Muto and Krishnan studied the performance of three steel moment frame building models in an Mw7.8 ShakeOut scenario earthquake on the San Andreas Fault [48, 57].
Base Line Model
Gravity loads are calculated using the full dead load and 30% live soil load. The same yield strength is assumed for horizontal springs and half the downward yield strength is assumed in the upward direction.
Retrofit Schemes
The vertical scale is the base displacement of the building normalized by the seismic design weight of the baseline model WBLM. These curves suggest that estimation of the global ductility of building models based on push-over curves can be misleading.
Design Criteria for Brace Retrofit Schemes
The SRSS spectra for the set of seven ground motion records and corresponding scaling factors are shown in Figure 2.9. The unscaled error-normal component ground accelerations, velocities, and displacements of the recorded ground motions used in the design are shown in Figures 2.10 and 2.11.
Finite Element Modeling in STEEL
In Section 3.4 we demonstrate the program's ability to model the cyclic loading of buckling restrained beam elements. A segment is used for the remainder of the element and given a larger area. The shear strain in the panel area is the difference between the end rotation of the beams and the end rotation of the connected columns.
The shear stiffness of the plate zone is given by the product of the volume of the plate zone and the shear modulus of the steel, G. The yield moment is given by the product of the volume of the plate area and the shear strength of the steel, τy = √σy. The dimensions and material properties of the zonal elements of the panels are taken from the connecting elements.
In the absence of columns (e.g., where braces abut beams in a chevron bracing configuration), material properties are taken from the beam, the depth and height of the panel zone are taken as the beam depth, and the thickness is taken as the beam web thickness.
Modeling of Connections
At the start of an analysis, the program runs over all segments of all elements and randomly draws from the pool of fracture strain values and assigns the signed values to all fibers of the same category in that segment. For pre-Northridge beam-to-column connections, distribution D1 is applied to beam top flange fibers (fibers 1 to 4) and distribution D2 is applied to beam bottom flange fibers (fibers 5 to 8) of the segment closest to the column face. For column base plate fractures, distribution D1 is applied to all fibers of the lower segment of all basement columns.
For column splices, distribution D1 is applied to all fibers in the fourth segment (from the bottom) of all columns at every second floor or as shown in Figure 2.3. The assumption is that the lateral displacement of the story would be sufficient to bring the web and flange plates out of alignment and therefore the bearing capacity would be dramatically reduced. However, if all fibers in a beam-to-column connection are broken, the shear transfer capacity is assumed to be retained.
If all fibers of a segment rupture, it is assumed that the element containing the segment is then unable to carry any load.
Modeling of Conventional Brace Elements
In this study, hollow square structural sections (HSS) or square tubes were used in the retrofit schemes. Two of the square tube sections were filled with grout intended to delay local buckling, and another specimen was reinforced mid-span and these are excluded. Three of the five specimens modeled were HSS4x4x1/4 square tube sections with detail ratios of 81 and two were HSS4x4x3/8 square tube sections with detail ratios of 84.
Axial loads are applied at small eccentricities adjusted to realize the same buckling loads as observed in experiments (except for specimen HSS1-2, which was first loaded and yielded in tension, for which a buckling load of 110 kips was modeled, compared to a measured bending load of 119 kips). Note that although local buckling is not modeled in STEEL, the models deteriorate at similar points to the samples in Fell et al. In the building analyses, axial loads are applied to conventional load-bearing members at an eccentricity of 4.3 mm (0.17 in).
Two material coupons were sampled from the corners of the cross-section, and two material models were sampled from the center of the walls of the cross-section.
Modeling of Buckling-Restrained Brace Elements
The steel core of specimen 3G cracked during the experiment and this is not captured in the modelling. The insert plate was thickened around the pin hole, but there was still plastic expansion of the pin hole. The axial strains of the strut specimens and the axial strains above the insert plates to which the strut specimens were connected were measured and the maximum displacements of each load cycle were reported.
In the current study, modeling of bolt slip or pin hole extension is neglected, and therefore the axial force versus deformation responses of the brace are of most interest. The ultimate strength, σu, of the material models used in STEEL takes into account the excess strength in compression, as described previously. In this study, we use simulated ground motions from three hypothetical earthquake scenarios causing strong shaking in the Los Angeles metropolitan area: motions from a simulated Mw7.9 1857-like San Andreas earthquake produced by Krishnan et al.
In the simulated earthquake scenarios, both the NW and NW orientation of planar building models are taken into account.
M w 7.9 1857-Like San Andreas Fault Earthquake
In this ground motion simulation, a variant of the classical Empirical Green's Function (EGF) method presented by Mourhatch and Krishnan [56] is applied to each of the 636 sites to produce high-frequency ground motion waveforms ( 0.5 - 5 Hz). . Amplification due to site-specific geology is not considered in the low-frequency part of the simulations. As for the high frequency part (0 - 5 Hz) of the simulations, the generated ground motion time histories are essentially constructed from real ground motions recorded at the ground surface at locations close enough to the target site and contain amplifications possible due to the specific geology of the country.
A map of the greater Los Angeles metropolitan area is presented in Figure 4.1, showing the locations of the 636 sites where ground motion time histories are generated and the building models analyzed. The relationship between the study area and the 290 km hypothetical fault of the San Andreas fault is shown in the inset. The red line in the inset shows the surface trace of the hypothetical 290 km rupture of the San Andreas fault.
In the inset, the extent of the greater Los Angeles metropolitan region, which is the geographic focus of this study, is indicated by a blue rectangle.
M w 7.8 ShakeOut Scenario Earthquake on San Andreas Fault
Black triangles represent the locations where ground motion time histories are generated and the building models are analyzed. The red line in the inset shows the surface trace of the hypothetical 305 km rupture on the San Andreas fault.
M w 7.2 Puente Hills Earthquake
Maps of peak ground acceleration (PGA), peak ground speeds (PGV) and peak ground displacements (PGD) realized in the earthquake scenario are shown for EW and NS directions in Figure 4.10. Time histories of ground acceleration, velocity, and displacement for four locations near downtown Los Angeles, Pasadena, Santa Monica, and Long Beach are shown in Figures 4.11 and 4.12. Black triangles represent locations where ground motion time histories are generated and the building models are analyzed.
The top rectangle represents the Los Angeles segment, and the bottom rectangle represents the Santa Fe and Coyote Hills segments.
Recorded Real Strong Ground Motions
Inter-story drift ratio refers to the ratio of relative horizontal displacement of two adjacent floors and the height of the story defined by the two floors. Building overall drift ratio refers to the ratio of the horizontal roof displacement relative to the horizontal displacement at ground level and the height of the building above the ground. The concrete walls at the basement level are stiff compared to the upper structure and the foundation springs.
The immediate occupancy capacity category is defined in FEMA 356 [17] as the capacity of a building where residual movement is negligible and the structure retains its original strength and stiffness. In some cases, the data are not well represented by a cumulative log-normal distribution function, and instead the calculated proportions of simulations that exceeded that particular performance category are plotted, with the data points aligned to the mean speed of each bin. The results of incremental dynamic analyzes using recorded ground motions due to actual earthquakes (Section 5.4) are presented in two types of graphs: bar charts summarizing the number of simulations for each building model that resulted in "repairable", "irrepairable", and "collapse" performance categories; and in table images showing the simulated performance categories for each of the ground motion records and the range of ground motion scaling factors used.
Section 5.5 compiles the data from all three simulated scenario earthquakes, and from the incremental dynamic analyzes using recorded ground motions from actual earthquakes, and the number of simulations that resulted in “repairable”, “irreparable” and “collapse” events. performance. - egos for each building model are summarized in bar charts.
Building Performance: M w 7.9 1857-Like San Andreas Fault Earth- quake
Building Performance: M w 7.2 Puente Hills Scenario Earthquake
Building Performance: Recorded Real Strong Ground Motions
As mentioned in the previous sections, it appears that span frames using buckling-restrained braces tend to have larger residual drifts. As before, the two retrofit schemes that implement bracing elements in the lower half of the building model while leaving the upper half unchanged (schemes RBR-3 and RBRB-3) are somewhat successful in that the schemes are more effective in reducing deformations in the lower half of the building model, compared to the moment-frame half-height retrofit schemes (RMF-1h, RMF-2h, and RMF-3h), thereby reducing to a greater extent global P-delta tilting moments. However, as mentioned in the previous sections, the resulting structures are stiffer than the moment frame configurations and consequently attract larger seismic forces, often leading to excessive drift in the upper half.
A retrofit scheme that implements bracing elements in the lower half of the building model in conjunction with improved beam-column moment connections in the upper half can present some additional improvements in building performance while keeping the architectural impact low. When the "rigid" foundation model was used, the foundation reactions were in the elastic range for all building models. When the "expected" foundation model was used, the foundation reactions were in the elastic range for all but four building models.
In the "soft" foundation model, the capacities of the foundation springs were often exceeded in all construction models.
