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 25 mm0.5 mP = 25 kN

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

P = 25 kNd = 25 mm
σ = MPa
2.Easy
300 kNØ25120 GPaØ120/50300 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 50 mm, E = 120 GPa). Both are 300 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 120 GPaL = 300 mm
σr = MPa
3.Medium
300 kNØ40110 GPaØ100/70800 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 70 mm, E = 110 GPa). Both are 800 mm long and are compressed together between rigid plates by 300 kN. Find the shortening δ.

P = 300 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 110 GPaL = 800 mm
δ = mm
4.Medium
200 kNØ20120 GPaØ100/50300 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 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: Ø100/Ø50 mm, E = 120 GPaL = 300 mm
δ = mm
5.Hard
P = ?Ø25120 GPaØ100/60400 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 60 mm, E = 120 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 160 MPatube: Ø100/Ø60 mm, E = 120 GPa, σallow = 70 MPa
Pmax = kN
6.Hard
Ø 25 mmSteel2 mØ 20 mmSteel1 mP = 100 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 = 100 kNsegment 1: Ø25 mm, 2 m, steel (E = 200 GPa)segment 2: Ø20 mm, 1 m, steel (E = 200 GPa)
σmax = MPa

Answer key

  1. 1. σ = 50.93 MPa
  2. 2. σr = 49.19 MPa
  3. 3. δ = 0.3469 mm
  4. 4. δ = 0.07795 mm
  5. 5. Pmax = 409.1 kN
  6. 6. σmax = 318.3 MPa

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