RAM Frame utilizes a non-iterative method to address P-Delta effects for rigid diaphragms in which global building stiffness are modified due to diaphragm mass\weights. Unfortunately, this method is strictly suited for only rigid diaphragm idealization where diaphragm response is represented with three degrees of freedom (two for lateral translation and one for rotation around global Z-axis).

The Preliminary P-Delta Analysis method is developed to be used for models with semirigid diaphragms. It involves a preliminary assessment of column\brace axial loads under only gravity or mass loads. Briefly,

• The model is run against only gravity loads (dead and live) or mass loads. Axial forces for columns and braces are stored (only columns and braces located inside a semirigid diaphragm are considered). These axial forces are also referred to as P-Delta Axial Forces.
• Element geometric stiffness matrix for each column and brace is calculated based on the P-Delta axial force of each element. Then, element stiffness matrix is modified with the geometric stiffness matrix. Note that this modification is applied only once.
• The program runs all load cases while modified element stiffnesses are used to assemble building stiffness matrix.

This process is automated and transparent to the user. It can be regarded as a 2 iteration analysis: in the 1^st iteration, P-Delta axial forces in columns\braces due to gravity\mass loads are detected and then, in the 2^nd iteration, these axial forces are used to predict P-Delta effects for all remaining load cases.

It should be noted that the current implementation fully satisfies equilibrium equations. The main assumption imposed with this approach is that axial forces due to gravity\mass loads do not significantly change under lateral loads (in fact, this is the same assumed for the non-iterative P-Delta method implemented for rigid diaphragms).

Note that P-Delta effects are reflected in each individual element stiffness matrix instead of in assembled building global stiffness matrix as observed in non-iterative P-Delta method. Thus, one may conclude that the non-iterative P-Delta method modifies global stiffness matrix whereas the Preliminary P-Delta Analysis method modifies each individual element stiffness matrix. In either case, geometric stiffness matrices are calculated.

In calculating P-Delta axial forces, it is important to note that primarily diaphragm's out-of-plane (bending) stiffness play an important role in distributing vertical loads (gravity or mass) loads to columns and braces. The diaphragm's in-plane stiffness (membrane stiffness) has a secondary impact. Thus, if a semirigid diaphragm is composed of one-way deck and if its out-of-plane stiffness is not included, then the vertical load distribution is carried our according to the diaphragm's in-plane (membrane stiffness) only.

Live load reductions are also applied to P-Delta axial forces for each column\brace.