A Beginner's Guide to Structural Mechanics/Analysis Continuous Beam Analysis (c) 2007, 2008 T. Bartlett Quimby
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Section CB.1

Continuous Beam Analysis

Last Revised: 11/04/2014

Statically indeterminate beams, particularly those of multiple spans, require more than basic statics to determine the internal forces.  Consequently the beams are referred to as statically indeterminate beams.  Additional principles of mechanics (usually load-deformation equations) are needed to provide the additional equations needed to solve for all the unknowns.  Typically these methods solve just enough of the unknown reactions to allow the rest of the problem to proceed using principles of Statics.

One of the most tedious tasks of structural analysis is to determine the envelope of values for shear and moment in statically indeterminate structural elements. The process requires determining the arrangement of live loads for maximum effects, analyzing the structure for the resulting load arrangements, and then comparing the results to get the envelope values. The process may lead to errors if the engineer is not diligent enough to analyze all the appropriate load arrangements. The process can also lead to an explosion of load arrangements in the interest of thoroughness.

There are two basic methods of analysis that can be used:  Elastic and Plastic.  They are discussed here.