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 kNØ20100 GPaØ80/50600 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 50 mm, E = 100 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: Ø20 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 100 GPaL = 600 mm
σr = MPa
2.Easy
80 kNØ25100 GPaØ120/60500 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 60 mm, E = 100 GPa). Both are 500 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 100 GPaL = 500 mm
σr = MPa
3.Medium
P = ?12300 mm500 mmØ40Ø60δ = 0.5 mm

A bar is made of a steel segment (diameter 40 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 60 mm, length 500 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, 300 mm, E = 200 GPasegment 2: aluminium, Ø60 mm, 500 mm, E = 70 GPaδ = 0.5 mm
P = kN
4.Medium
Ø 20 mmSteel1.5 mP = 50 kN

Find the axial strain ε in the steel bar, in microstrain (µε = 10⁻⁶).

P = 50 kNd = 20 mmL = 1.5 mE = 200 GPa
ε = µε
5.Hard
Ø 40 mmAluminium2 mØ 16 mmCopper2 mP = 45 kN

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

P = 45 kNsegment 1: Ø40 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø16 mm, 2 m, copper (E = 117 GPa)
δ = mm
6.Hard
P = ?Ø30110 GPaØ80/50600 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 50 mm, E = 110 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 120 MPatube: Ø80/Ø50 mm, E = 110 GPa, σallow = 60 MPa
Pmax = kN

Answer key

  1. 1. σr = 54.18 MPa
  2. 2. σr = 16.91 MPa
  3. 3. P = 134.4 kN
  4. 4. ε = 795.8 µε
  5. 5. δ = 4.849 mm
  6. 6. Pmax = 260.9 kN

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