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 kNØ30110 GPaØ80/50500 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 50 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 110 GPaL = 500 mm
σr = MPa
2.Easy
Ø 12 mm1 mP = 75 kN

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

P = 75 kNd = 12 mm
σ = MPa
3.Medium
50 kNØ25100 GPaØ120/50600 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 50 mm, E = 100 GPa). Both are 600 mm long and are compressed together between rigid plates by 50 kN. Find the shortening δ.

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 100 GPaL = 600 mm
δ = mm
4.Medium
250 kNØ40120 GPaØ80/60300 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 GPa). Both are 300 mm long and are compressed together between rigid plates by 250 kN. Find the shortening δ.

P = 250 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 300 mm
δ = mm
5.Hard
P = ?Ø40120 GPaØ120/50400 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 50 mm, E = 120 GPa, allowable stress 50 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 250 MPatube: Ø120/Ø50 mm, E = 120 GPa, σallow = 50 MPa
Pmax = kN
6.Hard
Ø 40 mmCopper2 mØ 20 mmAluminium1.5 mP = 15 kN

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

P = 15 kNsegment 1: Ø40 mm, 2 m, copper (E = 117 GPa)segment 2: Ø20 mm, 1.5 m, aluminium (E = 70 GPa)
δ = mm

Answer key

  1. 1. σr = 125.4 MPa
  2. 2. σ = 663.1 MPa
  3. 3. δ = 0.02905 mm
  4. 4. δ = 0.1456 mm
  5. 5. Pmax = 572 kN
  6. 6. δ = 1.227 mm

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