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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 plastic section modulus is calculated as the sum of the areas of the cross section on either side of the PNA, each multiplied by the distance from their respective local centroids to the PNA. [16] = + where: A C is the area in compression A T is the area in tension y C, y T are the distances from the PNA to their centroids. Plastic section ...
Deformation of a thin plate highlighting the displacement, the mid-surface (red) and the normal to the mid-surface (blue) The Kirchhoff–Love theory of plates is a two-dimensional mathematical model that is used to determine the stresses and deformations in thin plates subjected to forces and moments.
The typical thickness to width ratio of a plate structure is less than 0.1. [citation needed] A plate theory takes advantage of this disparity in length scale to reduce the full three-dimensional solid mechanics problem to a two-dimensional problem. The aim of plate theory is to calculate the deformation and stresses in a plate subjected to loads.
Strength depends upon material properties. The strength of a material depends on its capacity to withstand axial stress, shear stress, bending, and torsion.The strength of a material is measured in force per unit area (newtons per square millimetre or N/mm², or the equivalent megapascals or MPa in the SI system and often pounds per square inch psi in the United States Customary Units system).
, Young's modulus of the column material,, second moment of area of the cross section of the column (area moment of inertia),, unsupported length of column,, column effective length factor; This formula was derived in 1744 by the Swiss mathematician Leonhard Euler. [2]
The plate elastic thickness (usually referred to as effective elastic thickness of the lithosphere). The elastic properties of the plate; The applied load or force; As flexural rigidity of the plate is determined by the Young's modulus, Poisson's ratio and cube of the plate's elastic thickness, it is a governing factor in both (1) and (2).
where E is the Young's modulus of the plate material (assumed homogeneous and isotropic), υ is the Poisson's ratio, h is the thickness of the plate, w is the out–of–plane deflection of the plate, P is the external normal force per unit area of the plate, σ αβ is the Cauchy stress tensor, and α, β are indices that take values of 1 and ...