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 16 mm0.5 mP = 50 kN

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

P = 50 kNd = 16 mm
σ = MPa
2.Easy
80 kNØ30100 GPaØ100/50500 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 50 mm, E = 100 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: Ø30 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 100 GPaL = 500 mm
σr = MPa
3.Medium
P = ?12300 mm400 mmØ30Ø50δ = 0.4 mm

A bar is made of a steel segment (diameter 30 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 50 mm, length 400 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.4 mm in total.

segment 1: steel, Ø30 mm, 300 mm, E = 200 GPasegment 2: brass, Ø50 mm, 400 mm, E = 100 GPaδ = 0.4 mm
P = kN
4.Medium
Ø 12 mmCopper1 mP = 100 kN

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

P = 100 kNd = 12 mmL = 1 mE = 117 GPa
δ = mm
5.Hard
30 kN12600 mm400 mmØ30Ø60σ2​ = ?

A steel segment (diameter 30 mm, length 600 mm, E = 200 GPa) and a segment made of aluminium (diameter 60 mm, length 400 mm, E = 70 GPa) are joined end to end and fixed between two rigid walls. An axial load of 30 kN acts at the joint, towards segment 2. Find the magnitude of the stress σ2 in segment 2.

segment 1: steel, Ø30 mm, 600 mm, E = 200 GPasegment 2: aluminium, Ø60 mm, 400 mm, E = 70 GPaP = 30 kN
σ2 = MPa
6.Hard
P = ?Ø20100 GPaØ120/60800 mm

A steel rod (diameter 20 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 60 mm, E = 100 GPa, allowable stress 100 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø20 mm, E = 200 GPa, σallow = 200 MPatube: Ø120/Ø60 mm, E = 100 GPa, σallow = 100 MPa
Pmax = kN

Answer key

  1. 1. σ = 248.7 MPa
  2. 2. σr = 21.91 MPa
  3. 3. P = 96.17 kN
  4. 4. δ = 7.557 mm
  5. 5. σ2 = 7.188 MPa
  6. 6. Pmax = 911.1 kN

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