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 kNØ30120 GPaØ80/60300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 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: Ø30 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 300 mm
σr = MPa
2.Easy
150 kNØ20100 GPaØ100/70400 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 70 mm, E = 100 GPa). Both are 400 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 100 GPaL = 400 mm
σr = MPa
3.Medium
150 kNØ3070 GPaØ100/60400 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 60 mm, E = 70 GPa). Both are 400 mm long and are compressed together between rigid plates by 150 kN. Find the shortening δ.

P = 150 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 70 GPaL = 400 mm
δ = mm
4.Medium
50 kNØ4070 GPaØ80/60500 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 60 mm, E = 70 GPa). Both are 500 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 70 GPaL = 500 mm
δ = mm
5.Hard
80 kN12300 mm300 mmØ20Ø50σ2​ = ?

A steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) and a segment made of copper (diameter 50 mm, length 300 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 80 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø20 mm, 300 mm, E = 200 GPasegment 2: copper, Ø50 mm, 300 mm, E = 120 GPaP = 80 kN
σ2 = MPa
6.Hard
60 kN12300 mm500 mmØ40Ø30σ2​ = ?

A steel segment (diameter 40 mm, length 300 mm, E = 200 GPa) and a segment made of copper (diameter 30 mm, length 500 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 60 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø40 mm, 300 mm, E = 200 GPasegment 2: copper, Ø30 mm, 500 mm, E = 120 GPaP = 60 kN
σ2 = MPa

Answer key

  1. 1. σr = 39.48 MPa
  2. 2. σr = 64.74 MPa
  3. 3. δ = 0.1216 mm
  4. 4. δ = 0.06169 mm
  5. 5. σ2 = 32.17 MPa
  6. 6. σ2 = 14.29 MPa

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