Range-add load combination can be used is useful for pattern-type loading , such as to obtain the most extreme response over all possible combinations of individually loaded bays in maximum and minimum response from a range of possible load combinations.
For example, the bays of a multi-story building .
The beam below has 8 separate Load Cases, each of which loads a 1/8 length of the beam. Load Case 2 is shown:
Moment diagram for an Algebraic-Add Combo. All 8 Load Cases are added together, equivalent to uniform load on the entire beam:
Moment diagram for an Enveloping Combo. All 8 Load Cases are considered independently, only one acting at a time. Max and Min are shown:
For pattern type-loading, we want the envelope ofmay be subjected to many different vertical load patterns. The beam in Figure 1 is divided into eight equal-length segments to simulate the structural configuration of an eight-bay system. Any combination of bays may be loaded. A separate load case is defined for the loading of each individual bay. Range-add load combination is then implemented to envelope the response from all possible combinations.
Figure 1 - Structural configuration with second bay loaded
When all eight load cases are added together using an algebraic-add load combination, the beam is subjected to a uniformly-distributed load along its entire length. The moment diagram for this load combination is given in Figure 2:
Figure 2 - Moment from uniformly-distributed load
If each load case is applied independently, an envelope load combination may be applied to envelope the maximum and minimum response which results from the individual loading of each separate bay. This moment diagram is given in Figure 3:
Figure 3 - Moment from envelope load combination
For pattern-type loading, all possible load combinations are considered. An envelope is generated for response from the following combinations:
- Any single load case (same as the envelope combo previously shown), 8 permutations)
- Any pair of load cases , (28 permutations)
- Any three load cases , (56 permutations)
- Any four load cases, (70 permutations)
- Any five load cases, (56 permutations)
- Any six load cases, (28 permutations)
- Any seven load cases, (8 permutations)
- All eight cases (same as the additive combo previously shown), 1 permutation
For a total of 255 possible permutations!
In the past, we would have had to define 255 additive combos, plus one more combo that envelopes them all.
Now we can define a single Range Add combo to get the same results:
Simply list the 8 load cases as we would for adding or enveloping
- The computation starts with zero for Max and Min(1)
As a result, pattern-type loading involves 255 possible permutations. Without the range-add feature, definition would require 255 additive combinations, plus an additional combination to envelope response. The same output may be achieved using a single range-add load combination.
An summary of the range-add process is as follows:
- The computation begins with Max and Min results from zero loading
- For each contributing case:
- Positive values add to the Max
- Negative values add to the Min
- If the contributing case is another combocombination:
- Positive Max values add to the Max
- Negative Min values add to the Min
- The result represents a range of results that always includes zero
- The specification is easy, the computation is quick
Moment diagram for a single Range Add Combo. All 8 Load Cases are included. Equivalent to 255 additive and 1 enveloping combo:
...
- Results represent the envelope of all possible combinations
- Specification is streamlined, and computation is expedited
The moment diagram for a single range-add load combination, which includes all eight load cases and 256 permutations, is given in Figure 4:
Figure 4 - Moment from range-add load combination
See Also
Attachments
- Range-Add Load Combination PowerPoint Presentation presentation (PDF Format, size = 224 KB)