Effective Peak Ground Acceleration (EPGA)



Effective Peak Ground Acceleration (EPGA)EPGA= SMSg2.5where,SMS = Site class modified Maximum Considered Earthquake (MCER) response acceleration parameter for short periodsEnergy Releaselog10E=11.8+1.5Mwhere,E = earthquake energy radiated (ergs)M = Earthquake magnitude1 erg = 10-7 JAngular Frequencyω=Km=K×gWwhere,W = weight = m*gω = angular natural frequency (rad/s)g = 32.2 ft/s2 = 386.4 in/s2Linear Natural Frequency (f)f=ω2πwhere, f = linear frequency (Hz – cycles/sec)Natural Period (T)T=1f=2πω=2πWK×gDamping Ratio β=BBcriticalwhere,β = damping ratio (2% for flexible steel frame and 15% for light wood frame) – 0% for SDOFB = DampingRisk CategoryRisk Category I – Ie = 1.0Low hazard to human life in the event of failure as there is a probability of fewer occupantsLower and/or smallere.g., agricultural facilities, certain temporary facilities, minor storage facilitiesRisk Category II – Ie = 1.0Majority of buildingsRisk Category III – Ie = 1.25Substantial hazard to human life in the event of failureLarge number of occupants and/or those where occupants’ ability to exit is restrainedPotential high density of public assemblyE.g., prisons, Group 1-2 occupancy mental hospitals/nursing homes/etc. with >50 resident patients, detention centers, jails, prisonsPower generating facilities, water treatment facilities for potable water, wastewater treatment facilitiesRisk Category IV – Ie = 1.5Essential facilitiesHospitals with surgery or emergency treatment facilitiesFire, rescue, ambulance, police stations, and emergency vehicle garagesDesignated earthquake, hurricane, or other emergency sheltersPower-generating facilities & other public utility facilities required as emergency backup facilities for Risk Category IV facilitiesDesignated emergency preparedness, communication, and operation centersBuildings containing highly toxic materialsAviation control towers, air traffic control centers, and emergency aircraft hangersCritical national defense structuresWater storage facilities and pump stations required to maintain water pressure for fire suppressionBase Shear (V)V=m×Sa=WgSv=SaωSd=Svω=Saω2where,V = base shear m = massW = weightSa = Spectral AccelerationSv = Spectral VelocitySd = Spectral DisplacementSite Class Adjusted MCER Acceleration ParametersSMS=FaSsSM1=FvS1Where,SMS, SM1 = site class adjusted MCER acceleration parametersFa, Fv = site coefficientsSs = determined from the 0.2-second (short period) mapped MCER spectral response accelerationsS1 = determined from the 1-second mapped MCER spectral response accelerations**Ss and S1 – 1% probability of collapse in 50 yearsDesign Spectral Response Acceleration ParametersSDS=23SMS Table 3.2SD1=23SM1 Table 3.3whereSDS & SD1 = 5% damped design spectral response acceleration parameters at short periods and 1-second periods, respectivelySeismic Factors – R, Ω0, CdR=VEVSΩ0=VMVSCd=?M??Swhere,R = response modification coefficientVE = elastic base shearVM = maximum base shearVs = design base shear? = lateral driftCd = deflection amplification factorSeismic Base Shear, VV=CsWwhere,W = seismic weight (lb)Cs = seismic response coefficientSeismic Response Coefficient, CsThis equation governs when T<Ts which typically occurs with low rise and/or short period structures (i.e., < 3 stories)Cs=SDSRIeThis equation typically governs for longer period structures when Ts < T < TL but Cs minimum per ASCE 7 (12.8-5) and (12.8-6) needs to be consideredCs=SD1TRIe for T<TLThis equation can apply for very long periods (i.e., very tall) structures, when T>TL but Cs minimum per ASCE 7 (12.8-5) and (12.8-6) will typically govern over ASCE 7 (12.8-4)Cs=SD1TLT2RIe for T>TLMinimum CsCS=0.044SDSIe≥0.1 minimumFor structures where S1 > 0.6, Cs shall not be less than:Cs≥0.5S1RIe minimumTs=SD1SDS and TL determined from ASCE-Figure 22-12Period Determination, TT < 1.4Ta, where SD1>0.3T < 1.5Ta, where SD1=0.2T < 1.6Ta, where SD1=0.15T < 1.7Ta, where SD1<0.1Approximate Fundamental Period, TaSee Appendix CTa=Cthnxwhere,Ct and x are determined from ASCE 7 – Table 12.8-2hn = height in feet from base to the uppermost level of the structureSteel Moment-Resisting Frames (SMF, IMF & OMF)Ta=0.028hn0.8Or alternatively (for Steel MRF structures < 12 stories and average story height > 10 feetTa=0.1Nwhere,N = number of stories (i.e., levels) above the baseConcrete Moment-Resisting Frames (SMF, IMF & OMF)Ta=0.016hn0.9Or alternatively (for Concrete MRF structures < stories and average story height > 10 feet)Ta=0.1NSteel EBF, Steel BRBF, or Dual Systems with EBF & SMF –Ta=0.03hn0.75All Other Structural Systems (e.g., shear walls, CBF, Dual Systems)Ta=0.02hn0.75TsTS=SD1SDSSeismic Base Shear SpectraElastic CurveVE=RIeCSWInelastic (Actual) CurveVM=Ω0CSWIBC/ASCE 7 (ELF) Design CurveV=CsWVertical Distribution of Seismic Forces, FxFx=CvxVCvx=wxhxkwihikwhere,Cvx = vertical distribution factorV = seismic base sheark = 1 for T < 0.5 secondsk = 2 for T > 2.5 seconds = 2 0.5 second < T < 2.5 seconds…or determine k by linear interpolation using k=0.75+0.5TFor T < 0.5 secondsCvx=wxhxwihiFor T > 2.5 secondsCvx=wxhx2wihi2Story ShearStory Shear (Vx) in any story is the sum of the Fx forces acting above the storyVx=FiCalculated Deflection of a Levelδx=CdδxeIewhere,Cd = deflection amplification factor per ASCE 7 – Table 12.2-1δxe = deflection determined from an elastic analysis due to Fx forcesIe = seismic importance factorCalculated Story Drift, ΔxΔx=δx-δx-1where,Δx = maximum inelastic story driftδx = the amplified deflection at top of story x (i.e., Level x)δx-1 = the amplified deflection at bottom of story x (i.e., Level x-1)Allowable Story Drift (Δax)Structures < 4 StoriesΔax=0.025hsx Risk Category I or IIΔax=0.020hsx Risk Category IIIΔax=0.015hsx Risk Category IVMasonry Cantilever Shear Wall StructuresΔax=0.010hsx Risk Category I, II, III, or IVOther Masonry Shear Wall StructuresΔax=0.007hsx Risk Category I, II, III, or IVAll Other StructuresΔax=0.020hsx Risk Category I or IIΔax=0.015hsx Risk Category IIIΔax=0.010hsx Risk Category IVwhere,hsx = the story height below Level xMoment Frames Assigned to Seismic Design Category D, E, or FΔx≤Δaxρ for any storyP-Delta Effectsθ=PΔxIeVxhsxCdwhere,Px = total vertical design load (and above) Level xΔx = design story drift occurring simultaneously the story shear VxIe = Importance FactorVx = Seismic shear force acting between Level x and x-1hsx = story height below Level xCd = deflection amplification factorΘ = stability coefficientStability Coefficientθ=0.5βCd≤0.25where,β = ratio of shear demand to shear capacity for the story between Levels x and x-1. This ratio is permitted to be conservatively taken as 1.0*When θ is greater than θmax, the structure is potentially unstable and shall be redesignedMaximum Inelastic Response Displacement (δM)δM=CdδmaxIewhere,Cd = the deflection amplification factorδmax = maximum displacementIe = importance factorAdjacent Structures on the Same Property Separation (δMT)δMT=δM12+δM22where,δM1 = maximum inelastic displacement of adjacent structure 1δM2 = maximum inelastic displacement of adjacent structure 2Horizontal Cantilevers for SDC D,E, or FHorizontal cantilever structural members shall be designed for a minimum net upward force of 0.2 times the dead load in addition to applicable load combinationsOrthogonal Combinations Procedure100% of the forces for one direction plus 30% of the forces for the perpendicular direction(i.e., 100% of VN-S concurrently with 30% VE-W or VN-S concurrently with 100% VE-WSimplified Design ProcedureSDS=23FaSSwhere,Fa = 1.0 for rock sites, which may be assumed if there is < 10 ft of soil between the rock surface and the bottom of spread footings or mat foundation. 1.4 for soil sitesSs = mapped MCER short-period spectral acceleration but Ss need not exceed 1.5Seismic Base Shear, V Strength Design Force LevelV=FSDSRWwhere,F = 1.0 for one-story buildings (above grade plane) = 1.1 for two-story buildings (above grade plane) = 1.2 for three-story buildings (above grade plane)R = Response modification factorW = effective seismic weightOne-Story BuildingV=1.0SDSRWTwo-Story BuildingV=1.1SDSRWThree-Story BuildingV=1.2SDSRWVertical Distribution, FxFx=wxWVOrFx=F×SDSRwxDiaphragms, FpxFpx=wpxWV=F×SDSRwpxHorizontal Distribution of Shear, VxVx=FiDrift Limits and Building Separation (Simplified Design Procedure)δx=0.01hx?x=0.01hxxwhere,hx = the height above the base to Level xhxx = the story height below Level xSeismic Load EffectsE=Eh+Ev or E=Eh-EvE=ρQE+0.2SDSD or E=-ρQE-0.2SDSDwhere,E = seismic load effectEh = effect of horizontal seismic forces (due to horizontal ground motions)Ev = effect of vertical seismic forces (due to vertical ground motions)Horizontal Seismic Load Effect, EhEh=±ρQEwhere,QE = effects of horizontal seismic forces from the seismic base shear Vρ = redundancy factorVertical Seismic Load Effect, EvEv=±0.2SDSDExceptions: It is permitted to use Ev = 0 for either of the following conditions:In ASCE 7. Where SDS < 0.125In ASCE 7 (12.4-2) where determining demands on the soil-structure interface of foundationSeismic Load Effect Including Overstrength Factor, Ω0Em=Emh+Ev or Em=Emh-EvEm=Ω0QE+0.2SDSD or Em=-Ω0QE-0.2SDSDwhere,Em = seismic load effect including overstrength factor estimated maximum earthquake force that can be developed in the structureEmh = effect of horizontal seismic forces including structural overstrength (Ω0) as defined in ASCE 7-12.4.3.1. Emh can be positive or negative due to the cyclic nature of horizontal seismic ground motions.Strength Design Load CombinationsLC1=1.4DLC2=1.2D+1.6L+0.5(Lr or S or R)LC3=1.2(D)+1.6Lr or S or R+(1.0L or 0.5W)LC4=1.2(D)+1.0W+1.0L+0.5(Lr or S or R)LC5=1.2(D)+1.0E+1.0L+0.2SLC5=1.2(D)+1.0Eh+Ev+1.0L+0.2SLC5=1.2+0.2SDSD+ρQE+1.0L+0.2SLC6=0.9(D)+1.0WLC7=0.9D+1.0Ewhere,D = dead loadL = live loadLr = roof live loadS = snow loadR = rain loadW = wind loadE = earthquake loadAllowable Stress Design Load CombinationsLC1=DLC2=L+DLC3=D+(Lr or S or R)LC4=D+0.75L+0.75(Lr or S or R)LC5=D+0.6W or 0.7ELC5=1.0+0.14SDSD+0.7ρQELC6=1.0+0.10SDSD+0.525ρQE+0.75L+0.75SLC6a=D+0.75L+0.750.6W+0.75Lr or S or RLCb=D+0.75L+0.750.6E+0.75SLC7=0.6D+0.6WLC8=0.6D+0.7ELC8=0.6-0.14SDSD+0.7ρQELoad Combination with Overstrength FactorLC5=1.2+0.2SDSD+Ω0QE+1.0L+0.2SLC7=0.9-0.2SDSD+Ω0QE+Hwhere,H = load effects from lateral earth pressuresInelastic Story Driftsδx=CdδxeIewhere,δxe=displacemetn obtained from an elastic analysisCd = deflection amplification factorIe = importance factorSeismic Design Force, Fp for Nonstructural Components – Strength DesignFp=0.4apSDSWpRpIp1+2zh Fp≤1.6SDSIpWp Fp≥0.3SDSIpWpwhere,Fp = horizontal seismic design forceap = component amplification factor (1.0<ap<2.5) – (ASCE 7 – Table 13.5-1 or 13.6-1)Ip = component importance factorWp = component operating weightRp = component response factor (ASCE 7 – Table 13.5-1 or 13.6-1)z = component point of attachment elevationh = supporting structure average roof height relative to the baseDesign for Out-of-Plane Forces on Structural WallsFp=0.4SDSIeWw ≥0.10Ww minimumWall Anchorage ForcesThe anchorage of structural walls to supporting construction (e.g., roof or floor diaphragm)Fp=0.4SDSKaIeWp ≥0.2KaIeWp minimumwhere,Ka=1.0+Lf100≤2.0 maximumFp = design force in individual anchorsLf = flexible diaphragm span (feet), use 0 for rigid diaphragmWp = weight of masonry or concrete wall tributary to anchorWeight of Wall Tributary to AnchorWp=Wwallhw2+hp for one-story walls with a parapetWp=Wwallhw2 for one-story walls without a parapetFundamental Period, T of Nonbuilding StructureT=2πwiδi2gfiδiwhere,wi = effective seismic weight of Level ifi = lateral force at Level iδi = elastic deflection at Level I, relative to the baseg = acceleration due to gravity (32.2 ft/sec2 or 386.4 in/sec2)Single Degree of Freedom (SDOF) Nonbuilding StructureT=2πWK×gWhere,W = effective seismic weight (i.e., operating weight)K = stiffness of the nonbuilding structureg = acceleration due to gravity (32.2 ft/sec2 or 386.4 in/sec2)Seismic Base Shear for Nonbuilding StructuresV=0.3 ................
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