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A statically indeterminate structure can only be analyzed by including further information like material properties and deflections. Numerically, this can be achieved by using matrix structural analyses, finite element method (FEM) or the moment distribution method ( Hardy Cross ) .
The moment distribution method is a structural analysis method for statically indeterminate beams and frames developed by Hardy Cross. It was published in 1930 in an ASCE journal. [1] The method only accounts for flexural effects and ignores axial and shear effects.
The fixed end moments are reaction moments developed in a beam member under certain load conditions with both ends fixed. A beam with both ends fixed is statically indeterminate to the 3rd degree, and any structural analysis method applicable on statically indeterminate beams can be used to calculate the fixed end moments.
In structural engineering, the direct stiffness method, also known as the matrix stiffness method, is a structural analysis technique particularly suited for computer-automated analysis of complex structures including the statically indeterminate type.
Using these integration rules makes the calculation of the deflection of Euler-Bernoulli beams simple in situations where there are multiple point loads and point moments. The Macaulay method predates more sophisticated concepts such as Dirac delta functions and step functions but achieves the same outcomes for beam problems.
The cantilever method is considered one of the two primary approximate methods (the other being the portal method) for indeterminate structural analysis of frames for lateral loads. Its use is recommended for frames that are taller than they are wide, and therefore behave similar to a beam cantilevered up from the ground.
Figure 1: (a) This simple supported beam is shown with a unit load placed a distance x from the left end. Its influence lines for four different functions: (b) the reaction at the left support (denoted A), (c) the reaction at the right support (denoted C), (d) one for shear at a point B along the beam, and (e) one for moment also at point B. Figure 2: The change in Bending Moment in a ...
The Hardy Cross method is an adaptation of the Moment distribution method, which was also developed by Hardy Cross as a way to determine the forces in statically indeterminate structures. The introduction of the Hardy Cross method for analyzing pipe flow networks revolutionized municipal water supply design. Before the method was introduced ...