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 30 mm0.5 mP = 15 kN

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

P = 15 kNd = 30 mm
σ = MPa
2.Easy
250 kNØ30100 GPaØ80/50300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 50 mm, E = 100 GPa). Both are 300 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 100 GPaL = 300 mm
σr = MPa
3.Medium
Ø 30 mmCopper1.5 mP = 95 kN

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

P = 95 kNd = 30 mmL = 1.5 mE = 117 GPa
δ = mm
4.Medium
P = ?12400 mm500 mmØ40Ø50δ = 0.5 mm

A bar is made of a steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 50 mm, length 500 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.5 mm in total.

segment 1: steel, Ø40 mm, 400 mm, E = 200 GPasegment 2: aluminium, Ø50 mm, 500 mm, E = 70 GPaδ = 0.5 mm
P = kN
5.Hard
Ø 25 mmSteel2 mØ 12 mmAluminium2 mP = 65 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the largest normal stress σmax in the bar.

P = 65 kNsegment 1: Ø25 mm, 2 m, steel (E = 200 GPa)segment 2: Ø12 mm, 2 m, aluminium (E = 70 GPa)
σmax = MPa
6.Hard
P = ?Ø20120 GPaØ120/50600 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 50 mm, E = 120 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 200 MPatube: Ø120/Ø50 mm, E = 120 GPa, σallow = 70 MPa
Pmax = kN

Answer key

  1. 1. σ = 21.22 MPa
  2. 2. σr = 111.7 MPa
  3. 3. δ = 1.723 mm
  4. 4. P = 95.61 kN
  5. 5. σmax = 574.7 MPa
  6. 6. Pmax = 690.9 kN

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