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 kNØ20100 GPaØ80/50600 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 50 mm, E = 100 GPa). Both are 600 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø20 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 100 GPaL = 600 mm
σr = MPa
2.Easy
Ø 10 mm0.5 mP = 15 kN

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

P = 15 kNd = 10 mm
σ = MPa
3.Medium
Ø 12 mmSteel2 mP = 55 kN

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

P = 55 kNd = 12 mmL = 2 mE = 200 GPa
δ = mm
4.Medium
Ø 25 mmBrass0.5 mP = 40 kN

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

P = 40 kNd = 25 mmL = 0.5 mE = 100 GPa
ε = µε
5.Hard
P = ?Ø25110 GPaØ80/60600 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa, allowable stress 100 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 250 MPatube: Ø80/Ø60 mm, E = 110 GPa, σallow = 100 MPa
Pmax = kN
6.Hard
40 kN12400 mm500 mmØ40Ø40σ2​ = ?

A steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) and a segment made of aluminium (diameter 40 mm, length 500 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 40 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø40 mm, 400 mm, E = 200 GPasegment 2: aluminium, Ø40 mm, 500 mm, E = 70 GPaP = 40 kN
σ2 = MPa

Answer key

  1. 1. σr = 162.5 MPa
  2. 2. σ = 191 MPa
  3. 3. δ = 4.863 mm
  4. 4. ε = 814.9 µε
  5. 5. Pmax = 309.2 kN
  6. 6. σ2 = 6.963 MPa

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