SEISMIC HAZARD ANALYSIS. Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 1
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1 SEISMIC HAZARD ANALYSIS Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 1
2 Seismic Hazard Analysis Deterministic procedures Probabilistic procedures USGS hazard maps 2003 NEHRP Provisions design maps Site amplification NEHRP Provisions response spectrum UBC response spectrum Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 2
3 Hazard vs Risk Seismic hazard analysis describes the potential for dangerous, earthquake-related natural phenomena such as ground shaking, fault rupture, or soil liquefaction. Seismic risk analysis assesses the probability of occurrence of losses (human, social, economic) associated with the seismic hazards. Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 3
4 Approaches to Seismic Hazard Analysis Deterministic The earthquake hazard for the site is a peak ground acceleration of 0.35g resulting from an earthquake of magnitude 6.0 on the Balcones Fault at a distance of 12 miles from the site. Probabilistic The earthquake hazard for the site is a peak ground acceleration of 0.28g with a 2 percent probability of being exceeded in a 50-year period. Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 4
5 Probabilistic Seismic Hazard Analysis First addressed in 1968 by C. Allin Cornell in Engineering Seismic Risk Analysis, and article in the Bulletin of the Seismological Society (Vol. 58, No. 5, October). Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 5
6 Steps in Deterministic Seismic Hazard Analysis (1) Sources (2) Controlling Earthquake F1 Site Balcones Fault Fixed distance R Fixed magnitude M Area Source (3) Ground Motion Peak Acceleration Magnitude M Distance (4) Hazard at Site The earthquake hazard for the site is a peak ground acceleration of 0.35 g resulting from an earthquake of magnitude 6.0 on the Balcones Fault at a distance of 12 miles from the site. Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 6
7 Source Types Fault Site Fault Fault Localizing structure Area Source Seismotectonic province Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 7
8 Source Types Localizing structure: An identifiable geological structure that is assumed to generate or localize earthquakes. This is generally a concentration of known or unknown active faults. Seismotectonic province: A region where there is a known seismic hazard but where there are no identifiable active faults or localizing structures. Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 8
9 Maximum Earthquake Maximum possible earthquake: An upper bound to size (however unlikely) determined by earthquake processes (e.g., maximum seismic moment). Maximum credible earthquake: The maximum reasonable earthquake size based on earthquake processes (but does not imply likely occurrence). Maximum historic earthquake: The maximum historic or instrumented earthquake that is often a lower bound on maximum possible or maximum credible earthquake. Maximum considered earthquake: Described later. Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 9
10 Ground Motion Attenuation Ground Motion Parameter Magnitude M Distance Reasons: Geometric spreading Absorption (damping) Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 10
11 Attenuation with Distance Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 11
12 Comparison of Attenuation for Four Earthquakes Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 12
13 Ground Motion Attenuation Steps to Obtain Empirical Relationship 1. Obtain catalog of appropriate ground motion records 2. Correct for aftershocks, foreshocks 3. Correct for consistent magnitude measure 4. Fit data to empirical relationship of type: lnyˆ = ln b1 + f1( M ) + ln f2( R) + ln f3( M, R) + ln f4( Pi ) + lnε Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 13
14 Ground Motion Attenuation Basic Empirical Relationships lnyˆ = ln b1 + f1( M ) + ln f2( R) + ln f3( M, R) + ln f4( Pi ) + lnε Yˆ Ground motion parameter (e.g. PGA) f f 1 ( M b 1 ) f 2( R ) ( M, ) 3 R f ( P ) 4 i ε Scaling factor Function of magnitude Function of distance Function of magnitude and distance Other variables Error term Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 14
15 Ground Motion Attenuation Relationships for Different Conditions Central and eastern United States Subduction zone earthquakes Shallow crustal earthquakes Near-source attenuation Extensional tectonic regions Many others May be developed for any desired quantity (PGA, PGV, spectral response). Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 15
16 Ground Motion Attenuation Relationships Seismological Research Letters Volume 68, Number 1 January/February, 1997 Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 16
17 Earthquake Catalog for Shallow Crustal Earthquakes (Sadigh, Chang, Egan, Makdisi, and Youngs) Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 17
18 Earthquake Catalog for Shallow Crustal Earthquakes (Sadigh, Chang, Egan, Makdisi, and Youngs) Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 18
19 Attenuation Relation for Shallow Crustal Earthquakes (Sadigh, Chang, Egan, Makdisi, and Youngs) Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 19
20 Attenuation Relation for Shallow Crustal Earthquakes (Sadigh, Chang, Egan, Makdisi, and Youngs) ln( y) C + C2M + C3(8.5 M ) + C4 ln( rrup + exp( C5 + C6M )) + C7( r = 1 rup + 2) T C 1 C 2 C 3 C 4 C 5 C 6 C 7 PGA Table for Magnitude <= 6.5 Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 20
21 Attenuation Relation for Shallow Crustal Earthquakes (Sadigh, Chang, Egan, Makdisi, and Youngs) 1 Peak Ground Acceleration, G Magnitude Distance, KM Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 21
22 Attenuation Relation for Shallow Crustal Earthquakes (Sadigh, Chang, Egan, Makdisi, and Youngs) 0.2 Second Acceleration 1.0 Second Acceleration Sec. Spectral Acceleration, G Magnitude Sec. Spectral Acceleration, G Magnitude Distance, KM Distance, KM Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 22
23 Example Deterministic Analysis (Kramer) Source 3 Source 2 Source 1 D3 D1 D2 Site Source M D PGA (km) (g) Maximum on source Closest distance From attenuation relationship Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 23
24 Steps in Probabilistic Seismic Hazard Analysis (1) Sources (2) Recurrence F1 Area Source Site Balcones Fault Log # Quakes > M Magnitude M (3) Ground Motion (4) Probability of Exceedance Peak Acceleration M3 Distance Uncertainty M2 M1 Probability of Exceedance Ground Motion Parameter Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 24
25 Empirical Gutenberg-Richter Recurrence Relationship λ m Mean Annual Rate of Exceedance Magnitude log λ λ m m = a bm = mean rate of recurrence (events/year) 1 / = return period λ m a and b to be determined from data Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 25
26 Bounded vs Unbounded Recurrence Relationship 1000 Mean Annual Rate of Exceedance Magnitude Unbounded Bounded Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 26
27 Uncertainties Included in Probabilistic Analysis Attenuation laws Recurrence relationship Distance to site λ N N N S M R = v P[ Y > y * m, r ] P[ M ] P[ R = r y* i j k j k i= 1 j= 1 k = 1 = m ] Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 27
28 Example Probabilistic Analysis (Kramer) Source 3 Source 2 D1=? D3 D2=? Source 1 Site Source 3 M3=? A3=? Source 2 Source 1 Site M2=? A2=? M1=? A1=? Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 28
29 Result of Probabilistic Hazard Analysis Source 3 Source 2 Source 1 Site Mean Annual Rate of Exceedance SEISMIC HAZARD CURVE All Source Zones Source 2 Source 1 Source Peak Horizontal Acceleration (g) Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 29
30 Relationship Between Return Period, Period of Interest, and Probability of Exceedance Return period = -T/ln(1-P(Z>z)) 2475 Return Period (years) Period of Interest (years) 2% 10% 20% 30% 40% 50% Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 30
31 Use of PGA Seismic Hazard Curve 10% probability in 50 years Return period = 475 years Rate of exceedance = 1/475= Acceleration, g % in 50 year elastic response spectrum Period, T (sec) Mean Annual Rate of Exceedance SEISMIC HAZARD CURVE Peak Horizontal Acceleration (g) PGA=0.33g Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 31
32 Use of 0.2 Sec. Seismic Hazard Curve 10% probability in 50 years Return period = 475 years rate of exceedance = 1/475= Acceleration, g % in 50 year Elastic Response Spectrum Period, T (sec) Mean Annual Rate of Exceedance SEISMIC HAZARD CURVE Sec Spectral Acceleration (g) PGA = 0.55g Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 32
33 10% in 50 Year Elastic Response Spectrum 0.8 Acceleration, g Period, T (sec) Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 33
34 Uniform Hazard Spectrum Response Uniform hazard spectrum Large distant earthquake Small nearby earthquake Period Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 34
35 Uniform Hazard Spectrum Developed from probabilistic analysis All ordinates have equal probability of exceedance Represents contributions from small local, large distant earthquakes May be overly conservative for modal response spectrum analysis May not be appropriate for artificial ground motion generation Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 35
36 Probabilistic vs Deterministic Seismic Hazard Analysis The deterministic approach provides a clear and trackable method of computing seismic hazard whose assumptions are easily discerned. It provides understandable scenarios that can be related to the problem at hand. However, it has no way for accounting for uncertainty. Conclusions based on deterministic analysis can easily be upset by the occurrence of new earthquakes. Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 36
37 Probabilistic vs Deterministic Seismic Hazard Analysis The probabilistic approach is capable of integrating a wide range of information and uncertainties into a flexible framework. Unfortunately, its highly integrated framework can obscure those elements which drive the results, and its highly quantitative nature can lead to false impressions of accuracy. Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 37
38 USGS Probabilistic Hazard Maps (Project 97) 2.5 Spectral Response Acceleration (g) Period (sec) 2% in 50 years 10% in 50 years HAZARD MAP RESPONSE SPECTRA Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 38
39 USGS Probabilistic Hazard Maps (and NEHRP Provisions Maps) Earthquake Spectra, Seismic Design Provisions and Guidelines Theme Issue, Volume 16, Number 1, February 2000 Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 39
40 Maximum Considered Earthquake (MCE) The MCE ground motions are defined as the maximum level of earthquake shaking that is considered as reasonable to design normal structures to resist. Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 40
41 USGS Seismic Hazard Regions Note: Different attenuation relationships used for different regions. Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 41
42 USGS Seismic Hazard WUS Faults Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 42
43 USGS Seismic Hazard Curves for Various Cities Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 43
44 Uniform Hazard Spectra for San Francisco 2.5 Spectral Response Acceleration (g) Period (sec) 2% in 50 years 10% in 50 years Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 44
45 Uniform Hazard Spectra for Charleston, SC Spectral Response Acceleration (g) Period (sec) 2% in 50 years 10% in 50 years Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 45
46 USGS Seismic Hazard Map of Coterminous United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 46
47 USGS Seismic Hazard Map of Coterminous United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 47
48 USGS Seismic Hazard Map for Coterminous United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 48
49 USGS Map for Central and Eastern United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 49
50 USGS Map for Central and Eastern United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 50
51 USGS Map for Central and Eastern United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 51
52 USGS Map for Western United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 52
53 USGS Map for Western United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 53
54 USGS Map for Western United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 54
55 USGS Map for California Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 55
56 USGS Map for California Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 56
57 USGS Map for California Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 57
58 USGS Map for Pacific Northwest Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 58
59 USGS Map for Pacific Northwest Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 59
60 USGS Map for Pacific Northwest Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 60
61 USGS Seismic Hazard Map of Coterminous United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 61
62 USGS Seismic Hazard Map of Coterminous United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 62
63 USGS Seismic Hazard Map of Coterminous United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 63
64 USGS Map for Central and Eastern United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 64
65 USGS Map for Central and Eastern United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 65
66 USGS Map for Central and Eastern United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 66
67 USGS Map for Western United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 67
68 USGS Map for Western United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 68
69 USGS Map for Western United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 69
70 USGS Map for California Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 70
71 USGS Map for California Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 71
72 USGS Map for California Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 72
73 USGS Map for Pacific Northwest Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 73
74 USGS Map for Pacific Northwest Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 74
75 USGS Map for Pacific Northwest Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 75
76 USGS Website for Map Values The input zipcode is (DENVER) ZIP CODE LOCATION Lat Long. DISTANCE TO NEAREST GRID POINT kms NEAREST GRID POINT 39.7 Lat Long. Probabilistic ground motion values, in %g, at the Nearest Grid point are: 10%PE in 50 yr 5%PE in 50 yr 2%PE in 50 yr PGA sec SA sec SA sec SA CAUTION: USE OF ZIPCODES IS DISCOURAGED; LAT-LONG VALUES WILL GIVE ACCURATE RESULTS. Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 76
77 Relative PGAs for the United States Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 77
78 2000 NEHRP Recommended Provisions Maps 5% damped, 2% in 50 years, Site Class B (firm rock) 0.2 second and 1.0 second spectral ordinates provided On certain faults in California, Alaska, Hawaii, and CUS Provisions values are deterministic cap times 1.5. Outside deterministic areas, Provisions maps are the same as the USGS maps. USGS longitude/latitude and zipcode values are probabilistic MCE. To avoid confusion, ALWAYS use Provisions (adopted by ASCE and IBC) maps for design purposes. Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 78
79 Location of Deterministic Areas Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 79
80 Deterministic Cap Applies only where probabilistic values exceed highest design values from old (Algermissen and Perkins) maps. The deterministic procedure for mapping applies: For known active faults Uses characteristic largest earthquake on fault Uses 150% of value from median attenuation Use deterministic value if lower than 2% in 50 year value Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 80
81 NEHRP Provisions Maps 0.2 Second Spectral Response (S S ) Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 81
82 NEHRP Provisions Maps 1.0 Second Spectral Response (S 1 ) Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 82
83 2% in 50 Year 5% Damped MCE Elastic Spectra Site Class B (Firm Rock) Spectral Acceleration, g S s = 0.75g PGA Not mapped S 1 = 0.30g Period, sec. Curve is S 1 /T Constant displacement region beyond transition period T L Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 83
84 Site Amplification Effects Acceleration B A Sand Shale Rock B Time A Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 84
85 Site Amplification Effects Amplification of ground motion Longer duration of motion Change in frequency content of motion Not the same as soil-structure interaction Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 85
86 Site Amplification (Seed et al.) Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 86
87 Site Amplification: Loma Prieta Earthquake Soft Rock Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 87
88 Site Amplification: Loma Prieta and Mexico City Earthquakes Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 88
89 NEHRP Provisions Site Classes A Hard rock v s > 5000 ft/sec B Rock: 2500 < v s < 5000 ft/sec C Very dense soil or soft rock: 1200 < v s < 2500 ft/sec D Stiff soil : 600 < v s < 1200 ft/sec E V s < 600 ft/sec F Site-specific requirements Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 89
90 NEHRP Site Amplification for Site Classes A through E Amplification Fa Site Class A B C D E Short Period Ss (sec) Amplification Fv Site Class A B C D E Long Period S1 (sec) Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 90
91 2% in 50 Year 5% Damped MCE Elastic Spectra Modified for Site Class D 1.05 S MS = F A S S = 1.2(0.75)=0.9g Spectral Acceleration, g Basic S M1 = F V S 1 = 1.8(0.30) = 0.54g Site Amplified Period, sec. Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 91
92 Scaling of NEHRP Provisions Spectra by 2/3 for Margin of Performance Buildings designed according to current procedures assumed to have margin of collapse of 1.5 Judgment of lower bound margin of collapse given by current design procedures Design with current maps (2% in 50 year) but scale motions by 2/3 Results in 2/3 x 1.5 = 1.0 deterministic earthquake (where applicable) Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 92
93 2% in 50 Year 5% Damped Elastic Design Spectra (Scaled by 2/3) 1.00 Site Amplified Spectral Aceleration, g Basic S DS = (2/3)(0.90) = 0.60g S D1 = (2/3)(0.54) = 0.36g Period, sec. Scaled Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 93
94 Effect of Scaling in Western United States 2.5 Spectral Response Acceleration (g) Period (sec) 2% in 50 years 10% in 50 years 2/3 of 2% in 50 years Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 94
95 Effect of Scaling in Eastern United States 2.5 Spectral Response Acceleration (g) Period (sec) 2% in 50 years 10% in 50 years 2/3 of 2% in 50 years Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 95
96 2% in 50 Year 5% Damped Inelastic Design Spectra (R=6, I=1) Site Class D Spectral Acceleration, g Site Amplified Basic Scaled C S = S D1 /R = 0.90/6 = 0.15g C S = S DS /R = 0.36/6 = 0.06g Period, sec. Inelastic Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 96
97 Basis for Reduction of Elastic Spectra by R Inelastic behavior of structures Methods for obtaining acceptable inelastic response are presented in later topics Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 97
98 Directionality and Killer Pulse Earthquakes For sites relatively close to the fault, the direction of fault rupture can have an amplifying effect on ground motion amplitude. Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 98
99 Effect of Directionality on Response Spectra Towards Away Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 99
100 Effect of Directionality on Ground Motion Instructional Material Complementing FEMA 451, Design Examples Seismic Hazard Analysis 5a - 100
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