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Unformatted text preview: • Influence lines for reactions Influ r '"' Qualitative Influence Lines and Loading Patterns for an Multi-span Indeterminate Beam The MUller Breslau Principle, used previously to draw the influence lines for statically determinate structures, can also be extended to define the influence lines for indeterminate structures. This principle simply states that the influence line for a function is proportionally equivalent to the deflected shape of the structure when it undergoes a displacement as a result of the application of the function. For indeterminate structures, an understanding of how complex structures deflect and react when acted upon by a force is required in order to draw accurate diagrams. To determine the influence line for the support reaction at A, the Miiller Breslau Principle requires the removal of the support restraint and the application of a positive unit deformation at this point that corresponds to the direction of the force. In this case, apply a unit vertical displacement in the direction of Y A. A I B C E f ~ ;;:g;; I ;;:g;; c;;g;;; ;;;;g;;;; :iL SI S, ~ . ~ ; ....- _ ,8 C.. _ - ......... f + r U'-_..: ...... W :U b'" -_ _-0- --- c The resulting deflected shape, due to the application of the unit deformation, is then proportionally equivalent to the influence line for the support reaction at A. Notice that in statically indeterminate structures, the deflected shape is not a straight line, but rather a...
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This note was uploaded on 10/13/2011 for the course CE 377 taught by Professor Hosteng during the Fall '10 term at Iowa State.
- Fall '10