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 mm0.5 mP = 110 kN

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

P = 110 kNd = 25 mm
σ = MPa
2.Easy
300 kNØ3070 GPaØ80/50600 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 50 mm, E = 70 GPa). Both are 600 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 70 GPaL = 600 mm
σr = MPa
3.Medium
Ø 12 mmBrass0.5 mP = 75 kN

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

P = 75 kNd = 12 mmL = 0.5 mE = 100 GPa
δ = mm
4.Medium
P = ?12500 mm500 mmØ30Ø40δ = 0.5 mm

A bar is made of a steel segment (diameter 30 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 40 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, Ø30 mm, 500 mm, E = 200 GPasegment 2: aluminium, Ø40 mm, 500 mm, E = 70 GPaδ = 0.5 mm
P = kN
5.Hard
P = ?Ø3070 GPaØ120/70400 mm

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

rod: Ø30 mm, E = 200 GPa, σallow = 120 MPatube: Ø120/Ø70 mm, E = 70 GPa, σallow = 100 MPa
Pmax = kN
6.Hard
Ø 35 mmCopper1.5 mØ 12 mmBrass1.5 mP = 100 kN

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

P = 100 kNsegment 1: Ø35 mm, 1.5 m, copper (E = 117 GPa)segment 2: Ø12 mm, 1.5 m, brass (E = 100 GPa)
δ = mm

Answer key

  1. 1. σ = 224.1 MPa
  2. 2. σr = 168.6 MPa
  3. 3. δ = 3.316 mm
  4. 4. P = 54.22 kN
  5. 5. Pmax = 398.2 kN
  6. 6. δ = 14.6 mm

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