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 mm2 mP = 120 kN

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

P = 120 kNd = 10 mm
σ = MPa
2.Easy
200 kNØ20120 GPaØ100/60500 mmσr​ = ?

A steel rod (diameter 20 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 60 mm, E = 120 GPa). Both are 500 mm long and are compressed together between rigid plates by 200 kN. Find the compressive stress σr in the rod.

P = 200 kNrod: Ø20 mm, E = 200 GPatube: Ø100/Ø60 mm, E = 120 GPaL = 500 mm
σr = MPa
3.Medium
P = ?12300 mm300 mmØ40Ø30δ = 0.2 mm

A bar is made of a steel segment (diameter 40 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 30 mm, length 300 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.2 mm in total.

segment 1: steel, Ø40 mm, 300 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 300 mm, E = 70 GPaδ = 0.2 mm
P = kN
4.Medium
Ø 20 mmSteel2 mP = 40 kN

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

P = 40 kNd = 20 mmL = 2 mE = 200 GPa
δ = mm
5.Hard
Ø 30 mmBrass0.5 mØ 20 mmSteel2 mP = 70 kN

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

P = 70 kNsegment 1: Ø30 mm, 0.5 m, brass (E = 100 GPa)segment 2: Ø20 mm, 2 m, steel (E = 200 GPa)
δ = mm
6.Hard
P = ?Ø25110 GPaØ120/70400 mm

A steel rod (diameter 25 mm, E = 200 GPa, allowable stress 160 MPa) sits inside a tube made of bronze (outer diameter 120 mm, inner diameter 70 mm, E = 110 GPa, allowable stress 80 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø25 mm, E = 200 GPa, σallow = 160 MPatube: Ø120/Ø70 mm, E = 110 GPa, σallow = 80 MPa
Pmax = kN

Answer key

  1. 1. σ = 1528 MPa
  2. 2. σr = 60.06 MPa
  3. 3. P = 27.56 kN
  4. 4. δ = 1.273 mm
  5. 5. δ = 2.723 mm
  6. 6. Pmax = 668.3 kN

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