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
Ø 16 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 = 16 mm
σ = MPa
2.Easy
200 kNØ40110 GPaØ120/60800 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 60 mm, E = 110 GPa). Both are 800 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø40 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 110 GPaL = 800 mm
σr = MPa
3.Medium
Ø 12 mmSteel0.5 mP = 25 kN

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

P = 25 kNd = 12 mmL = 0.5 mE = 200 GPa
ε = µε
4.Medium
300 kNØ2570 GPaØ100/60400 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 60 mm, E = 70 GPa). Both are 400 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 70 GPaL = 400 mm
δ = mm
5.Hard
Ø 30 mmBrass0.5 mØ 16 mmAluminium1 mP = 120 kN

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

P = 120 kNsegment 1: Ø30 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø16 mm, 1 m, aluminium (E = 70 GPa)
δ = mm
6.Hard
P = ?Ø20100 GPaØ100/50300 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 50 mm, E = 100 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 200 MPatube: Ø100/Ø50 mm, E = 100 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σ = 149.2 MPa
  2. 2. σr = 33.77 MPa
  3. 3. ε = 1105 µε
  4. 4. δ = 0.2666 mm
  5. 5. δ = 9.375 mm
  6. 6. Pmax = 521.5 kN

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