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 = 120 kN

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

P = 120 kNd = 30 mm
σ = MPa
2.Easy
150 kNØ25100 GPaØ80/50400 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 50 mm, E = 100 GPa). Both are 400 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 100 GPaL = 400 mm
σr = MPa
3.Medium
Ø 16 mmSteel1 mP = 105 kN

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

P = 105 kNd = 16 mmL = 1 mE = 200 GPa
δ = mm
4.Medium
Ø 12 mmSteel2.5 mP = 15 kN

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

P = 15 kNd = 12 mmL = 2.5 mE = 200 GPa
ε = µε
5.Hard
50 kN12300 mm400 mmØ30Ø40σ2​ = ?

A steel segment (diameter 30 mm, length 300 mm, E = 200 GPa) and a segment made of copper (diameter 40 mm, length 400 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 50 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø30 mm, 300 mm, E = 200 GPasegment 2: copper, Ø40 mm, 400 mm, E = 120 GPaP = 50 kN
σ2 = MPa
6.Hard
20 kN12500 mm300 mmØ25Ø30σ2​ = ?

A steel segment (diameter 25 mm, length 500 mm, E = 200 GPa) and a segment made of aluminium (diameter 30 mm, length 300 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 20 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø25 mm, 500 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 300 mm, E = 70 GPaP = 20 kN
σ2 = MPa

Answer key

  1. 1. σ = 169.8 MPa
  2. 2. σr = 74.17 MPa
  3. 3. δ = 2.611 mm
  4. 4. ε = 663.1 µε
  5. 5. σ2 = 17.68 MPa
  6. 6. σ2 = 12.92 MPa

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