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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 ) .
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.
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.
A statically indeterminate structure has more unknowns than equilibrium considerations can supply equations for (see simultaneous equations). Such a system can be solved using consideration of equations of compatibility between geometry and deflections in addition to equilibrium equations, or by using virtual work .
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.
Example. The statically indeterminate beam shown in the figure is to be analysed. Members AB, BC, CD have the same length = . Flexural rigidities are EI, 2EI, EI respectively. Concentrated load of magnitude = acts at a distance = from the support A.
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 ...
A stationary object (or set of objects) is in "static equilibrium," which is a special case of mechanical equilibrium. A paperweight on a desk is an example of static equilibrium. Other examples include a rock balance sculpture, or a stack of blocks in the game of Jenga, so long as the sculpture or stack of blocks is not in the state of collapsing.