significant high-frequency input energy, can have response levels that are significantly less then would be predicted by conventional elastic or equivalent static analysis procedures. The
presence of even limited ductile energy absorbing capacity in component attachments, such as a weld, can lead to substantial reductions in response due to non-linear behavior. As an example, consider a small fillet weld with a yield displacement on the order of 0.001 inch (0.0254 mm) and the displacement at weld failure being 0.01 inch (0.254 mm). A 0.4g response at 25 Hz will require a displacement of 0.0063 inch (0.159 mm) while a 0.4g response at 5 Hz will involve a displacement of 0.157 inch (3.99 mm). The 20 Hz response level is within the ductile range of the weld while the 5 Hz response level has failed the weld. This example illustrates the so-called brittle behavior of welded anchorage associated with low frequency response while the high frequency response of the same anchorage is achieving ductile behavior. In Reference B7 the effects of ductility on high frequency response has been explored in great detail.
In order to develop a procedure for a reducing a floor spectrum for high frequency ductility effects, Reference B7 considered a squat item of equipment that is controlled by weld anchorage capacity subjected to a pure base shear as the limiting case. It was concluded in Reference B7 that it is conservative to use only a single-degree-of-freedom model to obtain response spectrum reduction factors. In terms of physical description, this conservative model corresponds to an electrical cabinet that is anchored at its base by a minimum 3/16-inch (4.8 mm) fillet weld loaded in the transverse direction. The equivalent length of the weld is taken to be 1 inch (25.4 mm) with a yield displacement of 0.001 inch (0.0254 mm) and ultimate displacement of 0.01 inch (0.254 mm) based on published test data. For this limiting example it was also conservatively
Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
assumed that there is no nonlinear response in the cabinet structure, in the connections mounting the electrical devices to the cabinet structure, or in the devices themselves. This case was denoted as the simplified sliding model in Reference B7 for which a seven-step iterative procedure was developed to obtain a reduced spectral ordinate at a given frequency. The procedure developed in Reference B7, reduces the ground spectrum rather than directly reduce an individual floor spectrum for ductility effects. This reduced level of input motion does not represent an actual reduced ground motion but is rather a pseudo ground motion or Damage Consistent Motion which yields the ductility reduced floor motion when the reduced input is applied to the elastic building analysis model. The amplification of the building is included in the sliding model procedure by requiring a larger input scale factor, , to be applied to the pseudo ground motion input level. The reason for utilizing this computational artifice is to allow the estimation of ductility reduced floor spectra using the elastic structure analysis model and direct spectra estimation methods. As a result, the scaling procedure developed for incoherence reduction of ground motion may also be used for estimation of high frequency ductility reduced floor spectra.
FSM
The sliding model procedure of Reference B7 was applied with the following basic guidance:
(a) the reduction is performed for frequencies 10 Hz and above; (b) the reduced pseudo ground response spectrum should be connected to the elastic spectrum at 8 Hz; (c) a spectral ordinate should not be reduced below a value equal to the peak spectral value at 10% damping divided by 1.6 or below the response level associated with just obtaining the yield displacement; and (d) for SMA evaluations the factor of safety for equipment mounted within a building should be taken as F = 3.0. The focus is on a spectrum reduction associated with a HCLPF capacity level rather than a median capacity level. The initial input ground motion applied to the base of the simplified sliding model is the incoherence reduced ground motion, since effects of foundation incoherence result in a reduction in actual motion input both to the structure and the equipment mounted therein.
SM
The reduction procedure detailed in Reference B7 was incorporated into an interactive spreadsheet that implemented the iterative procedure for the building. The combined
incoherence and high-frequency ductility-reduced pseudo-ground-motion was then obtained as a product of the UHS acceleration and building reduction function for the value of modal damping used in the corresponding building analysis.
( )
f ξ = R F ×SA( )
f ξSA g
µ
HFG , ( s ) , Equation B-15
Figures B-9 and B-10 provide a comparison of the results of both the horizontal and vertical high frequency ductility pseudo ground motion or damage consistent reduction with the unreduced ground spectra and the incoherence reduced ground spectra for Building E.
Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
Building E - Horizontal Ground Motion Spectra
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4
0 5 10 15 20 25 30 35 40 45 50
Frequency, Hz
SA, Hz
SAh SAh * Rs SAh*Rs/Fu
E-5 Input Motion
Incoherency Reduced Motion Damage Consistent Motion 4.5% Damping
Figure B-9
Reduced Horizontal Ground Motion Spectra for Building E
Building E - Vertical Ground Motion Spectra
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
0 5 10 15 20 25 30 35 40 45 50
Frequency, Hz
SA, g
SAv SAv * Rs SAv*Rs/Fu
E-5 Input Motion Incoherency Reduced Motion Damage Consistent Motion 4.5% Damping
Figure B-10
Reduced Vertical Ground Motion Spectra for Building E
Development of In-Structure Response Spectra for Seismic Margin or Seismic PRA Evaluation by Scaling
B.5 Estimation of Floor Spectra Compatible with High Frequency Ductility