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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.
The deflection must be considered for the purpose of the structure. When designing a steel frame to hold a glazed panel, one allows only minimal deflection to prevent fracture of the glass. The deflected shape of a beam can be represented by the moment diagram, integrated (twice, rotated and translated to enforce support conditions).
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
Historically a beam is a squared timber, but may also be made of metal, stone, or a combination of wood and metal [1] such as a flitch beam.Beams primarily carry vertical gravitational forces, but they are also used to carry horizontal loads such as those due to earthquake or wind, or in tension to resist rafter thrust or compression (collar beam).
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 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. [1]
The deflection downward positive. (Downward settlement positive) Let ABC is a continuous beam with support at A,B, and C. Then moment at A,B, and C are M1, M2, and M3, respectively. Let A' B' and C' be the final positions of the beam ABC due to support settlements. Figure 04-Deflection Curve of a Continuous Beam Under Settlement
A beam supported at its Airy points has parallel ends. Vertical and angular deflection of a beam supported at its Airy points. Supporting a uniform beam at the Airy points produces zero angular deflection of the ends. [2] [3] The Airy points are symmetrically arranged around the centre of the length standard and are separated by a distance equal to