VisualAnalysis Advanced Tutorials: Result Superposition Combinations
This example will use a two span continuous beam to illustrate the creation of Result Superposition Combinations. The primary purpose of such combinations is to combine loads that cannot be combined before an analysis. It is important that you recognize when such combinations are valid and how to interpret the results. For more information on these topics, consult the User's Guide (Help | Contents). The beams will be A992 Grade 50, W36x135 members with fixed supports at both ends and restrained in the Y-direction at the center.
Continuous Beam Geometry
Loading the Structure
To effectively demonstrate the use of Result Superposition Combinations, we will want to create a number of service load cases and load combinations.
Select the Live loads case in the Status Bar and apply a uniform load of -500 lb/ft to the second span.
Go to Load | Load Case Manager and click on the Service Case tab. Make sure standard self-weight is included in the Dead loads case.
Add a Moving Load load case by clicking the Advanced tab of the Load Case Manager and selecting the "Create Moving Load" box at the bottom of the screen.
Keep the default name of "Moving Load 1" and select BmX001.
Choose "HS 20 Short" in the "Select Truck" drop down list and be sure that "Reversible" is checked so that the loads can be applied in either direction. >>Click OK.
Now that we have our service cases defined, we would like to create an equation case using the dead loads.
Under the Load Combinations tab, Select the "Create Factored Combination" box.
Name the equation "1.4 DL" and change the dead load load case factor to 1.4. Click OK.
The next step is to create a Result Superposition Combination (or Super Combo, to use a shorter name).
Go to the Advanced tab and select the "Create Result Superposition..." box at the bottom of the window.
Name the Super Combo "1.4 DL + Moving Load 1."
Enter a factor of 1.0 for both the "1.4 DL" case and the "Moving Load 1." All result cases will be first order. Click OK.
Cases to Superimpose Dialog
Note: This combination could also be created by specifying a 1.0 factor for the "Moving Load 1" case and a 1.4 factor for the "Dead loads" case.
A Super Combo has been created. Now create another Super Combo named "DL + LL + Moving Load 1" that includes the Dead loads, Live loads, and Moving Loads 1 cases, all with factors of 1.0. You may now close the Load Case Manager.
Analyzing and Results
The last step before performing the analysis is to set the analysis options. From the Modify Tab in the Project Manager, select First Order for Static Method. You could calculate P-delta results as well, but the second order nature of these results makes the superposition principle used by the Super Combos invalid, so caution should be used (See the Advanced section of the User's Guide under Help | Contents for more information on this topic). Do not calculate any mode shapes either. Now perform an analysis.
After the analysis completes, you can view results for each of the various case. The Super Combo results can be viewed just like any other results. Change the case in the status bar to the "1.4 DL + Moving Load 1". Now, on the Filter Tab of the Project Manager you will see a drop down box with the title Result Type (shown below). This box can be toggled between High Extreme and Low Extreme.
High Extreme, Low Extreme
Set the Result type to Low Extreme. Note that the reaction at the right support is |1711lb. This is equivalent to the sum of the Low Extreme reaction at the right support of -6447lb for the Moving Load 1 case and the reaction at the support of 4736lb for the 1.4 DL factored case.
Extreme Min Results for 1.4 DL + Moving Load 1 Super Combo
Note the difference between the Super Combo results and Envelope results. The Super Combo simply adds the Low Extreme reaction for the Moving Load 1 case to that of the 1.4 DL equation case. The envelope simply reports the extreme value.
Another illustration of how Super Combos work is the "DL + LL + Moving Load 1" Super Combo. If this Super Combo is selected from the status bar and Low Extreme Result Type is selected, we get a plot similar to that shown below.
Low Extreme Results for DL +LL + Moving Load 1 Super Combo
As can be seen in the plot, in the left span, the displacements for the Dead loads and Moving Load 1 cases are adding to one another while the upward displacement for the Live loads case is subtracting from the combined value.
As an example, use the Report | Report Wizard command to create a custom report and include the Member Internal Forces report item for the beam of the first span. In the report shown below, the Result Case Name was included, as well as the bending moment, Mz.
Member Results Report
Notice that if you sum the moment values for the Dead loads, Live loads, and Moving Loads 1 cases at any offset, you get the value listed for the DL + LL + Moving Load 1 Result Super Combo case.
Result Super Position Combinations are a great way to combine moving loads with "normal' static results. You can also use them to combine dynamic Response or dynamic Time History results with static results.