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
Ø 30 mm0.5 mP = 40 kN

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

P = 40 kNd = 30 mm
σ = MPa
2.Easy
100 kNØ20110 GPaØ120/50300 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 50 mm, E = 110 GPa). Both are 300 mm long and are compressed together between rigid plates by 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø20 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 110 GPaL = 300 mm
σr = MPa
3.Medium
Ø 10 mmCopper1 mP = 75 kN

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

P = 75 kNd = 10 mmL = 1 mE = 117 GPa
δ = mm
4.Medium
Ø 20 mmSteel1 mP = 60 kN

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

P = 60 kNd = 20 mmL = 1 mE = 200 GPa
δ = mm
5.Hard
P = ?Ø30110 GPaØ80/60400 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 160 MPatube: Ø80/Ø60 mm, E = 110 GPa, σallow = 60 MPa
Pmax = kN
6.Hard
60 kN12300 mm200 mmØ40Ø30σ2​ = ?

A steel segment (diameter 40 mm, length 300 mm, E = 200 GPa) and a segment made of aluminium (diameter 30 mm, length 200 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 60 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø40 mm, 300 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 200 mm, E = 70 GPaP = 60 kN
σ2 = MPa

Answer key

  1. 1. σ = 56.59 MPa
  2. 2. σr = 18.33 MPa
  3. 3. δ = 8.162 mm
  4. 4. δ = 0.9549 mm
  5. 5. Pmax = 209.1 kN
  6. 6. σ2 = 19.35 MPa

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