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 kNØ40120 GPaØ100/50400 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa). Both are 400 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: Ø100/Ø50 mm, E = 120 GPaL = 400 mm
σr = MPa
2.Easy
250 kNØ20110 GPaØ120/70800 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 70 mm, E = 110 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: Ø20 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 110 GPaL = 800 mm
σr = MPa
3.Medium
200 kNØ20100 GPaØ80/60300 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 60 mm, E = 100 GPa). Both are 300 mm long and are compressed together between rigid plates by 200 kN. Find the shortening δ.

P = 200 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 100 GPaL = 300 mm
δ = mm
4.Medium
Ø 16 mmBrass2 mP = 35 kN

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

P = 35 kNd = 16 mmL = 2 mE = 100 GPa
ε = µε
5.Hard
Ø 40 mmAluminium2 mØ 12 mmAluminium2 mP = 35 kN

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

P = 35 kNsegment 1: Ø40 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 2 m, aluminium (E = 70 GPa)
δ = mm
6.Hard
60 kN12600 mm200 mmØ30Ø40σ2​ = ?

A steel segment (diameter 30 mm, length 600 mm, E = 200 GPa) and a segment made of bronze (diameter 40 mm, length 200 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, Ø30 mm, 600 mm, E = 200 GPasegment 2: bronze, Ø40 mm, 200 mm, E = 110 GPaP = 60 kN
σ2 = MPa

Answer key

  1. 1. σr = 62.62 MPa
  2. 2. σr = 56.59 MPa
  3. 3. δ = 0.2122 mm
  4. 4. ε = 1741 µε
  5. 5. δ = 9.638 mm
  6. 6. σ2 = 35.61 MPa

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