Location of Hinges in Cantilever Girder Systems with Variable Loads

Formulas are given for locating the girder-to-girder connections in cantilever and suspended span systems so that the maximum bending moments in the cantilevered girders are minimized, which facilitates least weight design. That optimum is achieved if the maximum positive moment on the backspan of each cantilevered girder is equal to the maximum magnitude of the negative moment over the support. An example derivation implements that concept and demonstrates that the formulas are based on principles of statics. The formulas cover an unlimited number of equally wide bays and include uniformly distributed loads as well as concentrated loads spaced at equal intervals. The formulas are valid for the general situation in which maximum loads occur at different times on different spans. A well-known design guide does not account for that situation and is shown to give results that may lead to designs that are not conservative with respect to strength.