Response Spectrum 2D and Response Spectrum 3D

) or (

) dataset selected from the and submenus, respectively, to perform a response spectrum analysis for a structural mechanics model. A response spectrum analysis is a modal-based method for estimating the structural response to a transient, nondeterministic event. Typical applications are dimensioning against earthquakes and shocks.

The input to a response spectrum is the results from an eigenfrequency computation, which you choose as one of the existing solution datasets from an eigenfrequency study, available in the list.

When you have selected a value other than from the list, you also need to include a number of stationary load cases. In those cases, also choose an applicable solution from the list. Computing the stationary load cases used here requires a special technique, as described in Performing a Response Spectrum Analysis in the Structural Mechanics Module User’s Guide.

In this section you specify the spectra used as loading for the response spectrum evaluation (“design response spectra”). The spectra must be defined as functions under either the node or under in a component. Spectra are commonly provided as functions of either natural frequency or period time. This is just an inversion of the abscissa, but you have the option to use either form.

From the list, choose a type for the spectrum: (the default), , or .

From the list, choose (the default) or to specify what the spectrum depends on.

	The functions you reference for the spectra are taken as entered, without any unit conversions. Thus, it is not meaningful to modify the unit fields available in the settings for many types of functions. The argument to the function is always either seconds or Hertz, depending on the choice in the Depends on list.

In a node, also specify the following settings:

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From the list, choose any available user-defined function that represents the primary horizontal spectrum. As a default, the primary spectrum acts along the global X-axis.

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From the list, choose any available user-defined function that represents the secondary horizontal spectrum. The secondary horizontal spectrum acts in a direction orthogonal to the primary horizontal spectrum. This option is only available when the method is or .

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In the field, enter a primary axis rotation (in degrees). This is the counterclockwise rotation in the XY-plane from the X-axis to the direction in which the primary horizontal spectrum acts. The allowed range is 0–90 degrees. This option is only available when the method is or .

The combination of the modes in the response spectrum method is in general done in two passes. First, all modes are combined into a response for each spatial direction of excitation, and then the result for the two or three directions are combined into a final result. There are, however, also evaluation methods where the total result is computed directly.

From the list, choose one of the following combination methods:

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The . In this method, the contribution from the worst direction is taken at full value, whereas the two (in 2D: one) other contributions are reduced. There are two variants in commonly in use, the 40% (100-40-40) method and the 30% (100-30-30) method. You enter the percentage for the reduced contributions in the field (default: 40[%]).

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The method (for datasets only). The CQC3 method extends the CQC (complete quadratic combination) principles to the spatial combination. In the CQC3 method, the modal and spatial combination are performed simultaneously. When you have selected this method, enter a (default: 0.5). In this method, the secondary horizontal spectrum is taken to differ from the primary horizontal spectrum only by this constant scalar factor. Also, select the check box to include the rigid response if desired.

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The method (for datasets only). The SRSS3 method is a special case of the CQC3 rule, in which the mode correlation is ignored. This method has the same additional settings as the CQC3 method.

For the and options, you need to decide on a method for the modal combination. From the list, choose a method for combining the modes:

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The method uses CQC (complete quadratic combination) with a Der Kiureghian correlation coefficient determining the degree of interaction between the modes. The coefficient depends on the damping and spacing between the frequencies.

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The method uses the sum of absolute values of the modes. This is a highly conservative method since it assumes that all modes reach their peak values at the same time.

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The (square root of sum of squares) method does not include any interaction between the modes and is applicable only when the eigenfrequencies for the used modes are well spaced.

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The method uses a double sum with a Rosenblueth correlation coefficient. This method resembles the CQC method in that the coupling between the modes depends on the damping and eigenfrequency spacing, but it also takes the duration of the event into account.

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The uses a scheme where grouping of modes are created based on the proximity eigenfrequencies. Within each group, the modes are assumed to interact completely, while there is no interaction between modes in different groups.

Depending on the method that you have selected from the list, the following additional settings are available:

Enter a (as a value between 0 and 1; the default is 0.05) for the CQC3, CQC (Der Kiureghian) and Double sum (Rosenblueth) methods. For the latter, also enter a time of duration (in seconds) in the field (default: 0).

Select the check box to use a more conservative assumption that the combination of two modes always gives a positive contributions to the total response. Without this assumption, the signs of the modal contributions are respected. This setting is available for , , and . For the method, you can select the corresponding check box. Later versions of NRC RG 1.92 state that the sign of the contribution should be respected, so this option is available only for compatibility with the first version of this regulatory guide.

	Respecting the sign of the coupling contributions is strictly speaking correct only when the result quantity is a linear function of the eigenmodes. This includes components of displacement, velocity, and acceleration vectors, as well as components of stress and strain tensors. Nonlinear quantities like total displacement and equivalent stress measures are always positive irrespective of the sign of the underlying mode shapes, so for such quantities you should consider selecting the Use absolute value for coupling terms check box in order to ensure a conservative result.

For all mode combination methods, the following settings are available:

From the list, choose (the default), , or . Some standards require a classification of the modes based on the natural frequency, where modes of with higher frequencies (“rigid modes”) are assumed to have a higher degree of correlation to each other. For the two methods that address this, Gupta and Lindley-Yow, additional settings are available:

Specify a (SI unit: 1/s). The default is 0. This is the frequency below which the modes are assumed to be fully periodic, and thus have the least degree of correlation. For the Lindley-Yow method, modes can be fully periodic even at higher frequencies, since there is an additional requirement stating that the acceleration spectrum must be monotonically decreasing before modes are considered to have a rigid part.

Specify a (SI unit: 1/s). The default is 0. For the Gupta method only. This is the frequency above which the modes are assumed to follow the base support acceleration as a rigid body, even if there can be some amplification.

Specify a (SI unit: 1/s). The default is 0. This is the frequency above which there is no periodic response, and the acceleration is equal to the of the excitation. For the Gupta method, this value is ignored, unless you also select to use the missing mass method.

In general, a mode superposition using a limited number of modes will miss some mass. With the assumption that the higher-order modes do not have any dynamic amplification, it is possible to device a correction by solving some extra static load cases, containing the acceleration excitation acting on the “lost mass”.

From the list, choose one of the following options:

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. In this model, the missing mass is computed from the eigenmodes as a distributed field over the structure, which can be seen as mass density distribution. This mass density is then used in stationary analysis to compute the extra displacements at a certain frequency. When you select this option, you must also select a stationary study in the list.

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(for Lindley-Yow only). In this method, there is no need to actually deduce the true missing mass. According to the Lindley-Yow method, all rigid modes have the acceleration at the zero period acceleration frequency, SZPA. This acceleration is given to the whole structure. The static load cases are thus just pure gravity loads but scaled by SZPA instead of the acceleration of gravity. When you select this option, you must also select a stationary study in the list.