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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) .
When =, the truss is said to be statically determinate, because the (m+3) internal member forces and support reactions can then be completely determined by 2j equilibrium equations, once we know the external loads and the geometry of the truss. Given a certain number of joints, this is the minimum number of members, in the sense that if any ...
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).
A three hinged bridge is isostatic, that is it is statically determinate; a two-hinged bridge is statically indeterminate in one degree of freedom, while a fixed arch bridge is indeterminate in three degrees of freedom. [5] [6] The statically determinate three-hinged arches were popular until the Second World War. Post-war, the advances in ...
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 inner truss of a Howe truss is statically indeterminate. There are two paths for stress during loading, a pair of diagonals in compression and a pair in tension. This gives the Howe truss a level of redundancy which allows it to withstand excessive loading (such as the loss of a panel due to collision). [23]
The Wichert truss is a modified type of continuous truss which is statically determinate and helps avoid some of the other shortcomings of continuous trusses. [35] It was patented in 1930 by Pittsburgh-based civil engineer Edward Martin Wichert (1883–1955). [36] [37]
Equations and are the solution for the primary system which is the original system that has been rendered statically determinate by cuts that expose the redundant forces . Equation ( 5 ) effectively reduces the set of unknown forces to X {\displaystyle \mathbf {X} } .