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 mm1.5 mP = 10 kN

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

P = 10 kNd = 16 mm
σ = MPa
2.Easy
80 kNØ20120 GPaØ100/70600 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 70 mm, E = 120 GPa). Both are 600 mm long and are compressed together between rigid plates by 80 kN. Find the compressive stress σr in the rod.

P = 80 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 120 GPaL = 600 mm
σr = MPa
3.Medium
P = ?12600 mm400 mmØ25Ø30δ = 0.4 mm

A bar is made of a steel segment (diameter 25 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 30 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, Ø25 mm, 600 mm, E = 200 GPasegment 2: brass, Ø30 mm, 400 mm, E = 100 GPaδ = 0.4 mm
P = kN
4.Medium
100 kNØ2570 GPaØ100/70300 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of aluminium (outer diameter 100 mm, inner diameter 70 mm, E = 70 GPa). Both are 300 mm long and are compressed together between rigid plates by 100 kN. Find the shortening δ.

P = 100 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 70 GPaL = 300 mm
δ = mm
5.Hard
40 kN12600 mm500 mmØ40Ø50σ2​ = ?

A steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) and a segment made of copper (diameter 50 mm, length 500 mm, E = 120 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, 600 mm, E = 200 GPasegment 2: copper, Ø50 mm, 500 mm, E = 120 GPaP = 40 kN
σ2 = MPa
6.Hard
20 kN12500 mm400 mmØ40Ø50σ2​ = ?

A steel segment (diameter 40 mm, length 500 mm, E = 200 GPa) and a segment made of aluminium (diameter 50 mm, length 400 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, Ø40 mm, 500 mm, E = 200 GPasegment 2: aluminium, Ø50 mm, 400 mm, E = 70 GPaP = 20 kN
σ2 = MPa

Answer key

  1. 1. σ = 49.74 MPa
  2. 2. σr = 29.44 MPa
  3. 3. P = 33.98 kN
  4. 4. δ = 0.07925 mm
  5. 5. σ2 = 10.79 MPa
  6. 6. σ2 = 4.136 MPa

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