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 = 70 kN

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

P = 70 kNd = 25 mm
σ = MPa
2.Easy
250 kNØ2570 GPaØ100/50400 mmσr​ = ?

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 400 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 400 mm
σr = MPa
3.Medium
Ø 16 mmSteel2.5 mP = 15 kN

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

P = 15 kNd = 16 mmL = 2.5 mE = 200 GPa
δ = mm
4.Medium
P = ?12300 mm500 mmØ20Ø30δ = 0.3 mm

A bar is made of a steel segment (diameter 20 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 30 mm, length 500 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.3 mm in total.

segment 1: steel, Ø20 mm, 300 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 500 mm, E = 70 GPaδ = 0.3 mm
P = kN
5.Hard
40 kN12500 mm300 mmØ30Ø50σ2​ = ?

A steel segment (diameter 30 mm, length 500 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 40 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø30 mm, 500 mm, E = 200 GPasegment 2: aluminium, Ø50 mm, 300 mm, E = 70 GPaP = 40 kN
σ2 = MPa
6.Hard
20 kN12400 mm400 mmØ40Ø60σ2​ = ?

A steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) and a segment made of aluminium (diameter 60 mm, length 400 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 20 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: aluminium, Ø60 mm, 400 mm, E = 70 GPaP = 20 kN
σ2 = MPa

Answer key

  1. 1. σ = 142.6 MPa
  2. 2. σr = 97.94 MPa
  3. 3. δ = 0.9325 mm
  4. 4. P = 20.16 kN
  5. 5. σ2 = 12.6 MPa
  6. 6. σ2 = 3.116 MPa

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