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 mm0.5 mP = 90 kN

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

P = 90 kNd = 10 mm
σ = MPa
2.Easy
300 kNØ25110 GPaØ100/70400 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 70 mm, E = 110 GPa). Both are 400 mm long and are compressed together between rigid plates by 300 kN. Find the compressive stress σr in the rod.

P = 300 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø70 mm, E = 110 GPaL = 400 mm
σr = MPa
3.Medium
P = ?12400 mm400 mmØ40Ø40δ = 0.5 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 40 mm, length 400 mm, E = 110 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.5 mm in total.

segment 1: steel, Ø40 mm, 400 mm, E = 200 GPasegment 2: bronze, Ø40 mm, 400 mm, E = 110 GPaδ = 0.5 mm
P = kN
4.Medium
200 kNØ30100 GPaØ100/60300 mmδ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of brass (outer diameter 100 mm, inner diameter 60 mm, E = 100 GPa). Both are 300 mm long and are compressed together between rigid plates by 200 kN. Find the shortening δ.

P = 200 kNrod: Ø30 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 100 GPaL = 300 mm
δ = mm
5.Hard
Ø 25 mmBrass1.5 mØ 20 mmAluminium2 mP = 15 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the largest normal stress σmax in the bar.

P = 15 kNsegment 1: Ø25 mm, 1.5 m, brass (E = 100 GPa)segment 2: Ø20 mm, 2 m, aluminium (E = 70 GPa)
σmax = MPa
6.Hard
30 kN12600 mm500 mmØ30Ø30σ2​ = ?

A steel segment (diameter 30 mm, length 600 mm, E = 200 GPa) and a segment made of bronze (diameter 30 mm, length 500 mm, E = 110 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: bronze, Ø30 mm, 500 mm, E = 110 GPaP = 30 kN
σ2 = MPa

Answer key

  1. 1. σ = 1146 MPa
  2. 2. σr = 111.4 MPa
  3. 3. P = 111.5 kN
  4. 4. δ = 0.09316 mm
  5. 5. σmax = 47.75 MPa
  6. 6. σ2 = 16.87 MPa

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