| Product(s): | RAM Structural System | ||
| Version(s): | Any | ||
| Area: | Analysis; Reports |
Center of Rigidity
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.
For technical information on the method Ram Frame uses to calculate it see the RamFrameAnalysis.pdf manual section "7.22 Center of Rigidity Calculation".
The Centers of Rigidity report lists the centers of rigidity of each rigid diaphragm at each of the levels that contain lateral members.
Center of Rigidity (CR) values reported are only used for load cases that require explicit calculation of CRs for use in calculation of load eccentricities (for example, ASCE 7-05 Wind Load Case). This information is never used directly for analysis, though it is used to determine the amount of eccentricity for some loads. It should be noted that analysis results always includes any torsional effects due to having center of rigidity and applied force resultant at different locations. In other words, the analysis always accounts for locations and stiffnesses of frame members and diaphragms. Hence, any torsional effects of the force being offset from the center are implicitly and correctly accounted in the analysis. The center of rigidity can be thought of as the location through which a lateral load would cause lateral deformation of the diaphragm (possibly at an angle) without causing rotation. The concept is analogous to that of a cross section’s “shear center”.
The report also lists the "Centers of Mass", and for rigid diaphragms specifically, it includes the Story Lateral Stiffness of each diaphragm. The reported story stiffness is the inverse of the interstory drift that is calculated according to a unit load applied at the story. This is useful for checking a number of code requirements such as the ASCE 7 Soft-Story limits.
Below are the results for a 30’x10’ structure, 10 stories tall, with walls on 3 sides. The walls here intersect to create a "C" shape, but individual wall out-of-plane stiffness is ignored and the diaphragms are rigid.
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 because the flexibility of the supporting structure keeps increasing. The higher the level, the more eccentric the center of rigidity. In other words, at the top a lateral load must be applied farther from the middle 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
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Channel Loaded Through Center of Rigidity |
Channel Loaded Through Long Wall |
It is worth noting that a structure like this with a high degree of eccentricity may also experience a significant shift in the center of rigidity location when using P-Delta analysis. For that reason, when closely evaluating the center of rigidity we recommend a first order analysis.
Why is more than one center of rigidity shown on a level?
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.
Why can't I plot the center of rigidity?
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.
See Also
RAM Frame - Seismic Loads [FAQ]