GPa). Both are 600 mm long and are compressed together between rigid plates by 200 kN. Find the shortening δ.

P = 200 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 70 GPaL = 600 mm
δ = mm
5.Hard
P = ?Ø4070 GPaØ100/60300 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 60 mm, E = 70 GPa, allowable stress 50 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 200 MPatube: Ø100/Ø60 mm, E = 70 GPa, σallow = 50 MPa
Pmax = kN
6.Hard
Ø 35 mmSteel2 mØ 16 mmCopper2 mP = 40 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 = 40 kNsegment 1: Ø35 mm, 2 m, steel (E = 200 GPa)segment 2: Ø16 mm, 2 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σr = 36.8 MPa
  2. 2. σr = 35.55 MPa
  3. 3. δ = 0.6366 mm
  4. 4. δ = 0.317 mm
  5. 5. Pmax = 430.8 kN
  6. 6. σmax = 198.9 MPa

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