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 = 65 kN

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

P = 65 kNd = 16 mm
σ = MPa
2.Easy
80 kNØ40110 GPaØ100/70600 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 70 mm, E = 110 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: Ø40 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 110 GPaL = 600 mm
σr = MPa
3.Medium
P = ?12300 mm300 mmØ25Ø60δ = 0.3 mm

A bar is made of a steel segment (diameter 25 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 60 mm, length 300 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.3 mm in total.

segment 1: steel, Ø25 mm, 300 mm, E = 200 GPasegment 2: brass, Ø60 mm, 300 mm, E = 100 GPaδ = 0.3 mm
P = kN
4.Medium
80 kNØ25110 GPaØ100/50400 mmδ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 80 kN. Find the shortening δ.

P = 80 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 400 mm
δ = mm
5.Hard
80 kN12600 mm200 mmØ30Ø60σ2​ = ?

A steel segment (diameter 30 mm, length 600 mm, E = 200 GPa) and a segment made of brass (diameter 60 mm, length 200 mm, E = 100 GPa) are joined end to end and fixed between two rigid walls. An axial load of 80 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: brass, Ø60 mm, 200 mm, E = 100 GPaP = 80 kN
σ2 = MPa
6.Hard
Ø 35 mmAluminium0.5 mØ 16 mmAluminium2 mP = 85 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the total elongation δ.

P = 85 kNsegment 1: Ø35 mm, 0.5 m, aluminium (E = 70 GPa)segment 2: Ø16 mm, 2 m, aluminium (E = 70 GPa)
δ = mm

Answer key

  1. 1. σ = 323.3 MPa
  2. 2. σr = 23.12 MPa
  3. 3. P = 72.87 kN
  4. 4. δ = 0.04289 mm
  5. 5. σ2 = 24.25 MPa
  6. 6. δ = 12.71 mm

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