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
100 kNØ3070 GPaØ100/50500 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 GPa). Both are 500 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 70 GPaL = 500 mm
σr = MPa
2.Easy
Ø 16 mm0.5 mP = 80 kN

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

P = 80 kNd = 16 mm
σ = MPa
3.Medium
P = ?12300 mm500 mmØ25Ø50δ = 0.25 mm

A bar is made of a steel segment (diameter 25 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of copper (diameter 50 mm, length 500 mm, E = 120 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.25 mm in total.

segment 1: steel, Ø25 mm, 300 mm, E = 200 GPasegment 2: copper, Ø50 mm, 500 mm, E = 120 GPaδ = 0.25 mm
P = kN
4.Medium
Ø 12 mmBrass1 mP = 70 kN

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

P = 70 kNd = 12 mmL = 1 mE = 100 GPa
ε = µε
5.Hard
100 kN12300 mm300 mmØ25Ø50σ2​ = ?

A steel segment (diameter 25 mm, length 300 mm, E = 200 GPa) and a segment made of copper (diameter 50 mm, length 300 mm, E = 120 GPa) are joined end to end and fixed between two rigid walls. An axial load of 100 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø25 mm, 300 mm, E = 200 GPasegment 2: copper, Ø50 mm, 300 mm, E = 120 GPaP = 100 kN
σ2 = MPa
6.Hard
P = ?Ø2070 GPaØ100/50500 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 50 mm, E = 70 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 250 MPatube: Ø100/Ø50 mm, E = 70 GPa, σallow = 60 MPa
Pmax = kN

Answer key

  1. 1. σr = 36.12 MPa
  2. 2. σ = 397.9 MPa
  3. 3. P = 48.28 kN
  4. 4. ε = 6189 µε
  5. 5. σ2 = 35.95 MPa
  6. 6. Pmax = 407.3 kN

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