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
80 kNØ2070 GPaØ120/70300 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 70 mm, E = 70 GPa). Both are 300 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 70 GPaL = 300 mm
σr = MPa
2.Easy
200 kNØ2570 GPaØ120/50500 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa). Both are 500 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 70 GPaL = 500 mm
σr = MPa
3.Medium
P = ?12500 mm200 mmØ20Ø30δ = 0.5 mm

A bar is made of a steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 30 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 0.5 mm in total.

segment 1: steel, Ø20 mm, 500 mm, E = 200 GPasegment 2: copper, Ø30 mm, 200 mm, E = 120 GPaδ = 0.5 mm
P = kN
4.Medium
P = ?12500 mm300 mmØ20Ø30δ = 0.2 mm

A bar is made of a steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 30 mm, length 300 mm, E = 110 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.2 mm in total.

segment 1: steel, Ø20 mm, 500 mm, E = 200 GPasegment 2: bronze, Ø30 mm, 300 mm, E = 110 GPaδ = 0.2 mm
P = kN
5.Hard
P = ?Ø2570 GPaØ80/60800 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of aluminium (outer diameter 80 mm, inner diameter 60 mm, E = 70 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 250 MPatube: Ø80/Ø60 mm, E = 70 GPa, σallow = 60 MPa
Pmax = kN
6.Hard
100 kN12400 mm200 mmØ30Ø60σ2​ = ?

A steel segment (diameter 30 mm, length 400 mm, E = 200 GPa) and a segment made of aluminium (diameter 60 mm, length 200 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 100 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: aluminium, Ø60 mm, 200 mm, E = 70 GPaP = 100 kN
σ2 = MPa

Answer key

  1. 1. σr = 27.34 MPa
  2. 2. σr = 53.16 MPa
  3. 3. P = 48.47 kN
  4. 4. P = 16.93 kN
  5. 5. Pmax = 216.1 kN
  6. 6. σ2 = 26.06 MPa

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