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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, the second moment of area of the beam cross-section about the axis of interest, length of the beam and beam boundary condition.
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.
By contrast, if a beam's weight is fixed, its cross-sectional dimensions are unconstrained, and increased stiffness is the primary goal, the performance of the beam will depend on Young's modulus divided by either density squared or cubed.
Geometric stiffness: a global characteristic of the body that depends on its shape, and not only on the local properties of the material; for instance, an I-beam has a higher bending stiffness than a rod of the same material for a given mass per length; Hardness: relative resistance of the material's surface to penetration by a harder body;
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, I is the second moment of area of the beam's cross-section, 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: [1]
Diagram of stiffness of a simple square beam (A) and universal beam (B). The universal beam flange sections are three times further apart than the solid beam's upper and lower halves. The second moment of inertia of the universal beam is nine times that of the square beam of equal cross section (universal beam web ignored for simplification)
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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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