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 12 mm2 mP = 70 kN

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

P = 70 kNd = 12 mm
σ = MPa
2.Easy
300 kNØ2070 GPaØ120/50500 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa). Both are 500 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 70 GPaL = 500 mm
σr = MPa
3.Medium
P = ?12500 mm300 mmØ20Ø30δ = 0.3 mm

A bar is made of a steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 30 mm, length 300 mm, E = 120 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, 500 mm, E = 200 GPasegment 2: copper, Ø30 mm, 300 mm, E = 120 GPaδ = 0.3 mm
P = kN
4.Medium
80 kNØ25110 GPaØ120/50600 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 50 mm, E = 110 GPa). Both are 600 mm long and are compressed together between rigid plates by 80 kN. Find the shortening δ.

P = 80 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 110 GPaL = 600 mm
δ = mm
5.Hard
60 kN12500 mm500 mmØ30Ø40σ2​ = ?

A steel segment (diameter 30 mm, length 500 mm, E = 200 GPa) and a segment made of copper (diameter 40 mm, length 500 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 60 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: copper, Ø40 mm, 500 mm, E = 120 GPaP = 60 kN
σ2 = MPa
6.Hard
Ø 35 mmCopper2 mØ 12 mmSteel2 mP = 70 kN

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

P = 70 kNsegment 1: Ø35 mm, 2 m, copper (E = 117 GPa)segment 2: Ø12 mm, 2 m, steel (E = 200 GPa)
δ = mm

Answer key

  1. 1. σ = 618.9 MPa
  2. 2. σr = 83.67 MPa
  3. 3. P = 26.1 kN
  4. 4. δ = 0.04262 mm
  5. 5. σ2 = 24.64 MPa
  6. 6. δ = 7.433 mm

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