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 10 mm1.5 mP = 60 kN

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

P = 60 kNd = 10 mm
σ = MPa
2.Easy
300 kNØ2570 GPaØ120/50400 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa). Both are 400 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 70 GPaL = 400 mm
σr = MPa
3.Medium
Ø 12 mmBrass0.5 mP = 90 kN

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

P = 90 kNd = 12 mmL = 0.5 mE = 100 GPa
ε = µε
4.Medium
150 kNØ30120 GPaØ80/60500 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 GPa). Both are 500 mm long and are compressed together between rigid plates by 150 kN. Find the shortening δ.

P = 150 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 500 mm
δ = mm
5.Hard
30 kN12400 mm500 mmØ40Ø60σ2​ = ?

A steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) and a segment made of copper (diameter 60 mm, length 500 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 30 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø40 mm, 400 mm, E = 200 GPasegment 2: copper, Ø60 mm, 500 mm, E = 120 GPaP = 30 kN
σ2 = MPa
6.Hard
Ø 30 mmCopper0.5 mØ 12 mmSteel0.5 mP = 70 kN

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

P = 70 kNsegment 1: Ø30 mm, 0.5 m, copper (E = 117 GPa)segment 2: Ø12 mm, 0.5 m, steel (E = 200 GPa)
δ = mm

Answer key

  1. 1. σ = 763.9 MPa
  2. 2. σr = 79.74 MPa
  3. 3. ε = 7958 µε
  4. 4. δ = 0.1851 mm
  5. 5. σ2 = 5.509 MPa
  6. 6. δ = 1.971 mm

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