As shown in the Figure below, P-Delta is a second-order effect due to the coupling of Normal Forces N and Bending Moments M. The P-delta effects, also known as geometric nonlinearity or 2nd Order Theory are considered in an RM Bridge CONNECT Edition V11 analysis if the P-Delta Effect box is ticked in the Recalc-pad. If more than one loading case is applied and it is intended to take the changes in stiffness due to each loading case into account, then this can be accomplished in two ways: by ticking either the Accumulate Stiffness or the Accumulate Permanent Loads box in the Recalc-Pad. A summation load case SumLC must also be defined. As the stiffness of a beam element becomes a function of the axial force present in the member at the time of loading. when P-delta effects are considered in an analysis of construction stages. The sequence of loading is therefore of great importance and can influence the result considerably. Moreover, during a construction stage analysis, the section force distribution changes with each structural modification and with each applied load.

   

A simple lateral load example is part of the RM Bridge installation and it can be loaded from Filex \ Examples \ FAQ. It includes the .tcl file and .pdf documentation. Three Variant schedules are presented to show the differences and technical comments are made. The difference between considering or not the 2nd order is shown in the plots below for displacements and bending moments.

   

Special considerations for the Analysis of Construction Stages with Cantilever Erection of Cable-Stayed Bridges are made, mainly about the restrictions of the implemented P-delta method with Accumulate Stiffness and with Accumulate Permanent Loads. Third-order theory, the large deflections, or the use of Erection Control, with Construction kink and add the necessary additional Fabrication Shape are presented as a solution.

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