A piping system can respond far differently to a dynamic load than it would to a static load of the same magnitude. Static loads are those which are applied slowly enough that the system has time to react and internally distribute the loads, thus remaining in equilibrium. In equilibrium, all forces and moments are resolved (that is, the sum of the forces and moments are zero) and the pipe does not move.
A dynamic load changes quickly with time. The piping system does not have time to internally distribute the loads. Forces and moments are not always resolved, resulting in unbalanced loads and pipe movement. Because the sum of forces and moments are not in equilibrium, the internally-induced loads can be different—either higher or lower—than the applied loads.
The software provides several methods for analyzing different types of system response under dynamic loads. Each method provides a trade-off of accuracy versus computing requirements. The methods include modal natural frequency calculations, harmonic analysis, response spectrum analysis, and time history analysis.
Modal natural frequency analysis measures the tendency of a piping system to respond to dynamic loads. The modal natural frequencies of a system typically should not be too close to equipment operating frequencies. Generally, higher natural frequencies usually cause less trouble than low natural frequencies. CAESAR II provides calculation of modal natural frequencies and animated plots of the associated mode shapes.
Harmonic analysis addresses dynamic loads that are cyclic in nature, such as fluid pulsation in reciprocating pump lines or vibration due to rotating equipment. These loads are modeled as concentrated forces or displacements at one or more points in the system. To provide the proper phase relationship between multiple loads, a phase angle can also be used. Any number of forcing frequencies can be analyzed for equipment start-up and operating modes. Harmonic responses represent the maximum dynamic amplitude the piping system undergoes and have the same form as a static analysis: node deflections and rotations, local forces and moments, restraint loads, and stresses. For example, if the results show an X displacement of 5.8 cm at a node, then the dynamic motion due to the cyclic excitation is from +5.8 cm. to -5.8 cm. at that node. The stresses shown are one half of, or one amplitude of, the full cyclic stress range.
Response spectrum analysis allows an impulse-type transient event to be characterized by response versus frequency spectra. Each mode of vibration of the piping system is related to one response on the spectrum. These modal responses are summed together to produce the total system response. The stresses for these analyses, summed with the sustained stresses, are compared to the occasional stress allowables defined by the piping code. Spectral analysis can be used in a wide variety of applications. For example, in uniform inertial loading, ground motion associated with a seismic event is supplied as displacement, velocity, or acceleration response spectra. The assumption is that all supports move with the defined ground motion and the piping system “catches up” to the supports. It is this inertial effect which loads the system. The shock spectra, which define the ground motion, can vary between the three global directions and can even change for different groups of supports (such as independent or uniform support motion). Another example is based on single point loading. CAESAR II uses this technique to analyze a wide variety of impulse-type transient loads. Relief valve loads, water hammer loads, slug flow loads, and rapid valve closure type loads all cause single impulse dynamic loads at various points in the piping system. The response to these dynamic forces can be predicted using the force spectrum method.
Time history analysis is one of the most accurate methods, because it uses numeric integration of the dynamic equation of motion to simulate the system response throughout the load duration. This method can solve any type of dynamic loading, but due to its exact solution, requires more resources (such as computer memory, calculation speed and time) than other methods. Time history analysis is not appropriate when, for example, the spectrum method offers sufficient accuracy.
Force versus time profiles for piping are usually one of three types: Random, Harmonic, or Impulse. Each profile has a preferred solution method. These profiles and the load types identified with them are described below.