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 12 mm1.5 mP = 45 kN

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

P = 45 kNd = 12 mm
σ = MPa
2.Easy
50 kNØ30100 GPaØ100/60800 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 60 mm, E = 100 GPa). Both are 800 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 100 GPaL = 800 mm
σr = MPa
3.Medium
Ø 10 mmCopper2 mP = 105 kN

Find the axial strain ε in the copper bar, in microstrain (µε = 10⁻⁶).

P = 105 kNd = 10 mmL = 2 mE = 117 GPa
ε = µε
4.Medium
P = ?12600 mm300 mmØ25Ø40δ = 0.25 mm

A bar is made of a steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 40 mm, length 300 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.25 mm in total.

segment 1: steel, Ø25 mm, 600 mm, E = 200 GPasegment 2: aluminium, Ø40 mm, 300 mm, E = 70 GPaδ = 0.25 mm
P = kN
5.Hard
P = ?Ø40120 GPaØ120/70400 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 70 mm, E = 120 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 160 MPatube: Ø120/Ø70 mm, E = 120 GPa, σallow = 60 MPa
Pmax = kN
6.Hard
Ø 25 mmAluminium1.5 mØ 20 mmSteel2 mP = 105 kN

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

P = 105 kNsegment 1: Ø25 mm, 1.5 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 2 m, steel (E = 200 GPa)
δ = mm

Answer key

  1. 1. σ = 397.9 MPa
  2. 2. σr = 15.53 MPa
  3. 3. ε = 11427 µε
  4. 4. P = 26.25 kN
  5. 5. Pmax = 573.3 kN
  6. 6. δ = 7.926 mm

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