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
250 kNØ4070 GPaØ120/50800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa). Both are 800 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 70 GPaL = 800 mm
σr = MPa
2.Easy
250 kNØ4070 GPaØ100/70800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 70 mm, E = 70 GPa). Both are 800 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 70 GPaL = 800 mm
σr = MPa
3.Medium
P = ?12600 mm400 mmØ20Ø60δ = 0.2 mm

A bar is made of a steel segment (diameter 20 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 60 mm, length 400 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.2 mm in total.

segment 1: steel, Ø20 mm, 600 mm, E = 200 GPasegment 2: brass, Ø60 mm, 400 mm, E = 100 GPaδ = 0.2 mm
P = kN
4.Medium
Ø 25 mmSteel0.5 mP = 80 kN

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

P = 80 kNd = 25 mmL = 0.5 mE = 200 GPa
ε = µε
5.Hard
50 kN12300 mm200 mmØ25Ø60σ2​ = ?

A steel segment (diameter 25 mm, length 300 mm, E = 200 GPa) and a segment made of brass (diameter 60 mm, length 200 mm, E = 100 GPa) are joined end to end and fixed between two rigid walls. An axial load of 50 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø25 mm, 300 mm, E = 200 GPasegment 2: brass, Ø60 mm, 200 mm, E = 100 GPaP = 50 kN
σ2 = MPa
6.Hard
Ø 35 mmBrass1.5 mØ 12 mmAluminium2 mP = 45 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 = 45 kNsegment 1: Ø35 mm, 1.5 m, brass (E = 100 GPa)segment 2: Ø12 mm, 2 m, aluminium (E = 70 GPa)
σmax = MPa

Answer key

  1. 1. σr = 55.21 MPa
  2. 2. σr = 94.04 MPa
  3. 3. P = 18.24 kN
  4. 4. ε = 814.9 µε
  5. 5. σ2 = 14.36 MPa
  6. 6. σmax = 397.9 MPa

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