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
50 kNØ40100 GPaØ80/60600 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 60 mm, E = 100 GPa). Both are 600 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 100 GPaL = 600 mm
σr = MPa
2.Easy
150 kNØ25120 GPaØ80/60400 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 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: Ø25 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 400 mm
σr = MPa
3.Medium
P = ?12500 mm200 mmØ30Ø60δ = 0.25 mm

A bar is made of a steel segment (diameter 30 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 60 mm, length 200 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, Ø30 mm, 500 mm, E = 200 GPasegment 2: aluminium, Ø60 mm, 200 mm, E = 70 GPaδ = 0.25 mm
P = kN
4.Medium
200 kNØ25120 GPaØ100/50600 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa). Both are 600 mm long and are compressed together between rigid plates by 200 kN. Find the shortening δ.

P = 200 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 120 GPaL = 600 mm
δ = mm
5.Hard
P = ?Ø25100 GPaØ120/60300 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 60 mm, E = 100 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 160 MPatube: Ø120/Ø60 mm, E = 100 GPa, σallow = 70 MPa
Pmax = kN
6.Hard
P = ?Ø40110 GPaØ120/60600 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of bronze (outer diameter 120 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 = 160 MPatube: Ø120/Ø60 mm, E = 110 GPa, σallow = 60 MPa
Pmax = kN

Answer key

  1. 1. σr = 21.22 MPa
  2. 2. σr = 82.86 MPa
  3. 3. P = 54.98 kN
  4. 4. δ = 0.1491 mm
  5. 5. Pmax = 662.5 kN
  6. 6. Pmax = 646 kN

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