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In mathematics, an Euler brick, named after Leonhard Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths. A primitive Euler brick is an Euler brick whose edge lengths are relatively prime. A perfect Euler brick is one whose space diagonal is also an integer, but such a brick has not yet been found.
A rectangular cuboid with integer edges, as well as integer face diagonals, is called an Euler brick; for example with sides 44, 117, and 240. A perfect cuboid is an Euler brick whose space diagonal is also an integer. It is currently unknown whether a perfect cuboid actually exists. [6]
Euler's critical load or Euler's buckling load is the compressive load at which a slender column will suddenly bend or buckle. It is given by the formula: [1]
The Euler–Bernoulli beam equation defines the behaviour of a beam element (see below). It is based on five assumptions: Continuum mechanics is valid for a bending beam. The stress at a cross section varies linearly in the direction of bending, and is zero at the centroid of every cross section.
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.
by the material used (stone, brick, concrete, steel) and construction approach. [26] For example, the wedge-shaped voussoirs of a brick arch can be made by cutting the regular bricks ("axed brick" arch) or manufactured in the wedge shape ("gauged brick" arch); [28] structurally, by the number of hinges (movable joints) between solid components ...
It is highly related to the slenderness limit that is the cut-off between elements being classed "slender" or "stocky". Slender walls are vulnerable to buckling failure modes, including Euler in-plane buckling due to axial compression, Euler out-of-plane buckling due to axial compression and lateral torsional buckling due to bending moment.
Brick – is building material used to make walls, pavements and other elements in masonry construction. Traditionally, the term brick referred to a unit composed of clay , but it is now used to denote rectangular units made of clay-bearing soil, sand, and lime , or concrete materials.