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
300 kNØ3070 GPaØ120/70800 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 70 mm, E = 70 GPa). Both are 800 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 70 GPaL = 800 mm
σr = MPa
2.Easy
Ø 20 mm1.5 mP = 50 kN

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

P = 50 kNd = 20 mm
σ = MPa
3.Medium
P = ?12300 mm200 mmØ30Ø50δ = 0.3 mm

A bar is made of a steel segment (diameter 30 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 50 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, Ø30 mm, 300 mm, E = 200 GPasegment 2: copper, Ø50 mm, 200 mm, E = 120 GPaδ = 0.3 mm
P = kN
4.Medium
P = ?12400 mm300 mmØ25Ø60δ = 0.25 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 brass (diameter 60 mm, length 300 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.25 mm in total.

segment 1: steel, Ø25 mm, 400 mm, E = 200 GPasegment 2: brass, Ø60 mm, 300 mm, E = 100 GPaδ = 0.25 mm
P = kN
5.Hard
60 kN12600 mm500 mmØ20Ø30σ2​ = ?

A steel segment (diameter 20 mm, length 600 mm, E = 200 GPa) and a segment made of bronze (diameter 30 mm, length 500 mm, E = 110 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, Ø20 mm, 600 mm, E = 200 GPasegment 2: bronze, Ø30 mm, 500 mm, E = 110 GPaP = 60 kN
σ2 = MPa
6.Hard
P = ?Ø20110 GPaØ80/60600 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 160 MPatube: Ø80/Ø60 mm, E = 110 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σr = 90.41 MPa
  2. 2. σ = 159.2 MPa
  3. 3. P = 101 kN
  4. 4. P = 48.68 kN
  5. 5. σ2 = 50.72 MPa
  6. 6. Pmax = 221.6 kN

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