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 kNØ25100 GPaØ100/60400 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 60 mm, E = 100 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: Ø25 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 100 GPaL = 400 mm
σr = MPa
2.Easy
Ø 12 mm2 mP = 95 kN

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

P = 95 kNd = 12 mm
σ = MPa
3.Medium
200 kNØ4070 GPaØ100/50600 mmδ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 GPa). Both are 600 mm long and are compressed together between rigid plates by 200 kN. Find the shortening δ.

P = 200 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 600 mm
δ = mm
4.Medium
Ø 25 mmCopper0.5 mP = 10 kN

Find the elongation δ of the copper bar under the axial load.

P = 10 kNd = 25 mmL = 0.5 mE = 117 GPa
δ = mm
5.Hard
P = ?Ø25120 GPaØ100/70800 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 200 MPatube: Ø100/Ø70 mm, E = 120 GPa, σallow = 80 MPa
Pmax = kN
6.Hard
Ø 35 mmAluminium0.5 mØ 12 mmAluminium1.5 mP = 60 kN

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

P = 60 kNsegment 1: Ø35 mm, 0.5 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 1.5 m, aluminium (E = 70 GPa)
δ = mm

Answer key

  1. 1. σr = 99.86 MPa
  2. 2. σ = 840 MPa
  3. 3. δ = 0.1808 mm
  4. 4. δ = 0.08706 mm
  5. 5. Pmax = 385.9 kN
  6. 6. δ = 11.81 mm

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