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 mP = 40 kN

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

P = 40 kNd = 10 mm
σ = MPa
2.Easy
200 kNØ3070 GPaØ100/50500 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 GPa). Both are 500 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 500 mm
σr = MPa
3.Medium
100 kNØ20120 GPaØ120/70400 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 70 mm, E = 120 GPa). Both are 400 mm long and are compressed together between rigid plates by 100 kN. Find the shortening δ.

P = 100 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 120 GPaL = 400 mm
δ = mm
4.Medium
Ø 16 mmBrass0.5 mP = 95 kN

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

P = 95 kNd = 16 mmL = 0.5 mE = 100 GPa
ε = µε
5.Hard
Ø 40 mmBrass0.5 mØ 20 mmSteel1 mP = 75 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 = 75 kNsegment 1: Ø40 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø20 mm, 1 m, steel (E = 200 GPa)
σmax = MPa
6.Hard
80 kN12400 mm400 mmØ40Ø60σ2​ = ?

A steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) and a segment made of brass (diameter 60 mm, length 400 mm, E = 100 GPa) are joined end to end and fixed between two rigid walls. An axial load of 80 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: brass, Ø60 mm, 400 mm, E = 100 GPaP = 80 kN
σ2 = MPa

Answer key

  1. 1. σ = 509.3 MPa
  2. 2. σr = 72.24 MPa
  3. 3. δ = 0.04175 mm
  4. 4. ε = 4725 µε
  5. 5. σmax = 238.7 MPa
  6. 6. σ2 = 14.98 MPa

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