Linear elastic analysis used to determine design forces and moments resulting from loads acting on a structure is first-order analysis, where small deflection behavior is assumed and equilibrium and kinematic relationships are based on the undeformed geometry of the structure. Solutions of these analyses are typically simple and straightforward. However, when lateral loads are applied to the structure, the configuration can deviate quietly noticeably from its undeformed configuration, which makes a second-order analysis necessary. In a second-order analysis, the equilibrium and kinematic relationships are applied to the deformed structure, which includes the effects of large displacement and stress stiffening.
P-Delta (large displacement and stress stiffening) effects may have appreciable effects in the following instances:
1) Pipe overhangs.
2) Vertical Risers
3) Compressive Axial Loads (Softening)
4) GRE Piping
5) Tall building structures supporting heavy column loads
For pipe overhangs, the pipe extends past the last support, turns upward and then runs another horizontal distance before encountering the next support. In this case, considerable sag of the pipe may occur if designers do not properly account for the increased flexibility along with the weight. Condensate can collect in these low, non-drained areas, further increasing the sag, ultimately resulting in a situation where unexpected slugging occurs in the line.
When vertical risers are permitted to move laterally, developed, compressive axial loads can reduce the lateral strength of the line, permitting additional lateral displacement and greater offset. These increased lateral displacements produce greater bending moments at the base of the riser.
When axial loads develop in long lines due to friction, the lateral load bearing capacity is reduced and large displacement can occur in the lateral direction as the pipe “conforms” to the axial load. Small displacements in the axial direction (thermal strains), can produce very large lateral displacements and binding or failure of supports.