In my previous article I finished up the discussion of modeling the properties of semirigid diaphragms. In this article I will return to a discussion of a topic relevant to each of the diaphragm types, Flexible, Rigid, and Semirigid.
A significant aspect of the modeling of the various types of diaphragms that hasn’t yet been discussed is the proper modeling of the lateral wind and seismic loads. The proper application, and the amount of work involved, varies greatly between those types. In each case the applied forces must properly represent the magnitude and location of the real loads.
In each case, calculate the seismic base shear and story forces, and wind pressures and story forces per the applicable building code, ASCE 7 for example. The determination of these values is independent of the types of diaphragms, except as the diaphragm stiffness impacts the fundamental period, which may slightly impact the magnitudes of the loads. Most codes also require that load cases be considered in which the loads are applied with a 5% eccentricity or an additional torsional moment.
The most simple diaphragm for modeling the lateral loads is the Rigid diaphragm. Shown here is the story force applied to the diaphragm at a location that is offset 5% from the center of mass.
Because the diaphragm is analytically infinitely rigid, the force can be applied as a concentrated load at a point on the diaphragm, and the diaphragm will distribute that force to the various frames – shown here as red members – based on their relative rigidities. The rigid diaphragm is free to translate and rotate, but cannot deform. Loads on rigid diaphragms are simple to calculate and simple to apply in analysis software, which is one more benefit of utilizing the rigid diaphragm assumption.
The application of loads to the semirigid diaphragm is vastly more complicated. The loads must be applied to the diaphragm model in a way that mimics the real forces. For example, seismic forces result from the acceleration of the masses, so the loads must be applied distributed the way that the masses are distributed. The image below shows the seismic loads distributed over the diaphragm, proportional to the tributary mass at each node. The code requirements that the loads be applied with a plus and minus 5% eccentricity still applies; if you look closely at the lower edge of the image below you can see that the applied forces are slightly larger on the left half of the diaphragm than on the right half of the diaphragm, to produce the correct eccentric loading effects.
By contrast, wind loads act on the perimeter of the structure, so the wind loads should be applied as a set of windward and leeward nodal forces, applied to the perimeter mesh nodes accordingly:
For some analysis programs these applied forces need to be determined manually and assigned to the individual mesh nodes, but this is all automated in the RAM Structural System.
It would be inappropriate to apply the story force as a concentrated force, or the 5% eccentricity effects as a concentrated moment, on the semirigid diaphragm, as is done for a rigid diaphragm. The reason is that, as the diaphragm elements nearest to the point of load application deformed under that load, they would dump most of the load onto the frame closest to that point load. The figure on the left below shows the resulting stresses in a semirigid diaphragm when the nodal forces, including the modifications for the 5% eccentricity, are correctly applied over the diaphragm; the figure on the right below shows the resulting stresses in the diaphragm when a torsional moment is applied to the centroid of the diaphragm in an attempt to account for the 5% eccentricity:
Obviously, the modified distributed loads more accurately represent the way that the seismic inertial forces will be applied to the diaphragm.
When the diaphragm is considered to be Flexible there is nothing in the analytical model that represents the diaphragm; there are no diaphragm elements. As a result, the lateral loads cannot be applied to the diaphragm, they must be applied directly to the frames as nodal loads, as shown here:
With a flexible diaphragm, the loads must be calculated and applied as nodal loads. Their magnitude is usually a function of the tributary area/mass for seismic loads and a function of tributary exposure for wind loads, taking into consideration the load path through the decking and through drag lines. The manual calculation of these nodal forces and their application in analysis software can be very tedious. The RAM Structural System has a feature to aid in this process that I believe is unique to that program; rather than going through the tedious process of determining and assigning nodal loads the user merely needs to assign the percent of the story force that is expected to go to each frame at each level. When the program has determined the story forces for each load case it then automatically creates and applies nodal loads that represent the assigned percentages.
One of the difficulties in modeling wind and seismic loads is that as the design process progresses, changes that affect the story masses or the frame stiffness can have an impact on the magnitude of the lateral loads. It requires that the loads be recalculated and reapplied. This is tedious and time-consuming for the engineer if these loads are not automatically determined and applied by the analysis software.
In the next and final article on diaphragms, Diaphragms: Conclusions and Recommendations, I will wrap it all up and give some parting recommendations.
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