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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.
The major difference being that with the addition of a fourth bearing the portion of the beam between the two loading points is put under maximum stress, as opposed to only the material right under the central bearing in the case of three-point bending.
Figure 1: (a) This simple supported beam is shown with a unit load placed a distance x from the left end. Its influence lines for four different functions: (b) the reaction at the left support (denoted A), (c) the reaction at the right support (denoted C), (d) one for shear at a point B along the beam, and (e) one for moment also at point B. Figure 2: The change in Bending Moment in a ...
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]
Shear and Bending moment diagram for a simply supported beam with a concentrated load at mid-span. Shear force and bending moment diagrams are analytical tools used in conjunction with structural analysis to help perform structural design by determining the value of shear forces and bending moments at a given point of a structural element such as a beam.
Sandwich theory [1] [2] describes the behaviour of a beam, plate, or shell which consists of three layers—two facesheets and one core. The most commonly used sandwich theory is linear and is an extension of first-order beam theory.
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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.