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 mm1 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
250 kNØ30100 GPaØ100/50300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 50 mm, E = 100 GPa). Both are 300 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 100 GPaL = 300 mm
σr = MPa
3.Medium
200 kNØ25100 GPaØ80/60600 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 60 mm, E = 100 GPa). Both are 600 mm long and are compressed together between rigid plates by 200 kN. Find the shortening δ.

P = 200 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 100 GPaL = 600 mm
δ = mm
4.Medium
Ø 20 mmBrass1 mP = 75 kN

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

P = 75 kNd = 20 mmL = 1 mE = 100 GPa
ε = µε
5.Hard
30 kN12600 mm300 mmØ20Ø50σ2​ = ?

A steel segment (diameter 20 mm, length 600 mm, E = 200 GPa) and a segment made of aluminium (diameter 50 mm, length 300 mm, E = 70 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, Ø20 mm, 600 mm, E = 200 GPasegment 2: aluminium, Ø50 mm, 300 mm, E = 70 GPaP = 30 kN
σ2 = MPa
6.Hard
Ø 35 mmCopper2 mØ 20 mmCopper2 mP = 60 kN

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

P = 60 kNsegment 1: Ø35 mm, 2 m, copper (E = 117 GPa)segment 2: Ø20 mm, 2 m, copper (E = 117 GPa)
δ = mm

Answer key

  1. 1. σ = 224.1 MPa
  2. 2. σr = 68.45 MPa
  3. 3. δ = 0.3773 mm
  4. 4. ε = 2387 µε
  5. 5. σ2 = 12.44 MPa
  6. 6. δ = 4.331 mm

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