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
80 kNØ40120 GPaØ80/60500 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 60 mm, E = 120 GPa). Both are 500 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø40 mm, E = 200 GPatube: Ø80/Ø60 mm, E = 120 GPaL = 500 mm
σr = MPa
2.Easy
Ø 30 mm1.5 mP = 100 kN

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

P = 100 kNd = 30 mm
σ = MPa
3.Medium
P = ?12500 mm200 mmØ25Ø40δ = 0.25 mm

A bar is made of a steel segment (diameter 25 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 40 mm, length 200 mm, E = 70 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, 500 mm, E = 200 GPasegment 2: aluminium, Ø40 mm, 200 mm, E = 70 GPaδ = 0.25 mm
P = kN
4.Medium
Ø 30 mmCopper2.5 mP = 55 kN

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

P = 55 kNd = 30 mmL = 2.5 mE = 117 GPa
δ = mm
5.Hard
P = ?Ø30100 GPaØ120/60300 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 150 MPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 60 mm, E = 100 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 150 MPatube: Ø120/Ø60 mm, E = 100 GPa, σallow = 70 MPa
Pmax = kN
6.Hard
20 kN12300 mm500 mmØ30Ø60σ2​ = ?

A steel segment (diameter 30 mm, length 300 mm, E = 200 GPa) and a segment made of aluminium (diameter 60 mm, length 500 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 20 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø30 mm, 300 mm, E = 200 GPasegment 2: aluminium, Ø60 mm, 500 mm, E = 70 GPaP = 20 kN
σ2 = MPa

Answer key

  1. 1. σr = 31.05 MPa
  2. 2. σ = 141.5 MPa
  3. 3. P = 33.94 kN
  4. 4. δ = 1.663 mm
  5. 5. Pmax = 692.7 kN
  6. 6. σ2 = 3.229 MPa

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