Bending stiffness

The bending stiffness (formula_1) is the resistance of a member against bending deformation. It is a function of the Young's modulus formula_2, the area moment of inertia formula_3 of the beam cross-section about the axis of interest, length of the beam and beam boundary condition. Bending stiffness of a beam can analytically be derived from the equation of beam deflection when it is applied by a force.
where formula_5 is the applied force and formula_6 is the deflection. According to elementary beam theory, the relationship between the applied bending moment formula_7 and the resulting curvature formula_8 of the beam is:
where formula_10 is the deflection of the beam and formula_11 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.