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 kNØ20120 GPaØ100/60600 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 60 mm, E = 120 GPa). Both are 600 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 120 GPaL = 600 mm
σr = MPa
2.Easy
50 kNØ30110 GPaØ100/50300 mmσr​ = ?

A steel rod (diameter 30 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 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 300 mm
σr = MPa
3.Medium
P = ?12400 mm300 mmØ40Ø30δ = 0.5 mm

A bar is made of a steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 30 mm, length 300 mm, E = 120 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.5 mm in total.

segment 1: steel, Ø40 mm, 400 mm, E = 200 GPasegment 2: copper, Ø30 mm, 300 mm, E = 120 GPaδ = 0.5 mm
P = kN
4.Medium
P = ?12500 mm300 mmØ40Ø30δ = 0.25 mm

A bar is made of a steel segment (diameter 40 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 30 mm, length 300 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.25 mm in total.

segment 1: steel, Ø40 mm, 500 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 300 mm, E = 70 GPaδ = 0.25 mm
P = kN
5.Hard
P = ?Ø40110 GPaØ100/60500 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of bronze (outer diameter 100 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: Ø40 mm, E = 200 GPa, σallow = 120 MPatube: Ø100/Ø60 mm, E = 110 GPa, σallow = 60 MPa
Pmax = kN
6.Hard
20 kN12500 mm200 mmØ20Ø60σ2​ = ?

A steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) and a segment made of copper (diameter 60 mm, length 200 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 20 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø20 mm, 500 mm, E = 200 GPasegment 2: copper, Ø60 mm, 200 mm, E = 120 GPaP = 20 kN
σ2 = MPa

Answer key

  1. 1. σr = 60.06 MPa
  2. 2. σr = 12.67 MPa
  3. 3. P = 97.5 kN
  4. 4. P = 31.05 kN
  5. 5. Pmax = 438.7 kN
  6. 6. σ2 = 6.586 MPa

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