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 = 15 kN

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

P = 15 kNd = 20 mm
σ = MPa
2.Easy
250 kNØ40120 GPaØ120/50300 mmσr​ = ?

A steel rod (diameter 40 mm, E = 200 GPa) sits inside a tube made of copper (outer diameter 120 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: Ø40 mm, E = 200 GPatube: Ø120/Ø50 mm, E = 120 GPaL = 300 mm
σr = MPa
3.Medium
Ø 16 mmCopper0.5 mP = 85 kN

Find the axial strain ε in the copper bar, in microstrain (µε = 10⁻⁶).

P = 85 kNd = 16 mmL = 0.5 mE = 117 GPa
ε = µε
4.Medium
P = ?12500 mm400 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 copper (diameter 30 mm, length 400 mm, E = 120 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: copper, Ø30 mm, 400 mm, E = 120 GPaδ = 0.4 mm
P = kN
5.Hard
Ø 35 mmAluminium2 mØ 16 mmCopper2 mP = 90 kN

The stepped bar is fixed at the wall and loaded at its free end. Find the largest normal stress σmax in the bar.

P = 90 kNsegment 1: Ø35 mm, 2 m, aluminium (E = 70 GPa)segment 2: Ø16 mm, 2 m, copper (E = 117 GPa)
σmax = MPa
6.Hard
P = ?Ø40110 GPaØ80/60300 mm

A steel rod (diameter 40 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of bronze (outer diameter 80 mm, inner diameter 60 mm, E = 110 GPa, allowable stress 60 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø40 mm, E = 200 GPa, σallow = 200 MPatube: Ø80/Ø60 mm, E = 110 GPa, σallow = 60 MPa
Pmax = kN

Answer key

  1. 1. σ = 47.75 MPa
  2. 2. σr = 36.42 MPa
  3. 3. ε = 3613 µε
  4. 4. P = 59.66 kN
  5. 5. σmax = 447.6 MPa
  6. 6. Pmax = 269 kN

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