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
150 kNØ4070 GPaØ100/70400 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 70 mm, E = 70 GPa). Both are 400 mm long and are compressed together between rigid plates by 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 70 GPaL = 400 mm
σr = MPa
2.Easy
300 kNØ2570 GPaØ80/60300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 60 mm, E = 70 GPa). Both are 300 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 70 GPaL = 300 mm
σr = MPa
3.Medium
Ø 12 mmBrass0.5 mP = 35 kN

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

P = 35 kNd = 12 mmL = 0.5 mE = 100 GPa
δ = mm
4.Medium
250 kNØ25120 GPaØ100/70400 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 GPa). Both are 400 mm long and are compressed together between rigid plates by 250 kN. Find the shortening δ.

P = 250 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 120 GPaL = 400 mm
δ = mm
5.Hard
40 kN12400 mm300 mmØ30Ø40σ2​ = ?

A steel segment (diameter 30 mm, length 400 mm, E = 200 GPa) and a segment made of copper (diameter 40 mm, length 300 mm, E = 120 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, 400 mm, E = 200 GPasegment 2: copper, Ø40 mm, 300 mm, E = 120 GPaP = 40 kN
σ2 = MPa
6.Hard
80 kN12500 mm400 mmØ30Ø60σ2​ = ?

A steel segment (diameter 30 mm, length 500 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 80 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, Ø60 mm, 400 mm, E = 70 GPaP = 80 kN
σ2 = MPa

Answer key

  1. 1. σr = 56.42 MPa
  2. 2. σr = 238 MPa
  3. 3. δ = 1.547 mm
  4. 4. δ = 0.1728 mm
  5. 5. σ2 = 18.69 MPa
  6. 6. σ2 = 18.01 MPa

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