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 kNØ20120 GPaØ100/70600 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 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: Ø20 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 120 GPaL = 600 mm
σr = MPa
2.Easy
300 kNØ25100 GPaØ80/60800 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 60 mm, E = 100 GPa). Both are 800 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 100 GPaL = 800 mm
σr = MPa
3.Medium
Ø 25 mmBrass2.5 mP = 70 kN

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

P = 70 kNd = 25 mmL = 2.5 mE = 100 GPa
δ = mm
4.Medium
P = ?12500 mm300 mmØ30Ø30δ = 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 bronze (diameter 30 mm, length 300 mm, E = 110 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: bronze, Ø30 mm, 300 mm, E = 110 GPaδ = 0.25 mm
P = kN
5.Hard
P = ?Ø4070 GPaØ100/60800 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of aluminium (outer diameter 100 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: Ø40 mm, E = 200 GPa, σallow = 150 MPatube: Ø100/Ø60 mm, E = 70 GPa, σallow = 80 MPa
Pmax = kN
6.Hard
P = ?Ø4070 GPaØ100/60600 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of aluminium (outer diameter 100 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: Ø40 mm, E = 200 GPa, σallow = 200 MPatube: Ø100/Ø60 mm, E = 70 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σr = 18.4 MPa
  2. 2. σr = 188.6 MPa
  3. 3. δ = 3.565 mm
  4. 4. P = 33.81 kN
  5. 5. Pmax = 452.4 kN
  6. 6. Pmax = 603.2 kN

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