Range-add load combination is useful for pattern-type loading to obtain the maximum and minimum response from a range of possible load combinations.
For example, the bays of a multi-story building may 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:
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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
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