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
150 kNØ40120 GPaØ100/50800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa). Both are 800 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 120 GPaL = 800 mm
σr = MPa
2.Easy
80 kNØ30110 GPaØ80/50600 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 50 mm, E = 110 GPa). Both are 600 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 110 GPaL = 600 mm
σr = MPa
3.Medium
Ø 25 mmCopper1.5 mP = 115 kN

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

P = 115 kNd = 25 mmL = 1.5 mE = 117 GPa
ε = µε
4.Medium
80 kNØ40110 GPaØ100/70400 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 70 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 80 kN. Find the shortening δ.

P = 80 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 110 GPaL = 400 mm
δ = mm
5.Hard
40 kN12400 mm300 mmØ25Ø30σ2​ = ?

A steel segment (diameter 25 mm, length 400 mm, E = 200 GPa) and a segment made of aluminium (diameter 30 mm, length 300 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 40 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø25 mm, 400 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 300 mm, E = 70 GPaP = 40 kN
σ2 = MPa
6.Hard
Ø 25 mmBrass0.5 mØ 20 mmSteel1.5 mP = 115 kN

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

P = 115 kNsegment 1: Ø25 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø20 mm, 1.5 m, steel (E = 200 GPa)
δ = mm

Answer key

  1. 1. σr = 31.31 MPa
  2. 2. σr = 33.45 MPa
  3. 3. ε = 2002 µε
  4. 4. δ = 0.04625 mm
  5. 5. σ2 = 22.74 MPa
  6. 6. δ = 3.917 mm

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