Response Spectra

A response spectrum represents maximum system responses for a group of single-mass oscillators (EMS) to a specific system excitation, for example the mean value from various earthquake recordings. The EMS have the same damping properties, but different natural periods. The maximum system responses of the individual EMS are shown versus the natural period of the EMS; this graph is the so-called response spectrum.

The response spectrum method has great advantages in terms of computation time. It is also a common method specified in various building standards. Please note, however, that this is an approximation method to determine the maximum internal forces of the model. For detailed information on the response spectrum method, see, for example, Wilson [1 ] or Tedesco [2 ].

A multimodal response spectrum method is available for the analysis. You can apply the relevant spectra in accordance with the standards or create them in a user-defined manner. The spectra used in the model are managed in the Response Spectrum dialog.

Base

In the Basic tab, you can specify the type of response spectrum and define the parameters.

Defintion Type

Determine how you want to define the response spectrum. There are four definition types to choose from in the list.

User-defined

If you describe a response spectrum in a user-defined manner, you can specify the characteristic values in the 'Periods and Accelerations' section: Enter the periods T or frequencies f with the associated accelerations S_a line by line in the table.

You can use the table to individually define the acceleration - period diagram or acceleration - frequency diagram. The order of the lines entered can be arbitrary. In this way, you can subsequently add value pairs that lie between values that have already been defined.

You can delete the selected table row with the button.

The button enables the table values of a diagram to be imported from Excel. You can use the button to export the user-defined response spectrum to Excel.

The functions of storing user-defined spectra in a library and reading them back in from there are still under development. Therefore the buttons are blocked.

If the value pairs have a constant time step below each other, activate the check box Δ_T below the table. Then enter the period step in the field next to it . If you now enter accelerations in the table, the time is automatically set with the steps_ΔT. You can adjust the step Δ_T at any time in order to enter further value pairs with a different time step. This function is in the chapter Accelerograms described.

User-defined with g-factor

With this option, you can manually define the table values of a response spectrum as described in section user-defined . Enter the values of the periods T or frequencies f with the associated accelerations S_a in the table ' Periods and Accelerations '.

The acceleration is dimensionless: Each value entered is multiplied by the g-factor that is stored in the basic data of the model (default setting: g = 10 m/s²). If necessary, you can adjust the value of the gravitational acceleration in the register Settings and Options .

Generate from Accelerogram

You can generate the response spectrum from one of the accelerograms that you have defined for the model or create a new one here in the dialog.

Select the accelerogram from the list. The button allows you to check the parameters of the selected accelerogram and adjust them if necessary. With the button you can create a new accelerogram according to user-defined criteria or from a Import library of recorded earthquakes. In the list, select the 'direction' of the global axis in which the response spectrum should be applied. Accelerograms can show different acceleration - period curves depending on the direction. image@030105@15#

With the other options you can adjust the 'conversion parameters' with which the response spectrum is generated from the accelerogram. After each change, the response spectrum is updated in the diagram. In the register 'table values' you can check the values of the period T and the acceleration S_a.

• The viscous 'damping' D is the damping of the group of single-mass oscillators (EMS) for which the maximum system responses are calculated. The higher the viscous damping is set, the smaller are the generated accelerations.
• The 'interval' describes the duration between the minimum time T_min as the period of the first EMS and the maximum time T_max as the period of the last EMS, which is applied when the response spectrum is generated.
• The 'number of samples' represents the number of steps between the minimum and maximum time (period). You can use this value to influence the number of data points generated. The number of samples also affects how finely the underlying accelerogram is approximated.

According to Standard

You can generate the response spectrum from the parameters that are stored in a standard. The standard that you specified in the Norms I tab in the basic model data is preset.

If you change the standard for the general data, the parameters and standard values adapt to the specifications of the set of rules.

If you have specified the geographical position of the building object in the model parameters , the accelerations of the corresponding location are applied.

You can select the parameters in the lists or define them manually depending on the parameter type and standard. Many sets of rules differentiate between a linear design spectrum using a ductility coefficient q and an elastic response spectrum using a coefficient for the damping η. Use the list to determine the ' spectrum shape '.

The 'spectrum direction' controls whether a horizontal or vertical response spectrum is applied.

Some cells are occupied by fixed parameters. For example, according to EN 1998-1 CEN, the parameters S, T_B, T_C and T_D are determined from the subsoil classes A to E; the values cannot be changed. If you still want to adjust these parameters, enter the subsoil class Other. This option is available for several standards. It enables the associated parameters.

Graph

The diagram of the response spectrum generated from the specifications is shown in the lower section. The functions of the diagram are described in the chapter Response spectrum described.

Table Values

The Tabular Values tab is only available if the response spectrum is generated using the definition type Generate from accelerogram .

In this register you can check the values of the periods T with the associated frequencies f and accelerations S_a. The table thus corresponds to the input of a response spectrum described in section user-defined . However, the values cannot be edited in this table.