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 mm1.5 mP = 20 kN

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

P = 20 kNd = 30 mm
σ = MPa
2.Easy
80 kNØ25120 GPaØ100/50800 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa). Both are 800 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 120 GPaL = 800 mm
σr = MPa
3.Medium
Ø 10 mmCopper0.5 mP = 20 kN

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

P = 20 kNd = 10 mmL = 0.5 mE = 117 GPa
δ = mm
4.Medium
200 kNØ2070 GPaØ120/70500 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 70 mm, E = 70 GPa). Both are 500 mm long and are compressed together between rigid plates by 200 kN. Find the shortening δ.

P = 200 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 70 GPaL = 500 mm
δ = mm
5.Hard
50 kN12600 mm400 mmØ25Ø50σ2​ = ?

A steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) and a segment made of brass (diameter 50 mm, length 400 mm, E = 100 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, Ø25 mm, 600 mm, E = 200 GPasegment 2: brass, Ø50 mm, 400 mm, E = 100 GPaP = 50 kN
σ2 = MPa
6.Hard
Ø 30 mmCopper2 mØ 12 mmBrass1.5 mP = 65 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 = 65 kNsegment 1: Ø30 mm, 2 m, copper (E = 117 GPa)segment 2: Ø12 mm, 1.5 m, brass (E = 100 GPa)
σmax = MPa

Answer key

  1. 1. σ = 28.29 MPa
  2. 2. σr = 19.87 MPa
  3. 3. δ = 1.088 mm
  4. 4. δ = 0.1709 mm
  5. 5. σ2 = 19.1 MPa
  6. 6. σmax = 574.7 MPa

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