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
250 kNØ20110 GPaØ120/60500 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 60 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 110 GPaL = 500 mm
σr = MPa
2.Easy
50 kNØ30100 GPaØ80/60500 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 60 mm, E = 100 GPa). Both are 500 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: Ø80/Ø60 mm, E = 100 GPaL = 500 mm
σr = MPa
3.Medium
P = ?12600 mm300 mmØ40Ø50δ = 0.4 mm

A bar is made of a steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 50 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 0.4 mm in total.

segment 1: steel, Ø40 mm, 600 mm, E = 200 GPasegment 2: aluminium, Ø50 mm, 300 mm, E = 70 GPaδ = 0.4 mm
P = kN
4.Medium
Ø 16 mmBrass3 mP = 120 kN

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

P = 120 kNd = 16 mmL = 3 mE = 100 GPa
δ = mm
5.Hard
Ø 25 mmSteel0.5 mØ 20 mmSteel1.5 mP = 30 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 30 kNsegment 1: Ø25 mm, 0.5 m, steel (E = 200 GPa)segment 2: Ø20 mm, 1.5 m, steel (E = 200 GPa)
δ = mm
6.Hard
P = ?Ø30120 GPaØ100/70500 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 200 MPatube: Ø100/Ø70 mm, E = 120 GPa, σallow = 60 MPa
Pmax = kN

Answer key

  1. 1. σr = 50.21 MPa
  2. 2. σr = 27.68 MPa
  3. 3. P = 87.53 kN
  4. 4. δ = 17.9 mm
  5. 5. δ = 0.869 mm
  6. 6. Pmax = 311 kN

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