TR.32.10.2 Time Varying Load for Response History Analysis
A STAAD.Pro model can include a dynamic load case that has loading that varies over a given time period.
For this to operate, STAAD.Pro must determine a set of mode shapes. These are obtained by creating a mass matrix and performing an eigen solution. The masses used to create the mass matrix can be specified as one of the following:
- the load specified in the first dynamic load case,
- if the first dynamic load case does not contain any loads, then by all primary load cases defined as LOADTYPE MASS,
- if there are no primary load cases defined as LOADTYPE MASS, then by all cases defined as LOADTYPE GRAVITY, or
- if there are no primary load cases defined as LOADTYPE MASS or GRAVITY, then by ALL reference load cases that are defined as LOADTYPE DEAD and LIVE (at least one case must be defined as LOADTYPE DEAD)
Refer to G.17.3.2 Mass Modeling for additional details.
For more information on the creation of modal analysis refer to TR.34.2 Modal Calculation Command
Time history loads are defined with the magnitude of acceleration, force, or moment that changes over a given time period (refer to TR.31.4 Definition of Time History Load). These are referred to as the forcing functions.
The forcing functions can either be assigned as variable force or moment loads to one or more superstructure nodes or as a ground motion which applies the forcing function to the all the supports on the model as a ground motion.
The load case can include both ground motion and super structure forcing functions applied simultaneously.
A set of results that are only produced with a time history load case are reported in the output file and additional layouts that can display the variation of displacement, velocity or acceleration in the three global directions.
The standard results sets that are provided for all load cases, both standard and dynamic, i.e. displacements, reactions, beam end forces, plate stresses, etc. will report the maximum values of the given attribute (either positive or negative) over the loading period.
When considering ground motion, then the results can either be reported as ABSOLUTE, i.e. taken relative to the original starting point, or RELATIVE which is taken relative to the ground motion position at the given time step.
The overall loading period that is considered for a time history load case is determined as the maximum time period from each time load application plus its arrival time.
For example if a model has two time loads applied
- A load on node 10 which is has a 10 second forcing function and an arrival time of 0 seconds (i.e. duration of 0 + 10 seconds)
- A load on node 20 which has an 8 second forcing function and an arrival time of 5 seconds (i.e. duration = 5+8 = 13 seconds)
The overall duration of the analysis will be maximum 10 and 13 seconds, thus 13 seconds.
General Format
The following set of commands may be used to apply one or more time varied load definitions (see TR.31.4 Definition of Time History Load) onto the structure which have been defined in the time history definitions.
TIME LOAD
joint-list *{ FX | FY | FZ | MX | MY | MZ } It Ia f2
GROUND MOTION { ABSOLUTE | (RELATIVE ) } { X | Y | Z } It Ia f2
Where:
| Parameter | Description |
|---|---|
| ABSOLUTE | Reported node displacements are relative on their original position |
| RELATIVE | Reported node displacements are
relative to the current displaced position of the supports at a
given time step. Hence all supports will show no displacement.
(Default) |
| It | ID of the forcing function
definition. (Refer to
TR.31.4 Definition of Time History Load). (No default) |
| Ia | Arrival time number (integer).
(default 1) This is the sequential number of the ARRIVAL TIME specified in the Time History definition block (Refer to TR.31.4 Definition of Time History Load. ) For example, if the ARRIAL TIME specifies 5 times of 0.0 0.1 0.2 10.0, to specify the third defined arrival time of 0.2 seconds, Ia would be 3 |
| f1 | Forcing function multiplication factor. The defined forcing function value is multiplied by this value at each time increment. (default = 1.0). |
Notes
- Multiple loads at a joint-direction pair for a particular ( It Ia ) pair will be aggregated.
- Up to four ( It Ia ) pairs may be associated with a particular joint-direction pair. Any more than four will be ignored an only the first four will be used.
- Forcing functions should not be applied to nodes that have been set as dependent joint directions. Any time history loads on these nodes will be ignored.
- For TIME LOAD data, multiple direction specifiers can be in one entry. Each direction followed by the three parameters It, Ia and f2, recall that if Ia or It are omitted, then default values of 1 will be used.
- The Node Displacement table reports the maximum displacement that occurs at each node over the entire time range.
- The displacement of the model at a specific time instance can be displayed by using the time slider bar on the Results toolbar when displaying a load case with time history loading.
- If any Node Groups are defined, the time history graphs can be set to display the average results for the group. The name of the selected node or group being displayed is given in the graph title bar.
- Time history loading can only be defined in a single load case before the first analysis command.
Example
A model that has a mass matrix defined by self-weight and a point weight of 7.5 defined in the time history load case, subject to forcing functions applied in the global X direction on nodes 2 , 3, 5, and 7 and simultaneously the structure being shaken by a different forcing function. The intensity of the forcing functions on all the super structure nodes is the same, although they start at different times.
LOAD 1 SELFWEIGHT X 1.0 SELFWEIGHT Y 1.0 SELFWEIGHT Z 1.0 MEMBER LOADS 5 CON GX 7.5 10.0 5 CON GY 7.5 10.0 5 CON GZ 7.5 10.0 TIME LOAD 2 3 FX 1 3 5 7 FX 1 6 GROUND MOTION REL X 2 1