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In continuum mechanics, plate theories are mathematical descriptions of the mechanics of flat plates that draw on the theory of beams. Plates are defined as plane structural elements with a small thickness compared to the planar dimensions. [1] The typical thickness to width ratio of a plate structure is less than 0.1.
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. This theory is an extension of Euler-Bernoulli beam theory and was developed in 1888 by Love [ 1 ] using assumptions proposed by Kirchhoff .
Where the plates meet, their relative motion determines the type of plate boundary (or fault): convergent, divergent, or transform. The relative movement of the plates typically ranges from zero to 10 cm annually. Faults tend to be geologically active, experiencing earthquakes, volcanic activity, mountain-building, and oceanic trench formation.
In a plate girder bridge, the plate girders are typically I-beams made up from separate structural steel plates (rather than rolled as a single cross-section), which are welded or, in older bridges, bolted or riveted together to form the vertical web and horizontal flanges of the beam. In some cases, the plate girders may be formed in a Z-shape ...
Simplified diagram of a convergent boundary. A convergent boundary (also known as a destructive boundary) is an area on Earth where two or more lithospheric plates collide. One plate eventually slides beneath the other, a process known as subduction.
A masonry skew arch bridge photographed shortly after its completion in 1898, showing the helicoidal nature of its stonework. Sickergill Skew Bridge over the River Raven at Renwick, near Penrith. A skew arch (also known as an oblique arch) is a method of construction that enables an arch bridge to span an obstacle at some angle other than a ...
A plate is a structural element which is characterized by a three-dimensional solid whose thickness is very small when compared with other dimensions. [ 1 ] The effects of the loads that are expected to be applied on it only generate stresses whose resultants are, in practical terms, exclusively normal to the element's thickness.
For rectangular plates, Navier in 1820 introduced a simple method for finding the displacement and stress when a plate is simply supported. The idea was to express the applied load in terms of Fourier components, find the solution for a sinusoidal load (a single Fourier component), and then superimpose the Fourier components to get the solution ...