Earthquake Design Using 1997 Uniform Building Code Dr. Hathairat Maneetes Department of Rural Roads

1971 San Fernando earthquake The UBC was introduced in the 1927… From the early 80’s, the earthquake design provisions in UBC changed rapidly and substantially in response to the lessons learned from several major earthquakes (e.g. 1971 San Fernando earthquake and 1994 Northridge earthquake) Soft story Spiral ties 1971 San Fernando earthquake Normal ties Confinement effects Another example of soft story

1994 Northridge earthquake 1997 UBC has several important modifications following the 1994 Northridge earthquake. 1994 Northridge earthquake

Some of the major changes include Strength-based (compared with allowable stress approach for the previous versions) Removal of pre-qualified steel connection details Requirements to consider liquefaction Addition of near-fault factor to base shear formulation Deformation compatibility requirements Redundancy requirements Stricter detailing for non-participating elements Aligned with NEHRP’s provisions for smooth transition into International Building Code (IBC) in 2000

Three model buildings codes for seismic design in the United States. Three model building codes in US: BOCA National Building Code (NBC) by BOCA Uniform Building Code (UBC) by ICBO Standard Building Code (SBC) by SBCCI NEHRP SEAOC Materials code accompanying IBC ASCE 7 Since the early 1900s, the system of building regulations in the United States was based on model building codes developed by three regional model code groups BOCA: Building Officials Code of Administrators International ICBO: International Conference of Building Officials SBCCI: Southern Building Code Congress International BOCA NBC SBC

There are three methods to estimate inertia or earthquake forces. Resultant (inertia) earthquake force distribution Response (time) history method Linear (elastic) or nonlinear (inelastic) Apply acceleration history directly to base of numerical model of structure Response spectrum method Linear (elastic) approach to calculate the modal (peak values) responses Modal responses combined (using SRSS or CQC) to give design values Equivalent static-force method Linear approach (assume response dominated by 1st mode response) Nonlinear approach used for rehabilitation (“Push-over” analysis) Ground acceleration There are basically 3 methods to estimate earthquake forces. They are response history, response spectrum and equivalent static-force methods. time Earthquake acceleration Complexity

Idealized for design purposes Typical response spectrum of a particular ground motion. Peak response acceleration, ar,peak Idealized for design purposes Actual Short to medium period Long Period Period (T) M Period This shows a typical response spectrum of a particular ground motion. The spectrum shows the peak response acceleration of a SDOF system with a given period under the given ground motion. For most seismic codes, it has been simplified to aid design analysis purposes. K a Ground acceleration time

Multiple (e.g. six) degrees of freedom The equivalent static force procedure is a simplification of the dynamic response spectrum method. Consider more than one mode to get realistic results Response Spectrum Method T6 T5 T4 T3 T2 T1 Building model Multiple (e.g. six) degrees of freedom Decoupled SDOF Consider only the fundamental (1st) mode to simply analysis Equivalent Static force Method The equivalent static force procedure is a simplified response spectrum method in that it only uses the first fundamental period to determine the peak response. T1

UBC-97 is specific about which analysis method may or must be used. Static Lateral-force Procedure limitations: Seismic Zones Regular structure Irregular structure 1 2A and 2B (with occupancy category 4 or 5) All structures (regular or irregular) in Seismic Zone 1 or in Zone 2 with occupancy category 4 or 5. Regular structures using one of the structural systems listed in Table 16-N if they are under 240 feet (7,315.2cm) in height. Irregular structures not more than 5 stories or 65 feet (1,981.2cm) in height. UBC-97 is specific about which analysis method may or must be used. The static-force method can be used under the following conditions. All structures (regular or irregular) in Seismic Zone 1 and in zone 2 with occupancy category 4 or 5. Regular structures using one of the structural systems listed in Table 16-N if they are under 240 feet (7,315.2cm) in height. Irregular structures not more than 5 stories or 65 feet (1,981.2cm) in height. 3,4 < 240 feet < 5 stories or 65 feet

If these conditions are not satisfied, the structure shall be designed using dynamic method. Structures with a flexible upper portion supported on a rigid lower portion if all of the following conditions are met: When both portions are considered separately, they can both be classified as regular. The average story stiffness of the lower portion is at least ten times the average story stiffness of the upper portion. The period of the whole structure is no more than 1.1 times the period of the upper portion considered as a separate structure fixed at the base. So how do we define building irregularities with respect to earthquake design? If these conditions are not satisfied, the structure shall be designed using the response spectrum or response history methods. So how do we define building irregularities with respect to earthquake design?

There are two types of irregularities, on plan or along the building height. Vertical Irregularities Kx < 0.7Kx+1 or Kx < 0.8 (Kx+1 + Kx+2 + Kx+3)/3 Where K is the story lateral stiffness x+3 x+2 x+1 There are two types of building irregularities: plan irregularities or vertical irregularities along the building height. UBC-97 categorizes five types of vertical irregularities. The first is stiffness irregularity or better known as soft story. The criteria is based on the relative stiffness of the story under consideration in comparison with the upper stories. x Stiffness irregularity – soft story UBC-97 Table 16-L

There are two types of irregularities, on plan or along the building height. Vertical Irregularities Wx+1 > 1.5Wx or Wx+1 > 1.5Wx+2 Where W is the story effective weight (or mass) x+2 x+1 x The 2nd vertical irregularities is referred as weight or mass irregularity. Here the effective seismic mass of any story is more than 150% of the adjacent story. Weight (mass) irregularity UBC-97 Table 16-L

Vertical Irregularities Vertical geometric irregularity There are two types of irregularities, on plan or along the building height. Vertical Irregularities Where bi: Horizontal dimension of lateral force-resisting system at story i b1 > 1.3b2 b2 Lateral force resisting elements For vertical geometric irregularity, the horizontal dimension of the lateral force resisting system in any story is more than 1.3 times of that in adjacent story. b1 Vertical geometric irregularity UBC-97 Table 16-L

There are two types of irregularities, on plan or along the building height. Vertical Irregularities l2: offset l1: length of lateral-load resisting elements l2 > l1 l2 The next category is in-plan discontinuity in vertical lateral force resisting element as shown in the figure. The offset between the lateral force resisting elements in adjacent story are more than the length of those elements. l1 In-plane discontinuity in vertical lateral-force resisting element UBC-97 Table 16-L

Vertical Irregularities Discontinuity in capacity – weak story There are two types of irregularities, on plan or along the building height. Vertical Irregularities Sx+1/Sx < 0.8 Where S: Total strength of lateral force resisting elements x+1 The last category of vertical irregularities is a weak story due to discontinuity in capacity as shown here. Next we will look at plan irregularities. x Discontinuity in capacity – weak story UBC-97 Table 16-L

There are two types of irregularities, on plan or along the building height. Plan Irregularities UBC-97 also categorizes five types of plan irregularities. The first type is torsional irregularity for rigid diaphragms. Torsional irregularity is considered to be present when the maximum story drift at one end of the structure is more than 120% percent of the average story drifts of the two ends of the structure. Torsional irregularity – to be considered when diaphragms are not flexible UBC-97 Table 16-M

There are two types of irregularities, on plan or along the building height. Deformation incompatibility leading to stress concentration Stiffer; less deformation Less stiff; more deformation Plan Irregularities Deformation incompatibility at re-entrant corners lead to stress concentrations and hence should be avoided. Alternatively these corners need to be strengthen and specifically detailed to withstand the stress concentrations. Stress concentrations Re-entrant corners UBC-97 Table 16-M

Diaphragm discontinuity There are two types of irregularities, on plan or along the building height. Plan Irregularities Aopening > 0.5Agross Agross Open Aopening In diaphragm discontinuity, there is abrupt discontinuities or changes in the diaphragm stiffness within a floor. Diaphragm discontinuity UBC-97 Table 16-M

There are two types of irregularities, on plan or along the building height. Vertical lateral force resisting elements offset out-of-plane Plan Irregularities Here out-of-plane offsets of vertical elements lead to discontinuity in the lateral force path. Out-of-plane offsets UBC-97 Table 16-M

There are two types of irregularities, on plan or along the building height. Plan Irregularities These lateral force resisting elements are not parallel to major axes These lateral force resisting elements are not parallel and symmetric to major axes The 5th plan irregularities refer to nonparallel systems where the vertical lateral load resisting elements are not parallel or symmetric about the major orthogonal axes of the lateral load resisting elements. Nonparallel systems UBC-97 Table 16-M

The UBC-97 governing equations are … Spectral Acceleration Estimation of Total Base Shear 2.5Ca Equation 30-4 But need not be greater than Equation 30-5 Ca With all the seismic inputs determined, the total base shear can be found as follows. Minimum base shear correspond to max. R = 8.5 i.e. (1/8.5) = 0.11. Limit the max. reduction of earthquake base shear. I will now talk about the individual seismic parameters But need to be at least Equation 30-6 T0 Ts Period (T) UBC-97 Design Spectra Equation 30-7 (for Seismic zone 4)

Rigid box of mass M fixed to the ground Inertial forces is developed from Newton’s Second Law. Damping Lumped mass (M) ar = a ar = f(M, K, a, c) ar = a F = M.a F = M ar F = M.a Flexible with stiffness K Infinitely rigid a a a For a rigid body, the inertial effects or dynamic force can be statically modeled using Newton’s second law of motion. The inertial force on the body is simply the product of mass and ground acceleration. For a non-rigid body, the inertial force is still a function of mass and acceleration. However, the response acceleration (ar) of the lumped mass is not equal to the ground acceleration. It is a function of the system mass, stiffness and damping, and ground acceleration. Rigid box of mass M fixed to the ground Ground acceleration time NON-RIGID BODY RIGID BODIES

UBC-97 has broadly zoned US territories into six seismic zones. 1 2A 2B 3 4 UBC-97 has broadly zoned US territories into six seismic zones. Zone 0 being one of least risk, 4 being the highest. The highest seismic risk regions in US are in the West (e.g. California), Alaska and Hawaii. Increasing seismic risk UBC-97 Figure 16-2: Seismic Zone Map of the United States

Each seismic zone is assigned a factor that corresponds to the maximum ground acceleration. Seismic Zone Factor Z 1 0.075 2A 0.15 2B 0.2 3 0.3 4 0.4 Each seismic zone is assigned a factor that corresponds to the maximum ground acceleration. The value is based on a reference soil profile, namely rock or SB soil profile as defined by UBC97. UBC-97 Table 16-I

The “effective” ground acceleration imparted to the structure is affected by the soil conditions. UBC-97 Table 16-J a = ag a  ag a a Reference soil type ag For each zone, the “effective” ground acceleration imparted to the structure is affected by the soil conditions. UBC-97 assign 6 soil profile types based on shear wave velocity, standard penetration test and undrained shear strength. Soil profile SB is the reference soil type. That is there is no reduction or amplification of the ground acceleration. Other soil profiles tend to amplify the ground acceleration impart to the structure base. Generally speaking, softer soil will amplify the soil more. The default category for undefined soil profile is SD Default soil profile Ground acceleration based on SB soil profile (i.e. rock). ag Other soil profiles tend to amplify the ground acceleration impart to the structure base a < ag (Hard rock, rock) a > ag (All other soil profiles)

“Short” to “medium” period Seismic coefficients represent the seismicity of the region and the characteristics of the soil. Seismic Coefficient Cv Seismic Coefficient Ca ag In UBC-97, the effect of soil profile on the base acceleration is accounted by the seismic coefficients Ca and Cv. Two seismic factors are necessary to quantify the soil profile effects because the soil profile has different effects on the structure with different periods. As evident from the table, softer soil amplify the ground motion significantly more for building with longer period. Ca applies to building with short to medium period while Cv is to cater for building with long period. UBC-97 Table 16-Q UBC-97 Table 16-R a “Short” to “medium” period “Long” period

Response Modification Factor to account for nonlinear building response. Need to consider the inherent ability of the structure to reduce the earthquake forces through overstrength, ductility and damping. A response reduction factor or R-factor is introduced to account for the beneficial effects of nonlinear building behavior. R-value greater than 1, inelastic response is assumed and earthquake forces is reduced. Base Shear Elastic response V Reduction in earthquake forces arising from nonlinear building response V/R “Actual” Inelastic response Based on past earthquake events, it was observed that structures that are more ductile and having higher degree of overstrength or damping generally experienced lower dynamic response, stresses and deformation. This is due to the dissipation of the earthquake energy through nonlinear structural behavior. To account for the beneficial effects of nonlinear building response, a response reduction factor is introduced. Higher ductility Displacement s M = (0.7R)s

Increase in inelastic response R-value is a convenient method to describe the nonlinear response of the structural system. Total Base Shear V System 1 V/R1 Increase in inelastic response System 2 V/R2 System 3 V/R3 Just to further illustrate the R-factor. It is a convenient (maybe too simplicity) way to describe nonlinear response of the structural system. System 2 is the most ductile (or has the most overstrength) whereas System 1 has limited ductility and overstrength R3 > R2 > R3 Displacement

UBC-97 categories 7 basic structural systems with R-values varying from 2.2 to 8.5 These are maximum values for each structural system type; lower value can be used if required. Great care must be exercised in selecting the R-value! The table summarizes some of the commonly used structural systems used for resisting lateral earthquake forces. Generally, structural systems (e.g. special steel moment frames, steel eccentrically braced frame) with higher degree of energy dissipation (through ductility or damping) have higher R-values and hence lower earthquake forces. On the other hand, systems (e.g., unreinforced masonry walls) that have limited inelastic response (or brittle behavior) are assigned lower R-values and hence less reduction in the design earthquake forces. It should be pointed out that great care should be exercised when selecting R-value. It is not sufficient to merely identify the proposed lateral force resisting system and to accord an R-value recommended by the seismic code. When specifying an R-value greater than 1, the designer must ensure that the building system he or she is designing can deform inelastically in a control manner. Btw, if you are wondering how these numbers came about. The numeric values for each system is selected based on the performance of similar structural systems in past earthquakes. It is based almost entirely on the professional judgment of the structural engineering community. It may be revised (normally reduced) as we learned more of each system performance in new earthquakes. UBC-97 Table 16-N

What are the common structural systems? Lateral Gravity Bearing wall Building frame Moment-resisting frame Dual system Supports all gravity and lateral loads Lack redundancy R-value varies from 2.8 to 5.5 Frame carries gravity (i.e. gravity frame Shear walls or braced frames carry lateral load Need to consider deformation compatibility R-value varies from 5.5 to 7.0 Specially detailed frame to support both gravity and lateral loads High level of ductility and redundancy R-value varies from 3.5 to 8.5 Similar to building frame system except the gravity frame also provide secondary lateral force resistance. R-value varies from 4.2 to 8.5 The four common structural systems or lateral force resisting systems are shown here. The systems are categorized based on how the gravity and lateral loads are supported.

Examples of structural systems Building frames Column Beam Concentric braced frames (CBF) Example of moment resisting connection Moment frame Here are more illustrative examples of buildings frames and special truss moment frame. Here you see examples of simple (gravity) connection and moment resisting connection. Steel eccentric braced frame (EBF) Example of simple shear connection Special truss moment frame

For essential or hazardous buildings, the margin of safety in seismic design needs to be higher The importance factor is used to increase the earthquake force Depends on the occupancy category. In UBC-97, I is 1.25 for essential facilities and hazards facilities; no enhancement for other facilities. For essential or hazardous buildings, the margin of safety in seismic design need to be higher to reduce damage. Specially, the earthquake force is increased by 25% in the code. UBC-97 Table 16-K

UBC-97 Load Combinations Strength level U = 1.2D + f1L + 1.0E U = 0.9D + 1.0E where E = Eh + Ev where Ev = 0.5CaID Working stress level F = D + (W or E/1.4) F = 0.9D + (E/1.4) F = D + 0.75 [L + (Lr or S) + (W or E/1.4)] OR F = 4/3[D + L + (W or E/1.4)] F = 4/3[D + L + (E/1.4)] f1 = 1.0 for public assembly LL>100 psf(4.9kN/m2) = 1.0 for garage LL = 0.5 for other LL Vertical component  Eh 1.2D + 0.5L + Ev

Numerical Example – Static lateral-force procedure Non-bearing shear wall Determine the design seismic forces for the three-story reinforced concrete shear wall shown using UBC-97 static lateral-force procedure. The building is located in Southeastern California on rock with a shear wave velocity of 3,000 ft/sec. The story dead loads are 2,200 kips, 2,000 kips and 1,700 kips for the 1st, 2nd and roof level, respectively. The shear walls do not carry significant vertical loads. (Adapted from Naeim (2001)) 11 ft 11 ft 13 ft Building is assumed to be located here IMPORTANT: Always check the applicability of the method Building of regular construction No plan or height irregularity Total height = 35 feet < 240 feet  UBC-97 static lateral-force method is applicable. Now we go through a simple numerical example to illustrate the static lateral-force procedure as outlined by UBC-97. This example is the same as that in the paper. The first step in the procedure is to always check the applicability of the method. Never assume it can be used all the time. UBC-97 Figure 16-2: Seismic Zone Map of the United States

Numerical Example – Static lateral-force procedure UBC-97 Table 16-I Seismic Importance Factor, I = 1.0 (Assumed non-essential facility) Location is in Seismic Zone 3  Seismic Zone Factor, Z = 0.3 Shear velocity = 3,000 ft/sec.  Soil Profile Type is SB i.e., rock Seismic Zone Seismic Zone Factor Z 1 0.075 2A 0.15 2B 0.2 3 0.3 4 0.4 UBC-97 Table 16-J Note corrections Seismic Coefficients: CV = 0.3, Ca = 0.3 Since the building is founded on soil profile type B, no modification to the ground acceleration is necessary. There is a correction here. Ca is 0.3 instead of 0.33. UBC-97 Table 16-Q UBC-97 Table 16-R

Numerical Example – Static lateral-force procedure UBC-97 Table 16-N Response modification factor: Non-load bearing shear wall, recommended highest R-value is 5.5 Height limit is 240 ft > 35 ft (OK) Note corrections The recommended R-value is 5.5. Note that this is the highest value recommended by UBC-97. It does not mean you need to use this value; a lower value can be used. There is a correction here. The nonbearing shear wall should be a building frame system, and not shear wall frame interaction system.

Numerical Example – Static lateral-force procedure V (kips) Estimation of Total Base Shear 1,109.7 804.5 194.7 But need not be greater than 0.29 Period (sec) With all the seismic inputs determined, the total base shear can be found as follows. But need to be at least  design base shear = 804.5 kips

Numerical Example – Static lateral-force procedure Vertical Distribution of the Earthquake Forces. Level x Story height hx (ft) Story weight wx (kips) Wxhx x 103 (kips.ft) Seismic force at each level Fx (kips) Story shear Vx (kips) Story over-turning moment Mx (kips.ft) 3 35 1,700 59.5 351.7 3,869 2 24 2,000 48.0 283.7 635.4 10,858 1 13 2,200 28.6 169.1 804.5 21,317 Σ 5,900 136.1 The total base shear is distributed vertically to each floor in accordance to the height and story weight. With the computed seismic forces and gravity loads, a static, elastic analysis of the building can be performed to obtain the design stresses and deformation for design of the structural elements. The appropriate load combinations are shown here. Use load combination! 351.7 kips Level 3 283.7 kips Level 2 U = 1.2D + 0.5L + 1.0E 169.1 kips Level 1 U = 0.9D + 1.0E

Numerical Example – Static lateral-force procedure Determine story drift limits Maximum inelastic response displacement: M = 0.7Rs Rearranging, we have s =  M/0.7R Where M < 0.025h for T < 0.7sec (UBC-97, Section 1630.10) 1st story: s < (0.025)(13)/0.7(5.5) = 1.01 in Other stories: s < (0.025)(11)/0.7(5.5) = 0.858 in The story drift limits are computed as shown here.

Other important considerations Orthogonal effects : 100% in one direction + 30% in the orthogonal effects (UBC-97 Section 1633.1) Multiple lateral force resisting systems; requirements of more restrictive one governs (UBC-97 Section 1633.2.2) Seismic design connections must be clearly detailed in drawings (UBC-97 Section 1633.2.3) Deformation compatibility (UBC-97 Section 1633.2.4) Familiarity with accompanying material codes , etc. For some structures (e.g. irregular), orthogonal effects shall be considered. For structures with multiple type of lateral force resisting systems, the more restrictive system shall govern the seismic design Connections designed for seismic forces must be clearly detailed in engineering drawings. Deformation compatibility shall be considered. This requires that non-participating structural elements be designed to ensure compatibility of deformations with the lateral force resisting system. In other words, the non-participating elements shall be capable of maintaining support for gravity loads at deformations expected due to the seismic forces. Collectors shall be designed to effectively transfer seismic forces originating in other portions of the structure to the elements providing the resistance to these forces. Detailed seismic provisions (esp. detailing requirements) spelt out in associated material codes (e.g., ACI 318, AISC Manual of Steel Construction)

Time History Analysis... Oakland, CA

The natural frequencies fell within the dominating frequency range of the ground motions. GILROY EL CENTRO According to the ASCE7, at least 3 different ground motions should be used in the analysis. If the no. of the selected ground motion is less than 7, the maximum response will be used in the design. But if the no. of the selected ground motion is more than 7, the average response can be used in the design. In this study, the 3 ground motions recorded from different station were selected. So the maximum response from these 3 scaled EQ will govern the structural design. HOLLISTER

The 3 OR 7 pairs of recorded ground motions were scaled to match the design spectrum. SRSS of GILROY (N-S and E-W) 0.2T 1.5T x scale factor1 PGA = 0.367 g Average response spectrum SRSS of EL CENTRO (N-S and E-W) x scale factor2 PGA = 0.371 g 1.4 x Design Spectrum Another important issue is scaling the EQ to match the design spectrum 2D : Average response spectrum above design spectrum 3D : Average response spectrum at 1.3 times above the design spectrum. SRSS of HOLLISTER (N-S and E-W) x scale factor3 PGA = 0.177 g If 3 analyses performed, use the maximum response. If 7 analyses performed, use the average response.

An Innovative Design – Structural Control

What’s an innovative design??? Conventional design ductility-based approach nonlinear behavior of the structure Some damage may occur Energy-based design ‘protective approach’ ‘structural control’ classified into 3 groups: passive, active and semi-active, hybrid controls

INTRODUCTORY - Passive Control Incorporating passive devices to control the structural motion and to modify its dynamic parameters (stiffness and damping). Seismic (base) isolation Passive EDS Mass damper

INTRODUCTORY - Passive Control Source-Sink Analogies [Popov et al., 1993]

Dampers

Viscous Fluid Damper 

How to choose the appropriate system for your building??? http://www.oiles.co.jp/en/menshin/building/index.html

INTRODUCTORY - Active Control Control motion of structure through some external energy source. Schematic Details [Chaidez, 2003] Analogy with Human Body (Servio Model)

INTRODUCTORY – Hybrid Systems A series or parallel combination of an active (or semi-active) system with a passive system. Active Control with Base Isolation System [Chaidez, 2003; Iemura, 1994]

Thank you for your attention! Any Questions ??? I have come to the end of my presentation. Thank you very much for your attention! Any questions?