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
100 kNØ4070 GPaØ120/60600 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 60 mm, E = 70 GPa). Both are 600 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 70 GPaL = 600 mm
σr = MPa
2.Easy
Ø 20 mm1.5 mP = 15 kN

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

P = 15 kNd = 20 mm
σ = MPa
3.Medium
300 kNØ40120 GPaØ80/50300 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 50 mm, E = 120 GPa). Both are 300 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 120 GPaL = 300 mm
δ = mm
4.Medium
300 kNØ25110 GPaØ100/50600 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa). Both are 600 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 600 mm
δ = mm
5.Hard
Ø 35 mmBrass2 mØ 20 mmAluminium0.5 mP = 35 kN

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

P = 35 kNsegment 1: Ø35 mm, 2 m, brass (E = 100 GPa)segment 2: Ø20 mm, 0.5 m, aluminium (E = 70 GPa)
δ = mm
6.Hard
60 kN12600 mm200 mmØ30Ø30σ2​ = ?

A steel segment (diameter 30 mm, length 600 mm, E = 200 GPa) and a segment made of copper (diameter 30 mm, length 200 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, 600 mm, E = 200 GPasegment 2: copper, Ø30 mm, 200 mm, E = 120 GPaP = 60 kN
σ2 = MPa

Answer key

  1. 1. σr = 23.67 MPa
  2. 2. σ = 47.75 MPa
  3. 3. δ = 0.1454 mm
  4. 4. δ = 0.2412 mm
  5. 5. δ = 1.523 mm
  6. 6. σ2 = 54.57 MPa

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