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 GPaØ100/60800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 60 mm, E = 120 GPa). Both are 800 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/Ø60 mm, E = 120 GPaL = 800 mm
σr = MPa
2.Easy
Ø 30 mm1 mP = 30 kN

A solid round bar carries an axial tensile load P. Find the normal stress σ in the bar.

P = 30 kNd = 30 mm
σ = MPa
3.Medium
Ø 25 mmBrass2.5 mP = 50 kN

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

P = 50 kNd = 25 mmL = 2.5 mE = 100 GPa
ε = µε
4.Medium
250 kNØ25120 GPaØ80/60800 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 GPa). Both are 800 mm long and are compressed together between rigid plates by 250 kN. Find the shortening δ.

P = 250 kNrod: Ø25 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 800 mm
δ = mm
5.Hard
Ø 30 mmAluminium2 mØ 12 mmAluminium1.5 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: Ø30 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 1.5 m, aluminium (E = 70 GPa)
δ = mm
6.Hard
P = ?Ø4070 GPaØ120/70300 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 70 mm, E = 70 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 150 MPatube: Ø120/Ø70 mm, E = 70 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σr = 70.22 MPa
  2. 2. σ = 42.44 MPa
  3. 3. ε = 1019 µε
  4. 4. δ = 0.5524 mm
  5. 5. δ = 8.046 mm
  6. 6. Pmax = 580.2 kN

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