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 20 mm1 mP = 120 kN

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

P = 120 kNd = 20 mm
σ = MPa
2.Easy
100 kNØ40100 GPaØ100/60300 mmσr​ = ?

A steel rod (diameter 40 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 100 kN. Find the compressive stress σr in the rod.

P = 100 kNrod: Ø40 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 100 GPaL = 300 mm
σr = MPa
3.Medium
Ø 30 mmAluminium2.5 mP = 15 kN

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

P = 15 kNd = 30 mmL = 2.5 mE = 70 GPa
δ = mm
4.Medium
P = ?12400 mm400 mmØ30Ø30δ = 0.5 mm

A bar is made of a steel segment (diameter 30 mm, length 400 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 30 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, Ø30 mm, 400 mm, E = 200 GPasegment 2: bronze, Ø30 mm, 400 mm, E = 110 GPaδ = 0.5 mm
P = kN
5.Hard
40 kN12500 mm300 mmØ30Ø40σ2​ = ?

A steel segment (diameter 30 mm, length 500 mm, E = 200 GPa) and a segment made of aluminium (diameter 40 mm, length 300 mm, E = 70 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, Ø30 mm, 500 mm, E = 200 GPasegment 2: aluminium, Ø40 mm, 300 mm, E = 70 GPaP = 40 kN
σ2 = MPa
6.Hard
Ø 35 mmBrass0.5 mØ 20 mmAluminium1.5 mP = 55 kN

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

P = 55 kNsegment 1: Ø35 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø20 mm, 1.5 m, aluminium (E = 70 GPa)
δ = mm

Answer key

  1. 1. σ = 382 MPa
  2. 2. σr = 26.53 MPa
  3. 3. δ = 0.7579 mm
  4. 4. P = 62.71 kN
  5. 5. σ2 = 16.2 MPa
  6. 6. δ = 4.037 mm

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