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
200 kNØ20120 GPaØ80/60300 mmσr​ = ?

A steel rod (diameter 20 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 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 300 mm
σr = MPa
2.Easy
Ø 16 mm0.5 mP = 65 kN

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

P = 65 kNd = 16 mm
σ = MPa
3.Medium
Ø 25 mmSteel3 mP = 80 kN

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

P = 80 kNd = 25 mmL = 3 mE = 200 GPa
δ = mm
4.Medium
P = ?12500 mm300 mmØ20Ø30δ = 0.4 mm

A bar is made of a steel segment (diameter 20 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 30 mm, length 300 mm, E = 120 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.4 mm in total.

segment 1: steel, Ø20 mm, 500 mm, E = 200 GPasegment 2: copper, Ø30 mm, 300 mm, E = 120 GPaδ = 0.4 mm
P = kN
5.Hard
P = ?Ø20120 GPaØ80/60600 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 250 MPatube: Ø80/Ø60 mm, E = 120 GPa, σallow = 80 MPa
Pmax = kN
6.Hard
P = ?Ø30100 GPaØ100/50800 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 50 mm, E = 100 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 120 MPatube: Ø100/Ø50 mm, E = 100 GPa, σallow = 70 MPa
Pmax = kN

Answer key

  1. 1. σr = 122.4 MPa
  2. 2. σ = 323.3 MPa
  3. 3. δ = 2.445 mm
  4. 4. P = 34.8 kN
  5. 5. Pmax = 217.8 kN
  6. 6. Pmax = 438.3 kN

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