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The Federal Emergency Management Agency (FEMA)/National Institute of Building Sciences (NIBS) Multi-Hazard Loss Estimation Technology (HAZUS-MH MR2) and, specifically, the HAZUS Advanced Engineering Building Module (AEBM) are used by the Office with building-specific parameters, described in this appendix, to evaluate the Probability of Collapse of SPC-1 buildings.

The Probability of Collapse, P[COL], is calculated by Equation (A6-1):

(A6-1)

where:

P[COL|STR5]=collapse factor of the HAZUS AEBM, as modified herein, and
P[STR5]=probability of Complete Structural Damage, based on HAZUS AEBM methods and parameters, as modified herein.

Building-specific properties are based on the building type (structural system), or Model Building Type (MBT), building height (number of stories above seismic base), building age (pre-1933, 1933 — 1961 or post-1961 design vintage), availability of materials testing data, and Significant Structural Deficiencies.

Table A6-1 lists Significant Structural Deficiencies. Table A6-1 includes older buildings (pre-1933 buildings) and buildings that do not have available materials test data, and treats these conditions as Significant Structural Deficiencies.

SPC-1 buildings with no Significant Structural Deficiencies are evaluated using "Baseline" values of building-specific properties. SPC-1 buildings with one or more Significant Structural Deficiencies are evaluated using Sub-Baseline (SubBase), or Ultra-Sub-Baseline (USB) building-specific properties, as specified in Table A6-1.

Building-specific properties include parameters related to (1) building capacity, (2) building response, (3) Complete Structural Damage, and (4) building collapse. Appendix H Sections 6-A4 through 6-A7, define the parameters of interest related to building capacity, building response, Complete Structural Damage and building collapse, respectively, and specify appropriate values of these parameters.

Building-specific capacity properties of interest include the yield capacity control point (Dy, Ay) and the ultimate capacity control point (Du, Au), as calculated by Equations (A6-2 through A6-5, respectively):

(A6-2)

(A6-3)

(A6-4)

(A6-5)

where:

Cs = seismic design coefficient — values of Cs are given in Tables A6-2a and A6-2b, respectively,

α1 = modal weight factor, Alpha 1 — values of α1 are given in Table A6-4,

Te = elastic period, in seconds — values of Te are given in Table A6-3,

γ = yield strength factor, Gamma — values of γ are given in Table A6-5,

λ = "overstrength" factor, Lambda — values of λ are given in Table A6-5, and

μ = "ductility" factor, Mu — values of μ are given in Table A6-6.

Building-specific response parameters of interest include the elastic damping factor, βE, and the degradation factor, Kappa. Values of βE are given in Table A6-7 and values of the Kappa factor are given in Table A6-8.

Building-specific damage parameters of interest include the median spectral displacement of the Complete Structural Damage state, SdC, and the associated lognormal standard deviation (Beta) factor, βC. Values of βC are given in Table A6-11. Median spectral displacement at the Complete Structural Damage state, SdC, is calculated using Equation (A6-6):

(A6-6)

where:

ΔC = interstory drift ratio (of the story with maximum drift) at the threshold of Complete Structural Damage — values of ΔC are given in Table A6-9,

HR = height of building at the roof level, in inches — default values of HR are given in Table A6-3 as a function of the number of stories above grade,

α2 = modal height factor, Alpha 2 — values of α2 are given in Table A6-4, and

α3 = modal shape factor, Alpha 3, relating maximum-story drift and roof drift, values of α3 are given in Table A6-10.

Building-specific values of the collapse factor, P[COL|STR5], that describe the fraction of the building likely to be collapsed given that the building has reached the Complete Structural Damage state, STR5, are given in Table A6-12.

TABLE A6-1—SIGNIFICANT STRUCTURAL DEFICIENCY MATRIX
SIGNIFICANT STRUCTURAL DEFICIENCY/CONDITION1CAPACITYRESPONSESTRUCTURAL DAMAGE - COMPLETE DAMAGE STATECOLLAPSE
Over-StrengthDurationFragility Curve Median4Fragility Curve Variability - Beta Factorc)Collapse Factor (P[COL |: STR5])
Gamma and Lambda FactorsDegradation (Kappa) FactorMaximum Story Drift Ratio (Δc)Mode Shape (Alpha 3) Factor
SubBaseUSBSubBaseUSB5SubBaseUSBSubBaseUSB6SubBaseUSB5SubBaseUSB6
Age (Pre-1933 buildings)XX7
Materials Testing (None)XX
No RedundancyXXX6
Weak Story IrregularityXXX6XX6
Soft Story IrregularityXXX6XX6
Mass IrregularityX
Vertical DescontinuityXX
Torsional IrregularityXXX6
Deflection Incompatibility2XXXX6
Short Column3XX
Wood DeteriorationXX
Steel DeteriorationXX
Concrete DeteriorationXX
Weak Column-SteelXX
Weak Column-ConcreteXXX
No Cripple Wall BracingXXX6XX6
Topping SlabXXXXX6
Inadequate Wall Anchorage/ Parapet BracingXX
Load Path/ Diaphragm OpeningsXXX6
URM Wall Thickness RatioXX6
  1. Sub-Baseline (SubBase) and Ultra-Sub-Baseline (USB) properties are based on one, or more, significant structural deficiencies.
  2. The Deflection Incompatibility structural deficiency applies only to concrete systems (C1, C2 and C3).
  3. The Short Column structural deficiency applies only to concrete and masonry systems (C1, C2, C3, RM1 and RM2).
  4. Effects of deficiencies related to drift and mode shape limited to a combined factor of 5 reduction in Complete median (of HAZUS default value).
  5. Grey shading indicates USB performance is not defined/used for deficiencies related to degradation (kappa) and fragility curve (beta) factors.
  6. USB performance required for systems with multiple, SubBase deficiencies related to either the mode shape (Alpha 3) factor or the collapse rate.
  7. USB performance required for pre-1933 buildings with other over-strength-related deficiencies (else use SubBase performance for pre-1933 buildings).
TABLE A6-2a—SEISMIC DESIGN COEFFICIENT, Cs UBC SEISMIC ZONE 4
NO. OF STORIESSeismic Design Coefficient, Cs - UBC Seismic Zone 4 Locations (Zone 3 of older editions of the UBC)
Structural System (MBT)
S1 and C1S2, S3, S4, S5, C2 and C3 (MH)W1, W2, PC1, PC2, RM1, RM2, URM
Post-61Pre-61Post-61Pre-61Post-61Pre-61
10.0720.1090.1000.1090.1330.109
20.0570.0920.1000.0920.1330.092
30.0500.0800.0860.0800.1140.080
40.0450.0710.0780.0710.1040.071
50.0420.0630.0730.0630.0980.063
60.0400.0570.0690.0570.0920.057
70.0380.0520.0660.0520.0880.052
80.0360.0480.0640.0480.0850.048
90.0350.0440.0620.0440.0820.044
100.0340.0410.0600.0410.0800.041
110.0320.0390.0580.0390.0780.039
120.0320.0360.0570.0360.0760.036
130.0310.0340.0560.0340.0740.034
140.0300.0320.0550.0320.0730.032
150.0290.0310.0540.0310.0720.031
160.0290.0290.0530.0290.0700.029
170.0280.0280.0520.0280.0690.028
180.0280.0270.0510.0270.0680.027
190.0270.0260.0510.0260.0670.026
> = 200.0270.0240.0500.0390.0670.024
TABLE A6-2b—SEISMIC DESIGN COEFFICIENT, Cs UBC SEISMIC ZONE 3
NO. OF STORIESSeismic Design Coefficient, Cs - UBC Seismic Zone 3 Locations (Zone 2 of older editions of the UBC)
Structural System (MBT)
S1 and C1S2, S3, S4, S5, C2 and C3 (MH)W1, W2, PC1, PC2, RM1, RM2, URM
Post-61Pre-61Post-61Pre-61Post-61Pre-61
10.0360.0550.0500.0550.0660.055
20.0280.0460.0500.0460.0660.046
30.0250.0400.0430.0400.0570.040
40.0230.0350.0390.0350.0520.035
50.0210.0320.0370.0320.0490.032
60.0200.0290.0350.0290.0460.029
70.0190.0260.0330.0260.0440.026
80.0180.0240.0320.0240.0430.024
90.0170.0220.0310.0220.0410.022
100.0170.0210.0300.0210.0400.021
110.0160.0190.0290.0190.0390.019
120.0160.0180.0290.0180.0380.018
130.0150.0170.0280.0170.0370.017
140.0150.0160.0270.0160.0360.016
150.0140.0150.0270.0150.0360.015
160.0140.0150.0260.0150.0350.015
170.0140.0140.0260.0140.0350.014
180.0140.0130.0260.0130.0340.013
190.0140.0130.0250.0130.0340.013
> = 200.0130.0120.0250.0120.0330.012
TABLE A6-3—DEFAULT BUILDING HEIGHTS AND ELASTIC PERIODS
NO. OF STORIESDEFAULT BUILDING HEIGHT, HR, AND ELASTIC PERIOD, Te. PROPERTIES
Structural System (MBT)
W1 AND W2 (MH)S1C1S2S4 AND S5C2, C3, PC2, RM1, RM2, URMS3 AND PC1
HR (ft)Te (sec)HR (ft)Te (sec)HR (ft)Te (sec)HR (ft)Te (sec)HR (ft)Te (sec)HR (ft)Te (sec)HR (ft)Te (sec)
1140.35140.40120.40140.40140.35120.35150.35
2240.38240.50200.40240.43240.35200.35250.39
3340.49360.69300.48360.59360.44300.39350.50
4440.60480.87400.62480.73480.55400.48
5540.70601.04500.76600.86600.65500.57
6721.20600.89720.99720.74600.65
7841.36701.03841.11840.84700.73
8961.51800.16961.22960.92800.81
91081.66901.291081.341081.01900.88
101201.811001.411201.451201.091000.95
111321.951101.541321.551321.171101.02
121442.091201.671441.661441.251201.09
131562.231301.791561.761561.331301.16
141682.361401.911681.861681.401401.23
151802.501502.041801.961801.481501.29
161922.631602.161922.061921.551601.35
172042.761702.282042.152041.621701.42
182162.891802.402162.252161.701801.48
192283.021902.522282.342281.771901.54
> = 202403.142002.642402.432401.842001.60
TABLE A6-4—ALPHA 1 AND ALPHA 2, MODAL FACTORS
NO. OF STORIESALPHA 1 (α1) - MODAL WEIGHT FACTORALPHA 2 (α2) - MODAL HEIGHT FACTOR
Structural System (MBT)Structural System (MBT)
S1 and C1W1, W2, S2, S3, S4, C2, C3, PC2, RM1 and RM2PC1 and URMMHMHAll Systems (except MH)
10.750.80.751.001.000.75
20.750.80.750.75
30.750.80.750.75
40.750.80.75
50.750.80.75
60.730.790.72
70.710.780.69
80.690.770.66
90.670.760.63
100.650.750.60
110.650.750.60
120.650.750.60
130.650.750.60
140.650.750.60
> =150.650.750.60
TABLE A6-5—LAMBDA FACTOR
NO. OF STORIESGamma Factor (γ)LAMBDA FACTOR (γ)
Baseline PerformanceSubBase PerformanceUSB Performance
Structural System (MBT)Structural System (MBT)Structural System (MBT)
W1, S1, C1W2, C2S4, C3Other MBTPC1, URMW1, S1, C1W2, C2S4 C3Other MBTPC1, URMW1, S1, C1W2, C2S4 C3Other MBTPC1, URM
12.702.002.001.831.671.331.751.751.631.501.251.501.501.421.331.17
22.502.002.001.831.671.331.751.751.631.501.251.501.501.421.331.17
32.252.002.001.831.671.331.751.751.631.501.251.501.501.421.331.17
42.002.002.001.831.671.331.751.751.631.501.251.501.501.421.331.17
51.882.002.001.831.671.331.751.751.631.501.251.501.501.421.331.17
61.802.002.001.831.671.331.751.751.631.501.251.501.501.421.331.17
71.752.002.001.831.671.331.751.751.631.501.251.501.501.421.331.17
81.712.002.001.831.671.331.751.751.631.501.251.501.501.421.331.17
91.692.002.001.831.671.331.751.751.631.501.251.501.501.421.331.17
101.672.002.001.831.671.331.751.751.631.501.251.501.501.421.331.17
111.652.002.001.831.671.331.751.751.631.501.251.501.501.421.331.17
121.652.002.001.831.671.331.751.751.631.501.251.501.501.421.331.17
131.652.002.001.831.671.331.751.751.631.501.251.501.501.421.331.17
141.652.002.001.831.671.331.751.751.631.501.251.501.501.421.331.17
> = 151.652.002.001.831.671.331.751.751.631.501.251.501.501.421.331.17
TABLE A6-6—DUCTILITY FACTOR Mu
NO. OF STORIESMu (μ) FACTOR (All Systems)
16.00
26.00
34.94
44.41
54.07
63.82
73.63
83.48
93.35
103.24
113.15
123.07
133.00
143.00
> = 153.00
TABLE A6-7—ELASTIC DAMPING
STRUCTURAL SYSTEM (MBT)βE ELASTIC DAMPING (% of Critical)
S1, S2, S3 and S45
C1, C2, PC1 and PC27
RM1 and RM27
C3 and S57
W1 and W210
TABLE A6-8—DEGRADATION KAPPA FACTORS
SCENARIO EARTHQUAKE CRITERIADEGRADATION (Kappa) FACTORS - (κs, κM and κL
Minimum Distance Site to Fault1 (km)Maximum Magnitude2Baseline PerformanceSubBase Performance
Post-61Pre-1961Post-61Pre-1961
< 5All0.80.70.60.5
5 - 10Mmax ≤ 6.50.80.70.60.5
5 - 10Mmax > 6.50.70.60.50.4
10 - 25Mmax ≤ 6.50.70.60.50.4
10 - 257.0 ≥ Mmax >6.50.60.50.40.3
10 - 25Mmax <7.00.50.40.30.2
25 - 50Mmax7.00.50.40.30.2
25 - 50Mmax >7.00.40.30.20.1
> 50All0.40.30.20.1
  1. Minimum distance to the fault that controls 1-second period ground motions at the building site.
  2. Maximum magnitude (Mmax) of fault that controls 1-second ground motions at the building site.
TABLE A6-9—INTERSTORY DRIFT RATIO — MEDIAN COMPLETE STRUCTURAL DAMAGE
STRUCTURAL SYSTEM (MBT)INTERSTORY DRIFT RATIO (max story) - MEDIAN COMPLETE STRUCTURAL DAMAGE (DC)
Baseline PerformanceSubBase PerformanceUSB Performance
Post-61Pre-61Post-61Pre-61Post-61Pre-61
W1 and W2 (MH)0.0750.0750.0600.0600.0380.038
S1, C1, S2 and C20.0600.0500.0500.0400.0300.025
S3, S4, PC1, PC2, RM1 and RM20.0530.0440.0440.0350.0270.022
S5, C3 and URM0.0350.0280.018
TABLE A6-10—ALPHA 3 (α 3) MODAL SHAPE FACTOR
No. of StoriesALPHA 3 (α3) MODAL SHAPE FACTOR - RATION OF MAXIMUM INTERSTORY DRIFT TO AVERAGE INTERSTORY DRIFT
When Combined with Baseline Interstory Drift Ratios (Table A6-9)When Combined with SubBase Interstory Drift Ratios (Table A6-9)When Combined with USB Interstory Drift Ratios (Table A6-9)
Baseline PerformanceSubBase PerformanceUSB PerformanceBaseline PerformanceSubBase PerformanceUSB PerformanceBaseline PerformanceSubBase PerformanceUSB Performance
11.001.001.001.001.001.001.001.001.00
21.211.622.031.211.622.031.211.622.03
31.352.042.731.352.042.731.352.042.50
41.452.363.271.452.363.271.452.362.50
51.542.633.721.542.633.721.542.502.50
61.622.874.111.622.874.001.622.502.50
71.693.074.461.693.074.001.692.502.50
81.753.264.771.753.264.001.752.502.50
91.813.435.001.813.434.001.812.502.50
101.863.595.001.863.594.001.862.502.50
111.913.735.001.913.734.001.912.502.50
121.963.875.001.963.874.001.962.502.50
132.004.005.002.004.004.002.002.502.50
142.044.125.002.044.004.002.042.502.50
> = 152.084.235.002.084.004.002.082.502.50
TABLE A6-11—LOGNORMAL STANDARD DEVIATION (BETA) VALUES — COMPLETE STRUCTURAL DAMAGE
NO. OF STORIESLOGNORMAL STANDARD DEVIATION (BETA) VALUES — COMPLETE STRUCTURAL DAMAGE (βc)
Baseline PerformanceSubBase Performance
Post-61Pre-61Post-61Pre-61
10.850.900.951.00
20.850.900.951.00
30.850.900.951.00
40.840.890.940.99
50.830.880.930.98
60.820.870.920.97
70.810.860.910.96
80.800.850.900.95
90.790.840.890.94
100.780.830.880.93
110.770.820.870.92
120.760.810.860.91
130.750.800.850.90
140.750.800.850.90
> =150.750.800.850.90
TABLE A6-12—COLLAPSE FACTOR
STRUCTURAL SYSTEM (MBT)COLLAPSE FACTOR - LIKELIHOOD OF COLLAPSE GIVEN COMPLETE STRUCTURAL DAMAGE - P[COL|STR5]
Baseline PerformanceSubBase PerformanceUSB Performance
W1 and W20.050.100.20
S1, S2, S3, S4 and S50.080.150.30
C1, C2 and C30.130.250.50
RM1 and RM20.130.250.50
PC1 and PC20.150.300.60
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