Multiframe allows you to apply dynamic loads to the structure which are used to perform a time history analysis.
Multiframe4D includes a Load Library which contains commonly used dynamic loads. These loads may be spectra from earthquake measurements (several common earthquakes are provided), acceleration spectra from measured vibrations, and may also be dynamically varying forces which can be applied at joints in the structure.
When Multiframe4D starts up it will look for a file called "Load Library" or "Load Library.llb" in the same way that Multiframe looks for "Sections Library", first looking in the same directory as Multiframe4D, then looking on the current volume. Then if the Load Library is not found, Multiframe4D will prompt you for the location of the current load library.
The Load Library shipping with Multiframe4D contains 9 earthquake spectra taken from 3 well known earthquakes. This includes accelerations in 3 orthogonal directions for each earthquake. The earthquakes are El Centro, Kobe Osaka.and Izmir, Turkey
All dynamic loads are stored in the Load Library as either a force series or acceleration series. You can add, edit or delete loads in the Load Library.
§ Choose Edit Load Library... from the Edit menu
The Load Library dialog will appear which displays the load and acceleration series currently stored in the library.
The list at the top left of the dialog lists all of the series stored in the Load Library. The name of the currently selected series is displayed below the list and may be edited there.
Each series has a number of attributes including start velocity and displacement, number of points and type of series (either force or acceleration).
To add a new series to the library
§ Click the Add button
§ Type in a new name for the series
Enter the attributes of the series and type the values for the series data in the table at the right hand side of the dialog. You can also copy and paste data into the table by selecting the cells to be pasted and using Paste in the Edit menu.
Remember that the final time value must be greater than any analysis time. Otherwise, the loading would be undefined. For a set load, the time could be any large number, as the load value does not vary.
You can import load data from a text file to the load library in addition to entering it by hand. To import load data
§ Click on the Import Series button
A dialog will appear allowing you to choose the format of the data in the text file.
If you select Variable Time, the data should be in tab delimited format with two values per data point, the first value being the time in seconds and the second value being the load value (force or acceleration as appropriate).
If you select Fixed Time Interval, the data should be in tab delimited format with one force or acceleration value per data point.
There are a number of different load cases that can be added in Multiframe. These include a self weight static load case, a normal static load case, a factored combination of static load cases, a Time History load case which can contain dynamically varying forces at one or more joints, and a seismic case which applies up to three orthogonal ground accelerations to any restrained joints.
To create a Time History Load Case
§ Select Time History... from the Add Load Case sub-menu
A dialog will appear allowing you to enter the name, number and duration of the time steps for this load case along with other relevant information.
To add a dynamic load to the current Time History load case
§ Go to the Load window
§ Select the joints to which you want to add the load
§ Choose Dynamic Load from the Load menu
This command is only available when a Time History loadcase has been created and selected. A dialog will appear allowing you to specify the direction of the load, a factor which will be multiplied by the values in the load series, and a pop-up to select the load series from the library.
§ Enter a load factor, if any
§ Select the series you want to add and the global direction in which it is to act
A force series needs to be created in the load library first. See Editing the Load Library for information on how to create a force series. Note that only force series may be applied when in a Time History load case and acceleration series can only be used in Seismic load cases.
To view the loads applied above while still in the current Time History load case
§ Choose Step Loads from the Data sub-menu under Display
In addition to creating Time History load cases that allow you to apply dynamically-varying forces to the structure, Multiframe4D allows you to create load cases that apply dynamically changing ground accelerations. The most common use for this is applying an earthquake spectrum to a frame, but it may also be used for any other ground-based acceleration. Analysis is carried out by applying the specified acceleration to all of the restrained joints in the structure. The assumption is that all restrained joints move with the ground acceleration. The results of the analysis are displayed relative to the ground position at each point in time. This means that the restrained joints all show zero deflection and the deflections of the frame are relative to the global axes as usual.
§ Select Seismic from the Add Load Case sub-menu under the Case menu
A dialog will appear allowing you to enter the name and number and duration of time steps, acceleration series to be applied, and the direction of the acceleration.
§ Enter the name of the load case
§ Enter the number of time steps to perform
§ Enter the duration of each time step
Multiframe will display the total duration of the analysis below these values.
§ Select the orientation of the axes along which the ground acceleration will be applied
The normal convention for these axes is to label them North, East and Up for the three directions. You can specify the orientation of the North axis relative to the global x axis by entering an angle (counter-clockwise about the y axis) in degrees from the x axis. You can also reverse the direction of any of the load axes by choosing the appropriate radio button beside the axis name. The drawing in the bottom right hand corner of the dialog will display your selection.
Finally, you can choose which acceleration series from the Load Library will be applied to which axes by choosing the appropriate names from the pop-up menus.
The time step you choose for a time history analysis (∆t) has the effect of including or excluding the effects of natural frequencies modes in response of the structure. As ∆t increases more modes are effectively excluded from the response behaviour as the time step. As a general rule if T is the period of the longest mode that is to be included in the response calculation you should choose ∆t such that
When adding either a dynamic or seismic case the user can specify if proportional damping is to be used in the analysis. To do so you need to specify non-zero values for the Rayleigh damping coefficients Alpha and Beta. If you are uncertain as to how to find the appropriate value for Alpha and Beta please refer to texts on the subject. Finite Element Procedures in Engineering Analysis Bathe, Klaus-Jürgen © 1982 by Prentice Hall Inc. ( pages 528-531) is a good reference.
Proportional damping assumes that the damping matrix is proportional to the mass and stiffness matrices M and K respectively.
To calculate these values you need to look at the first two modes and the corresponding critical damping values required at those modes. Then using the equations
Combing the equations gives
