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It indicates the possibility of self-stress (stress in the absence of an external load) that may be induced by mechanical or thermal action. Mathematically, this requires a stiffness matrix to have full rank. A statically indeterminate structure can only be analyzed by including further information like material properties and deflections.
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.
For example, consider a static uniform cantilever beam of length with an upward point load applied at the free end. Using boundary conditions, this may be modeled in two ways. In the first approach, the applied point load is approximated by a shear force applied at the free end.
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.
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.
Strength depends upon material properties. The strength of a material depends on its capacity to withstand axial stress, shear stress, bending, and torsion.The strength of a material is measured in force per unit area (newtons per square millimetre or N/mm², or the equivalent megapascals or MPa in the SI system and often pounds per square inch psi in the United States Customary Units system).
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.
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 beams. Although this occurs, the M/EI loading will provide the necessary "equilibrium" to hold the conjugate beam stable. [2]