Flexural modulus

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In mechanics (mechanics is a branch of physics), the flexural modulus or bending modulus[1] is the ratio of stress to strain in flexural deformation, or the tendency for a material to bend. It is determined from the slope of a stress-strain curve produced by a flexural test (such as the ASTM D 790), and uses units of force per area.[2] It is an intensive property.

For a 3-point test of a rectangular beam behaving as an isotropic linear material, where w and h are the width and height of the beam, L is the distance between the two outer supports and d is the deflection due to the load F applied at the middle of the beam, the flexural modulus:


E_{\mathrm{bend}} = \frac {L^3 F}{4 w h^3 d}

From elastic beam theory 
d = \frac {L^3 F}{48 I E } and for rectangular beam  I = \frac{1}{12}wh^3

thus 
E_{\mathrm{bend}} = E (Elastic modulus)

Ideally, flexural or bending modulus of elasticity is equivalent to the tensile or compressive modulus of elasticity. In reality, these values may be different, especially for plastic materials.

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