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 25 mm1.5 mP = 35 kN

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

P = 35 kNd = 25 mm
σ = MPa
2.Easy
100 kNØ30120 GPaØ120/60300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 60 mm, E = 120 GPa). Both are 300 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 120 GPaL = 300 mm
σr = MPa
3.Medium
Ø 25 mmCopper2.5 mP = 10 kN

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

P = 10 kNd = 25 mmL = 2.5 mE = 117 GPa
δ = mm
4.Medium
80 kNØ30110 GPaØ120/60300 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 60 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 80 kN. Find the shortening δ.

P = 80 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 110 GPaL = 300 mm
δ = mm
5.Hard
P = ?Ø30100 GPaØ120/50600 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 50 mm, E = 100 GPa, allowable stress 50 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 120 MPatube: Ø120/Ø50 mm, E = 100 GPa, σallow = 50 MPa
Pmax = kN
6.Hard
Ø 30 mmBrass0.5 mØ 16 mmSteel1 mP = 40 kN

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

P = 40 kNsegment 1: Ø30 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø16 mm, 1 m, steel (E = 200 GPa)
δ = mm

Answer key

  1. 1. σ = 71.3 MPa
  2. 2. σr = 17.25 MPa
  3. 3. δ = 0.4353 mm
  4. 4. δ = 0.02234 mm
  5. 5. Pmax = 538 kN
  6. 6. δ = 1.278 mm

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