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Re: P-Delta

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Computer programs based on the stiffness method typically handle PDELTA
ANALYSIS in the following manner :

1) For the load case being considered, first determine the nodal
displacements. As Charlie has mentioned, the load case should consist of
the lateral and vertical loads in order to be able to correctly account
for the PDELTA effect in the steps to follow. Next, for each member, do
the following.

2) Using the nodal displacements, determine the axial force in the

3) The relative displacement of the 2 ends of the member in the 2
orthogonal global directions is then measured.

4) The axial force is multiplied by the relative displacements to arrive
at the bending moment on the member in each of the two orthogonal

5) Each of these 2 moments is divided by the member length to arrive at
coupling forces (equal and opposite forces) at each end in the 2
orthogonal directions.

6) These forces are added to the global load vector and the nodal
displacements are recalculated. 

Steps 2 thru 6 are repeated if more cycles of PDELTA effects are

Because the forces which are obtained in step 5 form a couple, and hence
contribute no net force, the net additional horizontal force or vertical
force on the structure is zero. The only effect that PDelta analysis
should produce - when compared with a situation where PDelta effects are
not evaluated - is additional moments on the structure which should be
reflected in the support reactions. The software should not produce any
extra horizontal or vertical reaction forces.

Kris, STAAD Support Group

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