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
Ø 20 mm0.5 mP = 55 kN

A solid round bar carries an axial tensile load P. Find the normal stress σ in the bar.

P = 55 kNd = 20 mm
σ = MPa
2.Easy
300 kNØ40110 GPaØ100/50400 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa). Both are 400 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: Ø100/Ø50 mm, E = 110 GPaL = 400 mm
σr = MPa
3.Medium
Ø 30 mmSteel2 mP = 10 kN

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

P = 10 kNd = 30 mmL = 2 mE = 200 GPa
δ = mm
4.Medium
200 kNØ30120 GPaØ80/50800 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 50 mm, E = 120 GPa). Both are 800 mm long and are compressed together between rigid plates by 200 kN. Find the shortening δ.

P = 200 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 120 GPaL = 800 mm
δ = mm
5.Hard
Ø 40 mmCopper0.5 mØ 16 mmBrass0.5 mP = 65 kN

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

P = 65 kNsegment 1: Ø40 mm, 0.5 m, copper (E = 117 GPa)segment 2: Ø16 mm, 0.5 m, brass (E = 100 GPa)
δ = mm
6.Hard
P = ?Ø25120 GPaØ120/70300 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 70 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 = 150 MPatube: Ø120/Ø70 mm, E = 120 GPa, σallow = 50 MPa
Pmax = kN

Answer key

  1. 1. σ = 175.1 MPa
  2. 2. σr = 66.72 MPa
  3. 3. δ = 0.1415 mm
  4. 4. δ = 0.3144 mm
  5. 5. δ = 1.837 mm
  6. 6. Pmax = 414 kN

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