The bending

stiffness Stiffness is the extent to which an object resists deformation in response to an applied force. The complementary concept is flexibility or pliability: the more flexible an object is, the less stiff it is. Calculations The stiffness, k, of a b ...

(

K

) is the resistance of a member against bending deformation. It is a function of the

Young's modulus Young's modulus E, the Young modulus, or the modulus of elasticity in tension or compression (i.e., negative tension), is a mechanical property that measures the tensile or compressive stiffness of a solid material when the force is applied leng ...

E

, the

second moment of area The second moment of area, or second area moment, or quadratic moment of area and also known as the area moment of inertia, is a geometrical property of an area which reflects how its points are distributed with regard to an arbitrary axis. The ...

I

of the beam cross-section about the axis of interest, length of the beam and beam boundary condition. Bending

of a beam can analytically be derived from the equation of beam deflection when it is applied by a force. :

K = \frac

where

\mathrm

is the applied force and

\mathrm

is the deflection. According to elementary

beam theory Beam may refer to: Streams of particles or energy *Light beam, or beam of light, a directional projection of light energy **Laser beam *Particle beam, a stream of charged or neutral particles **Charged particle beam, a spatially localized grou ...

, the relationship between the applied bending moment

M

and the resulting

curvature In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonic ...

\kappa

of the beam is: :

M = E I \kappa = E I \frac{\mathrm{d} x^2}

where

w

is the deflection of the beam and

x

is the distance along the beam. Double integration of the above equation leads to computing the deflection of the beam, and in turn, the bending stiffness of the beam. Bending stiffness in beams is also known as

Flexural rigidity Flexural rigidity is defined as the force couple required to bend a fixed non- rigid structure by one unit of curvature, or as the resistance offered by a structure while undergoing bending. Flexural rigidity of a beam Although the moment M(x) an ...

External links

Efunda's beam calculator
Continuum mechanics Structural analysis

See also

External links