TR.37.2 PDelta Analysis Options
Used to perform a secondorder analysis, considering either large or smalldelta effects—or both—on the structure.
General Format
The following options are available in STAAD.Pro when performing a PDelta analysis:

PDelta analysis with Small & Large Delta effects or Large Delta effects only. With this option the global forces are adjusted with every iteration
PDELTA (n) ANALYSIS ( { LARGEDELTA  SMALLDELTA } ) (PRINT printoptions)
Where:
Parameter Description PDELTA n no. of iterations desired (default value of n = 1). LARGEDELTA  SMALLDELTA SMALLDELTA is the default 
PDelta analysis including stress stiffening effect of the KG matrix. With this option the global stiffness is adjusted with every iteration
PDELTA KG ANALYSIS (PRINT printoptions)
printoptions = { LOAD DATA  STATICS CHECK  STATICS LOAD  BOTH  ALL }
See TR.37.1 Linear Elastic Analysis for details.
Without one of these PDelta analysis commands, no PDelta analysis will be performed.
These ANALYSIS commands can be repeated if multiple analyses are needed at different phases.
A PDELTA ANALYSIS will correctly reflect the secondary effects of a combination of load cases only if they are defined using the REPEAT LOAD specification (TR.32.11 Repeat Load Specification). Secondary effects will not be evaluated correctly for load combinations.
PDelta effects are computed for frame members and plate elements only. They are not calculated for solid elements or curved beams.
Notes for Small or Large Delta (Option 1)
 This command
directs the program to perform the analysis that includes:
 Checking whether all information is provided for the analysis;
 Forming the joint stiffness matrix
 Checking the stability of the structure;
 Solving simultaneous equations, and
 Computing the member forces and displacements.
 For PDelta analysis, forces and displacements are recalculated, taking into consideration the chosen PDelta effect.
 If a RESPONSE SPECTRUM, TIME LOAD, or GROUND MOTION is specified within a load case or the MODAL CALCULATION command is used, a dynamic analysis is performed.
 In each of the iterations of the PDELTA ANALYSIS, the load vector will be modified to include the secondary effect generated by the displacements caused by the previous iterations.
 The default procedure of option 1 is based on "Psmall & large Delta" effects.(sometimes referred to as Pδ & PΔ). Enter the LargeDelta parameter to only include the "PlargeDelta" effects (PΔ only). SmallDelta is recommended.
 This PDELTA (n) ANALYSIS command (option 1) should specify 3 to 30 iterations to properly incorporate the PDelta effect. With this many iterations, the PDELTA (n) ANALYSIS SMALLDELTA command results are as good as or better than the PDELTA KG (option 2) command results for static analysis. The advantage of this PDELTA (n) ANALYSIS command comes from not having to reform and then triangular factorize the stiffness matrix for every iteration within every case. Also this command allows tension/compression.
 Be aware that global buckling can occur in PDelta analysis, resulting in large or infinite or NaN values for displacement. Do not use the results of such a case. Sometimes the loads from Repeat Load combination cases are too large; sometimes partial moment releases rather than the full release is needed, sometimes connectivity needs to be corrected. Always check the maximum displacements for PDelta analyses.
Example
Following are some examples on use of the command for PDelta analysis as described in option 1.
PDELTA ANALYSIS PDELTA 5 ANALYSIS PDELTA 20 ANALYSIS SMALLDELTA PRINT STATICS CHECK
STAAD.Pro allows multiple PDelta analyses in the same run (see the General Comments section of TR.37.1 Linear Elastic Analysis for details).
Notes for Stress Stiffening Matrix (Option 2)
The PDelta analysis also provides the option of including the stress stiffening effect of the Kg matrix into the member / plate stiffness.
 A regular STAAD PDelta Analysis (option 1) performs a first order linear analysis and obtains a set of joint forces from member/plates based on both large and small PDelta effects. In contrast, the PDelta KG Analysis (that is, with the Kg option selected) includes the effect of the axial stress after the first analysis is used to modify the stiffness of the member/plates. A second analysis is then performed using the original load vector. Large & small PDelta effects are always included in this KG option.
 This command
directs the program to perform the analysis that includes:
 Solving the static case.
 Reforming the global joint stiffness matrix to include the Kg matrix terms which are based on the computed tensile/compressive axial member forces.
 Solving simultaneous equations for displacements;
 If a RESPONSE SPECTRUM, TIME LOAD, or GROUND MOTION is specified within a load case or the MODAL CALCULATION command is used, a dynamic analysis is performed. The static cases solved for a PDELTA KG analysis command will be solved first then the dynamic analysis cases.
 A PDELTA KG ANALYSIS will correctly reflect the secondary effects of a combination of load cases only if they are defined using the REPEAT LOAD specification (TR.32.11 Repeat Load Specification). Secondary effects will not be evaluated correctly for load combinations since only final results are combined.
 PDelta KG effects are computed for frame members and plate elements only. They are not calculated for solid elements. The results are based on "Plarge & small Delta" effects.
 For static analysis, the other PDelta command [ PDELTA (n) ANALYSIS (SMALL) ] with 20 or more iterations (option 1) is preferred.
 Tension/compression only members are not allowed with this PDELTA KG command. You must use the PDELTA (n) ANALYSIS (SMALL) command instead.
 Be aware that global buckling can occur in a PDELTA KG ANALYSIS. This condition is usually detected by STAAD.Pro. A message is issued and the results for that case are set to zero. STAAD.Pro will continue with the next load case.
 Global buckling may not be detected which could result in a solution with large or infinite or NaN values for displacement or negative Lmatrix diagonals or stability errors. Do not use the results of such cases. This condition may require a nonlinear analysis. Sometimes the loads from Repeat Load combination cases are too large; sometimes partial moment releases rather than the full release is needed, sometimes connectivity needs to be corrected. Always check the maximum displacements for PDelta analyses.