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 mm2 mP = 30 kN

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

P = 30 kNd = 30 mm
σ = MPa
2.Easy
200 kNØ40100 GPaØ120/60800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 60 mm, E = 100 GPa). Both are 800 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 100 GPaL = 800 mm
σr = MPa
3.Medium
300 kNØ30100 GPaØ100/70300 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 70 mm, E = 100 GPa). Both are 300 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 100 GPaL = 300 mm
δ = mm
4.Medium
P = ?12400 mm200 mmØ25Ø60δ = 0.3 mm

A bar is made of a steel segment (diameter 25 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 60 mm, length 200 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, Ø25 mm, 400 mm, E = 200 GPasegment 2: copper, Ø60 mm, 200 mm, E = 120 GPaδ = 0.3 mm
P = kN
5.Hard
Ø 25 mmBrass1 mØ 20 mmAluminium2 mP = 50 kN

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

P = 50 kNsegment 1: Ø25 mm, 1 m, brass (E = 100 GPa)segment 2: Ø20 mm, 2 m, aluminium (E = 70 GPa)
δ = mm
6.Hard
80 kN12500 mm400 mmØ20Ø50σ2​ = ?

A steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) and a segment made of aluminium (diameter 50 mm, length 400 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 80 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø20 mm, 500 mm, E = 200 GPasegment 2: aluminium, Ø50 mm, 400 mm, E = 70 GPaP = 80 kN
σ2 = MPa

Answer key

  1. 1. σ = 42.44 MPa
  2. 2. σr = 36.38 MPa
  3. 3. δ = 0.1661 mm
  4. 4. P = 64.32 kN
  5. 5. δ = 5.566 mm
  6. 6. σ2 = 29.83 MPa

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