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Three point flexural test - Wikipedia, the free encyclopedia

Three point flexural test

From Wikipedia, the free encyclopedia


1940s flexural test machinery working on a sample of concrete
1940s flexural test machinery working on a sample of concrete

The three point bending flexural test provides values for the modulus of elasticity in bending EB, flexural stress σf, flexural strain εf and the flexural stress-strain response of the material. The main advantage of a three point flexural test is the ease of the specimen preparation and testing. However, this method has also some disadvantages: the results of the testing method are sensitive to specimen and loading geometry and strain rate.

[edit] Testing Method

Calculation of the flexural stress σf


\sigma_f = \frac{3 P L}{2 b d^2} for a rectangular cross section


\sigma_f = \frac{P L}{\pi R^3} for a circular cross section


Calculation of the flexural strain εf

\epsilon_f = \frac{6Dd}{L^2}

Calculation of Young's modulus EB

E_B = \frac{L^3 m}{4 b d^3}

in these formulas the following parameters are used:

  • σf = Stress in outer fibers at midpoint, (MPa)
  • εf = Strain in the outer surface, (%)
  • Eb = Modulus of elasticity in bending,(MPa)
  • P = load at a given point on the load deflection curve, (N)
  • L = Support span, (mm)
  • b = Width of test beam, (mm)
  • d = Depth of tested beam, (mm)
  • D = maximum deflection of the center of the beam, (mm)
  • m = Slope of the tangent to the initial straight-line portion of the load deflection curve, (N/mm)

[edit] See also

[edit] References

  • ASTM standard test methods for flexural properties of unreinforced and reinforced plastics and electrical insulating materials

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