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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) .
Here the conjugate beam has a free end, since at this end there is zero shear and zero moment. Corresponding real and conjugate supports are shown below. Note that, as a rule, neglecting axial forces, statically determinate real beams have statically determinate conjugate beams; and statically indeterminate real beams have unstable conjugate ...
A statically determinate structure can be fully analysed using only consideration of equilibrium, from Newton's Laws of Motion. A statically indeterminate structure has more unknowns than equilibrium considerations can supply equations for (see simultaneous equations).
Therefore, additional techniques such as linear superposition are often used to solve statically indeterminate beam problems. The superposition method involves adding the solutions of a number of statically determinate problems which are chosen such that the boundary conditions for the sum of the individual problems add up to those of the ...
While the influence lines of statically determinate structures (as mentioned above) are made up of straight line segments, the same is not true for indeterminate structures. Indeterminate structures are not considered rigid; therefore, the influence lines drawn for them will not be straight lines but rather curves.
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.
1874: Otto Mohr formalized the idea of a statically indeterminate structure. 1922: Timoshenko corrects the Euler–Bernoulli beam equation. 1936: Hardy Cross' publication of the moment distribution method, an important innovation in the design of continuous frames.
A statically determinate beam, bending (sagging) under a uniformly distributed load. A beam is a structural element that primarily resists loads applied laterally across the beam's axis (an element designed to carry a load pushing parallel to its axis would be a strut or column).