Abstract
Bend flexibility factor is defined as the ratio of rotation of a pipe bend to that of a straight pipe of the same diameter, wall thickness and length under the action of the same bending moment. In stress analysis of piping systems with the beam method, this factor is of great importance and plays a direct role in the formation of the stiffness matrix of a system. The exact calculation of this coefficient results in the precise amount of force and moment being obtained on anchor points (i.e., equipment nozzles) and also in stopper and guide restraints. Different codes such as ASME B31.3 and B31.1 present a formula for this factor without consideration of the end effect (constraint of bend ends by the adjacent straight pipe). Another limitation is that these formulas are valid only within the range of D/T ≤ 100 (diameter to thickness). In this paper the effect of adjacent straight pipes on in-plane flexibility factor of long radius 90-degree elbows has been investigated and it has also been demonstrated that the equation presented in ASME B31J-2017 as the minimum required length for the attached straight pipe is highly accurate and greater values do not have much effect on elbow flexibility. Finite element analysis (FEA) studies have been carried out on 31 models with various diameters and thicknesses for both D/T ≤ 100 and D/T > 100 and in all cases the high precision of the given equation in B31J-2017 is indicated. Also, a new formula of in-plane flexibility factor (with consideration of the end effect) for long radius-90degree elbows is presented that has acceptable accuracy in all ranges of D/T. The new formula reveals that the B31 equation also has an acceptable accuracy even for D/T > 100.
