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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.
Macaulay's notation is commonly used in the static analysis of bending moments of a beam. This is useful because shear forces applied on a member render the shear and moment diagram discontinuous. Macaulay's notation also provides an easy way of integrating these discontinuous curves to give bending moments, angular deflection, and so on.
The following procedure provides a method that may be used to determine the displacement and slope at a point on the elastic curve of a beam using the moment-area theorem. Determine the reaction forces of a structure and draw the M/EI diagram of the structure.
Francis Sowerby Macaulay FRS [1] (11 February 1862, Witney – 9 February 1937, Cambridge) was an English mathematician who made significant contributions to algebraic geometry. [2] He is known for his 1916 book The Algebraic Theory of Modular Systems (an old term for ideals ), which greatly influenced the later course of commutative algebra .
The Macaulay system showed that it was possible to solve actual problems in algebraic geometry using Gröbner basis techniques, but by the early 1990s, limitations in its architecture were becoming an obstruction. Using the experience with Macaulay, Grayson and Stillman began work on Macaulay2 in 1993.
The conjugate-beam methods is an engineering method to derive the slope and displacement of a beam. A conjugate beam is defined as an imaginary beam with the same dimensions (length) as that of the original beam but load at any point on the conjugate beam is equal to the bending moment at that point divided by EI .
Print/export Download as PDF ... The boundary condition u = 0 at x = 4 m allows us to solve for c = −7 Nm 2. See also. Macaulay brackets; Macaulay's method ...
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