The curves are linear up to a yielding or fracture point of the building model. Beyond those points, the building models either show some strain hardening that is followed by strength degrad- ing behavior, or directly show a strength degrading behavior. Some curves show a drop to zero base shear and are indicative of failure mechanisms that include the first few stories. Other curves show a more moderate drop in base shear and are indicative of failure mechanisms higher up in the building models. These curves suggest that estimating the global ductility of the building models based on push-over curves can be misleading. Since the push-over analyses are performed dynami- cally, stiffness changes that result from yielding of structural elements and, especially, fracturing of connections cause vibrations. The resulting vibrational oscillations are apparent in the figures.
RBR−1 RBR−2 RBR−3 RBRB−1 RBRB−2 RBRB−3
RMF−1h RMF−1 RMF−2h RMF−2 RMF−3h RMF−3
T = 2.44 s1 T = 2.37 s1 T = 2.78 s1 T = 2.52 s1 T = 2.49 s1 T = 2.79 s1 T = 3.31 s
T = 3.31 s1 1 T = 3.31 s1 T = 3.31 s1 T = 3.31 s1 T = 3.31 s1
Figure 2.4:A schematic overview of the retrofit schemes considered in this study and associated first mode natural periods. RMF refers to retrofit schemes that consist of upgrading the brittle moment- resisting beam-to-column connections, RBR refers to retrofit schemes that employ conventional brace elements, and RBRB refers to retrofit schemes that employ buckling-restrained brace ele- ments. Black triangles indicate pre-Northridge beam-to-column moment resisting connections.
Upgraded connections are indicated by enlarged triangles in red and the affected beams are indi- cated by thick red lines. Added conventional and buckling-restrained braces are shown in red as well.
0 0.02 0.04 0.06 0.08 0.1 0
0.05 0.1 0.15 0.2
Overall Drift Ratio Base Shear ( fraction of W BLM )
Building Model: RMF−1h
0 0.02 0.04 0.06 0.08 0.1
0 0.05 0.1 0.15 0.2
Overall Drift Ratio Base Shear ( fraction of W BLM )
Building Model: RMF−1
0 0.02 0.04 0.06 0.08 0.1
0 0.05 0.1 0.15 0.2
Overall Drift Ratio Base Shear ( fraction of W BLM )
Building Model: RMF−2h
0 0.02 0.04 0.06 0.08 0.1
0 0.05 0.1 0.15 0.2
Overall Drift Ratio Base Shear ( fraction of W BLM )
Building Model: RMF−2
0 0.02 0.04 0.06 0.08 0.1
0 0.05 0.1 0.15 0.2
Overall Drift Ratio Base Shear ( fraction of W BLM )
Building Model: RMF−3h
0 0.02 0.04 0.06 0.08 0.1
0 0.05 0.1 0.15 0.2
Overall Drift Ratio Base Shear ( fraction of W BLM )
Building Model: RMF−3
Figure 2.5:Push-over curves for the retrofit schemes that consider upgrading the brittle beam-to-column moment resisting connections (black curves), and for the base line model (gray curves). Three curves are shown for each building model that result from three runs that use different realiza- tions of the strengths of the beam-to-column moment resisting connections, column splices, and column base plates.
0 0.02 0.04 0.06 0.08 0.1 0
0.05 0.1 0.15 0.2
Overall Drift Ratio Base Shear ( fraction of W BLM )
Building Model: RBR−1
0 0.02 0.04 0.06 0.08 0.1
0 0.05 0.1 0.15 0.2
Overall Drift Ratio Base Shear ( fraction of W BLM )
Building Model: RBRB−1
0 0.02 0.04 0.06 0.08 0.1
0 0.05 0.1 0.15 0.2
Overall Drift Ratio Base Shear ( fraction of W BLM )
Building Model: RBR−2
0 0.02 0.04 0.06 0.08 0.1
0 0.05 0.1 0.15 0.2
Overall Drift Ratio Base Shear ( fraction of W BLM )
Building Model: RBRB−2
0 0.02 0.04 0.06 0.08 0.1
0 0.05 0.1 0.15 0.2
Overall Drift Ratio Base Shear ( fraction of W BLM )
Building Model: RBR−3
0 0.02 0.04 0.06 0.08 0.1
0 0.05 0.1 0.15 0.2
Overall Drift Ratio Base Shear ( fraction of W BLM )
Building Model: RBRB−3
Figure 2.6:Push-over curves for the retrofit schemes that consider implementing either conventional or buckling-restrained brace elements (black curves), and for the base line model (gray curves).
Three curves are shown for each building model that result from three runs that use different re- alizations of the strengths of the beam-to-column moment resisting connections, column splices, and column base plates.
−119˚ −118.75˚ −118.5˚ −118.25˚ −118˚ −117.75˚
33.75˚
34˚
34.25˚
1.4 1.4
1.6 1.6
1.6 1.6
1.6
1.8 1.8
1.8 1.8
1.8 1.8
2 2
2
2 2.2
2.2 2.2
2.2 2.2
2.4
2.4
−119˚ −118.75˚ −118.5˚ −118.25˚ −118˚ −117.75˚
33.75˚
34˚
34.25˚
−119˚ −118.75˚ −118.5˚ −118.25˚ −118˚ −117.75˚
33.75˚
34˚
34.25˚
Alhambra
Anaheim Azusa Baldwin Park Beverly Hills
Brea Burbank
Canoga Park Chatsworth
Compton
Diamond Bar Downey
El Segundo Encino
Fullerton Hollywood
Huntington Beach Inglewood
Irvine La Canada
La Puente
Long Beach Los Angeles Malibu
Monrovia
Montebello North Hollywood
Northridge
Norwalk Pasadena
Point Dume
San Fernando
Santa Ana Santa Monica
Seal Beach Simi Valley
Sunland Thousand Oaks
Torrance
Whittier
1.4 1.6 1.8 2.0 2.2 2.4 2.6
−−−−−− SXS used for design = 2.09 g SXS [ g ]
(a)
1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6
0 5 10 15 20
E[X]+STD = 2.09
SXS
Spectral Acceleration [g]
Number of Samples
(b)
Figure 2.7:(a) Map for the short-period (0.2 sec) spectral response acceleration parameter,SXS, in the region of interest. The locations whereSXSis sampled are shown as white triangles. (b) Histogram of theSXSsamples overlaid with a log normal PDF fit to the data set. For design purposes,SXSis taken to be the expected value plus one standard deviation (STD) of the log normal PDF (black dashed line).
−119˚ −118.75˚ −118.5˚ −118.25˚ −118˚ −117.75˚
33.75˚
34˚
34.25˚
0.8 0.8
0.8
0.8 0.8
0.9 0.9
0.9
0.9
0.9
0.9
1 1
1
1
1
1 1
1.1 1.1
1.1 1.1
1.2
1.2
1.2
1.3
−119˚ −118.75˚ −118.5˚ −118.25˚ −118˚ −117.75˚
33.75˚
34˚
34.25˚
−119˚ −118.75˚ −118.5˚ −118.25˚ −118˚ −117.75˚
33.75˚
34˚
34.25˚
Alhambra
Anaheim Azusa Baldwin Park Beverly Hills
Brea Burbank
Canoga Park Chatsworth
Compton
Diamond Bar Downey
El Segundo Encino
Fullerton Hollywood
Huntington Beach Inglewood
Irvine La Canada
La Puente
Long Beach Los Angeles Malibu
Monrovia
Montebello North Hollywood
Northridge
Norwalk Pasadena
Point Dume
San Fernando
Santa Ana Santa Monica
Seal Beach Simi Valley
Sunland Thousand Oaks
Torrance
Whittier
0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4
−−−−−− SX1 used for design = 1.07 g SX1 [ g ]
(a)
0.4 0.6 0.8 1 1.2 1.4
0 5 10 15 20
E[X]+STD = 1.07
SX1
Spectral Acceleration [g]
Number of Samples
(b)
Figure 2.8:(a) Map for the long-period (1 sec) spectral response acceleration parameter,SX1, in the region of interest. The locations whereSX1is sampled are shown as white triangles. (b) Histogram of theSX1samples overlaid with a log normal PDF fit to the data set. For design purposes,SX1is taken to be the expected value plus one standard deviation (STD) of the log normal PDF (black dashed line).
ground motion database user-interface [62], and seven records and corresponding scaling factors that give a close fit to the design spectrum are selected from the database. For each record, a square root of the sum of the squares (SRSS) 5%-damped response spectra is constructed from the scaled horizontal components. The records are then uniformly re-scaled such that the average of the seven SRSS response spectra does not fall below 1.3 times the design response spectrum for
periods from 0.2T to 1.5T (where T is the fundamental period of the building model), as prescribed inASCESeismic Rehabilitation of Existing Buildings [4]. The BSE-1 design spectrum is the BSE- 2 spectrum scaled down by a factor of 2/3. As a consequence, in this study the same set of seven records is used for the BSE-1 earthquake hazard level with the scaling factors reduced by 2/3. The building model is then subjected to the scaled fault normal component of the ground motion records, which is usually the dominant component. The braces added to frame A and cover plates added to strengthen the columns are sized to achieve a target peak transient inter-story drift ratio of 1.5%and 2.0%for the BSE-1 and BSE-2 seismic hazard levels, respectively, and such that the average peak element responses in the seven records is less than the limits required to achieve the Basic Safety Objective (BSO) for the two seismic hazard levels. The element deformation limits are summarized in Table 2.3. The “expected” realization of the foundation interactions is used for the design, but the sensitivity of the solution is also checked using the “soft” and “stiff” realization. The two partial brace retrofit schemes (RBR-3 and RBRB-3) are designed such that the lower braced portions of the buildings conform to the BSO design criteria, but large beam rotations and beam-to-column connection fractures are expected in the upper portions.
In the design phase, fracture susceptibility of pre-Northridge connections, column base plates, and column splices are modeled assuming fiber fracture strains equal to the geometric means of the probability functions described in Section 3.2, or as 3.5 times the yield strain for beam bottom flange fibers and 8.0 times the yield strain for beam top flange fibers, and all column fibers of column base plates and column splices. This is comparable to suggested modeling inASCERehabilitation of Existing Buildings [4] and FEMA State of the Art Report on Connection Performance [20].
Contributions of floor live loads to the seismic mass are omitted from the design process. The weight of added structural members and column cover plates are calculated and added to the dead loads. As designs are only carried out in the narrow dimension of the building, the weight of the retrofit elements in the long dimension cannot be calculated. Instead, the added weight in the long dimension is assumed to be the same as that calculated for the narrow dimension, and is added to the dead load applied on the exterior columns of the lumped frames B and C. Analyses are performed twice for different gravity loads, once for gravity loads taken as 1.1 times the sum of the dead loads and 30%of the floor live loads, and again for gravity loads taken as 0.9 times the dead loads only.
Because the six brace retrofit schemes have comparable first mode periods, the same set of seven ground motion records are used in their design, and for all six schemes, the same scaling factors are needed to satisfy the ground motion scaling criteria prescribed inASCERehabilitation of Existing
Table 2.3:Summary of design deformation limits for the Life Safety (LS) and Collapse Prevention (CP) performance levels [4].
Component/Action CP CP
Beams/Flexurea
a. 2tbf
f ≤ √52
Fye
andth
w ≤ √418
Fye 6θy 8θy
b.2tbf
f ≥ √65
Fye and th
w ≥ √640
Fye 2θy 3θy
c. Other Linear interpolation between the values on lines a and b for both flange slenderness
(first term) and web slenderness (second term) shall be performed, and the lower resulting value shall be used.
Column/Flexureb
ForP/PCL≤0.2
a. 2tbf
f ≤ √52
Fye
andth
w ≤ √300
Fye 6θy 8θy
b.2tbf
f ≥ √65
Fye and th
w ≥ √460
Fye 2θy 3θy
c. Other Linear interpolation between the values on lines a and b for both flange slenderness
(first term) and web slenderness (second term) shall be performed, and the lower resulting value shall be used.
For0.2≤P/PCL≤0.5
a. 2tbf
f ≤ √52
Fye
andth
w ≤ √260
Fye 8(1−53PP
CL)θy 11(1−53PP
CL)θy
b.2tbf
f ≥ √65
Fye
and th
w ≥ √400
Fye
0.5θy 0.8θy
c. Other Linear interpolation between the values on lines a and b for both flange slenderness
(first term) and web slenderness (second term) shall be performed, and the lower resulting value shall be used.
ForP/PCL≥0.5 No yielding is allowed
Column Panel Zonesc 8θy 11θy
HSS Braces/Compressiond
a. SlenderKlr ≥4.2q
E
Fye 5∆c 7∆c
b. Stockye Klr ≤2.1q
E
Fye 4∆c 6∆c
c. Other Linear interpolation between the values for slender and stock braces (after application
of all applicable modifiers) shall be used.
Braces/Tensionf 7∆T 9∆T
Pre-Northridge Connectionsg 0.0337-0.00086d 0.0284-0.00040d
Buckling-Restrained Braces Modeled strains in the yielding core need to be less than the maximum strains that
have been previously been demonstrated in experiments.
aBeams:θy= ZF6EIyelb
b
bColumns:θy= ZF6EIyelc
c
1−PP
ye
; PCLis the “lower-bound” critical axial loading.
cPanel Zones:θy= τGy
d∆cis the axial deformation at expected buckling load.
eSection compactness: Where the brace section is noncompact according to Table B5.1 ofAISCLRFD Specifications
[1], the acceptance criteria shall be multiplied by 0.5. For intermediate compactness conditions, the acceptance criteria shall be multiplied by a value determined by linear interpolation between the seismically compact and the noncompact cases.
f ∆Tis the axial deformation at expected tensile yielding load.
gdis the beam depth.
*bf - width of beam/column flange; tf - thickness of beam/column flange; h - height of beam/column web; tw -
thickness of beam/column web; Fye - expected yield strength; Klr - slenderness ratio; l - length of beam/column
memeber; I - moment of inertia; E - Young’s modulus;τy- shear yield strength; G - shear modulus; P - member axial
load; Py- axial load at yield.
Buildings [4]. The SRSS spectras of the set of seven ground motion records and corresponding scaling factors are shown in Figure 2.9. The unscaled fault-normal component ground accelera- tions, velocities, and displacements of the recorded ground motions used in the design are shown in Figures 2.10 and 2.11. The seismic design weights, the design first mode periods, the average peak base shears from the nonlinear analyses under the BSE-1 and BSE-2 earthquake hazard levels (VBSE−1and VBSE−2, respectively), the average peak inter-story drift ratios from the nonlinear anal- yses under the BSE-1 and BSE-2 earthquake hazard levels (IDRBSE−1and IDRBSE−2, respectively), and the designed brace sizes are presented in Table 2.4. Elevation views of frames A of the retrofit schemes showing the brace cross-sections and the locations and thicknesses of added column cover plates are shown in Figures 2.12, 2.13 and 2.14.
Figure 2.9:Response spectra of the seven ground motion records selected for retrofit schemes RBR-1, RBR- 2, RBRB-1, and RBRB-2, scaled accordingly to fit to the BSE-2 seismic hazard level.
−1.0 0.0 1.0
Northridge, Newhall Fire Station Fault Normal Component
Acc. (g)
−1.0 0.0 1.0
Vel. (m/s)
0 5 10 15 20 25 30 35
−1.0 0.0 1.0
Dsp. (m)
Time (sec)
−1.0 0.0 1.0
Northridge, Rinaldi Fault Normal Component
Acc. (g)
−1.0 0.0 1.0
Vel. (m/s)
0 5 10 15
−1.0 0.0 1.0
Dsp. (m)
Time (sec)
−1.0 0.0 1.0
Gazli, Karakyr Fault Normal Component
Acc. (g)
−1.0 0.0 1.0
Vel. (m/s)
0 5 10 15
−1.0 0.0 1.0
Dsp. (m)
Time (sec)
−1.0 0.0 1.0
Tabas, Tabas Fault Normal Component
Acc. (g)
−1.0 0.0 1.0
Vel. (m/s)
0 5 10 15 20 25 30
−1.0 0.0 1.0
Dsp. (m)
Time (sec)
Figure 2.10:Recorded ground motion accelerations, velocities, and displacements (fault-normal component) used in the seismic design of retrofit schemes.
−1.0 0.0 1.0
Duzce, Bolu Fault Normal Component
Acc. (g)
−1.0 0.0 1.0
Vel. (m/s)
0 5 10 15 20 25 30 35 40 45 50 55
−1.0 0.0 1.0
Dsp. (m)
Time (sec)
−1.0 0.0 1.0
Duzce, Ducze Fault Normal Component
Acc. (g)
−1.0 0.0 1.0
Vel. (m/s)
0 5 10 15 20 25
−1.0 0.0 1.0
Dsp. (m)
Time (sec)
−1.0 0.0 1.0
Northridge, Jensen Filter Plant Generator Fault Normal Component
Acc. (g)
−1.0 0.0 1.0
Vel. (m/s)
0 5 10 15 20 25
−1.0 0.0 1.0
Dsp. (m)
Time (sec)
Figure 2.11:Recorded ground motion accelerations, velocities, and displacements (fault-normal component) used in the seismic design of retrofit schemes (continued).
Table2.4:Designoverviewofthebracedretrofitschemes. RBR-1RBR-2RBR-3RBRB-1RBRB-2RBRB-3 W=32,247.1kNW=32,282.0kNW=31,832.5kNW=32,493.2kNW=32,516.5kNW=32,050.7kN T1(design)=2.36secT1(design)=2.29secT1(design)=2.68secT1(design)=2.43secT1(design)=2.41secT1(design)=2.70sec VBSE−1=8,511.4kNVBSE−1=8,619.1kNVBSE−1=6,321.8kNVBSE−1=7,301.6kNVBSE−1=7,350.7kNVBSE−1=6,064.0kN VBSE−2=9,652.0kNVBSE−2=9,821.8kNVBSE−2=7,664.3kNVBSE−2=8,493.3kNVBSE−2=8,424.5kNVBSE−2=7,234.9kN IDRBSE−1=0.88%IDRBSE−1=0.99%IDRBSE−1=0.70%*IDRBSE−1=1.13%IDRBSE−1=1.09%IDRBSE−1=0.80%* IDRBSE−2=1.91%IDRBSE−2=2.05%IDRBSE−2=1.46%*IDRBSE−2=1.92%IDRBSE−2=1.99%IDRBSE−2=1.77%* StoryNo.of Braces
Brace No.of Braces Brace No.of Braces Brace No.of Braces Yielding No.of Braces Yielding No.of Braces
Yielding Cross-Cross-Cross-CoreArea,CoreArea,CoreArea, SectionSectionSectionAsc(cm2)Asc(cm2)Asc(cm2) 202HSS5x5x1/42HSS5x5x1/40-29.729.70- 192HSS5x5x1/42HSS5x5x1/40-29.729.70- 182HSS5x5x1/42HSS5x5x1/40-29.729.70- 172HSS5x5x1/42HSS5x5x1/40-29.729.70- 162HSS6x6x3/82HSS6x6x3/80-222.6222.60- 152HSS6x6x3/82HSS6x6x3/80-222.6222.60- 142HSS6x6x3/82HSS6x6x3/80-232.3232.30- 132HSS6x6x3/82HSS6x6x3/80-232.3232.30- 122HSS7x7x3/86HSS5x5x1/40-238.7612.90- 112HSS7x7x3/86HSS5x5x1/40-238.7612.90- 102HSS7x7x3/86HSS5x5x1/44HSS5x5x1/4248.4616.1419.4 92HSS7x7x3/86HSS5x5x1/44HSS5x5x1/4248.4616.1419.4 86HSS5x5x3/86HSS5x5x3/84HSS5x5x1/4619.4619.4422.6 76HSS5x5x3/86HSS5x5x3/84HSS5x5x1/4619.4619.4422.6 66HSS5x5x3/86HSS5x5x3/84HSS5x5x1/4622.6622.6422.6 56HSS5x5x3/86HSS5x5x3/84HSS5x5x1/4622.6622.6422.6 46HSS5x5x1/26HSS5x5x1/24HSS5x5x3/8629.0629.0429.0 36HSS5x5x1/26HSS5x5x1/24HSS5x5x3/8629.0629.0429.0 26HSS5x5x1/26HSS5x5x1/24HSS5x5x3/8629.0629.0429.0 16HSS8x8x1/26HSS8x8x1/24HSS8x8x1/2641.9641.9441.9 *Averagepeakinter-storydriftratiosfromthenonlinearanalysesundertheBSE-1andBSE-2earthquakehazardlevelsinthelowerbracedportionofthebuilding models.Thecorrespondinginter-storydriftratiosfortheupperun-retrofittedportionofthebuildingmodelsresultedas3.00%and4.51%,respectively,forthe RBR-3retrofitscheme,and2.73%and3.76%,respectively,fortheRBRB-3retrofitscheme.
Level 19F El. 70.1 m (230’−6’’) Foundation
25.4 mm
cp
cp
41.9 cm2 29.0 cm 29.0 cm
25.4 mm
31.8 mm
31.8 mm
31.8 mm
31.8 mm 31.8 mm
31.8 mm 25.4 mm 34.9 mm
31.8 mm
31.8 mm
31.8 mm
31.8 mm 31.8 mm
31.8 mm 34.9 mm 3
1 2 4
Level Basement El. −5.5 m (−18’−0’’) 5.5 m (18’−0’’)
5.5 m (18’−0’’) Level 2F El. 5.5 m (18’−0’’) Level 3F El. 9.3 m (30’−6’’) 3.8 m (12’−6’’) Level 4F El. 13.1 m (43’−0’’) 3.8 m (12’−6’’) Level 5F El. 16.9 m (55’−6’’) 3.8 m (12’−6’’) Level 6F El. 20.7 m (68’−0’’) 3.8 m (12’−6’’) Level 7F El. 24.5 m (80’−6’’) 3.8 m (12’−6’’) Level 8F El. 28.3 m (93’−0’’) 3.8 m (12’−6’’)
Level 9F El. 32.1 m (105’−6’’) 3.8 m (12’−6’’)
Level 10F El. 35.9 m (118’−0’’) 3.8 m (12’−6’’)
Level 11F El. 39.7 m (130’−6’’) 3.8 m (12’−6’’)
Level 12F El. 43.5 m (143’−0’’) 3.8 m (12’−6’’)
Level 13F El. 47.3 m (155’−6’’) 3.8 m (12’−6’’)
Level 14F El. 51.1 m (168’−0’’) 3.8 m (12’−6’’)
Level 15F El. 54.9 m (180’−6’’) 3.8 m (12’−6’’)
Level 16F El. 58.7 m (193’−0’’) 3.8 m (12’−6’’)
Level 17F El. 62.5 m (205’−6’’) 3.8 m (12’−6’’)
Level 18F El. 66.3 m (218’−0’’) 3.8 m (12’−6’’)
3.8 m (12’−6’’)
Level 20F El. 73.9 m (243’−0’’) 3.8 m (12’−6’’)
Level Roof El. 77.7 m (255’−6’’)
Level Ground El. 0.0 m (0’−0’’) Simple Connection Moment Connection Column Splices Basement Wall
3.8 m (12’−6’’) RBR−1
Story Brace Sections:
HSS5x5x1/2 HSS5x5x1/2 HSS5x5x1/2 HSS5x5x3/8 HSS5x5x3/8 HSS5x5x3/8 HSS5x5x3/8 HSS7x7x3/8 HSS7x7x3/8 HSS7x7x3/8 HSS7x7x3/8 HSS6x6x3/8 HSS6x6x3/8 HSS6x6x3/8 HSS6x6x3/8 HSS5x5x1/4 HSS5x5x1/4 HSS5x5x1/4 HSS5x5x1/4
HSS8x8x1/2 19.1 mm
19.1 mm 25.4 mm
RBRB−1
19.1 mm 19.1 mm 3
1 2 4
Story Brace Yielding Core Area, A :sc
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
9.7 cm 9.7 cm 9.7 cm 9.7 cm
29.0 cm 22.6 cm 22.6 cm 19.4 cm 19.4 cm 48.4 cm 48.4 cm 38.7 cm 38.7 cm 22.6 cm
22.6 cm
32.3 cm
32.3 cm
25.4 mm
25.4 mm
31.8 mm
31.8 mm 34.9 mm
34.9 mm
31.8 mm
31.8 mm Column Cover
Plate Thick. t
Column Cover Plate Thick. t
Figure 2.12:Elevation view of frames A of retrofit schemes RBR-1 and RBRB-1.
Level 19F El. 70.1 m (230’−6’’) Foundation
25.4 mm
cp
41.9 cm2 29.0 cm 29.0 cm
cp
25.4 mm
31.8 mm
31.8 mm
31.8 mm
31.8 mm 31.8 mm
31.8 mm 25.4 mm 25.4 mm
31.8 mm 25.4 mm
31.8 mm 31.8 mm
31.8 mm 31.8 mm
31.8 mm
19.1 mm
19.1 mm
Level Basement El. −5.5 m (−18’−0’’) 5.5 m (18’−0’’)
5.5 m (18’−0’’) Level 2F El. 5.5 m (18’−0’’) Level 3F El. 9.3 m (30’−6’’) 3.8 m (12’−6’’) Level 4F El. 13.1 m (43’−0’’) 3.8 m (12’−6’’) Level 5F El. 16.9 m (55’−6’’) 3.8 m (12’−6’’) Level 6F El. 20.7 m (68’−0’’) 3.8 m (12’−6’’) Level 7F El. 24.5 m (80’−6’’) 3.8 m (12’−6’’) Level 8F El. 28.3 m (93’−0’’) 3.8 m (12’−6’’)
Level 9F El. 32.1 m (105’−6’’) 3.8 m (12’−6’’)
Level 10F El. 35.9 m (118’−0’’) 3.8 m (12’−6’’)
Level 11F El. 39.7 m (130’−6’’) 3.8 m (12’−6’’)
Level 12F El. 43.5 m (143’−0’’) 3.8 m (12’−6’’)
Level 13F El. 47.3 m (155’−6’’) 3.8 m (12’−6’’)
Level 14F El. 51.1 m (168’−0’’) 3.8 m (12’−6’’)
Level 15F El. 54.9 m (180’−6’’) 3.8 m (12’−6’’)
Level 16F El. 58.7 m (193’−0’’) 3.8 m (12’−6’’)
Level 17F El. 62.5 m (205’−6’’) 3.8 m (12’−6’’)
Level 18F El. 66.3 m (218’−0’’) 3.8 m (12’−6’’)
3.8 m (12’−6’’)
Level 20F El. 73.9 m (243’−0’’) 3.8 m (12’−6’’)
Level Roof El. 77.7 m (255’−6’’)
Level Ground El. 0.0 m (0’−0’’) Simple Connection Moment Connection Column Splices Basement Wall
3.8 m (12’−6’’) RBRB−2
19.1 mm 19.1 mm 3
1 2 4
3
1 2 4
RBR−2
Story Brace
HSS5x5x1/2
HSS8x8x1/2 HSS5x5x1/2 HSS5x5x1/2 HSS5x5x3/8 HSS5x5x3/8 HSS5x5x3/8 HSS5x5x3/8 HSS6x6x3/8 HSS6x6x3/8 HSS6x6x3/8 HSS6x6x3/8 HSS5x5x1/4 HSS5x5x1/4 HSS5x5x1/4 HSS5x5x1/4 Sections:
HSS5x5x1/4
HSS5x5x1/4
HSS5x5x1/4 HSS5x5x1/4
19.1 mm 19.1 mm 25.4 mm
Story Brace Yielding Core Area, A :sc
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
9.7 cm 9.7 cm 9.7 cm 9.7 cm
29.0 cm 22.6 cm 22.6 cm 19.4 cm 19.4 cm 22.6 cm
32.3 cm
32.3 cm 22.6 cm
12.9 cm
12.9 cm
16.1 cm
16.1 cm
25.4 mm
25.4 mm
31.8 mm
31.8 mm 31.8 mm
25.4 mm
25.4 mm
31.8 mm
19.1 mm
19.1 mm Plate Thick. t
Column Cover
Plate Thick. t Column Cover
Figure 2.13:Elevation view of frames A of retrofit schemes RBR-2 and RBRB-2.
Level 19F El. 70.1 m (230’−6’’) Foundation
41.9 cm2 29.0 cm 29.0 cm
31.8 mm
31.8 mm
31.8 mm
31.8 mm 31.8 mm
31.8 mm 31.8 mm
31.8 mm 31.8 mm
31.8 mm 31.8 mm
31.8 mm
Story Brace Yielding Core Area, A :sc Story Brace
Sections:
cp cp
Level Basement El. −5.5 m (−18’−0’’) 5.5 m (18’−0’’)
5.5 m (18’−0’’) Level 2F El. 5.5 m (18’−0’’) Level 3F El. 9.3 m (30’−6’’) 3.8 m (12’−6’’) Level 4F El. 13.1 m (43’−0’’) 3.8 m (12’−6’’) Level 5F El. 16.9 m (55’−6’’) 3.8 m (12’−6’’) Level 6F El. 20.7 m (68’−0’’) 3.8 m (12’−6’’) Level 7F El. 24.5 m (80’−6’’) 3.8 m (12’−6’’) Level 8F El. 28.3 m (93’−0’’) 3.8 m (12’−6’’)
Level 9F El. 32.1 m (105’−6’’) 3.8 m (12’−6’’)
Level 10F El. 35.9 m (118’−0’’) 3.8 m (12’−6’’)
Level 11F El. 39.7 m (130’−6’’) 3.8 m (12’−6’’)
Level 12F El. 43.5 m (143’−0’’) 3.8 m (12’−6’’)
Level 13F El. 47.3 m (155’−6’’) 3.8 m (12’−6’’)
Level 14F El. 51.1 m (168’−0’’) 3.8 m (12’−6’’)
Level 15F El. 54.9 m (180’−6’’) 3.8 m (12’−6’’)
Level 16F El. 58.7 m (193’−0’’) 3.8 m (12’−6’’)
Level 17F El. 62.5 m (205’−6’’) 3.8 m (12’−6’’)
Level 18F El. 66.3 m (218’−0’’) 3.8 m (12’−6’’)
3.8 m (12’−6’’)
Level 20F El. 73.9 m (243’−0’’) 3.8 m (12’−6’’)
Level Roof El. 77.7 m (255’−6’’)
Level Ground El. 0.0 m (0’−0’’) Simple Connection Moment Connection Column Splices Basement Wall
3.8 m (12’−6’’)
19.1 mm 19.1 mm 3
1 2 4
3
1 2 4
HSS5x5x1/4 HSS5x5x1/4
19.1 mm 19.1 mm
2
2
2
2
2
2
2
2
2
29.0 cm 22.6 cm 22.6 cm
31.8 mm
31.8 mm 31.8 mm
31.8 mm HSS8x8x3/8
HSS5x5x3/8 HSS5x5x3/8 HSS5x5x3/8 HSS5x5x1/4 HSS5x5x1/4 HSS5x5x1/4 HSS5x5x1/4
RBR−3 RBRB−3
22.6 cm 22.6 cm 19.4 cm
19.4 cm Plate Thick. t
Column Cover Plate Thick. t
Column Cover
Figure 2.14:Elevation view of frames A of retrofit schemes RBR-3 and RBRB-3.
Chapter 3
Modeling Considerations
Building analyses are carried out with a planar frame analysis program developed at Caltech called STEEL (also referred to as FRAME-2D). A brief summary that describes the capabilities and fea- tures of the program is included herein. Details of the formulation can be found in [9] and [36].
Several studies have been conducted to validate the program. Challa and Hall [9] showed that the behavior of a panel zone element which is used to model “joints” in STEEL agrees well with experimental data from a moment-frame subassembly test. Hall et al. [36] demonstrated a good aggreement with experimental data of a cantilever beam and a slender brace element under cyclic loading. Krishnan [43] extended the planar program into three dimensions and showed that both programs give similar results for a two dimensional moment-frame configuration, as well as good agreement with experimental data. In Section 3.3 we demonstrate further the ability of the program to model hysteretic buckling, postbuckling and tension yield of conventional brace elements. In sec- tion 3.4 we demonstrate the ability of the program to model cyclic loading of buckling-restrained brace elements.