A frequency analysis was accomplished for a short piping run. This analysis was entered into Cosmos/M 1.6. Dimensional points in space were entered. The unites for these points in space were entered in inches These points were connected to produce curves. The element group for piping was applied to these curve lines. Material specification for Alloy Steel were taken from the existing table in Cosmos. A mass group was applied to key points, and this mass was entered in slugs.
Initial conditions frequency analysis produced a max period of 1/(5.811_Hz) or .172_sec. The chosen maximum natural period for the piping is .16_sec so this first case failed. Another restraint was applied to the system and re-analyzed this produced an period of 1/(6.386_Hz) or .157_sec this met the criteria so this configuration was accepted.
Criteria for industrial design piping are dictated by ASME or ANSI codes. Most common failure criteria are specified as maximum allowable stress and deflection. Some times a maximum natural period of vibration or minimum natural frequency is also specified.
A direction in which a rigid body is free to move is called a degree of freedom. There are a maximum of six degrees of freedom. Three are a translation (or sliding) alone the x-axis, y-axis, and z-axis. The other three are rotation about the x-axis, y-axis, and z-axis. By adding a support certain degrees of freedom can be eliminated. For fixed ends all six degrees of freedom are arrested. This fixed connection is called an anchor. Normally at design stage a cookbook type of guideline is used. These are usually conservative approximation based on the above code criteria. In certain cases cookbook becomes too conservative making practical designs impossible. In such a case rigorous calculation have to be performed before a design is finished.
In addition to the stress and deflection criteria a set of piping will have maximum natural period or minimum natural frequency criteria to avoid resonance and subsequent failure similar to the famous "Tacoma Narrows Bridge". This criteria should be based on expected earthquake (or prevailing wind conditions in the case of the bridge). Further more the natural frequency or period of piping and its supports depend on the geometry and deflection under its own weight. Rigorous analysis may suggest rerouting or the use of an engineering hanger, snubbers, and springs. Analytical methods are too lengthy and tedious, if performed manually and may take weeks. Most computer programs are based on these methods and are much faster and are capable of determining displacement, reactions, or natural frequency loads and stresses under deadweight, seismic, or thermal conditions or any combination there of.
The following information is required for a pipe analysis to be conducted per the above discussion :
a) Specify the desired pipe or tubing including material used.
b) Specify the desired design pressure.
c) Specify the design and operating temperature.
d) Specify if the joints are welded, flanged etc.
e) Specify if bends or elbows will be used.
f) Specify the contents such as water, steam, or air.
g) Specify the code requirements.
h) Specify if there is any insulation.
i) Sketch or drawing showing the dimensions and routing.
A much simplified case was developed for analysis in Cosmos. The material is 1/2_inch pipe using Alloy steel and internal pressure of 2000_psi. Temperature information was not applied to this analysis. All joint were considered to be welded and no insulation was applied to this problem. A passing natural period of .16_sec will be considered acceptable.
The first case study had only beginning and ending restraints applied. In this first case the analysis produced a failing natural period of 1/(5.811_Hz) or .172_sec. This demonstrated the need of further restraints. Thus case two, the application of a central restraint was applied to the system, this produces a passing natural period of 1/(6.386_Hz) or .157_sec.
Case one of the simulation failed the acceptable natural period for the piping configuration chosen. Case two of the simulation was successful in finding a acceptable natural period of the piping configuration chosen.
When entering piping runs divide long runs up into many short run so as to develop many nodes. Restrains may only be applied at nodes. If nodes are not places at convenient restraint's location, reentering the design may be required.
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