Class 1 Branch Flexibilities - CAESAR II - Help

CAESAR II Users Guide

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CAESAR II Version
12

This analytical option was added to CAESAR II for the following reasons:

  • Automatic local flexibilities at intersections help you bound the true solution. Because the computer time to do an analysis is less expensive, more frequently you can run several solutions of the same model using slightly different input techniques to determine the effect of the modeling difference on the results. This gives you a degree of confidence in the numbers you get. For example, structural steel supporting structures can be modeled to see the effect of their stiffnesses, nozzle flexibilities can be added at vessel connections to see how these features redistribute load throughout the model, friction is added to watch its effect on displacements and equipment loads, and with CAESAR II you can include Class 1 intersection flexibilities. The characteristic that makes this option convenient to use is that you can enable or disable the Class 1 flexibilities using a single option in the setup file. No other modification to the input required.

  • In WRC 329, there are a number of suggestions made to improve the stress calculations at intersections. These suggestions are fairly substantial and are given in order of importance. The most important item, as felt by E. Rodabaugh, in improving the stress calculations at intersections is given, in part, as follows:

    "In piping system analyses, it may be assumed that the flexibility is represented by a rigid joint at the branch-to-run centerlines juncture. However, you should be aware that this assumption can be inaccurate and should consider the use of a more appropriate flexibility representation."

  • Use of the Class 1 Branch Flexibility feature may be summarized as follows: Include the Class 1 Branch Flex option in the setup file.

  • Where reduced branch geometry requirements are satisfied, CAESAR II constructs a rigid offset from the centerline of the header pipe to its surface, and then adds the local flexibility of the header pipe, between the end of the offset, at the header, and the start of the branch. Stresses computed for the branch are for the point at its connection with the header.

  • Where reduced branch geometry requirements are not satisfied, CAESAR II constructs a rigid offset from the centerline of the header pipe to its surface. The branch piping starts at the end of this rigid offset. There is NO local flexibility due to the header added. (It is deemed to be insignificant.) Stresses computed for the branch are for the point at its connection with the header.

The reduced branch geometry requirements that CAESAR II checks are

d/D £ 0.5 and D/T £ 100.0

Where:

d = Diameter of Branch

D = Diameter of Header

T = Wall thickness of Header

If you use the Class 1 branch flexibilities, intersection models in the analysis become stiffer when the reduced geometry requirements do not apply and become more flexible when the reduced geometry requirements do apply. Stiffer intersections typically carry more loads and thus have higher stresses lowering the stress in other parts of the system that have been unloaded. More flexible intersections typically carry less load and thus have lower stresses. This causes higher stresses in other parts of the system that have "picked up" the extra load.

The branch flexibility rules used in CAESAR II are taken from ASME III, Subsection NB, (Class 1), 1992 Edition, Issued December 31, 1992, from Code Sections NB-3686.4 and NB-3686.5.

When the reduced branch rules apply, use the following equations for the local stiffnesses:

TRANSLATIONAL:

AXIAL = RIGID

CIRCUMFERENTIAL = RIGID

LONGITUDINAL = RIGID

ROTATIONAL:

AXIAL = RIGID

CIRCUMFERENTIAL = (kx)d/EI

LONGITUDINAL = (kz)d/EI

Where:

RIGID = 1.0E12 lb./in. or 1.0E12 in.lb./deg.

d = Branch Diameter

E = Young’s Modulus

I = Cross Section Moment of Inertia

D = Header Diameter

T = Header Thickness

Tb = Branch Fitting Thickness

kx = 0.1(D/T)1.5[(T/t)(d/D)]0.5(Tb/T)

kz = 0.2(D/T)[(T/t)(d/D)]0.5(Tb/T)

For more information, see WRC 329 Section 4.9 Flexibility Factors. A brief quote from this section follows:

"The significance of "k" depends upon the specifics of the piping system. Qualitatively, if "k" is small compared to the length of the piping system, including the effect of elbows and their k-factors, then the inclusion of "k" for branch connections will have only minor effects on the calculated moments. Conversely, if "k" is large compared to the piping system length, then the inclusion of "k" for branch connections will have major effects. The largest effect will be to greatly reduce the magnitude of the calculated moments acting on the branch connection. To illustrate the potential significance of "k’s" for branch connections, we use the equation [above] to calculate "k" for a branch connection with D=30 in., d=12.75 in., and T=t=0.375 in.:

k = 0.1(80)1.5(0.425)0.5 * (1.0) = 46.6

This compares to the more typical rigid-joint interpretation that k=1, rather than k=46.6 !".

Further discussion in section 4.9 illustrates additional problems that can arise by overestimating the stiffness at branch connections. Problems arise by believing "mistakenly" that the stress at the intersection is too high. Further reference should be made to this section in WRC 329.

Branch automatic flexibility generation can be used where the user has only defined the branch element in the model, that is has left the header piping out of the analysis. In this case there will be no "offset" equal to one-half of the header diameter applied to the branch end. A "partial intersection" is one where either the header pipe is not modeled, is modeled with a single element, or is part of a geometric intersection where the header pipes are not colinear. In the case where there is no header pipe going to the intersection, there will be no modification to the model for the class 1 branch flexibilities. When at least a single header pipe is recognized, the local flexibility directions are defined by the branch alone and in accordance with the CAESAR II defaults for circumferential and longitudinal directions for the branch and header. You must build full intersection models at all times, not only when employing the class 1 branch flexibility. In most cases, building full intersection models eliminates problems caused by the assumptions necessary when a partial intersection is described.

In the equations in NB-3686.5 for tn, the thickness of the branch pipe is used in all cases.

When branches are skewed with respect to the header pipe, and where the two header pipes are colinear, the local Class 1 flexibilities are still taken to be the longitudinal and circumferential directions that are tangent to the header surface at its intersection with the branch.

Class 1 branch flexibilities can be formed at both ends of a single pipe element.

The offsets necessary to form the class 1 intersections are automatically generated by CAESAR II. There is no extra input required by you to have CAESAR II build these intersections.

If there are already user-defined offsets at an intersection end, the computed offset to get from the header centerline to its surface along the centerline of the branch is added to the already entered user offset.

Automatic offsets are generated providing that the distance from the header centerline to the header surface along the branch centerline is less than or equal to 98% of the total pipe straight length.

automaticoffset

When an element with a bend designation is part of an intersection model, the offset and flexibility calculations are not performed.