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
50 kNØ20120 GPaØ120/70300 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 70 mm, E = 120 GPa). Both are 300 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø70 mm, E = 120 GPaL = 300 mm
σr = MPa
2.Easy
Ø 20 mm0.5 mP = 20 kN

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

P = 20 kNd = 20 mm
σ = MPa
3.Medium
200 kNØ20120 GPaØ120/60400 mmδ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 60 mm, E = 120 GPa). Both are 400 mm long and are compressed together between rigid plates by 200 kN. Find the shortening δ.

P = 200 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 120 GPaL = 400 mm
δ = mm
4.Medium
Ø 10 mmAluminium1 mP = 30 kN

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

P = 30 kNd = 10 mmL = 1 mE = 70 GPa
ε = µε
5.Hard
P = ?Ø40100 GPaØ120/70400 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 70 mm, E = 100 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/Ø70 mm, E = 100 GPa, σallow = 50 MPa
Pmax = kN
6.Hard
100 kN12400 mm500 mmØ20Ø30σ2​ = ?

A steel segment (diameter 20 mm, length 400 mm, E = 200 GPa) and a segment made of copper (diameter 30 mm, length 500 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, Ø20 mm, 400 mm, E = 200 GPasegment 2: copper, Ø30 mm, 500 mm, E = 120 GPaP = 100 kN
σ2 = MPa

Answer key

  1. 1. σr = 10.44 MPa
  2. 2. σ = 63.66 MPa
  3. 3. δ = 0.07403 mm
  4. 4. ε = 5457 µε
  5. 5. Pmax = 498.7 kN
  6. 6. σ2 = 73.46 MPa

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