In the Recalc Window at the Non-linear Analysis inside the Basic Settings, the user can select the multiple possible options for the consideration of the non-linearities in the modeled structure including P-Delta, the 2nd Order effects of the geometric non-linearity caused by the additional moments due to the slightly deflected structure receiving the displaced usual normal force.

If the P-Delta effects need to be considered the "P-Delta effects" must be selected in the "Recalculation" dialog box. 

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. P-delta effects, also known as second-order effects or 2nd Order Theory, always happen at structures submitted to lateral loads because the gravity loads are applied at laterally deflected elements, causing even more displacements that will sum to an additional moment at the structure base, the moment of second order MII. Also, the final lateral displacement of the structure is different from the original displacement caused only by the lateral loads because the vertical loads, usually of a higher order, are now additionally contributing to the analysis of the deflections.

   

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. For the computation of the response to a singular load case on a given structural system, this leads to an iterative process whereby the occurring axial normal forces in the beam elements create additional bending moments.

For final stage analysis P-Delta effects should be considered for most of the bridges with significant spans or when the structure has considerable vertical loads or lateral displacements, due to wind, for example.

For construction stage analysis, when more than one loading case is applied and it is intended to take the changes in stiffness due to each loading case into account, this can be accomplished in two ways: by ticking either of the boxes in the Recalc-Pad:

• Accumulate Stiffness: The stiffness of each member is updated for each computed load case that is added to the summation load case. Consequently, P-Delta effects are only considered due to normal forces created by each loading case in addition to all previously computed loading cases.
• Accumulate Permanent Loads: Loading information is accumulated during a series of load cases; so, all previously applied loads in addition to a current loading case are applied.

The difference between these two procedures becomes immediately apparent in the FAQ example below.

communities.bentley.com/.../20-analysis---second-order-effects

A summation load case SumLC must also be defined. During a construction stage analysis, the section force distribution changes with each structural modification and with each applied load. If second-order effects should be considered in a construction stage analysis the normal forces in each member at the time of loading determine the starting stiffness of this member for this load case. The sequence of loading is therefore of great importance and can influence the result considerably. Therefore, in the context of pre-cambered bridge structures, the p-delta effect can be considered by using "accumulate stiffness (stage)" and in such a case, it is still possible to perform load combinations.

Note: On the other hand, there are restrictions of the implemented P-delta method to be used together with two of the most commonly used options possible to represent the structure in the following construction stages. This happens for both, Accumulate Stiffness and Accumulate Permanent Loads. In the construction stage analysis of some structures, when we consider the addition of a new segment during the cantilevered erection second-order effects could also be taken under consideration.

• Accumulate Stiffness: Second-order effects are in general underestimated if the prestressing is introduced after all other permanent loads.
• Accumulate Permanent Loads: As the structural system changes during each construction stage and each load case must be applied on the appropriate system at the time it's also not applicable.

Then, for general bridge design, using large deflection theory, third order, instead of second-order theory only, solves this dilemma; but, in the case of bridge construction control, the solution is to use Erection Control,, with Construction kink and add the necessary Fabrication Shape additional loads.