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Euler–Bernoulli beam theory (also known as engineer's beam theory or classical beam theory) [1] is a simplification of the linear theory of elasticity which provides a means of calculating the load-carrying and deflection characteristics of beams. It covers the case corresponding to small deflections of a beam that is subjected to lateral ...
Macaulay's method. Macaulay's method (the double integration method) is a technique used in structural analysis to determine the deflection of Euler-Bernoulli beams. Use of Macaulay's technique is very convenient for cases of discontinuous and/or discrete loading.
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] where. This formula was derived in 1744 by the Swiss mathematician Leonhard Euler. [2] The column will remain straight for loads less than the critical load.
The Euler pump and turbine equations are the most fundamental equations in the field of turbomachinery. These equations govern the power, efficiencies and other factors that contribute to the design of turbomachines. With the help of these equations the head developed by a pump and the head utilised by a turbine can be easily determined.
Aeroelasticity. Aeroelasticity is the branch of physics and engineering studying the interactions between the inertial, elastic, and aerodynamic forces occurring while an elastic body is exposed to a fluid flow. The study of aeroelasticity may be broadly classified into two fields: static aeroelasticity dealing with the static or steady state ...
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.
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 history of structural engineering dates back to at least 2700 BC when the step pyramid for Pharaoh Djoser was built by Imhotep, the first architect in history known by name. Pyramids were the most common major structures built by ancient civilizations because it is a structural form which is inherently stable and can be almost infinitely ...