Three point flexural test

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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 $E B$ , flexural stress $σ f$ , flexural strain $ε f$ 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 $σ f$

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

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

Calculation of the flexural strain $ε f$

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

Calculation of Young's modulus $E B$

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

in these formulas the following parameters are used:

$σ f$ = Stress in outer fibers at midpoint, (MPa)
$ε f$ = Strain in the outer surface, (%)
$E b$ = 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)