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R. C. Hibbeler states, in his book Structural Analysis, “All statically determinate beams will have influence lines that consist of straight line segments.” [5] Therefore, it is possible to minimize the number of computations by recognizing the points that will cause a change in the slope of the influence line and only calculating the ...
Procedure for analysis [ edit ] The following procedure provides a method that may be used to determine the displacement and deflection at a point on the elastic curve of a beam using the conjugate-beam 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.
Castigliano's method for calculating displacements is an application of his second theorem, which states: If the strain energy of a linearly elastic structure can be expressed as a function of generalised force Q i then the partial derivative of the strain energy with respect to generalised force gives the generalised displacement q i in the direction of Q i.
Hibbeler, R.C. Statics and Mechanics of Materials, SI Edition. Prentice-Hall, 2004. ISBN 0-13-129011-8. Lebedev, Leonid P. and Michael J. Cloud. Approximating Perfection: A Mathematician's Journey into the World of Mechanics. Princeton University Press, 2004. ISBN 0-691-11726-8.
In civil engineering and structural analysis Clapeyron's theorem of three moments (by Émile Clapeyron) is a relationship among the bending moments at three consecutive supports of a horizontal beam.
The moment-area theorem is an engineering tool to derive the slope, rotation and deflection of beams and frames. This theorem was developed by Mohr and later stated namely by Charles Ezra Greene in 1873.
Numerically, this can be achieved by using matrix structural analyses, finite element method (FEM) or the moment distribution method (Hardy Cross) . Practically, a structure is called 'statically overdetermined' when it comprises more mechanical constraints – like walls, columns or bolts – than absolutely necessary for stability.