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 30 mm1.5 mP = 60 kN

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

P = 60 kNd = 30 mm
σ = MPa
2.Easy
200 kNØ30110 GPaØ120/50600 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 50 mm, E = 110 GPa). Both are 600 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 110 GPaL = 600 mm
σr = MPa
3.Medium
P = ?12500 mm300 mmØ40Ø30δ = 0.4 mm

A bar is made of a steel segment (diameter 40 mm, length 500 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 30 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 0.4 mm in total.

segment 1: steel, Ø40 mm, 500 mm, E = 200 GPasegment 2: brass, Ø30 mm, 300 mm, E = 100 GPaδ = 0.4 mm
P = kN
4.Medium
Ø 10 mmBrass2.5 mP = 75 kN

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

P = 75 kNd = 10 mmL = 2.5 mE = 100 GPa
δ = mm
5.Hard
Ø 35 mmBrass0.5 mØ 20 mmCopper2 mP = 60 kN

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

P = 60 kNsegment 1: Ø35 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø20 mm, 2 m, copper (E = 117 GPa)
δ = mm
6.Hard
30 kN12500 mm500 mmØ40Ø50σ2​ = ?

A steel segment (diameter 40 mm, length 500 mm, E = 200 GPa) and a segment made of brass (diameter 50 mm, length 500 mm, E = 100 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, Ø40 mm, 500 mm, E = 200 GPasegment 2: brass, Ø50 mm, 500 mm, E = 100 GPaP = 30 kN
σ2 = MPa

Answer key

  1. 1. σ = 84.88 MPa
  2. 2. σr = 34.2 MPa
  3. 3. P = 64.17 kN
  4. 4. δ = 23.87 mm
  5. 5. δ = 3.577 mm
  6. 6. σ2 = 6.701 MPa

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