Cantilevered column P-delta example

P-delta analysis, a second-order effect required by most structural design codes, accounts for loading about the deflected position of the piping and structure. P-delta also accounts for real-world changes to element lateral stiffness under tension and compression loading. Tension loads increase lateral stiffness of pipes and frames whereas compressive load reduces lateral stiffness.

The following simple example will illustrate P-delta effects in a way that’s easy to understand. We have a slender 35 ft. tall cantilevered column “flagpole” of 8” STD pipe, A106-B anchored at the base, with a 5,000 lb. gravity-direction point load on a point 3’ offset from the tip of the flagpole which is rigidly connected to the tip of the pipe by a joint body constraint. This is similar to a scenario of a heavy valve operator offset from the piping centerline.

Without P-delta effects, we would expect to see a 15,000 ft/lb. bending moment at the anchor from the point load by itself, excluding selfweight of the pipe. However, with consideration of P-delta effects, we see an almost 18,747 ft/lb. bending moment. In this example, it would have been unconservative to ignore P-delta effects.

Below left, we see deflection results from the point load (selfweight excluded) without P-delta, 7.45". Below right are deflection results with P-delta effects considered, 8.99". When calculating the bending moment at the anchor, P-delta accounted for the almost 9” of displacement, using the more realistic 5,000 lbs. X 3’ 9” instead of 5,000 lbs. X 3’.

Furthermore, P-delta accounted for the fact that compression loading reduces lateral stiffness of the piping, thereby increasing lateral deflection in this example.