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The deflection of beam elements is usually calculated on the basis of the Euler–Bernoulli beam equation while that of a plate or shell element is calculated using plate or shell theory. An example of the use of deflection in this context is in building construction. Architects and engineers select materials for various applications.
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.
A tension member is a structural element designed to carry loads primarily through tensile forces, meaning it is subjected to stretching rather than compression or bending. These members are integral components in engineering and architectural structures, such as trusses , bridges , towers, and suspension systems, where they provide stability ...
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 ...
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 ...
Stress resultants are simplified representations of the stress state in structural elements such as beams, plates, or shells. [1] The geometry of typical structural elements allows the internal stress state to be simplified because of the existence of a "thickness'" direction in which the size of the element is much smaller than in other directions.
Attempts have been made to increase the safety of bridges with pin and hanger assemblies by adding some form of redundancy to the assembly. Retrofits that add redundancy to pin and hanger assemblies include adding a "catcher's mitt"—a short steel beam attached to the bottom of the cantilevered girder that extends out beneath the suspended girder to "catch" the suspended girder should ...
Shear (and tension) loads can be transferred between two structural elements by either a bearing-type connection or a slip-critical connection. In a slip-critical connection, loads are transferred from one element to another through friction forces developed between the faying surfaces of the connection. These friction forces are generated by ...