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The bending stiffness is the resistance of a member against bending deflection/deformation. It is a function of the Young's modulus E {\displaystyle E} , the second moment of area I {\displaystyle I} of the beam cross-section about the axis of interest, length of the beam and beam boundary condition.
Bending of plates, or plate bending, refers to the deflection of a plate perpendicular to the plane of the plate under the action of external forces and moments. The amount of deflection can be determined by solving the differential equations of an appropriate plate theory. The stresses in the plate can be calculated from these deflections.
where is the flexural modulus (in Pa), is the second moment of area (in m 4), is the transverse displacement of the beam at x, and () is the bending moment at x. The flexural rigidity (stiffness) of the beam is therefore related to both E {\displaystyle E} , a material property, and I {\displaystyle I} , the physical geometry of the beam.
The flexural strength is stress at failure in bending. It is equal to or slightly larger than the failure stress in tension. Flexural strength, also known as modulus of rupture, or bend strength, or transverse rupture strength is a material property, defined as the stress in a material just before it yields in a flexure test. [1]
Approximate specific stiffness for various materials. No attempt is made to correct for materials whose stiffness varies with their density. Material Young's modulus Density (g/cm 3) Young's modulus per density; specific stiffness (10 6 m 2 s −2) Young's modulus per density squared (10 3 m 5 kg −1 s −2) Young's modulus per density cubed ...
This results in a constant bending moment between the two supports. Consequently, a shear-free zone is created, where the specimen is subjected only to bending. This has the advantage that no additional shear force acts on the specimen, unlike in the 3-point bending test. [6] The bending modulus for a flat specimen is calculated as follows:
For very small strains in isotropic materials – like glass, metal or polymer – flexural or bending modulus of elasticity is equivalent to the tensile modulus (Young's modulus) or compressive modulus of elasticity. However, in anisotropic materials, for example wood, these values may not be equivalent.
Stiffness is the extent to which an object resists deformation in response to an applied force. [ 1 ] The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is.
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