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 mm1.5 mP = 50 kN

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

P = 50 kNd = 20 mm
σ = MPa
2.Easy
250 kNØ30120 GPaØ80/50300 mmσr​ = ?

A steel rod (diameter 30 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 80 mm, inner diameter 50 mm, E = 120 GPa). Both are 300 mm long and are compressed together between rigid plates by 250 kN. Find the compressive stress σr in the rod.

P = 250 kNrod: Ø30 mm, E = 200 GPatube: Ø80/Ø50 mm, E = 120 GPaL = 300 mm
σr = MPa
3.Medium
P = ?12300 mm500 mmØ30Ø30δ = 0.3 mm

A bar is made of a steel segment (diameter 30 mm, length 300 mm, E = 200 GPa) joined end to end with a segment made of aluminium (diameter 30 mm, length 500 mm, E = 70 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.3 mm in total.

segment 1: steel, Ø30 mm, 300 mm, E = 200 GPasegment 2: aluminium, Ø30 mm, 500 mm, E = 70 GPaδ = 0.3 mm
P = kN
4.Medium
Ø 25 mmBrass1 mP = 70 kN

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

P = 70 kNd = 25 mmL = 1 mE = 100 GPa
δ = mm
5.Hard
Ø 40 mmSteel2 mØ 16 mmAluminium2 mP = 85 kN

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

P = 85 kNsegment 1: Ø40 mm, 2 m, steel (E = 200 GPa)segment 2: Ø16 mm, 2 m, aluminium (E = 70 GPa)
δ = mm
6.Hard
P = ?Ø40120 GPaØ100/50600 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 250 MPa) sits inside a tube made of copper (outer diameter 100 mm, inner diameter 50 mm, E = 120 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 250 MPatube: Ø100/Ø50 mm, E = 120 GPa, σallow = 60 MPa
Pmax = kN

Answer key

  1. 1. σ = 159.2 MPa
  2. 2. σr = 98.24 MPa
  3. 3. P = 24.54 kN
  4. 4. δ = 1.426 mm
  5. 5. δ = 12.76 mm
  6. 6. Pmax = 479.1 kN

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