# International Building Code 2006 Section 1613 Earthquake Loads

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1 International Building Code 2006 Section 1613 Earthquake Loads Note: see original reference (the 2006 IBC Code) for full details The Code specifies that Every structure, and portion thereof, including nonstructural components that are permanently attached to structures and their supports and attachments, shall be designed and constructed to resist the effects of earthquake motions in accordance with ASCE 7 (ASCE SEI 7-05, see Appendix 1). As such, buildings and other structures shall be designed to sustain local damage with the structural system as a whole remaining stable (i.e., the Seismic Code ultimately aims to avoid catastrophic collapse of the structure). Base Shear per ASCE/SEI 7-05 EQUIVALENT LATERAL FORCE (ELF) Procedure The following method follows the provisions of the ASCE/SEI 7-05 and may be utilized for determining the seismic base shear. Calculation of the Seismic Base Shear, V - The seismic base shear, V, in a given direction shall be determined in accordance with the following equation: V C W (12.8-1) s where, C s is the seismic response coefficient, and W is the effective seismic weight. Evaluation of Effective Seismic Weight, W see Appendix 2 Determination of the Seismic Response Coefficient C s The seismic response coefficient, C s, is defined by: S DS Cs (12.8-2) R I where, S DS = design, 5 percent damped, spectral response acceleration parameter at short periods (Figure 1), 1

2 I is the occupancy importance factor, as shown in Appendix 3, and R is the response modification factor determined from Table (see Appendix 4). Check the value of C s versus the Need-Not-Exceed Limits - The value of C s computed in accordance with Eq need not exceed the following (see Figure 1): For T TL : C s S D1 R T I (12.8-3) For T TL : C s S D1 TL (12.8-4) 2 R T I where S D1 = design, 5 percent damped, spectral response acceleration parameter at a building Period T (see Appendix 5) of 1 second (Figure 1). Figure 1: Design Response Spectrum Configuration (from the 2006 IBC). 2

3 In the above, T S = S D1 / S DS and T L is specified as described in Appendix 6. In the Design Response Spectrum above, the spectral response acceleration segments are specified on the basis of geotechnical site amplification studies that show overall envelopes/averages that resemble the configuration depicted in Figure 1. Check on minimum value of C s - Cs shall not be less than: C 0.01 (12.8-5) s In addition, for structures located where S 1 (the one-second period spectral acceleration, see Appendix 7) is equal to or greater than 0.6g, C s shall not be less than (to implicitly account for near source effects): 0.5 S1 C s R I (12.8-6) Determination of S DS and S D1 These spectral values are defined by the following expressions: 2 S DS S MS 3 (11.4-3) 2 S D1 S M 1 3 (11.4-4) where, M denotes Maximum Considered Earthquake (MCE), an expression that represents ground motions with a 2% probability of being exceeded in 50 years (average return period of approximately 2,500 years); with exceptions where deterministic estimates govern the MCE design motions in certain higher seismic regions near active faults (Crouse et al. 2006). S MS is the MCE, 5 percent damped, spectral response acceleration at short periods adjusted for Site Class effects, and S M1 is the MCE, 5 percent damped, spectral response acceleration at a Period of 1.0 second adjusted for Site Class effects. These spectral accelerations are defined by: 3

4 S F S (11.4-1) S MS a s M1 Fv S 1 (11.4-2) where the site-specific short period (S s ) and one-second period (S 1 ) spectral accelerations are defined following the procedures in Appendix 7, and the Site coefficients F a and F v are defined in Tables and below, respectively. Table Site Coefficient, F a (see Appendix 8 for site Class) Mapped Maximum Considered Earthquake Spectral Response Acceleration Parameter at Short Period Site Class S S 0.25 S S = 0.5 S S = 0.75 S S = 1.0 S S 1.25 A B C D E F See Section (see Appendix 9) Table Site Coefficient, F v (see Appendix 8 for site Class) Mapped Maximum Considered Earthquake Spectral Response Acceleration Parameter at 1-s Period Site Class S S 1 = 0.2 S 1 = 0.3 S 1 = 0.4 S A B C D E F See Section (see Appendix 9) Vertical Distribution of Seismic Forces The lateral seismic force (F x ) (kip or kn) induced at any level shall be determined, in accordance with ASCE/SEI 7-05 Section , from the following equations: Fx CvxV ( ) and 4

5 C vx n w h i 1 x k x w h k i i ( ) where, C vx = vertical distribution factor, w i and w x = the portion of the total effective seismic weight of the structure (W) located or assigned to Level i or x, h i and h x = the height (ft or m) from the base to Level i or x, n = total number of stories, k = an exponent related to the structure period as follows: for structures having a period of 0.5 s or less, k = 1, for structures having a period of 2.5 s or more, k = 2, for structures having a period between 0.5 and 2.5 s, k shall be 2 or shall be determined by linear interpolation between 1 and 2. Horizontal Distribution of Forces - The seismic design story shear in any story (V x ) (kip or kn) shall be determined, in accordance with ASCE/SEI 7-05 Section , from the following equation: n V ( ) x F i i x where F i is the portion of the seismic base shear (V) (kip or kn) induced at Level i. Determination the Seismic Design Category For Material Design Sections of the Code Appendix 10 see The Seismic Design Category classification is employed for additional code considerations as shown in Appendix 4. References C.B. Crouse, E.V. Leyendecker, P.G. Somerville, M. Power, and W.J. Silva, development of seismic ground-motion criteria for the ASCE 7 standard, Proceedings of the 8th U.S. National Conference on Earthquake Engineering April 18-22, 2006, San Francisco, California, USA, Paper No. 533). 5

7 Appendix Calculate the Effective Seismic Weight, W The effective seismic weight shall include the total dead load and other loads listed below: 1. In areas used for storage, a minimum of 25 percent of the floor live load (floor live load in public garages and open parking structures need not be included). 2. Where provision for partitions is required by Section in the floor load design, the actual partition weight or a minimum weight of 10 psf (0.48 kn/m 2 ) of floor area, whichever is greater. 3. Total operating weight of permanent equipment. 4. Where the flat roof snow load, P f, exceeds 30 psf (1.44 kn/m 2 ), 20 percent of the uniform design snow load, regardless of actual roof slope. 7

8 Appendix 3 Determination of the Building s Importance Factor, I The Importance Factor I is a factor assigned to each structure according to its Occupancy Category. In turn, the Occupancy Category is defined as follows: Building s Occupancy Category - Buildings and other structures shall be classified, based on the nature of occupancy, according to Table 1-1 for the purposes of applying flood, wind, snow, earthquake, and ice provisions. The occupancy categories range from I to IV, where Occupancy Category I represents buildings and other structures with a low hazard to human life in the event of failure and Occupancy Category IV represents essential facilities. Each building or other structure shall be assigned to the highest applicable occupancy category or categories. Assignment of the same structure to multiple occupancy categories based on use and the type of load condition being evaluated (e.g., wind or seismic) shall be permissible. OCCUPANCY: The purpose for which a building or other structure, or part thereof, is used or intended to be used. The Occupancy Category is determined from Table 1-1 OCCUPANCY CATEGORY OF BUILDINGS AND OTHER STRUCTURES FOR FLOOD, WIND, SNOW, EARTHQUAKE, AND ICE LOADS. 8

9 On this basis, the importance factor, I, shall be assigned to each structure by: Occupancy Category Importance Factor, I I 1.0 II 1.0 III 1.25 IV 1.5 Note: The NEHRP 1997 Provisions in Section 1.1, identifies two purposes of the Occupancy Importance Factor, one of which specifically is to improve the capability of essential facilities and structures containing substantial quantities of hazardous materials to function during and after design earthquakes. This is achieved by introducing the occupancy importance factor of 1.25 for Seismic Use Group III structures and 1.5 for Seismic Use Group IV structures. The NEHRP Commentary Sections 1.4, 5.2, and explain that the factor is intended to reduce the ductility demands and result in less damage. When combined with the more stringent drift limits for such essential or hazardous facilities the result is improved performance of such facilities. 9

10 Appendix 4 -- R factor; and Seismic Design Category (see Appendix 10) 10

11 11

12 In this table, the overstrength factor, 0, dictates increase in seismic load for the critical structural elements that would be expected to remain in the elastic state (e.g., to prevent collapse), and the deflection amplification factor, C d dictates increases to the code-derived deflections, to be representative of the actual expected peak deflection values (since the Code specifies much lower forces to calculate building shear forces). 12

13 Determination of Design Coefficients and Factors for Building s Seismic Force-Resisting System(s) The structural system used shall be in accordance with the Seismic Design Category and height limitations indicated in Table above. The appropriate response modification coefficient, R, system overstrength factor, 0, and the deflection amplification factor, C d, indicated in Table shall be used in determining the base shear, element design forces, and design story drift. Different seismic force resisting systems are permitted to be used to resist seismic forces along each of the two orthogonal axes of the structure. Where different systems are used, the respective R, C d, and 0 coefficients shall apply to each system, including the limitations on system use contained in Table above. Where different seismic force resisting systems are used in combination to resist seismic forces in the same direction of structural response, other than those combinations considered as dual systems, the more stringent system limitation contained in Table shall apply and the design shall comply with the requirements of this section. 13

14 Appendix 5 Determination of the Approximate Fundamental Period of Structure The approximate fundamental period (T a ), in seconds, shall be determined from the following equation: T C h (12.8-7) a t x n where h n is the height in ft above the base to the highest level of the structure and the period coefficients C t and x are determined from Table TABLE VALUES OF APPROXIMATE PERIOD PARAMETERS C t AND x Structural Type C t x Moment-resisting frame systems in which the frames resist 100% of the required seismic force and are not enclosed or adjoined by components that are more rigid and will prevent the frames from deflecting where subjected to seismic forces: Steel moment-resisting frames 0.28 (0.0724)* Concrete moment-resisting frames (0.0466)* Eccentrically braced steel frames 0.03 (0.0731)* All other structural systems 0.02 (0.0488)* * Metric equivalents are shown in parentheses For structures not exceeding 12 stories in height in which the seismic force resisting system consists entirely of concrete or steel moment resisting frames and the story height is at least 10 ft, it is permitted to determine the approximate fundamental period (Ta), in s, from the following equation: T a = 0.1 N (12.8-8) where N = number of stories. 14

15 Appendix 6 -- Map for obtaining T L (please see sample map below) 15

16 Appendix 7 Determination of S S and S 1 (site-specific short period and one-second period spectral accelerations) S S = mapped MCE, 5 percent damped, spectral response acceleration at short periods (0.2 seconds). S 1 = mapped MCE, 5 percent damped, spectral response acceleration at a period of 1 second. The above parameters are readily available for Site Class B (see Site Classes in Appendix 8): For values over the Internet, go to: 16

17 17

18 Conversely, maps (see samples below) are available in the Code (Figs through 22-14, see sample maps on the following pages). 18

19 19

20 20

21 21

22 Appendix 8 -- Site Class 5. Determination of Site Classification - Based on the site soil properties, the site shall be classified as Site Class A, B, C, D, E, or F in accordance with Chapter 20. The site soil shall be classified in accordance with Table and Section 20.3 based on the upper 100 ft (30 m) of the site profile. Where the soil properties are not known in sufficient detail to determine the site class, Site Class D shall be used unless the authority having jurisdiction or geotechnical data determines Site Class E or F soils are present at the site. Site Classes A and B shall not be assigned to a site if there is more than 10 ft of soil between the rock surface and the bottom of the spread footing or mat foundation. vs is the average shear wave velocity in the upper 100 ft of the site profile and is calculated as: v n i 1 s n i 1 d d v i i si d i is the thickness of any layer between 0 and 100 ft (30 m). v si is the shear wave velocity in ft/s (m/s). (20.4-1) N ~ Average Field Standard Penetration Resistance and N ~ ch, Average Standard Penetration Resistance for Cohesionless Soil Layers. N ~ and N ~ ch shall be determined in accordance with the following formulas: ~ N n i 1 n i 1 d d N i i i (20.4-2) 22

23 ~ N ch m i 1 d s d N i i (20.4-3) where N i and d i in Eq are for cohesionless soil layers only and m di i 1 d s where d s is the total thickness of cohesionless soil layers in the top 100 ft (30 m). N i is the standard penetration resistance (ASTM D1586) not to exceed 100 blows/ft (328 blows/m) as directly measured in the field without corrections. Where refusal is met for a rock layer, N i shall be taken as 100 blows/ft (328 blows/m). su is the Average Undrained Shear Strength. u formula: s shall be determined in accordance with the following s u k d c d i 1 s i ui (20.4-4) where k di i 1 d c and d c = the total thickness of cohesive soil layers in the top 100 ft (30 m) PI = the plasticity index as determined in accordance with ASTM D4318 w = the moisture content in percent as determined in accordance with ASTM D2216 s ui = the undrained shear strength in psf (kpa), not to exceed 5,000 psf (240 kpa) as determined in accordance with ASTM D2166 or ASTM D

24 Appendix 9 -- Site Specific Procedure 24

25 Note: Material below is from the 2003 Seismic Code Provisions 25

26 26

27 27

28 Appendix 10 Determination of the Seismic Design Category The Seismic Design Category is a classification assigned to a structure based on its Occupancy Category (Appendix 3) and the severity of the design earthquake ground motion at the site. Seismic Design Category is an important parameter in the material design sections of the Code (Appendix 4). Occupancy Category I, II, or III structures located where the mapped spectral response acceleration parameter at 1-s period, S 1, is greater than or equal to 0.75 g (Appendix 7) shall be assigned to Seismic Design Category E. Occupancy Category IV structures located where the mapped spectral response acceleration parameter at 1-s period, S 1 (Appendix 7), is greater than or equal to 0.75 g shall be assigned to Seismic Design Category F. All other structures shall be assigned to a Seismic Design Category based on their Occupancy Category and the design spectral response acceleration parameters, S DS and S D1. Each building and structure shall be assigned to the more severe Seismic Design Category in accordance with Table or , irrespective of the fundamental period of vibration of the structure, T (Appendix 5). A geotechnical investigation report shall be provided for a structure assigned to Seismic Design Category C, D, E, or F. TABLE SEISMIC DESIGN CATEGORY BASED ON SHORT PERIOD RESPONSE ACCELERATION PARAMETER Occupancy Category Value of S DS I or II III IV S DS < A A A S DS < 0.33 B B C 0.33 S DS < 0.50 C C D 0.50 S DS D D D TABLE SEISMIC DESIGN CATEGORY BASED ON 1-S PERIOD RESPONSE ACCELERATION PARAMETER Occupancy Category Value of S DS I or II III IV S D1 < A A A S D1 < B B C S D1 < 0.20 C C D 0.20 S D1 D D D 28

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