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 20 mm2 mP = 35 kN

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

P = 35 kNd = 20 mm
σ = MPa
2.Easy
200 kNØ20100 GPaØ120/70600 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 70 mm, E = 100 GPa). Both are 600 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 100 GPaL = 600 mm
σr = MPa
3.Medium
50 kNØ2570 GPaØ100/50300 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 GPa). Both are 300 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 300 mm
δ = mm
4.Medium
Ø 12 mmAluminium1 mP = 40 kN

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

P = 40 kNd = 12 mmL = 1 mE = 70 GPa
δ = mm
5.Hard
Ø 30 mmSteel2 mØ 16 mmSteel0.5 mP = 55 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 = 55 kNsegment 1: Ø30 mm, 2 m, steel (E = 200 GPa)segment 2: Ø16 mm, 0.5 m, steel (E = 200 GPa)
σmax = MPa
6.Hard
40 kN12300 mm200 mmØ20Ø40σ2​ = ?

A steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) and a segment made of bronze (diameter 40 mm, length 200 mm, E = 110 GPa) are joined end to end and fixed between two rigid walls. An axial load of 40 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø20 mm, 300 mm, E = 200 GPasegment 2: bronze, Ø40 mm, 200 mm, E = 110 GPaP = 40 kN
σ2 = MPa

Answer key

  1. 1. σ = 111.4 MPa
  2. 2. σr = 49.45 MPa
  3. 3. δ = 0.02938 mm
  4. 4. δ = 5.053 mm
  5. 5. σmax = 273.5 MPa
  6. 6. σ2 = 24.43 MPa

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