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## Tips July - September 2005

### Modeling Snubbers

**Question:** A hanger catalog typically indicates hydraulic or mechanical snubber ratings in LBS and no spring rate associated with either type. Normally, if properly maintained, hydraulic or mechanical snubbers move with little resistance to the slow thermal expansion movements of a piping system, but in the event of an upset condition (e.g., earthquake, SRV blowdown) snubbers will act having a specified maximum load. Can hydraulic or mechanical snubbers be specified properly within CAEPIPE?

**Reply:** Yes, however a snubber, either hydraulic or mechanical, is normally considered rigid with respect to the pipe it supports. In CAEPIPE then, the user only needs to accept the default "Rigid" stiffness shown in the snubber input. Upon analyzing the piping system, the user can check the manufacturer’s catalog to see if the snubber is overloaded, i.e., the analysis load on the snubber does not exceed the “Maximum Load” permitted by the manufacturer. Using the default “Rigid” stiffness will yield a conservative load, which could be reduced by a detailed evaluation of the snubber and the support load path stiffnesses and inputting the combined stiffness in the CAEPIPE snubber stiffness input in place of “Rigid.” Likewise, any gaps in the snubber load path are ignored by CAEPIPE, but should the user want to consider a gap, multiplying the analysis load by a factor of two will provide a conservative dynamic amplification to account for the impact of an applied load rapidly closing the gap.

### Sway Braces With Preload-Modeling Technique

**Question:** Grinnell/Lisega hanger catalogs show a sway brace to be a horizontal spring normally used to control vibration or possibly to limit creep migration. Sway brace details typically specify an minimum load (or preload), a spring rate, and a maximum load in some form with varying terminology (it is observed that for some sway braces the minimum load, in lbs., and the spring rate, in lbs./in., are the same). Can a sway brace with a preload be specified properly within CAEPIPE?

**Reply:** Yes, however, you’ll have to “trick” CAEPIPE with an iterative process to do what you want it to do (this appears to be occasionally necessary with all computer programs). First, if the sway brace is intended to be unloaded or in a neutral position in the operating condition, the CAEPIPE “Reference temperature” must be the operating temperature. This means that the thermal expansion stress range will be from the “hot” condition to the “cold” condition rather than from the “cold” condition to the “hot” condition, the latter being the more often analyzed situation. If this is the case, a separate sustained load analysis may be necessary. Note, also if this is the case in the CAEPIPE thermal expansion analysis, the “operating” condition (W+P1+T1) will be the “cold” condition. (Make sure your coefficients of thermal expansion are properly input).

Second, the user will need to initially analyze the piping system with a rigid strut at the location of the desired sway brace. The CAEPIPE “skewed restraint” is useful here because the stiffness can be initially specified as “Rigid” and later changed to a numerical value, if necessary. This initial analysis is to determine whether the load on the sway brace is sufficient to overcome the preload. If the analyzed load is less than or equal to the preload, then you are done and the CAEPIPE results load in the “operating” condition is the design load on the sway brace.

But if the analyzed load is higher than the preload, then an iterative process must be undertaken. Based on the analyzed load and the characteristics of the selected sway brace, determine a trial deflection. For example, if a sway brace has a specified preload of 900 lb and a spring rate of 900 lb/in and the initial analysis with a “Rigid” sway brace disclosed a load of 3491 lb on the sway brace in the “operating” condition (W+P1+T1), then a trial deflection of the sway brace could be (3491-900)/900 = 2.879 in (this should always be a conservative deflection). The first iterative analysis can then be performed with a sway brace spring stiffness of 3491/2.879 = 1213 lb/in. The “operating” condition results of the first iterative analysis discloses a results load of 174 lb on the sway brace and a deflection of 0.145 in; this translates to a sway brace load of (900+900*0.145) = 1031 lb. A second iterative analysis can then be performed with a sway brace spring stiffness of (900+(900*0.145))/0.145 = 7107 lb/in. The “operating” condition results of the second iterative analysis discloses a results load of 827 lb on the sway brace and a deflection of 0.116 in; this translates to a sway brace load of (900+900*0.116) = 1004 lb. A third iterative analysis can then be performed with a sway brace spring stiffness of (900+(900*0.116))/0.116 = 8659 lb/in.

The third iteration yields a sway brace load of 1000 lb; a fourth yields a snubber load of 998 lb. Two iterations yield sufficiently accurate results for this model.

Download all the test models plus results tabulation in an Excel spreadsheet.

*Author: Mr. Ron Haupt, P. E., of Pressure Piping Engineering (www.ppea.net) is a member of several piping code committees (B31, B31.1, B31.3, BPTCS, and others). He consults with us in the capacity of Nuclear QA Manager.*

### Stiffness Matrix Not Positive Definite

**Question:** What does the message "Stiffness matrix not positive definite" mean in CAEPIPE? How can I correct it?

**Reply:** This message simply means that the piping model is incompletely restrained (model is "statically indeterminate"). The model has to be restrained properly in all six degrees of freedom (three translations and three rotations). For example, inputting a rigid Anchor at a node ought to fix this message. Or, a combination of all supports should collectively restrain the six degrees of freedom.

This message could appear when a model does not have the shear and the hoop moduli specified for the FRP material that you may have in your model.

This message could appear when you have only one anchor in the model and you have released all 6 directions for hanger design. When they are released, there is nothing to support the model in these directions during hanger design. This is an unusual situation. Typically only vertical direction is released or there are other supports in the model.

This message could also appear when you have jacketed piping in the model, and you don't have a Jacket Endcap at any node along the jacketed piping. A tricky situation could be when you have a component such as a valve that separates the jacketed piping into two and you don't have a Jacket endcap on one side.