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 kNØ4070 GPaØ120/60500 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 60 mm, E = 70 GPa). Both are 500 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 70 GPaL = 500 mm
σr = MPa
2.Easy
200 kNØ2570 GPaØ120/60600 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 60 mm, E = 70 GPa). Both are 600 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/Ø60 mm, E = 70 GPaL = 600 mm
σr = MPa
3.Medium
Ø 25 mmAluminium1 mP = 15 kN

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

P = 15 kNd = 25 mmL = 1 mE = 70 GPa
ε = µε
4.Medium
P = ?12600 mm300 mmØ25Ø50δ = 0.5 mm

A bar is made of a steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 50 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 0.5 mm in total.

segment 1: steel, Ø25 mm, 600 mm, E = 200 GPasegment 2: brass, Ø50 mm, 300 mm, E = 100 GPaδ = 0.5 mm
P = kN
5.Hard
P = ?Ø40110 GPaØ100/70400 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 70 mm, E = 110 GPa, allowable stress 100 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 200 MPatube: Ø100/Ø70 mm, E = 110 GPa, σallow = 100 MPa
Pmax = kN
6.Hard
Ø 35 mmAluminium0.5 mØ 20 mmCopper2 mP = 90 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the largest normal stress σmax in the bar.

P = 90 kNsegment 1: Ø35 mm, 0.5 m, aluminium (E = 70 GPa)segment 2: Ø20 mm, 2 m, copper (E = 117 GPa)
σmax = MPa

Answer key

  1. 1. σr = 71 MPa
  2. 2. σr = 57.81 MPa
  3. 3. ε = 436.5 µε
  4. 4. P = 65.45 kN
  5. 5. Pmax = 629 kN
  6. 6. σmax = 286.5 MPa

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