Earthquake Design involves 3 analysis catagories in accordance with the UBC 97.
 Equivalent Static Load Method (Static Procedure)
 Response Spectrum Analysis (pseudo dynamic analysis)
 Time History Analysis (Real Dynamic Analysis)
Lateral load produced by horizontal inertia forces are determined using structural dynamic properties and expected ground acceleration.
This method needs response spectrum curves relation between natural periods of building having single degree of freedom versus spactral accelerations of building.
Responsespectrum analysis seeks the likely maximum response to motion equations. The earthquake ground acceleration in each direction is given as a digitized responsespectrum curve of pseudospectral acceleration response versus period of the structure.
Magnitude of design response spectrum can be defined by one of following three methods.
Magnitude of design response spectrum can be defined by one o following three methods
 UBC 97 elastic design response spectrum containing damping of 5%
Spectral Accelerations (g’s) is equal to Ca at period of 0 sec, 2.5Ca between To and Ts, linearly varied between 0 sec to To and Cv/T when period is greater then Ts. Where Ts is Cv/2.5Ca and To is 0.2 times Ts. The seismic response coefficients Ca and Cv account for the potential amplification of the ground vibration generated at a specific site by an earthquake.
 Sitespecific design spectrum from the actual building location.
 A spectrum ground motion time history analysis using accelerometer data from one or more earthquake can be performed.
Dynamic/Modal analysis must be active and choose one method and apply appropriate information
 Eigen Vector Analysis
This method determines the undamped freevibration mode shapes and frequencies of the system. These natural modes provide an excellent insight into the behaviour of the structure.
 RitzVector Analysis
This method seeks to find modes that are excited by a particular loading. Ritz vectors can provide a better basis then do eigenvectors when used for responsespectrum or timehistory analyses that are based on modal superposition. Dynamic analyses based on a special set of loaddependent Ritz vectors yield more accurate results then the use of the same number of natural mode shapes.
The first Ritz vector is the static displacement vector corresponding to the starting load vector.
You may specify any number of starting load vectors. Each starting load vector may be one of the following:
 An Acceleration Load in the global X, Y, or Z direction

 A Load Case
For responsespectrum analysis, only the Acceleration Loads are needed. For modal timehistory analysis, one starting load vector is needed for each Load Case or Acceleration Load that is used in any modal timehistory analysis.
 Construct a Lumped Mass
 Calculate a modeshape factors
 Calculate the period Tm for each mode
 Calculate the spectral acceleration (Sa,m) and seismic design coefficient for each mode from the UBC normalized response spectra
 Calculate the base shear for each mode
 Calculate the participating mass fraction (PM) for each mode
 Combine the base shears into the design dynamic lateral force, Vdyne using SRSS method. (Sum of PM >= 0.9)
 Calculate the lateral force Vstatic according to equivalent lateral force procedure
 Determine the scaling factor for structure
 Regular structure scale = 0.9*Vstatic/Vdyne
 Irreegular structure scale = Vstatic/Vdyne
 Regular structure scale = 0.8*Vstatic/Vdyne when siteresponse spectrum is used
 Distribute the scaledup base shear to each level
 Determine the raw deflections and element forces
 Combine the raw results using SRSS method
 Define mass
 Select menu item: Define > Mass Source
 Select mass definition option: From Loads
 Add load case: Dead (with multiplier of 1)
Note: The dead load is automatically divided by gravity.
 Define Response Spectrum Function
 Select menu item: Define > Response Spectrum Functions
 Choose function type: Add UBC 97 Spectrums
 Click: Add New Function Parameter (Ca, Cv)
 Type function name: FUNC1
 Define Modal Analysis Case
 Select menu item: Set Analysis Option
 Set Dynamic Analysis Parameter
 Click: Eigenvectors
 Enter maximum number of modes = 5
 Define Response Spectra Analysis Case
 Select menu item: Define > Response Spectrum Cases
 Click: Add New Spectrum
 Type case name = EQX
 Set Structural and Function Damping = 0.05
 Select Modal Combination SRSS
 Select Directional Combination SRSS
 Input Response Spectra
 Choose FUNC1 for U1 and Enter Scale Factor = 32.2 (response values in G’s, unit dependent)
 Click: Ok
 Define Load Combination
 Select menu item: Define > Combinations
 Click: Add New Combo
 Make Necessary Design Load Combination or Let Software to Define
Note: Response spectrum will automatically give +/ values
 Perform Response Spectrum Analysis
 Select menu item: Analyze > Run Analysis
 Click: Run Now
 Display output results in tabular form
 Verification computations
 Verify: dead load reaction = total weight = 1183.75 kip
 Verify: total mass = total dead load / gravity = 1183.75 / (32.2 x 12) = 3.064
 Mass = 3.1497 (Export joint masses to Excel and sum)
 Weight = Mass x Gravity = 3.1497 x 12 x 32.2 = 1217 kips
 Verify: modal participating mass ratio > 90%
 Ratio = 92.766% for UX
 Ratio = 93.192% for UY
 Verify: response spectra base shear = response x weight = 246.96 kip
 Response for period = 1.272 sec => 0.25 G => 0.25 x 1183.75 = 295.94 kip
 Period for Response= 0.209 G => 1.53 sec
 0.209 x (1183.75) = 246.96 kips
 Verify: fundamental period
 Limiting that period by 1.4TA for zone 2,3 and 1.3 for zone 4 (Method B – UBC)
 TA=Ct x Hn^{0.75} = 0.03 x 63^{0.75} = 0.671 => 1.4 x 0.671 = 0.939 sec <= use this
 Structure period T=2pi sqrt(W/(GK))
K = 1 kips / 0.025268 in = 39.576 k/in (from unit load case)
T = 2 x 3.1416 x sqrt[1183.75 / (32.2 x 39.576 x 12)] = 1.748 sec
 Compare the Base Shear results against dynamic base shear determined from clause 1631.5.4
 Vdynamic = (90% regular ) or (100% irregular) x statics
 Minimum Vdynamic = V dynamic from Spectrum/R
Vdynamic = 295.94/5.5 = 53.807 kip
Vstatic = (Cv I / RT ) W = 0.23 /(5.5 x 0.939) x 1183.75 = 52.718 kip
[0.11 Ca I W < V < (2.5 Ca I /R) W ] => 28.647 < 52.718 < 118.373
Vstatic = 0.9 x 52.718 = 47.446
 Use the greatest value to determine the scale factor => Scale Factor = Vstatic / Vdynamic
Scale = 47.446 / 53.807 < 1 <= Scale=1
 Reenter scale factor I/RxGxScale instead of G [32.2 ft/sec^{2}]
 Notes
 It is preferred to have the same stiffness for you building in both directions in order to resist the earthquake forces…
 UBC97 load combination is very close to ACI318 combinations
 Earthquake force in UBC97 is factored by 1.4, so in service load combination you will notice that earthquake force is divided by 1.4
 Mass participation should be at least 90% in both direction X, Y
 For Z direction you need to perform vibration analysis
 Pdelta analysis needs to be performed as geometrical nonlinearity
 Check if PushOver analysis is needed because Mechanism may occur before reaching targeted displacement (calculated from linear analysis procedure).
 Orthogonal load combinations (100%Rx + 30%Ry….ect) can be used if you do not use SRSS (square root of sum of squares) and CQC (completing Quadratic combinations)
 Ductility of you structure is very important and you need to check it with acceptance percentage specified
 UBC References
 Seismic Zone Factor ( UBC Tbl 16 – I)
 Soil profile type ( UBC Tbl 16 – J)
 Seismic Dynamic Response spectrum coefficients Ca & Cv ( UBC Tbl 16 – R & 16 –Q)
 Importance Factor I (UBC Tbl 16 – K)
 Measure of Over Strength R (UBC Tbl 16 N)
 Weak Storey ( Tbl 16 – L)
 Torsional Irregularity (Tbl 16M)
 If there is any Torsional Irregularity exists, orthogonal effects shall be considered (Ref. 1633.1)
 Remarks
 In order for a structure to have equal resistance to earthquake motions from all directions, the CQC3 method should be used to combine the effects of earthquake spectra applied in three dimensions. The percentage rule methods have no theoretical basis and are not invariant with respect to the reference system.
 The CQC method has a sound theoretical basis.
 Engineers, however, should clearly understand that the response spectrum method is an approximate method used to estimate maximum peak values of displacements and forces and that it has significant limitations.
 It will never be accurate for nonlinear analysis of multidegree of freedom structures.
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