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
300 kNØ40110 GPaØ80/60800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 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: Ø40 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 110 GPaL = 800 mm
σr = MPa
2.Easy
200 kNØ2570 GPaØ120/50800 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa). Both are 800 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 70 GPaL = 800 mm
σr = MPa
3.Medium
P = ?12300 mm300 mmØ30Ø30δ = 0.25 mm

A bar is made of a steel segment (diameter 30 mm, length 300 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 0.25 mm in total.

segment 1: steel, Ø30 mm, 300 mm, E = 200 GPasegment 2: copper, Ø30 mm, 300 mm, E = 120 GPaδ = 0.25 mm
P = kN
4.Medium
Ø 25 mmCopper1 mP = 85 kN

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

P = 85 kNd = 25 mmL = 1 mE = 117 GPa
δ = mm
5.Hard
Ø 30 mmCopper1.5 mØ 12 mmCopper2 mP = 120 kN

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

P = 120 kNsegment 1: Ø30 mm, 1.5 m, copper (E = 117 GPa)segment 2: Ø12 mm, 2 m, copper (E = 117 GPa)
δ = mm
6.Hard
P = ?Ø25120 GPaØ80/60600 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 GPa, allowable stress 50 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 250 MPatube: Ø80/Ø60 mm, E = 120 GPa, σallow = 50 MPa
Pmax = kN

Answer key

  1. 1. σr = 121.6 MPa
  2. 2. σr = 53.16 MPa
  3. 3. P = 44.18 kN
  4. 4. δ = 1.48 mm
  5. 5. δ = 20.31 mm
  6. 6. Pmax = 150.9 kN

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