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
50 kNØ2570 GPaØ100/70500 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 70 mm, E = 70 GPa). Both are 500 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 70 GPaL = 500 mm
σr = MPa
2.Easy
150 kNØ30110 GPaØ100/50600 mmσr​ = ?

A steel rod (diameter 30 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 150 kN. Find the compressive stress σr in the rod.

P = 150 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 600 mm
σr = MPa
3.Medium
Ø 20 mmSteel2.5 mP = 50 kN

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

P = 50 kNd = 20 mmL = 2.5 mE = 200 GPa
δ = mm
4.Medium
P = ?12600 mm200 mmØ40Ø30δ = 0.5 mm

A bar is made of a steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 30 mm, length 200 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.5 mm in total.

segment 1: steel, Ø40 mm, 600 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 200 mm, E = 70 GPaδ = 0.5 mm
P = kN
5.Hard
P = ?Ø2070 GPaØ100/50800 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 GPa, allowable stress 100 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 120 MPatube: Ø100/Ø50 mm, E = 70 GPa, σallow = 100 MPa
Pmax = kN
6.Hard
80 kN12600 mm400 mmØ25Ø60σ2​ = ?

A steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) and a segment made of copper (diameter 60 mm, length 400 mm, E = 120 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, Ø25 mm, 600 mm, E = 200 GPasegment 2: copper, Ø60 mm, 400 mm, E = 120 GPaP = 80 kN
σ2 = MPa

Answer key

  1. 1. σr = 26.42 MPa
  2. 2. σr = 38.01 MPa
  3. 3. δ = 1.989 mm
  4. 4. P = 77.77 kN
  5. 5. Pmax = 285.1 kN
  6. 6. σ2 = 23.72 MPa

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