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
200 kNØ3070 GPaØ80/50800 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 50 mm, E = 70 GPa). Both are 800 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 70 GPaL = 800 mm
σr = MPa
2.Easy
200 kNØ25110 GPaØ120/60300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 60 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 110 GPaL = 300 mm
σr = MPa
3.Medium
Ø 25 mmAluminium2.5 mP = 40 kN

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

P = 40 kNd = 25 mmL = 2.5 mE = 70 GPa
δ = mm
4.Medium
Ø 10 mmBrass1 mP = 100 kN

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

P = 100 kNd = 10 mmL = 1 mE = 100 GPa
ε = µε
5.Hard
Ø 25 mmAluminium1.5 mØ 20 mmBrass0.5 mP = 120 kN

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

P = 120 kNsegment 1: Ø25 mm, 1.5 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 0.5 m, brass (E = 100 GPa)
δ = mm
6.Hard
P = ?Ø2070 GPaØ80/60800 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 60 mm, E = 70 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 120 MPatube: Ø80/Ø60 mm, E = 70 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σr = 112.4 MPa
  2. 2. σr = 38.79 MPa
  3. 3. δ = 2.91 mm
  4. 4. ε = 12732 µε
  5. 5. δ = 7.148 mm
  6. 6. Pmax = 130.1 kN

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