3. Seismic Design Requirements of

Structural System Selection 41

Structural System Selection Combinations of Framing Systems in Different Directions Different seismic force resisting resisting systems permitted resist seismic forces along each of two orthogonal axes of the structure. Respective R, C d, and 0 coefficients shall apply to each system R (E-W), C d (E-W), and 0 (E-W) R (N-S), C d (N-S), and 0 (N-S) 44

Structural System Selection Combinations of Framing Systems in the Same Direction Where different seismic force resistingresisting systems used in combination to resist seismic forces in the same direction, other than those combinations considered as dual systems, stems more stringent system stem limitation contained in Table 12.2-1 applies R 1 R 2 R 2 <R 1 R 2 applies 46

Structural System Selection R, C d,andω Ω 0 Values for Vertical Combinations Value of response modification coefficient, R, used for design at any story shall not exceed lowest value of R used in the same direction at any story above that story. Deflection amplification factor, C d, and system over strength factor, 0, used at any story shall not be less than largest value of 0 used in the same direction at any story above that story. Exceptions: Rooftop structures not exceeding two stories in height and 10 percent of the total structure weight. Other supported structural systems with a weight equal to or less than 10 percent of the weight of the structure. Detached one- and two-family dwellings of light-frame construction. 47

Structural System Selection RC R, d, and Ω 0 Values for Vertical Combinations Resulting DesignValues R = 7, C d = 3.0, 0 = 5.5 R = 7, C d = 3.0, 0 = 5.5 R = 8, C d = 2.0, 0 = 4.0 R = 7, C d = 3.0, 0 = 5.5 R = 6, C d = 2.5, 0 = 5.0 R = 6, C d = 3.0, 0 = 5.5 R = 5, C d = 3.0, 0 = 5.5 R = 5, C d = 3.0, 0 = 5.5 R = 8, C d = 3.0, 0 = 5.5 R = 5, C d = 3.0, 0 = 5.5 R = 7, C d = 3.0, 0 = 5.5 R = 5, C d = 3.0, 0 = 5.5 48

Structural System Selection R, C d,andω Ω 0 Values for Vertical Combinations Two-stage equivalent lateral force procedure permitted for structures having flexible upper portion above a rigid lower portion, provided: Stiffness of lower portion at least 10 times the stiffness of upper portion Period of entire structure not greater than 1.1 times period of upper portion considered as a separate structure fixed at the base Flexible upper portion designed as a separate structure using appropriate values of R and ρ Rigid lower portion designed as a separate structure using appropriate values of R and ρ Reactions from upper portion determined from analysis of upper portion amplified by ratio of the R/ρ of the upper portion over R/ρ of the lower portion. This ratio shall not be less than 1.0. 49

Diaphragm Flexibility Rigid id diaphragm: Torsional analysis required Flexible diaphragm: Design forces proportional to tributary areas 50

Diaphragm Flexibility 51

Structural Irregularities Horizontal Irregularities 52

Structural Irregularities Vertical Irregularities 58

Redundancy Factor, For structures assigned to Seismic Design Category D, E, or F, ρ = 1.3 unless one of the following two conditions is met, whereby ρ is permitted to be taken as 1.0: Each story resisting more than 35 percent of the base shear in the direction of interest shall comply with Table 12.3-3. Structures that are regular in plan at all levels provided that the seismic i force resisting iti systems consist itof at tleast ttwo bays of seismic force resisting perimeter framing on each side of the structure in each orthogonal direction at each story resisting more than 35 percent of the base shear. The number of bays for a shear wall shall be calculated as the length of shear wall divided by the story height or two times the length of shear wall d 64

Redundancy Factor 65

Seismic Load Effects and Combinations Basic Combinations for Strength Design (1.2 + 0.2S DS )D + ρq E + L + 0.2S (0.9 02S 0.2S DS )D + ρq E +16H 1.6H D = dead load effect L = live load effect S = snow load effect H = load due to lateral earth pressure, ground water pressure, or pressure of bulk materials = 0 if counteracts Q E Q E = effects of horizontal seismic forces from V or F p 66

Seismic Load Effects and Combinations Basic Combinations for Strength Design 67

Seismic Load Effects and Combinations Basic Combinations for Strength Design with Overstrength Factor (1.2 + 0.2S DS )D + o Q E + L + 0.2S (0.9 0.2S DS )D + o Q E + 1.6H D = dead load effect L = live load effect S = snow load effect H = load due to lateral earth pressure,,ground water pressure, or pressure of bulk materials = 0 if counteracts Q E Q E = effects of horizontal seismic forces from V or F p 68

Seismic Load Effects and Combinations Basic Combinations for Strength Design with Overstrength Factor 69

Analysis Procedure Selection 70

Seismic Base Shear, V Effective Seismic Weight, W Total dead load plus following loads: In areas used for storage: 25 percent of floor live load Total operating weight of permanent equipment. 20% percent of design snow load if exceeds 30 psf 71

Seismic Response Coefficient, C s 72

Seismic Response Coefficient, C s Value of C s need not exceed the following: C s shall not be less than For structures located where S 1 > 0.6g, C s shall not be less than 73

Fundamental Period Determination Analysis Fundamental period, T,, obtained from analysis shall not exceed product of coefficient for upper limit on calculated period C u and approximate fundamental period, T a 74

Fundamental Period Determination Approximate fundamental period, T a, in sec 75

Fundamental Period Determination 76

Fundamental Period Determination 79

Vertical Distribution of Seismic Forces Lateral seismic force, F x, at any level determined from the following equations: 80

Vertical Distribution of Seismic Forces 81

Vertical Distribution of Seismic Forces 82

Horizontal Distribution of Forces Story shear in any story, V x, determined from: 83

Story Drift Determination Design story drift ( ) computed as the difference of deflections at centers of mass at top and bottom of story. 84

Story Drift Determination 85

Story Drift Determination 86

Story Drift Limit 87

P-Delta Effects P-delta effects on story shears, moments drifts not required to be considered if stability coefficient (θ) equation is less than 0.10 89

P-Delta Effects 90

P-Delta Effects 91

P-Delta Effects 92

P-Delta Effects 93

P-Delta Effects 94

Torsional Effects Inertia forces produced by an earthquake act through centre of mass, CM, of the structure If structure is not uniform, CM and centre of rigidity, CR, do not coincide and torsional moments are produced CM CR e 95

Torsional Effects Torsional moment, T x, on a horizontal plan at a given floor x must be calculated by: T x= F x 1.0e A 0. 05 x A x = Amplification factor for accidental eccentricity D nx = Dimension of structure perpendicular to direction of applied forces 0.05 D nx = Accidental eccentricity D nx 96

Torsional Effects 97

Torsional Effects Amplification of Accidental Eccentricity Structures assigned to Seismic Design Category C, D, E, or F, where Type 1a or 1b torsional irregularity exists as defined in Table 12.3-1 98

Torsional Effects Amplification of Accidental Eccentricity 99

Torsional Effects Amplification of Accidental Eccentricity 100

Torsional Effects To calculate torsional moments, position of CM and CR must be evaluated Position of CM is easy to evaluate Position of CR is complex to determine 101

X Y CR CR = = n i=1 n Position of the Centre of Rigidity (CR) K n i=1 i=1 n i=1 K yi K xi K Relative Stiffness Criterion (Blume at al. 1961) X yi Y xi i i Position of CR can evaluated in a similar fashion as position of centre of gravity of a section K xi and K yi lateral stiffness of the n lateral load resisting elements in the x and y directions, respectively Requires same type of resisting elements over the entire height CR is, in theory, constant over the entire height 102

Position of the Centre of Rigidity (CR) No Rotation of All Floors Criterion (Stafford-Smith and Vezina 1985 ) X CR,r = n i=1 V yi,r F -V y,r yi, r-1 X i 103

Position of the Centre of Rigidity (CR) Shear Centre Criterion (Tso 1990) 104

Torsional Analysis without Determining the Position of the Centre of Rigidity Goel and Chopra (1993) showed that torsion could be taken into account without t directly calculating l position of CR Consider design eccentricity e x worst case of: e e x = e D or e D nx x = nx D nx =Dimension of structure perpendicular to direction of applied forces Note for ASCE 7-05: = =1.0; = 0.05 A x 105

Torsional Analysis without Determining the Position of the Centre of Rigidity Step 1: Building analysed with seismic lateral loads applied to CM of each floor, but the floors are not allowed to rotate. Results (deflections and internal forces) represented by r 1 Step 2: Same analysis as step 1 is but with floors allowed to rotate. Results represented by r 2 Step 3 Building analyzed when subjected only to accidental torsional moments, T x, applied to the CM of each level x and given by: T x = D nx F x Results represented by r 3 106

Torsional Analysis without Determining the Position of the Centre of Rigidity Step 4: Total effect of the lateral loads and the torsional moments, r c, are obtained by combining the results of the three previous analyses with one of the two equations which will produce the most unfavorable effect in the members. = 1 r1+ r or + r rc 2 3 = 1 r1 + r2 - r rc 3 107

Modal Response Spectrum Analysis Number of Modes At least 90 percent of actual mass in each orthogonal horizontal direction Modal Response Parameters Design Response Spectrum of ASCE 7-05 Design modal force response parameters divided by R/I Displacement and drift quantities multiplied by C d /I p q p y d Combined Response Parameters Sum of the squares method (SRSS) or complete quadratic combination method (CQC CQC method shall be used for closely spaced modes that have significant cross-correlation of translational and torsional response 108

Seismic Response History Procedures Linear Response History Procedure Ground Motions Suite of not less than three appropriate ground motions 2D Analysis:» scaled such that average 5% damped response spectra not less than design response spectrum for periods ranging from 0.2T to 1.5T where T is fundamental natural period of the structure 3D Analysis:» pair of motions scaled such that each period between 0.2T and 1.5T, average of SRSS spectra from all horizontal component pairs does not fall below1.3 times corresponding ordinate of design response spectrum Response Parameters» force response parameters divided by R/I» If 3 ground motions are used: design for maximum response» If 7 ground motions are used: design for average response 109

Seismic Response History Procedures Linear Response History Procedure Ground Motions 110

Seismic Response History Procedures Linear Response History Procedure Ground Motions 111

Seismic Response History Procedures Nonlinear Response History Procedure Dead and Live Loads 100% dead load; at least 25% live load Design review required by independent team 112