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
50 kNØ25110 GPaØ100/50500 mmσr​ = ?

A steel rod (diameter 25 mm, E = 200 GPa) sits inside a tube made of bronze (outer diameter 100 mm, inner diameter 50 mm, E = 110 GPa). Both are 500 mm long and are compressed together between rigid plates by 50 kN. Find the compressive stress σr in the rod.

P = 50 kNrod: Ø25 mm, E = 200 GPatube: Ø100/Ø50 mm, E = 110 GPaL = 500 mm
σr = MPa
2.Easy
Ø 12 mm1.5 mP = 55 kN

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

P = 55 kNd = 12 mm
σ = MPa
3.Medium
P = ?12600 mm200 mmØ20Ø60δ = 0.5 mm

A bar is made of a steel segment (diameter 20 mm, length 600 mm, E = 200 GPa) joined end to end with a segment made of brass (diameter 60 mm, length 200 mm, E = 100 GPa). It is fixed at one end and pulled at the other. Find the axial load P that stretches it by 0.5 mm in total.

segment 1: steel, Ø20 mm, 600 mm, E = 200 GPasegment 2: brass, Ø60 mm, 200 mm, E = 100 GPaδ = 0.5 mm
P = kN
4.Medium
Ø 10 mmBrass1.5 mP = 100 kN

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

P = 100 kNd = 10 mmL = 1.5 mE = 100 GPa
ε = µε
5.Hard
Ø 35 mmBrass1.5 mØ 20 mmAluminium1.5 mP = 10 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 = 10 kNsegment 1: Ø35 mm, 1.5 m, brass (E = 100 GPa)segment 2: Ø20 mm, 1.5 m, aluminium (E = 70 GPa)
σmax = MPa
6.Hard
P = ?Ø30100 GPaØ120/50300 mm

A steel rod (diameter 30 mm, E = 200 GPa, allowable stress 200 MPa) sits inside a tube made of brass (outer diameter 120 mm, inner diameter 50 mm, E = 100 GPa, allowable stress 70 MPa). They are compressed together between rigid plates. Find the largest load Pmax.

rod: Ø30 mm, E = 200 GPa, σallow = 200 MPatube: Ø120/Ø50 mm, E = 100 GPa, σallow = 70 MPa
Pmax = kN

Answer key

  1. 1. σr = 13.4 MPa
  2. 2. σ = 486.3 MPa
  3. 3. P = 48.75 kN
  4. 4. ε = 12732 µε
  5. 5. σmax = 31.83 MPa
  6. 6. Pmax = 753.2 kN

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