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In order to review the center of rigidity for a structure, a special Centers of Rigidity load case must be created under Loads – Load cases in RAM Frame. Once the analysis of that load case has been performed, a “Centers of Rigidity” report becomes available under the reports menu.
The Centers of Rigidity report lists the centers of rigidity of each diaphragm at each of the levels that contain lateral members. The report also lists the center of mass and Story Lateral Stiffness of each diaphragm.
The center of rigidity can be thought of as the location through which a lateral load would cause lateral deformation of the diaphragm without causing rotation. The concept is analogous to that of a cross section’s “shear center”.
Below are the results for a 30’x10’ structure, 10 stories tall, with walls on 3 sides.
Isometric view of “C” shaped wall model, center of mass at (15,5)
For buildings with torsional irregularity, the lateral load may always be on the same side of the center of rigidity even after considering a 5% accidental eccentricity of the load. In this case, the torsion will always be “adding” to the shear on one side of the building and “subtracting” shear from the other side. To ignore these effects, an additional lateral load case with the same magnitude as the generated load, but with a location exactly at the center of rigidity can be added. This, pure shear load case, can then be included in the load combos to yield a conservative design for the frame elements that otherwise would benefit from the eccentricity. Some codes may require such a conservative approach, but most building codes recognize the reality of the eccentricity and the effect it has on the structure. In those cases, the code may simply want an increase in the accidental torsion to be considered. This can be changed under Loads – Masses, within the Analysis mode of RAM Frame.
Returning to the example above, an interesting phenomenon occurs in regard to the “Yr” location. Even though the levels are identical, the center of rigidity shifts from level to level. The higher the level, the more eccentric the center of rigidity. In other words, a load must be applied from the long wall in order to bend the channel without twisting it.
A load applied to the diaphragm in line with the long wall (y=10’), actually produces a large diaphragm rotation. For a load applied to the center of the diaphragm (y=5’) the effect is even worse
Channel Loaded Through Center of Rigidity
Channel Loaded Through Long Wall
The Center of Rigidity location is not directly used in determining the loads or in the finite element analysis. The exception to this rule is in the determination of some wind loads where the eccentricity affects the applied loads directly.
The center of rigidity is always calculated using a rigid diaphragm analysis, even where semi rigid or flexible diaphragms are called out.
The program calculates and reports a center of rigidity for each diaphragm on every level. The plotted center of rigidity values using Process - Results - Center of Rigidity are only for rigid diaphragms.
First a Center of Rigidity load case must be created and analyzed in order to plot the location using Process - Results - Center of Rigidity.
Furthermore, this graphical result is only provided for rigid diaphragms.
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