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羂聿膂螈袈肈芄薁螄膇莆螇虿膆葿蕿羈膆膈莂袄膅莁薈袀膄蒃蒁螆膃膂蚆蚂膂芅葿羁膁莇蚄袇芀葿蒇螃芀腿蚃虿艿芁蒅肇芈蒄蚁羃芇薆薄衿芆芆蝿螅袃莈薂蚁袂蒀螇羀袁膀薀袆羀节螆螂罿莅蕿蚈羈薇莁肆羈芆蚇羂羇荿蒀袈羆蒁蚅螄羅膁蒈蚀肄芃蚃罿肃莅蒆袅肂蒈蚂螁肂芇蒅螇肁莀螀蚃肀蒂薃羂聿膂螈袈肈芄薁螄膇莆螇虿膆葿蕿羈膆膈莂袄膅莁薈袀膄蒃蒁螆膃膂蚆蚂膂芅葿羁膁莇蚄袇芀葿蒇螃芀腿蚃虿艿芁蒅肇芈蒄蚁羃芇薆薄衿芆芆蝿螅袃莈薂蚁袂蒀螇羀袁膀薀袆羀节螆螂罿莅蕿蚈羈薇莁肆羈芆蚇羂羇荿蒀袈羆蒁蚅螄羅膁蒈蚀肄芃蚃罿肃莅蒆袅肂蒈蚂螁肂芇蒅螇肁莀螀蚃肀蒂薃羂聿膂螈袈肈芄薁螄膇莆螇虿膆葿蕿羈膆膈莂袄膅莁薈袀膄蒃蒁螆膃膂蚆蚂膂芅葿羁膁莇蚄袇芀葿蒇螃芀腿蚃虿艿芁蒅肇芈蒄蚁羃芇薆薄衿芆芆蝿螅袃莈薂蚁袂蒀螇羀袁膀薀袆羀节螆螂罿莅蕿蚈羈薇莁肆羈芆蚇羂羇荿蒀袈羆蒁蚅螄羅膁蒈蚀肄芃蚃罿肃莅蒆袅肂蒈蚂螁肂芇蒅螇肁莀螀蚃肀蒂薃羂聿膂螈袈肈芄薁螄膇莆螇虿膆葿蕿羈膆膈莂袄膅莁薈袀膄蒃蒁螆膃膂蚆蚂膂芅葿羁膁莇蚄袇芀葿蒇螃芀腿蚃虿艿芁蒅肇芈蒄蚁羃芇薆薄衿芆芆蝿螅袃莈薂蚁袂蒀螇羀袁膀薀袆羀节螆螂罿莅蕿蚈羈薇莁肆羈芆蚇羂羇荿蒀袈羆蒁蚅螄羅膁蒈蚀肄芃蚃罿肃莅蒆袅肂蒈 Control Parameter3 Static Load Case for Nonlinear Restraint Status动态分析是线性的分析,在开始建立分析模型之前,我们选择哪个工况作为开始。STATIC LOAD CASE FOR NONLINEAR RESTRAINT STATUS (Active for: Harmonic, Spectrum, Modal, Range, and Time History) Currently all of CAESAR IIs dynamic analyses act only on linear systems, so any non-linearities must be linearized prior to analysis. This means that one-directional restraints will not lift off and reseat, gaps will not open and close, and friction will not act as a constant effort force. Therefore, for dynamic analyses, all non-linear effects must be modeled as linear - for example, a one-directional restraint must be modeled as either seated (active) or lifted off (inactive), and a gap must be either open (inactive) or closed (active). This process is automated when the static load case is selected here - CAESAR II automatically activates the non- linear restraints in the system to correspond to their status in the selected load case (the user may think of this as being the loading condition - for example Operating - of the system at the time at which the dynamic load occurs). It must be noted that this automated linearization does not always provide an appropriate dynamic model, and it may be necessary to select other static load cases or even to manually alter the restraint condition in order to simulate the correct dynamic response. A static load case must precede the dynamics job whenever: 1) There are spring hangers to be designed in the job. The static runs must be made in order to determine the spring rate to be used in the dynamic model. 2) There are non-linear restraints, such as one-directional restraints, large-rotation rods, bi-linear restraints, gaps, etc. in the system. The static analysis must be made in order to determine the active status of each of the restraints for linearization of the dynamic model. 3) There are frictional restraints in the job, i.e. any restraints with a nonzero (mu) value. 0.0 Stiffness Factor for Friction (0.0-Not Used)解释这个含义 STIFFNESS FACTOR FOR FRICTION (0.0-NOT USED) (Active for: Harmonic, Spectrum, Modal, Range, and Time History) All of CAESAR IIs dynamic analyses are currently linear, so non-linear effects must be linearized. Modeling of friction in dynamic models presents a special case, since friction actually impacts the dynamic response in two ways - static friction (prior to breakaway) affects the stiffness of the system, by providing additional restraint, while kinetic friction (subsequent to breakaway) actually affects the damping component of dynamic response; due to mathematical constraints, damping is ignored for all analyses except time history (for which it is only considered on a system-wide basis). CAESAR II allows friction to be taken into account through the use of this Friction Stiffness Factor. CAESAR II approximates the restraining effect of friction on the pipe by including stiffnesses transverse to the direction of the restraint at which friction was specified. The stiffness of these frictional restraints is computed as: Kfriction = (F)*()*(Fact) Where: Kfriction = stiffness of frictional restraint inserted by CAESAR II F = the force at the restraint taken from the static solution = mu, friction coefficient at restraint, as defined in the static model Fact = Friction Factor from the control spreadsheet This factor should be adjusted as necessary in order to make the dynamic model simulate the systems actual dynamic response (note that use of this factor does not correspond to any actual dynamic parameter, but is actually a tweak factor to modify system stiffness). Entering a friction factor greater than zero causes these friction stiffnesses to be inserted into the dynamics job. Increasing this factor correspondingly increases the effect of the friction. Entering a friction factor equal to zero ignores any frictional effect in the dynamics job. 0 Max. No. of Eigenvalues Calculated (0 - Not Used)解释这个含义 MAX. NO. OF EIGENVALUES CALCULATED (0-NOT USED) (Active for: Spectrum, Modal, and Time History) The first stage of the Spectrum, Modal, and Time History analyses, is the use of the Eigensolver algorithm to extract the piping systems natural frequencies and mode shapes. For the Spectrum and Time History analyses, the response under loading is calculated for each of the modes, with the system response being the sum of the individual modal responses. Obviously, the more modes that are extracted, the more the sum of those modal responses resembles the actual system response. The problem is that this algorithm uses an iterative method for finding successive modes, so extraction of a large number of modes usually requires much more time than does a static solution of the same piping system. The object is to extract sufficient modes to get a suitable solution, without straining computational resources. CAESAR II permits the user to specify - either through a mode number cutoff or a frequency cutoff - the number of modal responses to be included in the system results. This parameter is used, in combination with the Frequency Cutoff described below, to limit the maximum number of modes of vibration to be extracted during the dynamic analysis. If this parameter is entered as 0, the number of modes extracted is limited only by the frequency cutoff (and potentially, the number of degrees-of-freedom in the system model). If the analyst is more interested in providing an accurate representation of the system displacements, it may only be necessary to request the extraction of a few modes, allowing a rapid calculation time. However, if an accurate estimate of the forces, stresses, etc. in the system is the objective, calculation time grows as it becomes necessary to extract far more modes. This is particularly true in the case when solving a fluid hammer problem in the presence of axial restraints; often modes with natural frequencies of up to 300 Hz can be large contributors to the solution.The usual procedure for determining how many modes are sufficient is to extract a certain number of modes and review the results; then to repeat the analysis while extracting 5 to 10 additional modes, and comparing the new results to the old. If there is a significant change between the results, a new analysis is made, again extracting 5 to 10 more modes above those that were extracted for the second analysis. This iterative process continues until the results taper off, becoming asymptotic. This procedure has two drawbacks, the first one obvious - the time involved in making the multiple analyses, as well as the time involved in extracting the potentially large number of modes. The second drawback, occurring with Spectrum analysis, is less obvious - a degree of conservatism is introduced when combining the contributions of the higher order modes. Possible spectral mode summation methods include SRSS, ABSOLUTE, and GROUP - all methods that combine modal results as same-sign (positive) values. In reality, theory states that the rigid modes actually act in phase with each other, and should therefore be combined algebraically, thus permitting the response of some rigid modes to cancel the effect of other rigid modes (this is actually what occurs in a time history analysis). Because of this conservatism, it is actually possible to get results which exceed twice the applied load, despite the fact that the Dynamic Load Factor (DLF) of an impulse load cannot be greater than 2.0. An alternative method of ensuring that sufficient modes are considered in the dynamic model is through the use of the Included Mass Data Report. This report (available from the Dynamic Output Screen) is compiled for all spectrum and time history shock cases, whether missing mass (see description in the section Include Missing Mass Components) is to be included or not. It displays the percent of system mass along each of the three global axes, as well as the percent of total force, which has been captured by the extracted modes. The percent of system mass active along each of the three global axes (X-, Y-, and Z-) is calculated by summing the modal mass (corresponding to the appropriate directional degree-of-freedom) attributed to the extracted modes and dividing that sum by the sum of the system mass acting in the same direction. 40 Frequency Cutoff (Hz)Frequency Cutoff (HZ) (Active for: Spectrum, Modal, and Time History) As noted above, CAESAR II permits the user to specify either a number of modes or a frequency cutoff for extracting modes to be considered in the dynamic analysis. Modal extraction ceases when the Eigensolver extracts either the number of modes requested, or extracts a mode with a frequency above that of the Frequency Cutoff, whichever comes first. One recommendation for selection of a frequency cutoff point is that the user extract modes up to, but not far beyond, a recognized rigid frequency, and then include the missing mass correction (discussed in the section Include Missing Mass Components). Choosing a cutoff frequency to the left of the response spectrums resonant peak will provide a non-conservative result, since resonant responses may be missed. During spectrum analysis, using a cutoff frequency to the right of the peak, but still in the resonant range, will yield either overly- or underly-conservative results, depending upon the method used to extract the ZPA from the response spectrum. (In the case of time history analysis, selecting a cutoff frequency to the right of the peak, but still in the resonant range, will probably yield non-conservative results, since the missing mass force is applied with a dynamic load factor of 1.0). Extracting a large number of rigid modes for calculation of the dynamic response may be conservative in the case of Spectrum analysis, since all spectral modal combination methods (SRSS, GROUP, ABS, etc.) give conservative results versus the algebraic combination method (always used during time history analysis), which gives a more realistic representation of the net response of the rigid modes. When the analysis type is SPECTRUM, MODES, or TIMEHIST, either this parameter or the previous one must be entered. 0.1 Closely Spaced Mode Criteria解释这个含义CLOSELY SPACED MODE CRITERIA/TIME HISTORY TIME STEP (MS) (Active for: Spectrum/GROUP and Time History) This parameter does double duty, depending upon the analysis type. For a Spectrum analysis type with GROUP modal Combination Method (as defined by USNRC Regulatory Guide 1.92), this parameter specifies the frequency spacing defining each modal group - i.e., the percent (of the base frequency) between the lowest and highest frequency of the group. Regulatory Guide 1.92 specifies the group spacing criteria as 10% (entered here as 0.1), so it is unlikely that the user would ever wish to change the Closely Spaced Mode Criteria from the CAESAR II default value of 0.1. For a Time History analysis type, this parameter is used to enter the length of the time slice, in milliseconds, to be used by the program during its step-by-step integration of the equations of motion for each of the extracted modes (CAESAR II uses the unconditionally stable Wilson q integration method, so any size time step will provide a solution, with a smaller step providing greater accuracy - and more strain on computational resources). The time step should be sufficiently small that it can accurately map the force vs. time load profile (i.e., the time step should be smaller than typical force ramp times). Additionally, the time step must be small enough that the contribution of the higher order modes is not filtered from the response. For this reason, it is recommended that the time step should be selected such that Time Step (in seconds) times Maximum Modal Frequency (in Hz) be less than 0.1. For example, if the modal frequency cutoff is set to 50 Hz, the time step should be set to a maximum of milliseconds: 0.002 sec x 50 Hz = 0.1N Re-use Last Eigensolution (Frequencies and Mode Shapes)解释这个含义Re-use Last Eigensolution (Active for: Spectrum and Time History) When repeating a dynamic analysis, this parameter may be set to Yes, causing CAESARII to skip the eigensolution (reusing the results of the earlier analysis), and only perform the computations for displacements, reactions, forces, and stresses. Activating this option is only valid after an initial eigensolution has been performed and is still available. Additionally, the mass and stiffness parameters of the model must be unchanged or the previous eigensolution is invalid. MODAL Spatial or Modal Combination First解释这个含义 Spatial or Modal Combination First (Active for: Spectrum) This directive tells CAESAR II whether to combine the Spatial components or the Modal components of the load case first. When performing a spectrum analysis, each of the modal responses must be summed. In addition, if multiple shocks have been applied to the structure in more than one direction, the results from different directions must be combined - for example, spatially combining the X-direction, Y-direction, and Z-direction results. The question arises as to whether the spatial summations should precede or follow the modal summations. A difference in the final results (of Spatial first vs. Modal first) arises whenever different methods are used for the spatial and modal combinations. The combination of Spatial components first implies that the shock loads are dependent, while the combination of Modal components first implies that the shock loads are independent. Dependent and Independent refer to the time relationship between the X, Y, and Z components of the earthquake. With a dependent shock case, the X, Y, and Z components of the earthquake have a direct relationship - a change in the shock along one direction produces a corresponding change in the other directions. For example, this would be the case when the earthquake acts along a specific direction having components in more than one axis - such as when a fault runs at a 30o angle between the X- and Z-axes. In this case, the Z-direction load would be a scaled (by a factor of tan 30o), but otherwise identical version of the X-direction load. In this case, spatial combinations should be made first. An Independent shock is one where the X, Y, and Z time histories produce related frequency spectra but have completely unrelated time histories. It is the Independent type of earthquake that is far more common, and thus in most cases the modal components should be combined first. For example, IEEE 344-1975 (IEEE Recommended Practices for Seismic Qualification of Class 1E Equipment for Nuclear Power Generating Stations) states: Earthquakes produce random ground motions which are characterized by simultaneous but statistically INDEPENDENT horizontal and vertical components. This is usually less of an issue for force spectrum combinations, since normally there are no separate spatial components to combine - i.e., there are not X-, Y-, and Z-shocks acting simultaneously. However, in the event that there is more than one potential force load (such as when there is a bank of relief valves that can

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