Rhythmic Excitation of Monumental Stairs in RAM Elements

Question

Any advice for the determining the rhythmic excitation of monumental stairs? I have a cantilevered stair that I'm worried about. I have a copy of Davis & Murray's 2009 "Slender Monumental Stair Vibration Serviceability" paper which recommends a natural frequency greater than 10hz. 
 
 My initial thought was to call the landing a rigid diaphragm and assign the mass of the floor to one node. This is not accurate, however, because it ignores any mass contribution from the treads and risers. The next option would be to assign mass to each node at a tread/stringer intersection as well as at the nodes defining the landing. If i take this approach should I remove all rigid diaphragm constraints? I was not planning on modelling any slabs, or the treads/risers, but if that would better determine the frequency I certainly could.

Next, what is the forcing function used to determine the dynamic response? Should I be entering data in the response spectrum input tab? If I don' t, what is being used? Or should I be using the "earthquake acceleration" tab to be entering info? I know SRSS doesn't use damping and CQC does, is there an advantage to one over the other? 
 
 Finally, when I'm running under my assumptions ( mass at all nodes, no data entered for response spectrum or acceleration) I'm getting very large nodal displacements (i.e. 9") Could this truly be correct? Gravity vertical displacements at the maximum point of radius are about .25". I'm also getting a fundamental frequency of 6.67hz which seems to be in range for the current sizes chosen. 
 
 Thanks for any and all guidance on this topic.

Seth Guthrie · Accepted Answer

If no scale factor or acceleration is given then there is no forcing function at all. (I thought that was required in Ram Elements to even get frequency results, but it must have been changed.) 
From the first post I assumed you were looking at displacements from the rsp analysis which do require the scale factor, direction and acceleration. 
Modal displacements are another matter. Magnitude of modal displacements are irrelevant because they are normalized. Only the relative magnitude of one node compared to another matters. This effectively defines the mode shape. In one of our other programs we have a note that clarifies: 
"Mode shapes are normalized with respect to building mass matrix: Qi^T x M x Qi = 1 where Qi: ith mode shape and M is the mass matrix"

Seth Guthrie · Answer

The response spectrum (acceleration and time data) is irrelevant if you only want the natural frequencies, but in Ram Elements something must be entered for the dynamic analysis to run. Depending on what you enter for the rsp, the scale factor and the direction, that's all going to impact deflections for that load case, but again, it does not matter if you are only after the frequencies.
As to the mass distribution, that's really up to you. If you are going to lump the masses to a point and use a diaphragm, then it's important to enter the mass moment of inertia (rotation about Y mass in Elements) as well. If you spread the masses to various nodes and forego the diaphragm, then MMI is less important.
Modeling the treads would not impact behavior if they are all parallel and pinned, but if they are modeled with fixed ends, they would alter the stiffness significantly.