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 mm2 mP = 90 kN

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

P = 90 kNd = 16 mm
σ = MPa
2.Easy
50 kNØ30120 GPaØ120/60400 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 mm, inner diameter 60 mm, E = 120 GPa). Both are 400 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø30 mm, E = 200 GPatube: Ø120/Ø60 mm, E = 120 GPaL = 400 mm
σr = MPa
3.Medium
P = ?12600 mm200 mmØ40Ø30δ = 0.3 mm

A bar is made of a steel segment (diameter 40 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of bronze (diameter 30 mm, length 200 mm, E = 110 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.3 mm in total.

segment 1: steel, Ø40 mm, 600 mm, E = 200 GPasegment 2: bronze, Ø30 mm, 200 mm, E = 110 GPaδ = 0.3 mm
P = kN
4.Medium
Ø 25 mmAluminium3 mP = 30 kN

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

P = 30 kNd = 25 mmL = 3 mE = 70 GPa
δ = mm
5.Hard
P = ?Ø40100 GPaØ120/50500 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 120 MPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 50 mm, E = 100 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 120 MPatube: Ø120/Ø50 mm, E = 100 GPa, σallow = 60 MPa
Pmax = kN
6.Hard
Ø 25 mmAluminium2 mØ 12 mmSteel0.5 mP = 90 kN

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

P = 90 kNsegment 1: Ø25 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø12 mm, 0.5 m, steel (E = 200 GPa)
δ = mm

Answer key

  1. 1. σ = 447.6 MPa
  2. 2. σr = 8.626 MPa
  3. 3. P = 60.49 kN
  4. 4. δ = 2.619 mm
  5. 5. Pmax = 711.6 kN
  6. 6. δ = 7.228 mm

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