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 10 mm1.5 mP = 45 kN

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

P = 45 kNd = 10 mm
σ = MPa
2.Easy
100 kNØ30100 GPaØ80/50800 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 80 mm, inner diameter 50 mm, E = 100 GPa). Both are 800 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: Ø80/Ø50 mm, E = 100 GPaL = 800 mm
σr = MPa
3.Medium
P = ?12400 mm500 mmØ40Ø50δ = 0.25 mm

A bar is made of a steel segment (diameter 40 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 50 mm, length 500 mm, E = 110 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, Ø40 mm, 400 mm, E = 200 GPasegment 2: bronze, Ø50 mm, 500 mm, E = 110 GPaδ = 0.25 mm
P = kN
4.Medium
Ø 12 mmCopper2.5 mP = 85 kN

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

P = 85 kNd = 12 mmL = 2.5 mE = 117 GPa
δ = mm
5.Hard
60 kN12500 mm500 mmØ40Ø40σ2​ = ?

A steel segment (diameter 40 mm, length 500 mm, E = 200 GPa) and a segment made of copper (diameter 40 mm, length 500 mm, E = 120 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, 500 mm, E = 200 GPasegment 2: copper, Ø40 mm, 500 mm, E = 120 GPaP = 60 kN
σ2 = MPa
6.Hard
P = ?Ø4070 GPaØ120/50500 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of aluminium (outer diameter 120 mm, inner diameter 50 mm, E = 70 GPa, allowable stress 100 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 200 MPatube: Ø120/Ø50 mm, E = 70 GPa, σallow = 100 MPa
Pmax = kN

Answer key

  1. 1. σ = 573 MPa
  2. 2. σr = 44.68 MPa
  3. 3. P = 64 kN
  4. 4. δ = 16.06 mm
  5. 5. σ2 = 17.9 MPa
  6. 6. Pmax = 905.6 kN

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