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 kNØ25110 GPaØ100/50300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 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: Ø25 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 300 mm
σr = MPa
2.Easy
80 kNØ2070 GPaØ100/50800 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 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: Ø20 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 800 mm
σr = MPa
3.Medium
300 kNØ25120 GPaØ80/50600 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 50 mm, E = 120 GPa). Both are 600 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 120 GPaL = 600 mm
δ = mm
4.Medium
Ø 30 mmAluminium1.5 mP = 15 kN

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

P = 15 kNd = 30 mmL = 1.5 mE = 70 GPa
δ = mm
5.Hard
Ø 30 mmBrass0.5 mØ 20 mmAluminium0.5 mP = 25 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 = 25 kNsegment 1: Ø30 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø20 mm, 0.5 m, aluminium (E = 70 GPa)
σmax = MPa
6.Hard
P = ?Ø25110 GPaØ80/60800 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 200 MPatube: Ø80/Ø60 mm, E = 110 GPa, σallow = 60 MPa
Pmax = kN

Answer key

  1. 1. σr = 40.21 MPa
  2. 2. σr = 33.67 MPa
  3. 3. δ = 0.3865 mm
  4. 4. δ = 0.4547 mm
  5. 5. σmax = 79.58 MPa
  6. 6. Pmax = 185.5 kN

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