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Overview In order to determine dynamic response of a structure LinPro performs linear time-history analysis. As a solution method LinPro uses mode superposition method.The load, r(t), applied in a time-history analysis may be an arbitrary function of space and time. It can be written as a finite sum of spatial load vectors, pi , multiplied by time functions, fi(t), as: r(t)= Σ fi(t)·pi The program uses Load Cases or Acceleration Load to represent the spatial load vectors. The time functions can be arbitrary functions of time. If Acceleration Load is used, the displacements are measured relative to the ground. The time function associated with the Acceleration Load mx is the corresponding component of uniform ground acceleration, üx. In the next two examples dynamic analysis with LinPro will be demonstrated. One example is with loads as time dependent forces and another if load is ground acceleration. The results are compared with SAP2000. Example 1: Time varying forces Model and load that will be analyzed is on the next picture.
Creating structure is explained in Static Analysis, so you can create structure and apply forces and masses. Apply forces as static load CASE1 and in the next section you will be instructed how to define time dependence of load CASE1. In this version of LinPro you have to apply masses explicitly. When you finish creating this model main window of LinPro should look like on this picture. Dynamic Load In menu Load/Mass click on Dynamic Load. In window Dynamic Load, for Load type select Load, and for Load Name CASE1. Input time and value data:
Click on button Define and dynamic load will be defined and name CASE1 will be added in the list with applied dynamic loads. Here you can see how window Dynamic Load looks like. Analysis In menu Analysis click on Dynamic Analysis. In window that is opened input
This window you can open from menu Analysis-> Dynamic Analysis Options. Modal analysis will be performed and then dynamic analysis.
Results
Here you can compare results between SAP2000 and LinPro: Periods of oscilation Displacement function of joint 6 Moment diagram in time 0.05 Moment diagram in time 10.0 Example 2: Ground acceleration Model that will be analyzed is on the next picture.
Accelerogram that will be used, you should find in your installation directory of LinPro\Data\ALTADENA-1.TH Creating structure is explained in Static Analysis, so you can create structure and apply masses. In this version of LinPro you have to apply masses explicitly. When you finish creating this model main window of LinPro should look like on this picture. Accelerogram Click on menu item Load/Mass-> Dynamic Load. In window Dynamic Load, for Load Type select Acceleration. Now, for time history function program expects accelerations in m/s² Click on button Open under Time History Function table in order to import accelerogram. Program should open Data directory in your installation directory of LinPro. Select file ALTADENA-1.TH and click Open. In window that is opened now you can preview tekst in file ALTADENA-1.TH. This is important because only text that program recognizes as numbers will be imported. And this text is written in green colour. Here you can see window Preview text. In file ALTADENA-1.TH you can read in second row that these values are at interval 0.02 sec and unit is cm/s², so in window Preview Text for function definition select "Values at equal Interval of" and input 0.02. Finally click on button Import. If everything is regular accelerogram values should be imported in table Time History function and accelerogram should be drawn. Since unit of values in file ALTADENA-1.TH is cm/s² and LinPro expects m/s² click on button Scale and input 0.01 for Scale Factor. Click Ok and now you have values in m/s². In window Dynamic Load click on button Define and Dynamic load will be defined and its name will be added to the list Applied Dynamic Loads. Close window clicking on OK. Analysis In menu Analysis click on Dynamic Analysis. In window that is opened input
Click on Button Ok and dynamic analysis will be performed. Results Results are displayed in the same way as it's already explained for time dependent forces. Here you can compare results between SAP2000 and LinPro: Displacement function of joint 6 Moment function on member 0 at joint 2 Moment diagram in time 2.67 |
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