Concrete Construction Engineering Handbook, Second Edition · 2010-01-11 · 32-2 Concrete...

32-1

32Seismic-Resisting

Construction

Walid M. Naja, S.E.*

Christopher T. Bane, S.E.**

32.1 Fundamentals of Earthquake Ground Motion ...............32-2Introduction • Recorded Ground Motion • Characteristics of Earthquake Ground Motion • Factors Influencing Ground Motion • Evaluating Seismic Risk at a Site • Estimating Ground Motion

32.2 International Building Code (IBC 2006).........................32-7IBC Design Criteria • Design Requirements for Seismic Design Category A • Design Requirements for Seismic Design Categories B, C, D, E, and F • Equivalent Lateral Force Procedure • Modal Response Spectrum Analysis • Seismic Load Combinations • Diaphragms, Chords, and Collectors • Building Separation • Anchorage of Concrete or Masonry Walls • Material-Specific Design and Detailing Requirements • Foundation Design

32.3 Design and Construction of Concrete and Masonry Buildings...................................................32-29Preface • Concrete Buildings • Design of Masonry Buildings • Shear-Wall Foundation Analysis and Design • Nomenclature

32.4 Seismic Retrofit of Existing Buildings ...........................32-42Introduction • Structure Weakness • Creation of Adequate Load Path • Establish Deformation Compatibility • Establish Adequate Lateral-Load-Resisting System

32.5 Seismic Analysis and Design of Bridge Structures .......32-48Seismic Analysis of Bridge Structures • Seismic Design of Bridge Structures •

32.6 Retrofit of Earthquake-Damaged Bridges .....................32-56Introduction • Background • Seismic Analysis Approach • Design Approaches

32.7 Defining Terms ................................................................32-62References ...................................................................................32-62

* Principal, FBA, Inc., Structural Engineers, Hayward, California; expert in the design and construction of concretestructures in seismically active regions, particularly low- to mid-rise buildings.** Senior Project Engineer, FBA, Inc., Structural Engineers, Hayward, California; expert in the design of post-tensioned concrete structures and the design and retrofit of buildings in seismic regions.

© 2008 by Taylor & Francis Group, LLC

32-2 Concrete Construction Engineering Handbook

32.1 Fundamentals of Earthquake Ground Motion

32.1.1 Introduction

When transmitted through a structure, ground acceleration, velocity, and displacements (referred to asground motion) are in most cases amplified. The amplified motion can produce forces and displacementsthat may exceed those the structure can sustain. Many factors influence ground motion and its amplifi-cation. An understanding of how these factors influence the response of structures and equipment isessential for a safe and economical design. Earthquake ground motion is usually measured by a strong-motion accelerograph that records the acceleration of the ground at a particular location. Record accel-erograms, after they are corrected for instrument errors and adjusted for baseline, are integrated to obtainvelocity and displacement-time histories. The maximum values of the ground motion (peak groundacceleration, peak ground velocity, and peak ground displacement) are of interest for seismic analysisand design. These parameters, however, do not by themselves describe the intensity of shaking thatstructures or equipment experience. Other factors, such as the earthquake magnitude, distance from faultor epicenter, duration of strong shaking, soil condition of the site, and frequency content of the motion,also influence the response of a structure. Some of these effects, such as the amplitude of motion, durationof strong shaking, frequency content, and local soil conditions, are best represented through the responsespectrum (1.1 to 1.4), which describes the maximum response of a damped, single-degree-of-freedomoscillator to various frequencies or periods. The response spectra from a number of records are oftenaveraged and smoothed to obtain design spectra, which also represent the amplification of ground motionat various frequencies or periods of the structure. This section discusses earthquake ground motion. Theinfluence of earthquake parameters such as earthquake magnitude, duration of strong motion, soilcondition, and epicentral distance on ground motion is presented and discussed.

32.1.2 Recorded Ground Motion

Ground motion during an earthquake is measured by a strong-motion accelerograph that records theacceleration of the ground at a particular location. Three orthogonal components of the motion, two inthe horizontal direction and one in the vertical, are recorded by the instrument. The instruments maybe located in a free field or mounted in structures. Accelerograms are generally recorded on photographicpaper or film. The records are digitized for engineering applications, and during the digitization processerrors associated with instruments and digitization are removed. The digitization, correction, and pro-cessing of accelerograms have been carried out by the Earthquake Engineering Research Laboratory ofthe California Institute of Technology in the past and are now carried out by the U.S. Geological Survey.

32.1.3 Characteristics of Earthquake Ground Motion

Characteristics of earthquake ground motion that are important in earthquake engineering applicationsinclude:

• Peak ground motion (peak ground acceleration, peak ground velocity, and peak ground displace-ment)

• Duration of strong motion• Frequency content

Each of these parameters influences the response of a structure. Peak ground motion primarily influencesthe vibration amplitudes. Duration of strong motion has a pronounced effect on the severity of shaking.A ground motion with a moderate peak acceleration and long duration may cause more damage than aground motion with a larger acceleration and a shorter duration. Frequency content and spectral shapesrelate to frequencies or periods of vibration of a structure. In a structure, ground motion is most amplifiedwhen the frequency content of the motion and the vibration frequencies of the structure are close toeach other. Each of these characteristics is briefly discussed below.


Seismic-Resisting Construction 32-3

32.1.3.1 Peak Ground Acceleration

Peak ground acceleration has been widely used to scale earthquake design spectra and acceleration-timehistories. As will be discussed later, recent studies recommend that in addition to peak ground acceler-ation, peak ground velocity, and displacement should be used for scaling purposes.

32.1.3.2 Duration of Strong Motion

Several investigators have proposed procedures for computing the strong-motion duration of an accel-erogram. Page et al. (1972) and Bolt (1969) proposed the bracketed duration, which is the time intervalbetween the first and the last acceleration peaks greater than a specified value (usually 0.05 g). Trifunacand Brady (1985) defined the duration of the strong motion as the time interval in which a significantcontribution to the integral of the square of the acceleration (òa2dt, referred to as the accelerogramintensity) takes place. They selected the time interval between the 5% and the 95% contributions as theduration of strong motion. The noted procedures usually result in different values for the duration ofstrong motion. This is to be expected, as the procedures are based on different criteria. Because there isno standard definition of strong-motion duration, the selection of a procedure for computing it for astudy depends on the purpose of the study. The bracketed duration proposed in Page et al. (1972) andBolt (1969) may be more appropriate when computing elastic and inelastic response.

32.1.3.3 Frequency Content

The frequency content of ground motion can be examined by transforming the motion from time domainto frequency domain through a Fourier transform. The Fourier amplitude spectrum and power spectraldensity, which are based on this transformation, may be used to characterize the frequency content. Forfurther discussion regarding frequency content, the reader is encouraged to consult The Seismic DesignHandbook (Naeim, 1989). When the power spectral density of ground motion at a site is established,random-vibration methods may be used to formulate probabilistic procedures for computing theresponse of structures.

32.1.4 Factors Influencing Ground Motion

Earthquake ground motion and its duration at a particular location are influenced by a number of factors,the most important being: (1) earthquake magnitude, (2) distance of the source of energy release(epicentral distance or distance from causative fault), (3) local soil conditions, (4) variation in geologyand propagation of velocity along the travel path, and (5) earthquake-source conditions and mechanism(fault type, stress conditions, stress drop). Past earthquake records have been used to study some of theseinfluences. Although the effect of some of these parameters, such as local soil conditions and distancefrom source of energy release, are fairly well understood and documented, the influence of the sourcemechanism and the variation of geology along the travel path are more complex and difficult to quantify.Several of these influences are interrelated; consequently, it is difficult to discuss them individually withoutincorporating the others. Some of these influences are discussed below.

32.1.4.1 Distance

The variation of ground motion with distance to the source of energy release has been studied by manyinvestigators. In most studies, peak ground motion (usually peak ground acceleration) is plotted as afunction of distance. A smooth curve based on a regression analysis is fitted to the data, and the curveor its equation is used to predict the expected ground motion as a function of distance. These relation-ships, referred to as motion attenuation, are sometimes plotted independently of the earthquake magni-tude. This was the case in earlier studies because of the lack of sufficient numbers of earthquake records;however, with the availability of a large number of records, particularly during the 1971 San Fernandoearthquake and subsequent seismic events, the database for attenuation studies was increased and anumber of investigators reexamined their earlier studies, modified their proposed relationships forestimating peak accelerations, and included earthquake magnitude as a parameter. Donovan (1973)



compiled a database of more than 500 recorded accelerations from seismic events in the United States,Japan, and elsewhere, and later increased it to more than 650. A plot of peak ground acceleration vs.fault distance for different earthquake magnitudes from his database shows that, for a good portion ofthe data, the peak acceleration decreases as the distance from the source of energy release increases. Ithas been reported by Housner (1965), Donovan (1973), and Seed and Idriss (1982) that at distancesaway from the fault or the source of energy release (far field), the earthquake magnitude influences theattenuation, whereas at distances close to the fault (near field) the attenuation is affected by smallerearthquake magnitudes and not by the larger ones. The majority of attenuation studies and the relation-ships presented in Table 32.1 are mainly from data in the western United States. It is believed by severalseismologists that ground acceleration attenuates more slowly in the eastern United States and easternCanada. The variation of peak ground velocity with distance from the source of energy release (velocityattenuation) has also been studied by several investigators. Velocity attenuation curves have similar shapesand follow similar trends to the acceleration attenuation; however, velocity attenuates somewhat fasterthan acceleration, and, unlike acceleration attenuation, velocity attenuation depends on soil condition.

TABLE 32.1 Typical Attenuation Relationships

Data Source Relationships Ref.

1 San Fernando earthquake, February 9, 1971

a = 190/R1.83 Donovan (1973)

2 California earthquake

where log yo = –(b + 3) + 0.81m – 0.027m2, where b is a site factor

Blume et al. (1992)

3 California and Japanese earthquakes

where Q = 0.167 – 1.83/R; TG = fundamental period of site

Yamabe and Kanai (1988)

4 Cloud (1963) Milne and Davenport (1969)

5 Cloud (1963) a = 1.24e0.67m/(R + 25)2 Esteva (1969)

6 USC and USGS Cloud and Perez (1967)

7 303 instrumental values a = 1.325e0.67m/(R + 25)1.6 Donovan (1973)

8 Western U.S. records a = 0.093e0.8m/(R + 400) Donovan (1973)

9 U.S., Japan, etc. a = 1.35e0.58m/(R + 25)1.52 Donovan (1973)

10 Western U.S. records, USSR, Iran

ln a = 3.99 + 1.28m – 1.75 ln [R + 0.147e0.732m] Campbell (1997)

11 Western U.S. records, worldwide

log a = –1.02 + 0.249m – log (R2 + 7.32)1/2 – 0.00255(R2 + 7.32)1/2

Idriss (1993)

12 Western U.S. records ln a = ln α(m) – β(m) ln(R + 20)

where m = surface-wave magnitude, m ≥ 6; local magnitude, m < 6; R = smallest distance to source, m ≥ 6; hypocentral distance, m < 6; α(m) and β(m) are magnitude-dependent coefficients

Seed and Idriss (1982)

13 Italian records log a = –1.562 + 0.306m – log(R2 + 5.82)1/2 + 0.169S

where S = 1.0 for soft sites and 0 for rock

Sabetta and Pugliese(1987, 1996)

Note: Acceleration a is in g; distance to causative fault R is in kilometers; epicentral distance R′ is in miles; local depth his in miles.

ay

R h=

+ ′0

21 ( / )

aTG

m P R Q= − +0 0051100 61. . log

ae

e R

m

m=

+0 0069

1 1

1 64

1 1 2

.

.

.

.

log. log( )

aR= − ′ +6 5 2 80

981



Distance also influences the duration of strong motion. Correlation of the duration of strong motionwith epicentral distance has been studied by Page et al. (1972), Trifunac and Brady (1975), Krinitzskyand Chang, and others. Page et al. (1972), using the bracketed duration, concluded that for a givenmagnitude the duration decreases with an increase in the distance from the source.

32.1.4.2 Site Geology

Soil conditions influence ground motion and its attenuation. Several investigators, such as Boore et al.(1978, 1980) and Seed and Idriss (1982), have presented attenuation curves for soil and rock. Accordingto Boore et al., the peak horizontal acceleration is not appreciably affected by soil condition (it is nearlythe same for rock and for soil). Seed and Idriss compared the acceleration attenuation for rock fromearthquakes with Richter magnitudes of approximately 6.6 with that for alluvium from the 1979 ImperialValley earthquake (Richter magnitude, 6.8). Their comparison, shown in Figure 32.1, indicates that, ata given distance from the source of energy release, peak accelerations on rock are somewhat greater thanthose on alluvium. The effect of soil condition on peak acceleration is illustrated in Figure 32.2. Accordingto this figure, the difference in acceleration in rock and in stiff soil is practically negligible. There seemsto be general agreement among various investigators that soil condition has a pronounced influence onvelocities and displacements. Larger peak horizontal velocities are more likely to be expected in soil thanin rock.

32.1.4.3 Magnitude

As expected, at a given distance from the source of energy release, larger earthquake magnitudes resultin larger peak ground accelerations, velocities, and displacements. Because of the lack of adequate datafor earthquake magnitudes greater than approximately 7.5, the effect of magnitude on peak groundmotion and duration is generally determined through extrapolation of data from earthquake magnitudessmaller than 7.5.

FIGURE 32.1 Comparison of attenuation curves for rock sites and the Imperial Valley earthquake of 1979. (Adaptedfrom Seed, H.B. and Idris, I.M., Ground Motions and Soil Liquefaction during Earthquakes, Earthquake EngineeringResearch Institute, Berkeley, CA, 1982.)

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.01 2 5 10 20 50

Closest Horizontal Distance from Zone

of Energy Release (km)

Mean for Imperial Valley

1979 earthquake, Ms = 6.8

Mean for rock sites,

Ms = 6.6

Peak

Ho

rizo

nta

l Acc

ele

rati

on

(g

)



32.1.5 Evaluating Seismic Risk at a Site

Seismic-risk evaluation is based on information from three sources: (1) the recorded ground motion,(2) the history of seismic activity in the vicinity of the site, and (3) the geological data and fault activitiesof the region. For most regions of the world this information, particularly that from the first source, isvery limited and may not be sufficient to predict the size and recurrence intervals of future earthquakes.Nevertheless, earthquake engineers have relied on this limited information to establish some acceptablelevels of risk. Seismic-risk analysis usually begins with developing mathematical models that are used toestimate the recurrence intervals of future earthquakes with certain magnitudes and/or intensities. Thesemodels, together with the appropriate attenuation relationships, are commonly utilized to estimateground-motion parameters such as the peak acceleration and velocity corresponding to a specifiedprobability and return period. The provisions of the International Building Code (IBC) use the spectralaccelerations determined from maximum considered earthquake ground motion maps prepared by theU.S. Geological Survey (USGS). The ground motion accelerations are modified for specific site charac-teristics to determine actual design-level accelerations. The USGS maps are extremely detailed and maybe referenced in ASCE 7-05 or on the USGS website. For a discussion regarding the use of such mappedaccelerations, refer to Section 32.2.1.1.

32.1.6 Estimating Ground Motion

Seismic-risk procedures and attenuation relationships are primarily developed for estimating the expectedpeak horizontal acceleration at the site. A statistical summary of the peak ground acceleration ratios for allfour soil categories (rock, 30 ft of alluvium underlain by rock, 30 to 200 ft of alluvium underlain by rock,alluvium) is presented in Table 32.2. The table includes the ratio of the smaller to the larger of the twopeak horizontal accelerations and the ratio of the vertical to the larger of the two peak horizontal acceler-ations. In each column, the ratios are generally close to each other, indicating that the soil condition doesnot influence the acceleration ratios. The 2/3 ratio of the vertical to horizontal acceleration, which has beenrecommended by Newmark and has been employed in seismic design, is closer to the 84.1 percentile thanto the 50 percentile ratio. Although the 2/3 ratio is conservative, its use has been justified as taking intoaccount variations greater than the median and uncertainties in the ground motion in the vertical direction.

FIGURE 32.2 Relationship between peak accelerations of rock and soil. (Adapted from Seed, H.B. and Idriss, I.M.,Ground Motions and Soil Liquefaction during Earthquakes, Earthquake Engineering Research Institute, Berkeley, CA,1982.)

0.6

0.5

0.4

0.3

0.2

0.1

00 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Peak Horizontal Acceleration on Rock (g)

Deep soil sites

Stiff soil sites

Rock

Peak

Ho

rizo

nta

l Acc

ele

rati

on

(g

)



32.2 International Building Code (IBC 2006)

32.2.1 IBC Design Criteria

The International Building Code (ICC, 2006) references the provisions of ASCE 7-05 (ASCE, 2005) forlateral seismic loads. The ASCE 7-05 seismic design criteria are in turn based on the NEHRP RecommendedProvisions for Seismic Regulations for New Buildings and Other Structures (FEMA, 2003). The provisions

a minor seismic event should cause little or no damage, and a major seismic event should not result inthe collapse of the structure. Accordingly, the building is expected to behave elastically when subjectedto frequently occurring earthquakes and exhibit inelastic behavior when influenced only by infrequentstrong earthquakes. Most low-rise concrete buildings fall into the regular structure type of the Interna-tional Building Code and accordingly are designed for a loading condition resulting from equivalentstatic lateral force. This static load depends on the site geology and soil characteristics, the buildingoccupancy, the building configuration and height, and the structural system being used to support thelateral load. It is important to note that code static loads are no more than one quarter to one third ofthe expected earthquake action. This can be justified in concrete structures where the anticipated crackingresults in increased energy absorption only where ductility in each resisting member and between all theresisting members can be maintained.

32.2.1.1 Mapped Acceleration Parameters

Chapter 22 of ASCE 7-05 contains the mapped maximum considered earthquake (MCE) ground motionparameters Ss and S1. Both Ss and S1 are spectral response acceleration parameters with 5% damping; SS

is determined from a 0.2-second response acceleration, and S1 is determined from a 1-second responseacceleration. Chapter 22 provides detailed maps developed by the U.S. Geological Survey (USGS), but itis not practical to determine site parameters from the maps provided. The recommended method ofobtaining these parameters is to use the Ground Motion Parameter Calculator, provided on the USGSwebsite (http://earthquake.usgs.gov/research/hazmaps/), which allows for the input of a Zip Code or alatitude and longitude to obtain the response parameters. It is recommended that the latitude andlongitude for the specific site be used, as the response parameters can vary significantly over the regionof an entire Zip Code. Websites such as http://terraserver.microsoft.com/ may be used to obtain latitudeand longitude information for a particular address.

32.2.1.2 Site Class

Site class has replaced the term soil profile type, which was used in past codes such as the 1997 UniformBuilding Code. Because the soil type on which a structure is founded has a great impact on the groundmotion at the site, different soil types are assigned values, depending on their stiffness, from Site ClassA for rocklike material to Site Class F for a soil profile that requires a site-specific analysis. Table 32.3lists the site coefficients for different soil types. Site class should not be confused with seismic design

TABLE 32.2 Summary of Peak Ground Acceleration Ratios (Lognormal Distribution)

Soil Category

as/al av/al

Percentile

Mean

Percentile

Mean50 84.1 50 84.1

Rock 0.81 0.99 0.82 0.48 0.69 0.52<30 ft of alluvium underlain by rock 0.89 0.98 0.89 0.47 0.62 0.4630–200 ft of alluvium underlain by rock 0.82 0.96 0.83 0.40 0.66 0.46Alluvium 0.75 0.96 0.79 0.42 0.61 0.45

Note: as is the smaller of the two horizontal components; al is the larger peak acceleration of the two horizontal components;av is the peak acceleration of the vertical component.


and commentary may be found at www.bassconline.org. The basic guideline of the IBC provisions is that

http://earthquake.usgs.gov

http://terraserver.microsoft.com


category, as both use the letters A through F to define different soil types or seismic design categories.Site class is one of the elements used to determine the seismic design category. When not enoughinformation is available to determine the site class, Site Class D shall be used except when the authorityhaving jurisdiction determines that Site Class E or Site Class F is appropriate.

32.2.1.3 Site Coefficients and Adjusted Maximum Considered Earthquake Spectral Response Acceleration Parameters

The mapped acceleration parameters contained in Chapter 22 of ASCE 7-05 are based on Site Class B.When the actual site class varies from Site Class B, the acceleration parameters must be modified based onthe actual site class; for example, SS must be multiplied by an adjustment factor (Fa) to determine SMS, themaximum considered earthquake (MCE) spectral response acceleration at short periods adjusted for siteclass effects. The same holds true for the MCE spectral acceleration at a period of 1 second; S1 is multipliedby Fv to determine SM1. Refer to Table 32.4 and Table 32.5 for the site coefficients Fa and Fv, respectively.

32.2.1.4 Design Spectral Acceleration Parameters

The design earthquake spectral response acceleration parameters are determined by multiplying themodified MCE spectral response acceleration parameters by 2/3:

32.2.1.5 Design Response Spectrum

When required by ASCE 7-05 and the IBC, the design response spectrum shall be developed as shownin Figure 32.3.

32.2.1.6 Importance Factor and Occupancy Category

The importance factor (I) depends on the occupancy category of a given structure. The InternationalBuilding Code and ASCE 7-05 distinguish between four different categories:

• Buildings and other structures that represent a low hazard to human life in the event of failure• All other structures besides those listed in Occupancy Categories I, III, and IV• Buildings and structures that represent a substantial hazard to human life in the event of failure• Essential facilities and structures containing highly toxic substances

TABLE 32.3 Site Classification

Site Class vs (ft/sec) N or Nch Su (psf)

A Hard rock >5,000 NA NAB Rock 2500 to 5000 NA NAC Very dense soil and soft rock 1200 to 2500 >50 >2000 psfD Stiff soil 600 to 1200 15–50 1000–2000 psfE Soft clay soil <600 <15 <1000 psf

Any profile with more than 10 ft of soil having the following characteristics:-Plasticity index PI > 20,-Moisture content w ≥ 40%,and-Undrained shear strength su < 500 psf

F Soils requiring site response analysis in accordance with Section 21.1 of ASCE 7-05

See Section 20.3.1 of ASCE 7-05.

Note: For SI units, 1 ft/sec = 0.3048 m/sec; 1 lb/ft2 = 0.0479 kN/m2.Source: ASCE, Minimum Design Loads for Buildings and Other Structures, ASCE 7-05, American Society of Civil Engineers,Reston, VA, 2005. With permission.

S S S SDS MS D M= =2

3

2

31 1,



Essential facilities, in addition to having an importance factor of 1.5, require special construction review,inspection, and observation procedures. It is argued that the additional measures can improve perfor-mance more effectively than solely relying on increased design force levels. Refer to Table 32.6 for thedetailed description of the various occupancy categories. Refer to Table 32.7 for importance factor I basedon the occupancy category.

TABLE 32.4 Site Coefficient Fa

Site Class

Mapped Maximum Considered Earthquake Spectral Response Acceleration Parameter at a Short Period

SS ≤ 0.25 SS = 0.5 SS = 0.75 SS = 1.0 SS ≥ 1.25

A 0.8 0.8 0.8 0.8 0.8B 1.0 1.0 1.0 1.0 1.0C 1.2 1.2 1.1 1.0 1.0D 1.6 1.4 1.2 1.1 1.0E 2.5 1.7 1.2 0.9 0.9F See Section 11.4.7 of ASCE 7-05.

Note: Use straight-line interpolation for intermediate values of SS.Source: ASCE, Minimum Design Loads for Buildings and Other Structures, ASCE 7-05, American Society of Civil Engineers,Reston, VA, 2005. With permission.

TABLE 32.5 Site Coefficient FV

Site Class

Mapped Maximum Considered Earthquake Spectral Response Acceleration Parameter at 1-Second Period

S1 ≤ 0.1 S1 = 0.2 S1 = 0.3 S1 = 0.4 S1 ≥ 0.5

A 0.8 0.8 0.8 0.8 0.8B 1.0 1.0 1.0 1.0 1.0C 1.7 1.6 1.5 1.4 1.3D 2.4 2.0 1.8 1.6 1.5E 3.5 3.2 2.8 2.4 2.4F See Section 11.4.7 of ASCE 7-05.

Note: Use straight-line interpolation for intermediate value of S1.Source: ASCE, Minimum Design Loads for Buildings and Other Structures, ASCE 7-05, American Society of Civil Engineers,Reston, VA, 2005. With permission.

FIGURE 32.3 Design response spectrum. (From ASCE, Minimum Design Loads for Buildings and Other Structures,ASCE 7-05, American Society of Civil Engineers, Reston, VA, 2005, Figure 11.4-1. With permission.)

Sa = SDS (0.4 + 0.6 )TTD

T0

SDS

SD1

TS TL1.0

Sa = SD1

T

Sa = SD1TL

T2

Period (T) (sec)

Spe

ctra

l Re

spo

nse

Acc

ele

rati

on

(S a

) (g

)



TABLE 32.6 Occupancy Category of Buildings and Other Structures for Flood, Wind, Snow, Earthquake, and Ice Loads

Nature of OccupancyOccupancy Category

Buildings and other structures that represent a low hazard to human life in the event of failure, including, but not limited to:

Agricultural facilitiesCertain temporary facilitiesMinor storage facilities

I

All buildings and other structures except those listed in Occupancy Categories I, III, and IV II

Buildings and other structures that represent a substantial hazard to human life in life in the event of failure, including, but not limited to:

Buildings and other structures where more than 300 people congregate in one areaBuildings and other structures with daycare facilities with a capacity greater that 150Buildings and other structures with elementary school or secondary school facilities with a capacity

greater than 250Buildings and other structures with a capacity greater than 500 for colleges or adult education facilitiesHealthcare facilities with a capacity of 50 or more resident patients but not having surgery or emergency

treatment facilitiesJail and detention facilities

Buildings and other structures, not included in Occupancy Category IV, with potential to cause a substantial economic impact and/or mass disruption of day-to-day civilian life in the event of failure, including, but not limited to:

Power-generating stationsa

Water-treatment facilitiesSewage treatment facilitiesTelecommunication centers

Buildings and other structures not included in Occupancy Category IV (including, but not limited to, facilities that manufacture, process, handle, store, use, or dispose of such substances as hazardous fuels, hazardous chemicals, hazardous waste, or explosives) containing sufficient quantities of toxic or explosive substances to be dangerous to the public if released

Buildings and other structures containing toxic or explosive substances shall be eligible for classification as Occupancy Category II structures if it can be demonstrated to the satisfaction to the authority having jurisdiction by a hazard assessment as described in. Section 1.5.2 that a release of the toxic or explosive substances does not pose a threat to the public.

III

Buildings and other structures designated as essential facilities, including, but not limited to:Hospitals and other healthcare facilities having surgery or emergency treatment facilitiesFire, rescue, ambulance, police station and emergency vehicle garagesDesignated earthquake, hurricane, or other emergency sheltersDesignated emergency preparedness, communication, and operation centers and other facilities required

for emergency responsePower generating stations and other public utility facilities required in and emergency

Ancillary structures (including, but not limited to, communication towers, fuel storage tanks, cooling towers, electrical substation structures, fire water storage tanks or other structures housing or supporting water or other fire- suppression material or equipment) required for operation of Occupancy Category IV Structures during an emergency

Aviation control towers, air traffic control centers, and emergency aircraft hangarsWater-storage facilities and pump structures required to maintain water pressure for fire suppressionBuildings and other structures having critical national defense functionsBuildings and other structures (including, but not limited to, facilities that manufacture, process, handle,

store, use, or dispose of such substances as hazardous fuels, hazardous chemicals, or hazardous waste) containing highly toxic substances where the quantity of the material exceeds a threshold quantity established by the authority having jurisdiction

Buildings and other structures containing highly toxic substances shall be eligible for classification as Occupancy Category II structures if it can be demonstrated to the satisfaction of the authority having jurisdiction by a hazard assessment as described in Section 1.5.2 that a release of the highly toxic substances does not pose a threat to the public. This reduced classification shall not be permitted if the buildings or other structures also function as essential facilities.

IV

a Cogeneration power plants that do not supply power on the national grid shall be designated Occupancy Category II.Source: ASCE, Minimum Design Loads for Buildings and Other Structures, ASCE 7-05, American Society of Civil Engineers,Reston, VA, 2005. With permission.



32.2.1.7 Seismic Design Category

Structures shall be assigned the more severe seismic design category as determined from Table 32.8 orTable 32.9 regardless of the period of vibration of the structure. In addition, when the mapped spectralresponse acceleration parameter at the 1-second period (S1) is greater than or equal to 0.75, then thestructures in Occupancy Categories I, II, or III shall be assigned to Seismic Design Category E, andstructures in Occupancy Category IV shall be assigned to Seismic Design Category F. There are exceptionsthat allow for the seismic design category to be determined from Table 32.8 alone. To use this exception,S1 must be less than 0.75, and all of the following requirements must be met:

• The approximate fundamental period of vibration (Ta), as determined by Equation 32.4 in eachof the two orthogonal directions, is less than 0.8TS, where TS = SD1/SDS.

• The fundamental period of the structure that is used to calculate the story drift in the twoorthogonal directions is less than TS.

• The seismic response coefficient (CS) is determined by Equation 32.2.• The diaphragms are rigid or, where diaphragms are considered flexible, the spacing between

vertical elements of the lateral-force-resisting system does not exceed 40 feet.

TABLE 32.7 Importance Factors

Occupancy Category I

I or II 1.0

III 1.25

IV 1.5

Source: ASCE, Minimum Design Loads forBuildings and Other Structures, ASCE 7-05,American Society of Civil Engineers, Reston,VA, 2005. With permission.

TABLE 32.8 Seismic Design Category Based on Short Period Response Acceleration Parameter

Value of SDS

Occupancy Category

I or II III IV

SDS < 0.167 A A A

0.167 ≤ SDS < 0.33 B B C

0.33 ≤ SDS < 0.50 C C D

0.50 ≤ SDS D D D

Source: ASCE, Minimum Design Loads for Buildings and Other Structures, ASCE 7-05, American Societyof Civil Engineers, Reston, VA, 2005. With permission.

TABLE 32.9 Seismic Design Category Based on 1-Second Period Response Acceleration Parameter

Value of SD1

Occupancy Category

I or II III IV

SD1 < 0.067 A A A

0.067≤ SD1< 0.133 B B C

0.133 ≤ SD1 < 0.20 C C D

0.20 ≤ SD1 D D D

Source: ASCE, Minimum Design Loads for Buildings and Other Structures, ASCE 7-05, American Societyof Civil Engineers, Reston, VA, 2005. With permission.



32.2.2 Design Requirements for Seismic Design Category A

Structures designated to Seismic Design Category A are designed for minimal seismic forces. A lateralforce of 1% of the dead load of each level shall be applied in each of two orthogonal directions indepen-dently. Load path connections must be designed to transfer the lateral forces induced by the elementsbeing connected. Smaller portions of a structure are required to be tied to the remainder of the structurewith a strength of at least 5% of the weight of the smaller portion. Connections to supporting elementsrequire a positive connection to resist a horizontal force acting parallel to the member being connected.This positive connection may be obtained by connecting an element to slabs designed to act as dia-phragms, but the supporting element must then be connected to the diaphragm with a connectionstrength of 5% of the dead plus live load reaction. Concrete and masonry walls are required to be anchoredto all floors and the roof, as well as members that provide lateral support for the wall or that are supportedby the wall.

32.2.3 Design Requirements for Seismic Design Categories B, C, D, E, and F

Similar to Seismic Design Category A, Seismic Design Categories B through F have some minimumrequirements with respect to member design, connection design, and load path. These requirements maybe found at the beginning of Chapter 12 of ASCE 7-05. The design of building structures assigned toSeismic Design Categories B through F requires the following steps:

• Determine the structural system or systems (may include a combination of systems in differentdirections, in the same direction, or vertical combinations).

• Determine if any structural irregularities exist.• Determine redundancy factor ρ if the structure is assigned to Seismic Design Categories D through F.• Determine the appropriate analytical procedure (i.e., equivalent lateral force analysis, modal

response spectrum analysis, or seismic response history procedure).• Apply the appropriate seismic load combinations to determine member design forces.• Determine the diaphragm, chord, and collector design requirements.• Check allowable story drift and determine building separation requirements, if necessary.• Check deformation compatibility of members not included in the seismic-force-resisting system.• Address foundation design requirements.• Address material specific seismic design and detailing requirements of the structural system.

32.2.3.1 Structural System Selection

The maximum elastic response acceleration of a structure during a severe earthquake can be several timesthe magnitude of the maximum ground acceleration and depends on the mass and stiffness of thestructure and the amplitude of the damping. Because it is unnecessary to design a structure to respondin the elastic range to the maximum seismic inertia forces, it is of the utmost importance that a well-designed structure be able to dissipate seismic energy by inelastic deformations in certain localized regionsof the lateral-force-resisting system. This translates into accomplishing flexural yielding of the membersand avoiding all forms of brittle failure. The code-specified design seismic force recognizes such inelasticbehavior and damping and scales down the inertia forces corresponding to a fully elastic response basedon the structural system used. This is accounted for in the response modification factor (R). The structuralsystems for buildings and the corresponding R values are listed in Table 32.10 and are defined as follows:

• Bearing wall system—A structural system without a complete vertical-load-carrying frame. Bearingwalls provide support for all or most gravity loads. Resistance to lateral load is provided by shearwalls or light-frame walls with flat-strap bracing. In Seismic Design Categories D, E, and F, concreteand masonry shear walls must be specially detailed to satisfy IBC requirements. These specialreinforced-concrete or masonry shear walls are limited to a height of 160 feet in Seismic DesignCategories D and E, while they are limited to a height of 100 feet in Seismic Design Category F.



• Building frame system—A structural system with an essentially complete frame providing supportfor gravity loads. Resistance to lateral load is provided by shear walls or braced frames. Shear wallsin Seismic Design Categories D, E, and F are required to be specially designed and detailed tosatisfy the IBC requirements. In addition, other structural elements not designated part of thelateral-load-resisting system must be able to sustain their gravity load-carrying capacity at a lateraldisplacement equal to a multiple times the computed elastic displacement of the lateral-force-resisting system under code-specified design seismic forces. The IBC restricts the building framesystem to a maximum height of 160 feet for Seismic Design Categories D and E but lowers thelimit to 100 feet for Seismic Design Category F.

• Moment-resisting frame system—A structural system with an essentially complete frame providingsupport for gravity loads. Moment-resisting frames provide resistance to lateral loads primarilyby flexural action of members. In Seismic Design Category B, the moment-resisting frames canbe ordinary moment-resisting frames (OMRFs) proportioned to satisfy the IBC requirements. InSeismic Design Category C, reinforced-concrete frames resisting forces induced by earthquakemotions at minimum must be intermediate moment-resisting frames (IMRFs). In Seismic DesignCategories D, E, and F, reinforced-concrete frames resisting forces induced by earthquake motionsmust be special moment-resisting frames (SMRFs).

• Dual system—Structural system with the following features: (1) an essentially complete frame thatprovides support for gravity loads; (2) resistance to lateral load provided by shear walls or bracedframes and moment-resisting frames (SMRFs and IMRFs), with the moment-resisting frames designedto independently resist at least 25% of the design base shear; and (3) designed to resist total designbase shear in proportion to relative rigidities considering the interaction of the dual system at all levels.

• Shear wall–frame interactive system—A structural system with ordinary reinforced-concretemoment frames and ordinary reinforced-concrete shear walls. This system is permitted only inSeismic Design Category B.

• Cantilevered column system—A structural system consisting of cantilevered column elementsdetailed to conform to the requirements of various moment frame systems.

32.2.3.2 Combinations of Framing Systems in Different Directions

Any combination of moment-resisting frame systems, dual systems, building frame systems, or bearingwall systems may be used to resist seismic forces in each of the two orthogonal directions of the structure.Where different systems are used, the respective R, Cd, and ΩO coefficients shall apply to each system,including the limitations on system use contained in Table 32.10.

32.2.3.3 Combination of Framing Systems in the Same Direction

Where different seismic-force-resisting systems are used in the same direction but do not meet therequirements of a dual system, the more stringent response modification factor, deflection amplificationfactor, and overstrength factor shall be used in the analysis and design. Resisting elements are permittedto be designed for the least value of R for the different structural systems found in each independent lineof resistance if the following three conditions are met:

• Occupancy Category I or II building• Two stories or less in height• Use of light-frame construction or flexible diaphragms

32.2.3.4 Vertical Combinations

The International Building Code requires that the value of the response modification factor (R) used inthe design of any story be less than or equal to the value of R used in the given direction for the storyabove. The deflection amplification factor (Cd) and the system overstrength factor (ΩO) used for thedesign of any story shall not be less than the largest value of these factors used in the given direction forthe story above. Exceptions to these requirements include:


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TABLE 32.10 Design Coefficients and Factors for Seismic-Force-Resisting Systems

Seismic-Force-Resisting System

ASCE 7 Section Specifying Detailing

Requirements

Response Modification

Coefficient (R)a

System Overstrength Factor (ΩO)g

Deflection Amplification Factor (Cd)b

Structural System Limitations and Building Height (ft) Limitc

Seismic Design Category

B C Dd Ed Fe

A Bearing Wall Systems1 Special reinforced-concrete shear walls 14.2, 14.2.3.6 5 2-1/2 5 NL NL 160 160 1002 Ordinary reinforced-concrete shear walls 14.2, 14.2.3.4 4 2-1/2 4 NL NL NP NP NP3 Detailed plain concrete shear walls 14.2, 14.2.3.2 2 2-1/2 2 NL NP NP NP NP4 Ordinary Plain concrete shear walls 14.2, 14.2.3.1 1-1/2 2-1/2 1-1/2 NL NP NP NP NP5 Intermediate precast shear walls 14.2, 14.2.3.5 4 2-1/2 4 NL NL 40k 40k 40k

6 Ordinary precast shear walls 14.2, 14.2.3.3 3 2-1/2 3 NL NP NP NP NP7 Special reinforced masonry shear walls 14.4, 14.4.3 5 2-1/2 3-1/2 NL NL 160 160 1008 Intermediate reinforced masonry shear walls 14.4, 14.4.3 3-1/2 2-1/2 2-1/2 NL NL NP NP NP9 Ordinary reinforced masonry shear walls 14.4 2 2-1/2 1-1/2 NL 160 NP NP NP

10 Detailed plain masonry shear walls 14.4 2 2-1/2 1-1/2 NL NP NP NP NP11 Ordinary plain masonry shear walls 14.4 1-1/2 2-1/2 1-1/2 NL NP NP NP NP12 Prestressed masonry shear walls 14.4 1-1/2 2-1/2 1-1/2 NL NP NP NP NP13 Light-framed walls sheathed with wood structural panels

rated for shear resistance or steel sheets14.1, 14.1.4.2, 14.5 6-1/2 3 4 NL NL 65 65 65

14 Light-framed walls sheathed with shear panels of all other materials

14.1, 14.1.4.2, 14.5 2 2-1/2 2 NL NL 35 NP NP

15 Light -framed wall systems using flat strap bracing 14.1, 14.1.4.2, 14.5 4 2 3-1/2 NL NL 65 65 65

B Building Frame Systems1 Steel eccentrically braced frames, moment-resisting,

connections at columns away from links14.1 8 2 4 NL NL 160 160 100

2 Steel eccentrically braced frames, non-moment-resisting, connections at columns away from links

14.1 7 2 4 NL NL 160 160 100

3 Special steel concentrically braced frames 14.1 6 2 5 NL NL 160 160 1004 Ordinary steel concentrically braced frames 14.1 3 1/4 2 3-1/2 NL NL 35j 35j NPj

5 Special reinforced-concrete shear walls 14.2, 14.2.3.6 6 2-1/2 5 NL NL 160 160 1006 Ordinary reinforced-concrete shear walls 14.2, 14.2.3.4 5 2-1/2 4-1/2 NL NL NP NP NP7 Detailed plain concrete shear walls 14.2, 14.2.3.2 2 2-1/2 2 NL NP NP NP NP8 Ordinary plain concrete shear walls 14.2, 14.2.3.1 1-1/2 2-1/2 1-1/2 NL NP NP NP NP9 Intermediate precast shear walls 14.2, 14.2.3.5 5 2-1/2 4-1/2 NL NL 40k 40k 40k

10 Ordinary precast shear walls 14.2, 14.2.3.3 4 2-1/2 4 NL NP NP NP NP


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11 Composite steel and concrete eccentrically braced frames 14.3 8 2-1/2 4 NL NL 160 160 10012 Composite steel and concrete concentrically braced

frames14.3 5 2 4-1/2 NL NL 160 160 100

13 Ordinary composite steel and concrete braced frames 14.3 3 2 3 NL NL NP NP NP14 Composite steel plate shear walls 14.3 6-1/2 2-1/2 5-1/2 NL NL 160 160 10015 Special composite reinforce concrete shear walls with

steel elements14.3 6 2-1/2 5 NL NL 160 160 100

16 Ordinary composite reinforced-concrete shear walls with steel elements

14.3 5 2-1/2 4-1/2 NL NL NP NP NP

17 Special reinforced masonry shear walls 14.4 5-1/2 2-1/2 4 NL NL 160 160 10018 Intermediate reinforced masonry shear 14.4 4 2-1/2 4 NL NL NP NP NP19 Ordinary reinforce masonry shear walls 14.4 2 2-1/2 2 NL 160 NP NP NP20 Detailed plain masonry shear walls 14.4 2 2-1/2 2 NL NP NP NP NP21 Ordinary plain masonry shear walls 14.4 1-1/2 2-1/2 1-1/2 NL NP NP NP NP22 Prestressed masonry shear walls 14.4 1-1/2 2-1/2 1-1/2 NL NP NP NP NP23 Light-framed walls sheathed with wood structural panels

rated for shear resistance or steel sheets14.4,14,1.4.2, 14.5 7 2-1/2 4-1/2 NL NL 65 65 65

24 Light-framed walls with shear panels of all other materials

14.1,14.1.4.2, 14.5 2-1/2 2-1/2 2-1/2 NL NL 35 NP NP

25 Buckling-restrained braced frames, non-moment-resisting beam–column connections

14.1 7 2 5-1/2 NL NL 160 160 100

26 Buckling-restrained braced frames, moment-resisting beam–column connection

14.1 8 2-1/2 5 NL NL 160 160 100

27 Special steel plate shear wall 14.1 7 2 6 NL NL 160 160 100

C Moment-Resisting Frame Systems1 Special steel moment frames 14.1, 12.2.5.5 8 3 5-1/2 NL NL NL NL NL2 Special steel truss moment frames 14.1 7 3 5-1/2 NL NL 160 100 NP3 Intermediate steel moment frames 12.2.5.6, 12.2.5.7,

12.2.5.8, 12.2.5.9, 14.1

4.5 3 4 NL NL 35h NPh NPi

4 Ordinary steel moment frames 12.2.5.6, 12.2.5.7, 12.2.5.8, 14.1

3.5 3 3 NL NL NPh NPh NPi

5 Special reinforced-concrete moment 12.2.5.5, 14.2 8 3 5-1/2 NL NL NL NL NL6 Intermediate reinforced-concrete moment frames 14.2 5 3 4-1/2 NL NL NP NP NP7 Ordinary reinforced-concrete moment frames 14.2 3 3 2-1/2 NL NP NP NP NP8 Special composite steel and concrete moment frames 12.2.5.5, 14.3 8 3 5-1/2 NL NL NL NL NL9 Intermediate composite moment frames 14.3 5 3 4-1/2 NL NL NP NP NP

(continued)


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TABLE 32.10 (cont.) Design Coefficients and Factors for Seismic-Force-Resisting Systems

Seismic-Force-Resisting System

ASCE 7 Section Specifying Detailing

Requirements

Response Modification

Coefficient (R)a

System Overstrength Factor (ΩO)g

Deflection Amplification Factor (Cd)b

Structural System Limitations and Building Height (ft) Limitc


B C Dd Ed Fe

10 Composite partially restrained moment frames 14.3 6 3 5-1/2 160 160 100 NP NP11 Ordinary composite moment frames 14.3 3 3 2-1/2 NL NP NP NP NP

D Dual Systems with Special Moment Frames Capable of Resisting at Least 25% of Prescribed Seismic Forces

12.2.5.1 — — — — — — — —

1 Steel eccentrically braced frames 14.1 8 2-1/2 4 NL NL NL NL NL2 Special steel concentrically braced frames 14.1 7 2-1/2 5-1/2 NL NL NL NL NL3 Special reinforced-concrete shear walls 14.2 7 2-1/2 5-1/2 NL NL NL NL NL4 Ordinary reinforced-concrete shear walls 14.2 6 2-1/2 5 NL NL NP NP NP5 Composite steel and concrete eccentrically braced frames 14.3 8 2-1/2 4 NL NL NL NL NL6 Composite steel and concrete concentrically braced

frames14.3 6 2-1/2 5 NL NL NL NL NL

7 Composite steel plate shear walls 14.3 7-1/2 2-1/2 6 NL NL NL NL NL8 Special composite reinforced-concrete shear walls with

steel elements14.3 7 2-1/2 6 NL NL NL NL NL

9 Ordinary composite reinforced shear walls with steel elements

14.3 6 2-1/2 5 NL NL NP NP NP

10 Special reinforced masonry shear walls 14.4 5-1/2 3 5 NL NL NL NL NL11 Intermediate reinforced masonry shear walls 14.4 4 3 3-1/2 NL NL NP NP NP12 Buckling-restrained braced frame 14.1 8 2-1/2 5 NL NL NL NL NL13 Special steel plate shear walls 14.1 8 2-1/2 6-1/2 NL NL NL NL NL

E Dual Systems with Intermediate Moment Frames Capable of Resisting at Least 25% of Prescribed Seismic Forces

12.2.5.1 — — — — — — — —

1 Special steel concentrically braced framesf 14.1 6 2-1/2 5 NL NL 35 NP NPh,k

2 Special reinforced-concrete shear walls 14.2 6-1/2 2-1/2 5 NL NL 160 100 100


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3 Ordinary reinforced masonry shear walls 14.4 3 3 2-1/2 NL 160 NP NP NP4 Intermediate reinforced masonry shear walls 14.4 3-1/2 3 3 NL NL NP NP NP5 Composite steel and concrete concentrically braced

frames14.3 5-1/2 2-1/2 4-1/2 NL NL 160 100 NP

6 Ordinary composite braced frames 14.3 3-1/2 2-1/2 3 NL NL NP NP NP7 Ordinary composite reinforced-concrete shear walls with

steel elements14.3 5 3 4-1/2 NL NL NP NP NP

8 Ordinary reinforced-concrete shear walls 14.2 5-1/2 2-1/2 4-1/2 NL NL NP NP NP

F Shear Wall-Frame Interactive System with Ordinary Reinforced Concrete Moment Frames and Ordinary Reinforced Concrete Shear Walls

12.2.5.10, 14.2 4-1/2 2-1/2 4 NL NP NP NP NP

a Response modification coefficient (R) for use throughout the standard. Note that R reduces forces to a strength level, not an allowable stress level.b Deflection amplification factor (Cd) for use in ASCE 7-05, Sections 12.8.6, 12.8.7, and 12.9.2c NL = not limited and NP = not permitted. For metric units, use 30.5 m for 100 ft and use 48.8 m for 160 ft. Heights are measured from the base of the structure as defined in ASCE7-05, Section 11.2.d See ASCE 7-05, Section 12.2.5.4, for description of building systems limited to buildings with a height of 240 ft (73.2 m) or less.e See ASCE 7-05, Section 12.2.5.4, for building systems limited to buildings with a height of 160 ft (48.8m) or less.f Ordinary moment frame is permitted to be used in lieu of intermediate moment frame for Seismic Design Categories B or C.g The tabulated value of the overstrength factor (Ω0) is permitted to be reduced by subtracting one half for structures with flexible diaphragms but shall not be taken as less than 2.0 forany structure.h See ASCE 7-05, Sections 12.2.5.6 and 12.2.5.7, for limitations for steel OMFs and IMFs in structures assigned to Seismic Design Category D or E.i See ASCE 7-05, Sections 12.2.5.8 and 12.2.5.9, for limitations for steel OMFs and IMFs in structures assigned to Seismic Design Category F.j Steel ordinary concentrically braced frames are permitted in single-story storage building up to height of 60 ft (18.3 m) where the dead load of the roof does not exceed 20 psf (0.96kN/m2)and in penthouse structures.k Increase in height to 45 ft (13.7 m) is permitted for single story storage warehouse facilities.Source: Adapted from ASCE, Minimum Design Loads for Buildings and Other Structures, ASCE 7-05, American Society of Civil Engineers, Reston, VA, 2005, Table 12.2-1. With permission.



• Rooftop structures not exceeding two stories in height and 10% of the weight of the entire structure• Other supported structural systems with a weight equal to or less than 10% of the weight of the

entire structure• Detached one- and two-family dwellings of light-frame construction

A two-stage equivalent lateral force procedure is permitted to be used for structures having a flexibleupper portion supported by a rigid lower portion, provided that the design of the structure complieswith the following:

• The stiffness of the lower portion must be at least 10 times the stiffness of the upper portion.• The period of the entire structure shall not be greater than 1.1 times the period of the upper

portion considered as a separate structure fixed at the base.• The flexible upper portion shall be designed as a separate structure using the appropriate values

of R and ρ.• The rigid lower portion shall be designed as a separate structure using the appropriate values of

R and ρ. The reactions from the upper portion shall be those determined from analysis of theupper portion amplified by the 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.

32.2.3.5 Combination Framing Detailing RequirementsStructural components that are common to different framing systems used to resist seismic motions inany direction shall be detailed in accordance with the requirements of ASCE 7-05, Chapter 12, for thehighest response modification factor (R) of the connected framing systems. More stringent detailing isrequired with the higher response modification factor.

32.2.3.6 System-Specific RequirementsA series of system-specific requirements either imposes additional limitations on system use or notesexceptions to system use in particular seismic design categories. These requirements are included in ASCE7-05, Section 12.2.5.

32.2.3.7 Diaphragm FlexibilityThe relative stiffness of the diaphragms of a structure shall be considered in the analysis unless thediaphragms can be idealized as rigid or flexible. Certain types of construction may be idealized as eitherflexible or rigid diaphragms. When the diaphragm cannot be idealized as flexible or rigid, the structuralanalysis performed shall explicitly include the stiffness of the diaphragm. The inclusion of the diaphragmstiffness in the analysis is often referred to as semirigid modeling, which is often available as an option incommercially available structural analysis software. Concrete slabs and concrete-filled metal deck slabswith span-to-depth ratios of 3 or less in structures with no horizontal irregularities are allowed to beidealized as rigid diaphragms.

32.2.3.8 Structural IrregularitiesThe IBC and ASCE 7-05 require that a structure be designated as regular or irregular. Regular structureshave no significant physical discontinuities in plan or vertical configurations or in their lateral-force-resisting systems. Two assumptions apply for regular structures. First, the equivalent static force distri-bution provides a conservative envelope of the forces and deformations due to the actual dynamicresponse. Second, the cyclic inelastic deformation demands during a major level of seismic ground motionwill be reasonably uniform in all elements. Irregular structures are those with irregular features asdescribed in Table 32.11 and Table 32.12. Vertical irregularities are defined as a distribution of mass,stiffness, or strength that results in lateral forces or deformations, over the height of the structure, thatare significantly different from the linearly varying distribution obtained from an equivalent lateral forceanalysis. Plan irregularities are encountered where diaphragm characteristics create significant diaphragmdeformations or stress concentrations. As will be seen in the next section, only structures with certaintypes of irregularities require a dynamic analysis.



In Seismic Design Categories E and F, structures with horizontal irregularity Type 1b or verticalirregularities Type 1b, Type 5a, and Type 5b are not permitted. Structures having vertical irregularityType 5b in Seismic Design Category D are not permitted. Structures with a Type 5b vertical irregularityare not permitted to exceed 2 stories or 30 feet in height except when the weak story is designed to resistthe forces determined by the special seismic load combinations including ΩO. Overturning moments ondiscontinuous shear-resisting elements are to be carried as loads to the foundation. In Seismic DesignCategories B through F, columns, beams, trusses, or slabs supporting the overturning forces of discon-tinuous shear walls or frames of structures are to be designed to resist the axial forces resulting from thespecial seismic load combinations including ΩO. The columns carrying these factored loads may bedesigned considering the maximum force that can be transferred from the supported element above andmust meet special detailing requirements to ensure their ductile behavior under cyclic loading.

32.2.3.9 Analysis Procedure Selection

The IBC and ASCE 7-05 recognize three different analysis procedures for the determination of seismiceffects on structures. Refer to Table 32.13 for the applicability of each of the three analysis options. Theequivalent lateral force analysis procedure is allowed when certain criteria of building period, occupancy,and regularity are met; the modal response spectrum analysis (dynamic analysis) procedure is alwayspermissible for design. The third analysis option is the seismic response history procedure, which is

TABLE 32.11 Horizontal Structural Irregularities

Irregularity Type and Description

ASCE 7-05 Reference Section


Application

1a Torsional irregularity is defined to exist where the maximum story drift, computed including accidental torsion, at one end of the structure transverse to an axis is more that 1.2 times the average of the story drifts at the two ends of the structure. Torsional irregularity requirements in the reference sections apply only to structures in which the diaphragms are rigid or semirigid.

12.3.3.412.8.4.312.7.312.12.1Table 12.6-116.2.2

D, E, and FC, D, E, and FB, C, D, E, and FC, D, E, and FB, C, D, E, and F

1b Extreme torsional irregularity is defined to exist where the maximum story drift, computed including accidental torsion, at one ends of the structure transverse to an axis is more than 1.4 times the average of the story drifts at the two ends of the structure. Extreme torsional irregularity requirements in the reference sections apply only to structures in which the diaphragms are rigid or semirigid.

12.3.3.112.3.3.412.7.312.8.4.312.12.1Table 12.6-116.2.2

E and FDB, C, and DC and DDB, C, and D

2 Reentrant corner irregularity is defined to exist where both plan projections of the structure beyond a reentrant corner are greater than 15% of the plan dimension of the structure in the given direction.

12.3.3.4Table 12.6-1

D, E, and FD, E, and F

3 Diaphragm discontinuity irregularity is defined to exist where there are diaphragms with abrupt discontinuities or variations in stiffness, including those having cutout or open areas greater than 50% of the gross enclosed diaphragm area, or changes in effective diaphragm stiffness of more that 50% from one story to the next.

12.3.3.4Table 12.6-1

D, E, and FD, E, and F

4 Out-of-plane offsets irregularity is defined to exist where there are discontinuities in a lateral force-resistance path, such as out -of-plan offsets of the vertical elements.

12.3.3.412.3.3.312.7.3Table 12.6-116.2.2

D, E, and FB, C, D, E, and FB, C, D, E, and FD, E, and FB, CD, E, and F

5 Nonparallel systems irregularity is defined to exist where the vertical lateral-force-resisting elements are not parallel to or symmetric about the major orthogonal axes of the seismic-force-resisting system.

12.5.312.7.3Table 12.6-116.2.2

C,D, E and FB, C, D, E, and FD, E, and FB, C, D, E, and F

Source: ASCE, Minimum Design Loads for Buildings and Other Structures, ASCE 7-05, American Society of CivilEngineers, Reston, VA, 2005. With permission.



beyond the scope of this chapter. The scope of this chapter is primarily dedicated to the equivalent lateralforce analysis procedure, but modal response spectrum analysis is briefly touched upon. Equivalent lateralforce analysis is acceptable for use with all structures, regular or irregular, in Seismic Design CategoriesB and C. Equivalent lateral force analysis may be used for regular and irregular structures in SeismicDesign Categories D, E, and F with a fundamental period of vibration, in each of the two orthogonaldirections, less than 3.5TS, except when a Type 1a or Type 1b horizontal irregularity or Type 1a, Type1b, Type 2 or Type 3 vertical irregularity exists. Additional structural characteristics that allow the useof the equivalent lateral force analysis procedure are noted in Table 32.13.

32.2.3.10 Redundancy

A redundancy factor (ρ) shall be assigned to the seismic-force-resisting system in each of two orthogonaldirections for all structures. Redundancy factor ρ is permitted to equal 1.0 for the following:

• Structures assigned to Seismic Design Categories B or C• Drift calculations and P-delta effects• Design of nonbuilding structures that are not similar to buildings• Design of collector elements, splices, and their connections for which the load combinations

including the overstrength factor ΩO are used• Design of members or connections where the load combinations including the overstrength factor

ΩO are required for design

TABLE 32.12 Vertical Structural Irregularities

Irregularity Type and Description

ASCE 7-05 Reference Section


Application

1a Stiffness-soft story irregularity is defined to exist where there is a story in which the lateral stiffness is less than 70% of that in the story above or less than 80% of the average stiffness of the three stories above.

Table 12.6-1 D,E, and F

1b Stiffness-extreme soft story irregularity is defined to exist where there is a story in which the lateral stiffness is less than 60% of that in the story above or less than 70% of the average stiffness of the three stories above.

12.3.3.1Table 12.6-1

E and FD, E, and F

2 Weight (mass) irregularity is defined to exist where the effective mass of any story is more than 150% of the effective mass of an adjacent story. A roof that is lighter than the floor below need not be considered.

Table 12.6-1 D, E, and F

3 Vertical geometric irregularity is defined to exist where the horizontal dimension of the seismic-force-resisting system in any story is more than 130% of that in an adjacent story.

Table 12.6-1 D, E, and F

4 In-plane discontinuity in vertical lateral-force-resisting element irregularity is defined to exist where an in-plane offset of the lateral-force-resisting element is greater than the length of those elements or there exists a reduction in stiffness of the resisting element in the story below.

12.3.3.312.3.3.4Table 12.6-1

B, C, D, E, and FD, E, and FD, E, and F

5a Discontinuity in lateral strength-weak story irregularity is defined to exist where the story lateral strength is less than 80% of that in the story above. The story lateral strength is the total lateral strength of all seismic resisting elements sharing the story shear for the direction under consideration.

12.3.3.1Table 12.6-1

E and FD, E, and F

5b Discontinuity in lateral strength-extreme weak story irregularity is defined to exist where the story lateral strength is less than 65% of that in the story above. The story strength is the total strength of all seismic resisting elements sharing the story shear for the direction under consideration.

12.3.3.112.3.3.2Table 12.6-1

D, E, and FB and CD, E, and F

Source: ASCE, Minimum Design Loads for Buildings and Other Structures, ASCE 7-05, American Society of CivilEngineers, Reston, VA, 2005. With permission.



• Diaphragm loads determined using Equation 32.18• Structures with damping systems designed in accordance with ASCE 7-05, Chapter 18.

The redundancy factor (ρ) shall equal 1.3 for structures assigned to Seismic Design Categories D, E, orF, unless one of the following conditions is met, whereby ρ is permitted to be taken as 1.0:

• Each story resisting more than 35% of the base shear in the direction of interest shall comply withTable 32.14.

• Structures are regular in plan at all levels, provided that the seismic-force-resisting systems consistof at least two bays of seismic-force-resisting perimeter framing on each side of the structure ineach orthogonal direction at each story resisting more than 35% of the base shear. The numberof bays for a shear wall shall be calculated as the length of the shear wall divided by the storyheight or two times the length of the shear wall divided by the story height for light-frameconstruction.

32.2.4 Equivalent Lateral Force Procedure

The International Building Code and ASCE 7-05 require that structures be designed for seismic forcesin each of the two orthogonal directions. Such forces may be assumed to act nonconcurrently in thedirection of each principal axis of the structure except for structures with certain plan irregularities. Eventhough not all structures are permitted to be designed using the equivalent lateral force analysis procedure,the procedure is often used to help determine those structures that require more exhaustive analysis.When a dynamic analysis is to be preformed, an equivalent lateral force analysis generally has to be thefirst step of the process.

TABLE 32.13 Permitted Analytical Procedures

Seismic Design

Category Structural Characeristics

Equivalent Lateral Force Analysis

(Section 32.2.4)

Modal Response Spectrum Analysis

(Section 32.2.5)

Seismic Response History Procedures

(ASCE 7-05, Chapter 16)

B, C Occupancy Category I or II buildings of light-framed construction not exceeding 3 stories in height

P P P

Other Occupancy Category I or II buildings not exceeding 2 stories in height

P P P

All other structures P P PD, E, F Occupancy Category I or II buildings of

light-framed construction not exceeding 3 stories in height

P P P

Other Occupancy Category I or II buildings not exceeding 2 stories in height

P P P

Regular structures with T < 3.5Ts and all structures of light-framed construction

P P P

Irregular structures with T < 3.5Ts and having only horizontal irregularities Type 2, 3, 4, or 5 of Table 32.11 or vertical irregularities Type 4, 5a, or 5b of Table 32.12

P P P

All other structures NP P P

Note: P, permitted; NP, no permitted.Source: ASCE, Minimum Design Loads for Buildings and Other Structures, ASCE 7-05, American Society of Civil Engineers,Reston, VA, 2005.



32.2.4.1 Effective Seismic Weight (W)

The effective seismic weight of a building (W) is the total dead load and applicable portions of other loads:

• In occupancies where partition loads are used in the floor design, a load of not less than 10 psfshall be included.

• In occupancies such as storage and warehouses, a minimum of 25% of the floor live load shall beincluded.

• In areas subjected to flat roof snow loading greater than 30 psf, 20% of the snow load shall beincluded in the design regardless of actual roof slope.

• In buildings with permanent equipment, the weight of such equipment shall be included as partof the total dead load (W).

32.2.4.2 Seismic Base Shear

The International Building Code equation for calculating the total design lateral force at the base of abuilding in a given direction is as follows:

(32.1)

The seismic response coefficient (CS) is determined by:

(32.2)

The value of CS need not exceed the following:

(32.3a)

(32.3b)

TABLE 32.14 Requirements for Each Story Resisting More Than 35% of the Base Shear

Lateral-Force-Resisting Element Requirement

Braced frames Removal of an individual brace, or connection thereto, would not result in more than a 33% reduction in story strength nor does the resulting system have an extreme torsional irregularity (horizontal structural irregularity Type 1b).

Moment frames Loss of moment resistance at the beam-to-column connections at both ends of a single beam would not result in more than a 33% reduction in story strength nor does the resulting system have an extreme torsional irregularity (horizontal structural irregularity Type 1b).

Shear walls or wall pier with a height-to-length ratio greater than 1.0

Removal of a shear wall or wall pier with a height-to-length ratio greater than 1.0 within any story, or collector connections thereto, would not result in more than 33% reduction in story strength nor does the resulting system have an extreme torisional irregularity (horizontal structural irregularity Type 1b).

Cantilever columns Loss of moment resistance at the base connections of any single cantilever column would not result in more than 33% reduction in story strength nor does the resulting system have an extreme torsional irregularity (horizontal structural irregularity Type 1b).

Other No requirements.

Source: ASCE, Minimum Design Loads for Buildings and Other Structures, ASCE 7-05, American Society of Civil Engineers,Reston, VA, 2005. With permission.

V C Ws=

CS

R

I

sDS=

CS

TR

I

T TsD

L=

≤1 for

CS T

TR

I

T TSD L

L=

>1

2

for



In addition, for structures located where S1 is greater than or equal to 0.6g, CS shall not be less than:

(32.3c)

where:

CS = seismic response coefficient.W = total seismic dead load of the system.I = importance factor in Table 32.7.R = response modification coefficient per Table 32.10.T = fundamental period of vibration of the building.TL = long-period transition point.V = total design lateral force or shear at the base.SDS = design, 5% damped, spectral response acceleration at short periods of vibration.SD1 = design, 5% damped, spectral response acceleration at a period of 1 second.S1 = mapped MCE, 5% damped, spectral response acceleration at a period of 1 second.

The fundamental period of the structure (T) shall be determined using the structural properties anddeformation characteristics of the resisting elements in a properly substantiated analysis. As an alternativeto performing an analysis to determine the fundamental period (T), it is permitted to use the approximatebuilding period (Ta). For all buildings, the value Ta may be approximated from the following formula:

(32.4)

where hn is the height in feet above the base to the highest level of the structure, and the numericalcoefficients Ct and x are determined from Table 32.15.

The fundamental period (T) calculated by methods other than the approximate method shall notexceed an upper limit as determined from:

(32.5)

where Cu is determined from Table 32.16.Alternatively, the approximate period may be determined from the following equations when the

structure does not exceed 12 stories in height and consists entirely of concrete or steel moment resistingframes with a story height of at least 10 feet:

(32.6)

where N = number of stories.

TABLE 32.15 Values of Approximate Period Parameters Ct and x

Structure Type Cta x

Moment-resisting frame systems in which the frames resist 100% of the required seismic force and are not enclosed of adjoined by components that are more rigid and will prevent the frames from deflecting where subjected to seismic forces:

Steel moment-resisting framesConcrete moment-resisting frames

0.028 (0.0724) 0.80.016 (0.0466) 0.9

Eccentrically braced steel frames 0.03 (0.0731) 0.75All other structural systems 0.02 (0.0488) 0.75

a Metric equivalents are shown in parentheses.Source: ASCE, Minimum Design Loads for Buildings and Other Structures, ASCE 7-05, American Society of Civil Engineers,Reston, VA, 2005. With permission.

CS

R

I

S =

0 5 1.

T C ha t nx=

T C Tu a≤

T Na = 0 1.



For concrete or masonry shear-wall structures, the approximate period (Ta) may be determined fromthe following formula:

(32.7)

where hn is defined in the proceeding text, and CW is calculated from the following formula:

(32.8)

where:

AB = area of base of structure (ft2).Ai = web area of shear wall i (ft2).Di = length of shear wall i (ft).hi = height of shear wall i (ft).x = number of shear walls in the building effective in resisting lateral forces in the direction under

consideration.

32.2.4.3 Vertical Distribution of Force

The total seismic force shall be distributed to each level of the structure in accordance with the following:

(32.9)

and

(32.10)

where:

Cvx = vertical distribution factor.V = total design lateral force at the base of the structure (kips or kN).wi, wx = the portion of the total effective seismic weight (W) located or assigned to level i or x.hi, hx = the height (ft or m) from the base of the structure to level i or x.k = an exponent related to the structure period as follows: (1) when T < 0.5 seconds, k = 1, and

(2) when T ≥ 2.5 seconds, k = 2; for structures having a period between 0.5 and 2.5 sec, kshall be taken equal to 2 or shall be determined by linear interpolation between 1 and 2.

TABLE 32.16 Coefficient for Upper Limit on Calculated Period

Design Spectral Response Acceleration Parameter at 1 Second (SD1) Coefficient Cu

0.4 1.40.3 1.40.2 1.5

0.15 1.6≤0.1 1.7

Source: ASCE, Minimum Design Loads for Buildings and Other Structures, ASCE 7-05,American Society of Civil Engineers, Reston, VA, 2005. With permission.

TC

ha

W

n

0 0019.

CA

h

h

A

h

D

WB

n

ii

x

i

i

i

=

+

=∑100

1 0 831

2

2

.

F C Vx vx=

Cw h

w h

vxx x

k

i ik

i

n=

=∑

1



32.2.4.4 Horizontal Distribution of Shear and Horizontal Torsional Moments

The seismic design story shear (Vx, the sum of the forces Fi above that story) in any story shall bedistributed to the various elements of the vertical lateral-force-resisting system in proportion to theirrigidities, considering the rigidity of the diaphragm. Furthermore, the IBC and ASCE 7-05 require thatprovisions be made for the increased shears resulting from horizontal torsion where diaphragms are notflexible. To account for the uncertainties in load locations, the IBC and ASCE 7-05 further require thatthe mass at each level be assumed to be displaced from the calculated center of mass in each direction adistance equal to 5% of the building dimension at that level perpendicular to the direction of the forceunder consideration. This is often referred to as the accidental torsion. The torsional design moment ata given story is the moment resulting from the combination of this accidental torsional moment and theinherent torsional moment between the applied design lateral forces and the center of rigidity of thevertical lateral-force-resisting elements in that story (see Figure 32.5). When seismic forces are appliedconcurrently in two orthogonal directions, the required 5% displacement of the center of mass need notbe applied in both orthogonal directions at the same time but shall be applied in the direction thatproduces the greater effect.

32.2.4.5 Story Drift Determination and Limitation

The IBC and ASCE 7-05 define story drift as the relative displacement between adjacent stories (aboveor below) due to the design lateral forces. The design story drift is computed as the difference of thedeflections at the center of mass at the top and bottom of the story under consideration. ASCE 7-05further expands on the requirements for calculating story drift by stating that, for structures withsignificant torsional deflections, the maximum story drift must include torsional effects. For structuresassigned to Seismic Design Categories C, D, E, or F having horizontal irregularities of Type 1a or Type1b, the design story drift (∆) shall be computed as the largest difference of the deflections along any ofthe edges of the structure at the top and bottom of the story under consideration. The design story drift(∆) shall not exceed the allowable story drift (∆a) determined from Table 32.17.

The deflections used to determine the design story drift shall be determined from the following equation:

(32.11)

TABLE 32.17 Allowable Story Drift (∆a)

Structure

Occupancy Category

I or II III IV

Structures, other than masonry shear walls structures, 4 stories or less with interior walls, partitions, ceilings and exterior wall systems that have been designed to accommodate the story drifts.

0.25hsxa 0.020hsx 0.015hsx

Masonry cantilever shear wall structuresb 0.010hsx 0.010hsx 0.010hsx

Other masonry shear wall structures 0.007hsx 0.007hsx 0.007hsx

All other structures 0.020hsx 0.015hsx 0.010hsx

a There shall be no drift limit for single-story structures with interior walls, partitions, ceilings, and exterior wall systemsthat have been designed to accommodate the story drifts. The structure separation requirement of ASCE 7-05 Section 12.12.3is not waived.b Structure in which the basic structural system consists of masonry shear walls designed as vertical elements cantileveredfrom their base or foundation support which are so constructed that moment transfer between shear walls (coupling) isnegligible.Note: hxs is the story height below level x. For seismic-force-resisting systems comprised solely of moment frames in SeismicDesign Categories D, E, and F, the allowable story drift shall comply with the requirements of ASCE 7-05, Section 12.12.1.1.Source: ASCE, Minimum Design Loads for Buildings and Other Structures, ASCE 7-05, American Society of Civil Engineers,Reston, VA, 2005. With permission.

δ δx

d xeC

I=



where:

Cd = the deflection amplification factor in Table 32.10.δxe = the deflection determined by elastic analysis without the upper limit on the fundamental period

(CuTa).I = the importance factor determined from Table 32.7.

Past codes, such as the Uniform Building Code, did not elaborate on how story drift is determinedfrom analysis results. As a result, it was often assumed that the drift should be calculated at the structureextremities as is now required by ASCE 7-05 only in certain seismic design categories and when torsionalirregularities exist. This can have a liberalizing effect on drift requirements of moment frame structuresthat are often governed by drift. Whereas these requirements seem to loosen drift requirements thatwould impact moment frame structures, a limitation has been put into place on the allowable story driftrequiring that the design story drift not exceed ∆a/ρ for structures assigned to Seismic Design CategoriesD, E, or F.

32.2.4.6 P-Delta Effects

P-delta effects on story shears and moments, the resulting member forces and moments, and the storydrifts induced by these effects are not required to be considered where the stability coefficient θ, asdetermined by the following equation, is less than or equal to 0.10:

(32.12)

where:

Px = total vertical design load at and above level x (kips or kN); when computing Px, no individualload factor need exceed 1.0.

∆ = design story drift occurring simultaneously with Vx (in. or mm).Vx = seismic shear force acting between levels x and x – 1 (kips or kN).hsx = story height below level x (in. or mm).Cd = deflection amplification factor in Table 32.10.

The stability coefficient θ shall not exceed θmax determined as follows:

(32.13)

where β is the ratio of shear demand to shear capacity for the story between levels x and x – 1. This ratiomay conservatively be taken equal to 1.0.

When 0.10 < θ ≤ θmax, the incremental factor related to P-delta effects on displacement and memberforces shall be determined by rational analysis. As an alternative, it is permitted to multiply displacementsand member forces by 1.0/(1 – θ). When θ > θmax, the structure is potentially unstable and shall beredesigned. Where P-delta effects are included in an automated analysis, Equation 32.13 will still besatisfied; however, the value of θ computed from Equation 32.12 using the results of the P-delta analysisis permitted to be divided by (1 + θ) before checking Equation 32.13.

32.2.4.7 Deformation Compatibility

For structures assigned to Seismic Design Categories D, E, or F, all framing elements not required bydesign to be part of the lateral-force-resisting system must be investigated and shown to be adequate forvertical-load-carrying capacity when subjected to the design story drift (∆) resulting from the requireddesign lateral force. Reinforced concrete frame members not designed as part of the lateral-force-resistingsystem shall comply with Section 21.9 of ACI 318.

θ = P

V h Cx

x sx d

∆

θβmax

..= ≤0 5

0 25Cd



32.2.5 Modal Response Spectrum Analysis

ASCE 7-05 sets some rather general requirements regarding modal response spectrum analysis (dynamicanalysis). The following is a summary of the requirements:

• The analysis shall include a sufficient number of natural modes of vibration for the structure suchthat the modal mass participation in each direction is at least 90% of the actual mass.

• The design forces shall be determined using the properties of each mode and the response spectrumdefined in either Section 32.2.1.5 or Section 21.2 of ASCE 7-05 divided by R/I. When calculatingdisplacement and drift, values shall be multiplied by Cd/I.

• The value for each response parameter shall be combined using either the square root sum of thesquares (SRSS) method or the complete quadratic combination (CQC) method, in accordancewith ASCE 4.

• A base shear shall be calculated in each of the two orthogonal directions using the equivalentlateral force procedure of Section 32.2.4. When the fundamental period of vibration exceeds thecap CuTa, then CuTa shall be used in lieu of T in that direction.

• Where the combined response for the modal base shear (Vt) is less than 85% of the calculatedbase shear (V) using the equivalent lateral force procedure, the forces, but not the drifts, shall bemultiplied by 0.85V/Vt.

• The horizontal distribution of shear shall be in accordance with the horizontal distributionrequirements of the equivalent lateral force procedure except that the amplification of the torsionaleffects required when a horizontal irregularity Type 1a or Type 1b exists is not required whenaccidental torsional effects are included in the dynamic analysis model.

• P-delta effects are determined in accordance with the same requirements as the equivalent lateralforce procedure, as well as the story shears and story drifts.

• A soil structure interaction reduction is permitted where determined using ASCE 7-05, Chapter 19.

As can be seen from the above requirements, even though a separate method of analysis is being employed,the requirements of the equivalent lateral force procedure still play a large role in the modal responsespectrum analysis.

32.2.6 Seismic Load CombinationsThe basic load combinations for strength design are as follows:

(32.14)

(32.15)

The basic load combinations for strength design with the overstrength factor (ΩO) are as follows:

(32.16)

(32.17)

where:

D = dead loads or related internal moments and forces.L = live loads or related internal moments and forces.QE = effects of horizontal seismic forces from V or Fp.ρ = redundancy factor from Section 32.2.3.10.SDS = design spectral acceleration parameter defined in Section 32.2.1.4.H = load due to earth pressure, ground water pressure, or pressure of bulk materials.S = snow load.ΩO = overstrength factor.

1 2 0 2 0 2. . .+( ) + + +S D Q L SDS Eρ

0 9 0 2 1 6. . .−( ) + +S D Q HDS Eρ

1 2 0 2 0 2. . .+( ) + + +S D Q L SDS O EΩ

0 9 0 2 1 6. . .−( ) + +S D Q HDS O EΩ



The load factor applied to the live load in the above load combinations is permitted to equal 0.5 for alloccupancies where the live load is less than or equal to 100 psf with the exception of garages or areas ofpublic assembly. The load factor on H in the above load combinations shall be set equal to zero if thestructural action due to H counteracts that due to E. Where lateral earth pressure provides resistance tostructural actions other than seismic, it shall not be included in H but shall be included in the designresistance. When utilizing the load combinations including the overstrength factor, the required designstrength for an element need not exceed the maximum force that can be developed in the element asdetermined by rational, plastic mechanism analysis, or nonlinear response analysis utilizing realisticexpected values of material strengths.

32.2.7 Diaphragms, Chords, and Collectors

Floor and roof diaphragms are required to be designed to resist the forces determined in the followingformula:

(32.18)

The force (Fpx) determined in the above formula need not exceed 0.4SDSIwpx but shall not be less than0.2SDSIwpx. For structures assigned to Seismic Design Categories D, E, and F, redundancy factor ρ shallbe used in the diaphragm design. For inertial forces calculated in accordance with Equation 32.18, theredundancy factor shall equal 1.0. For transfer forces, the redundancy factor shall be the same as thatused for the structure. For structures assigned to Seismic Design Categories D, E, or F and having ahorizontal structural irregularity of Types 1a, 1b, 2, 3, or 4 from Table 32.11 or a vertical irregularity ofType 4 from Table 32.12, the design forces determined from Section 32.2.2.2 shall be increased 25% forconnections of diaphragms to vertical elements and to collectors. Collectors and their connections shallbe designed for these increased forces unless they are designed for the load combinations that includethe overstrength factor.

32.2.8 Building Separation

All structures have to be separated from adjoining structures a distance sufficient to avoid damagingcontact under total deflection δx. ASCE 7-05 does not further expand on what is considered a sufficientdistance; however, past codes allowed the separation to be based on the square root sum of the squaresof the estimated maximum seismic displacement due to code-specified seismic forces of the two struc-tures. The separation was calculated as , where δx1 and δx2 are the displacement of adjacentbuildings and δS is the calculated required building separation.

32.2.9 Anchorage of Concrete or Masonry Walls

Concrete or masonry walls shall be provided with a positive direct connection to all floors and roofs thatprovide them lateral support. Such connections shall be capable of resisting the horizontal forces inducedby the seismic excitement and as specified in the code. ASCE 7-05, Section 12.11, should be consultedfor further information.

32.2.10 Material-Specific Design and Detailing Requirements

The IBC and ASCE 7-05 make a series of modifications to ACI 318. The IBC in turn makes a series ofmodifications to both ASCE 7-05 and ACI 318 in Chapters 16 and 19. ASCE 7-05 lists the requiredmodification as part of Chapter 14.

FF

w

wpx

ii x

n

i

i x

n px= =

=

∑∑

δ δ δS x x= +12

22



32.2.11 Foundation Design

The foundation shall be designed to resist the forces developed and accommodate the movementsimparted to the structure by the design ground motions. Importantly, overturning effects at the soil–foun-dation interface are permitted to be reduced by 25% for foundations of structures that are designed inaccordance with the equivalent lateral force analysis procedure provided the structure is not an invertedpendulum or cantilevered column type structure. Overturning effects at the soil–foundation interfaceare permitted to be reduced by 10% for foundation of structures designed in accordance with the modalresponse spectrum analysis procedure. Refer to ASCE 7-05, Section 12.13, for additional foundationdesign requirements.

32.3 Design and Construction of Concrete and Masonry Buildings

32.3.1 Preface

This section is intended to serve as a guide to engineers in the design of reinforced-concrete and masonrybuildings to resist earthquake forces in conformance with the 2006 IBC and ASCE 7-05 (refer to Section32.2). The lateral-load-resisting system, including horizontal diaphragms, is addressed. Please note thatterm definitions, notations, and symbols used in this chapter are provided in the 2006 IBC and ASCE 7-05.

32.3.2 Concrete Buildings

32.3.2.1 Introduction

As discussed in Section 32.2, reinforced-concrete buildings in general are designed to have adequatestrength to resist the equivalent static lateral load and appropriate ductility to allow the structure todisplace as a result of dynamic earthquake excitement. The building strength is achieved by selecting theappropriate member sizes, concrete strength, proper placement, and adequate size of reinforcing steel sothe nominal capacity decreased by a reduction factor of each member meets or exceeds the ultimatedemands. Ductility is achieved by providing confinement to the concrete section at critical locations byintroducing closely spaced and appropriately anchored bars transversely to the longitudinal reinforcementin beams, columns, and boundary members such as at the ends of a shear wall (see Figure 32.9).

When designing a building to resist the seismic forces obtained in Section 32.2, the engineer wouldgo through selection of the lateral-force-resisting system. This section addresses shear walls and specialmoment-resisting frames, as they are primarily used in Seismic Design Categories D, E, and F. Thedecision of whether to choose shear walls or moment frames or a combination of the two depends onthe architectural layout of the structure. The structural engineer’s role in most cases is limited to locatingand sizing the lateral resisting elements. The following steps are then followed in the lateral design of thestructure:

• Select the lateral-force-resisting system.• Calculate the building weight and base shear (see Section 32.2).• Distribute lateral load to each floor and calculate the story shear (see Section 32.2).• Distribute story shear to the various lateral-force-resisting elements at each floor based on member

stiffness (see Section 32.2.4.4).• Design and detail lateral-force-resisting components (shear wall or moment frame) for the applied

forces.• Design and detail diaphragms to transfer story shear into shear walls or moment frames.

32.3.2.2 Horizontal Distribution of Shear and Torsional Moments

The following discussion addresses the distribution of shear and torsional moments on the basis thatthe lateral-force-resisting system consists of shear walls. The same discussion also applies to buildings



with moment frames or combination of shear walls and moment frames. The center of mass of thefloor is first calculated as follows:

(32.19)

(32.20)

Figure 32.4 serves as a good illustration for the above formulas. Next, the rigidity of each wall iscalculated. The deflection at the top of the wall is calculated based on the following formula:

(32.21)

where r is the rigidity or stiffness of the wall panel equal to 1/deflection (see Figure 32.4, Figure 32.5,and Figure 32.6). The center of rigidity of the floor is then calculated as follows:

(32.22)

(32.23)

Refer to Figure 32.7 for the shear distribution formulation.

FIGURE 32.4 Schematic center of mass in shear wall.

FIGURE 32.5 Cantilever shear-wall deflection.

4

3

2

1

l, y

l, x

X

Floor

+C.M.

–

Y–

∆T ∆F ∆S

+=

L

h

Xwx

wm = ∑

∑

Ywy

wm = ∑

∑

∆ ∆ ∆T F SC G

Ph

E I

Ph

AE= + = +

3

3

1 2.

xr x

rr

x

y

=∑

yr y

rr

x

x

=∑



32.3.2.3 Design of Vertical Lateral-Force-Resisting Elements

This section illustrates the design and reinforcement requirements for shear walls and moment-resistingframes through practical examples.

Example 32.1. Shear-Wall Design and Reinforcement Requirements(See Figure 32.8.) The given values are as follows:

fc′ = 4000 psi.t (wall thickness) = 12 in.

FIGURE 32.6 Schematic center of rigidity in a shear wall.

FIGURE 32.7 Shear distribution formulation.

4ry

rx

ry

rx

+C.R.

1

2

Y–

X– 3

3 VS

cg cr

V1

2

EQ.

EQ.

4 VS

(a)

V

V13

d1 d2

d3

d4

Vt2

Vt4

Vs2Vs1

Vt1

e

cg cr

1

(b)



Vu = 980 kips = shear force.Mu = 73,500 kip-ft = overturning moment.Pu = 2800 kips = total load on wall, includes wall weight.SDS = 1.1 (site class D).L = 53 ft.H = 75 ft.

Note that walls with a height-to-width ratio (H/W) greater than 2.0 behave primarily as bending mem-bers, whereas walls with H/W below 2.0 resist lateral forces in a predominantly truss-type behavior. Themaximum shear stress in walls is limited to .

• The vertical steel in the wall is required to equal the horizontal steel.• At least two curtains of reinforcement shall be used in a wall if the in-plane factored shear force

assigned to the wall exceeds . Acv is the cross-sectional area bounded by the wall lengthparallel to the direction of the shear force and the wall thickness.

Check number of curtains required:

• Required vertical and horizontal wall reinforcement:

FIGURE 32.8 Typical shear wall elevation.

Footing (see plan & schedule)

Cla

ss “

B”

lap

fo

r

con

cre

te (

30

" m

in.)

&

48

Db la

p f

or

CM

U,

typ

ical

Footing dowel

12

–#

11

Ve

rt.

Ve

rt.

Concrete

or CMU

wall

See

schedule

End

ve

rt.

5"

CLR

.

12" typical

Horiz.

OptionalFloor slab

Top dowels (see wall

schedule for dowel

size and spacing)

2 ′fc

2A fcv c′

2 2 12 53 12 4000 1000 965 4A f

V

cv c

u

′ = × × ×( ) =( ) . kips

==

> ′ ∴

980

2

kips

two curtains of reinfoV A fu cv c rrcement are required

Minimum rebar ratio,

Area of steel

ρv = 0 0025.

in each, in. 12 in. = 0ρv cvA = × ×0 0025 12. ..36 in. /ft2



• Try #5 bars in each direction at each face at 18 in. on-center ≤ Smax = 18 in.

• Check:

Boundary member requirement: Boundary members shall be provided where the maximum compressiveand extreme-fiber stress under factored forces exceeds 0.2fc′.

• Gross section properties:

• Check axial capacity of 36 × 36-in. boundary member with 12 #11:

• Use 36 × 36-in. boundary members with 12 #11.

A

h l

m

w w

= × × =

=

2 0 31 12 18 0 413

75

. / .

/

in.

ft/53 ft

2

.. = 1.42 < 2

V A f f

A

n cv c c n y

cv

= ′ +( )= × ×

α ρ

12 53 12(( ) =

=

7632

3 0

in.

varies linearly from

2

α αc c. 33.0 for to 2.0 forwh l h lw w w

n

/ . / .= =( )1 5 2 0

ρ == × × =

=

2 0 31 12 18 0 0029

0 6

. /( ) .

.φ

V A f

V

n cv c

n

≤ ′

= + ×

10

7632

10003 4000 0 0029 6

.

. 00 000 2776

10 10 7632 4000 1000

,

/

( ) =

′ = × ×

kips

A fcv c == ∴ < ′4827 10kips (OK)V A fn cv c

1 53

53 12 12 7632

=

= × × =

ft, = 12 in.

in.2

t

A

I

cv

y == × × =

= +

12 53 12 12 257 259 4563( ) , , in.4

f P A M lc U g u ww y

u

u

c

I

P

M

f

/

,

2

2800

73 500

2800

( )=

=

=

kips

kip-ft

77632

73 500 12 53 12 2

257 259 4561 46+ × × × =, /

, ,. ksi

0..2 ksi < 1.46 ksi provide boundfc = × = ∴0 2 4 0 8. . aary member

A

A

y

st

g

= × =

= × =

=

36 36 1296

12 1 56 18 72

in.

in.

2

2. .

ρ 118 72 1296 0 0144

0 01 0 06

. / .

. .min max

=

= < < =ρ ρ ρg (OK))

kP P f A A f Au n c y st y st= = ′ −( )+ =φ 0 6 0 85 3279. . iips (OK)> Pu



• Check boundary reinforcement for tension load for load combination:

Other requirements: (1) Required cross-sectional area of confinement reinforcement should be in accor-dance with ACI 318-05; see Nawy (2008) for a detailed example. (2) All continuous reinforcement inshear walls must be anchored or spliced as required by IBC and ACI.

32.3.3 Design of Masonry Buildings


The majority of construction in the masonry industry involves smaller buildings, and these are oftendesigned with the code-equivalent static loads. It is the intent of this section to briefly demonstrate howthe building must be designed to resist these equivalent static lateral forces. Again, for computationalconvenience, the effects of ground motion are considered as if the motion acts only in one directionparallel to the perpendicular axes of the building. Several different types of structural systems are usedto resist the static lateral forces and carry them into the foundation. Such systems include shear walls,braced frames, and moment-resisting space frames. Because it has not been possible, so far, to feasiblyconstruct masonry moment-resisting frames, this chapter is limited to the discussion of concrete masonryshear walls.

32.3.3.2 General Behavior of Box Buildings

A box system does not have an independent vertical-load-carrying frame but rather depends on the wallsnot only to carry the vertical loads but also to provide the necessary lateral stability. Walls that areperpendicular to the assumed direction of the ground motion must span vertically between the floordiaphragms. The inertial effect of one half the wall height, both above and below the floor level inquestion, is considered to be transferred to that floor diaphragm. In addition, the inertial effect of thediaphragm dead load itself must be taken by the diaphragm. The diaphragm essentially behaves as ahorizontal plate girder, wherein the diaphragm boundary members serve as the girder flanges and thefloor functions as the web. The diaphragm therefore spans between the supporting shear walls. Throughthe diaphragm-to-wall connection, the total horizontal shear is transferred directly to the shear wall.Depending on the rigidity of the diaphragm, this lateral shear transfer to any shear wall may be basedon the adjacent tributary area or the relative rigidities of the various shear walls. Where rigid diaphragmssuch as reinforced or post-tensioned concrete floor slabs are used, each wall experiences a torsional shearin addition to the direct shear when the building center of gravity and the center of rigidity of the verticallateral-force-resisting elements do not coincide. The total direct lateral shear and the torsional shear arecombined so the sum becomes the total UBC-design force imposed upon the shear wall. Figure 32.7provides an illustration of the total shear force, lateral load combination.

32.3.3.3 Shear Walls

32.3.3.3.1 Shear-Wall DesignRoof and floor seismic forces may be carried down to the building foundation by the strength and rigidityof the building walls in a bearing wall system or building frame system. Such walls are called shear walls.In tall buildings, design of the shear walls is generally governed by flexure, whereas in low buildings shearis often the governing criteria. The shear wall is basically a cantilever member with the shear force resistedby the combined shear strength of the masonry and the horizontal rebar in the wall, while the vertical

T S D E

P

T

u DS

D

u

= −( ) ±

=

= −

0 9 0 2

1400

73 500 53

. .

, /(

kips

33 0 9 0 2 1 1 1400 0 5 994) ( . . . ) .

/

− − × × × =

=

kips

A T fs u yφ == × =994 0 9 60 18 41/( . ) . in. (OK)2



boundaries (end reinforcement) provide the capacity to resist tension and compression caused by thebending moment and axial forces on the wall. A shear wall by definition is a wall resisting in-planehorizontal shear forces. In addition to horizontal force, the wall is investigated for the effects of thevertical loads it is subjected to. Example 32.2 provides a good illustration for the design of a concretemasonry wall subjected to both gravity and seismic forces.

32.3.3.3.2 Shear-Wall DetailingFor a masonry wall to function properly as a shear wall, it must be capable of resisting the diagonaltensile forces imposed by the design shear forces and the vertical compressive or tensile stresses causedby the overturning moment due the same design shear forces. A typical detail for placing reinforcingsteel in a masonry wall is shown in Figure 32.9. The horizontal rebar is anchored with a 90° standardhook to ensure that the bar can be fully developed in tension. Also shown in Figure 32.9 is the endreinforcement for a four-bar condition to resist tensile forces. Figure 32.8 shows an elevation of the samewall with the wall-to-floor and wall-to-footing connections properly shown. It is important to note thatthe designer must take into account the limited amount of space in the cells when specifying the bar sizeand spacing so the placement of reinforcement does not become impossible.

Example 32.2. Masonry Shear-Wall DesignThe given values are as follows:

Masonry, CMU fm′ = 1500 psiGrout, type M, 2000 psiSteel, Gr 60Special inspection requiredWall length, 31 ftWall thickness, 12 inWall height, 12 ftShear force, 203.45 kipsMoment, 3051.7 kip-ftAxial loading, 95.00 kips

The following items are required:

Stress checkReinforcement requirements

FIGURE 32.9 Typical placement of reinforcement in masonry shear wall.

Vertical reinforcement,

#5 @ 16" o.c.

Horizontal reinforcement,

#5 @ 16" o.c.

8" CMU wall

#3 ties

@ 8" o.c.

Hook into

wall

4 #9



The following calculations are necessary (calculations are based on design UBC 1991):

Em = 750 × 1500 = 1125 ksi.Es = 29,000 ksi.Ratio of moduli = 29,000/1125 = 25.78.Allowable steel stress (Fs) = 24,000 psi.Increase for seismic design (1.33Fs) = 1.33 × 24,000 = 31,920 psi.Allowable bending stress (Fb) = 0.33fm′ = 0.33 × 1500 = 495 psi.Increase for seismic design (1.33Fb) = 658.35 psi.Allowable axial stress (Fa/R) = 0.2fm′ = 0.2 × 1500 = 300 psi.Increase for seismic design = 399 psi.

The design for bending and axial load is as follows:

Allowable axial stress (Fa) = 399 × 0.97 = 387 psi.

Axial stress ratio (fa/Fa) = 21.97/387 = 0.057.

Hence, fb/Fb = 1 – 0.057 = 0.943.Assume that masonry stress governs and check for steel stress. If steel stress as calculated exceeds its

allowable stress, then discard the assumption and proceed by assuming steel reaches its maximumallowable value first.

(I) Masonry stress governs.

where d = 12 × 3 ft – 18 in. = 354 in.

R h t

h

t

= −( )

= × =

=

1 42

12 12 144

11 625

3/

.

in.

foor in./in. CMU12

1144

42 11 6250

3

R = −×

=.

..

.

97

95 1000

31 12 11 62522f

P

Aa = = ×

× ×≅ psi

f

F

f

Fa

a

b

b

+ = 1

f

jkM

f bd

b

b

= × =

= = ×

0 943 658 35 621

2 2 3051 702

. .

.

psi

××× ×

=12 000

620 98 11 625 3540 081

2

,

. ..

− + =3 3 02k k jk

kk k

k

f nfk

ks b

2 3 3 0 081 0

0 0833

125

− + × =

=

−

=

.

.

.778 620 981 0 0833

0 0833176 128 3× −

= >..

., psi 11 920, psi N.G.∴



(II) Steel stress governs.

where j = jk/k = 0.81/0.0833 = 0.972.

Check compressive stress in the masonry:

The bending stress ratio is:

The combined bending and axial stress ratio is:

Check shear stresses:

where d ≅ 0.8 × 31.

The allowable ranges for design with rebar are:

Hence, the design stress is Fv = 77.27 + (1 – 0.6)(103.02 – 77.27) = 87.33 psi, and the governing stressvalue is Fv = 87.33 psi.

The actual stress value is:

The shear stress ratio is:

AM

f jds

s

= = ×× ×

=3051 12 000

31 920 0 972 3543 33

,

, .. in.. = area of jamb reinforcement2

ρ

ρ ρ

= = × = ×

= +(

−A bd

k n n

s / . / . .3 33 11 625 354 8 09 10

2

4

2 )) − = × × × + × ×( ) −− −ρn 2 8 09 10 25 78 25 78 8 09 104 42

. . . . 88 09 10 25 78 0 23

1 3 1 0 23 3 0 923

4. . .

/ . / .

× × =

= − = − =

−

j k

ffM

jkbdb = = × ×

× ×2 2 3051 70 12 000

0 923 0 162 112

. ,

. . .6625 354336 658 35

2×= < ∴psi psi OK.

f

Fb

b

= = ∴336

658 350 51

.. OK

f

F

f

Fa

a

b

b

+ = + = < ∴0 06 0 51 0 57 1. . . OK

M

Vd=

× ×( ) = < ∴3051 7

203 45 0 8 310 6 1

.

. .. OK

for psiM Vd Fv/ , . . . .= = × = < ×1 1 33 1 5 1500 77 27 1 33 75 ppsi OK

for psi

∴

= = × = <M Vd Fv/ , . .0 1 33 2 1500 103 02 1..33 120× ∴psi OK

Fv = + − − =77 27 1 0 6 103 02 77 27 87 33. ( . )( . . ) . psi

FV

bjdv

u= = × ×× ×

=1 5 203 45 1000

11 625 0 923 35480

. .

. ...34 psi

f

Fv

v

= = ∴80 34 87 33 0 92. / . . OK



Calculate the shear reinforcement:

Hence, minimum ρu governs: Av = 0.0007 × 11.625 × 12 = 0.1 in./ft.

32.3.4 Shear-Wall Foundation Analysis and Design

32.3.4.1 Background

The analysis and design presented herein pertain to the sizing of the shear-wall foundations and deter-mination of their structural adequacy. The algorithm adopted is aimed at obtaining economical foun-dation dimensions with due consideration of all the major parameters such as the actions from the shearwall, the permissible soil pressure, concrete strength, the shear-wall foundation, and grade beam dimen-sions. The analysis and design are directed toward the seismic-loading case only. The adequacy of thefoundation under gravity loading is to be established separately. Under normal conditions, however, thesize and reinforcement of a shear-wall foundation is governed by the seismic case. The gravity case checkwill be conducted for unusual cases and dimensions. The analysis is based on the limit design concept.A probable failure mechanism is assumed (refer to the free body diagrams in Figure 32.10). By satisfyingthe requirements of statics, the actions (shears and moments) at critical sections are determined, andthe cross-sectional area and reinforcement at such sections are evaluated. The failure mechanism selectedmay not be the optimum for all cases, but it is consistently conservative.

The soil pressure is checked by determining the soil stress ratio (SSR). This is the ratio of the calculatedunfactored soil pressure to the permissible soil pressure. SSR is to be kept less than 1. The analysis assumesthat the foundation is tied to the remainder of the structure through grade beams. If the foundation byitself can resist the applied loading without need for grade beams, the calculated shear transfer (parameterG) between the foundation and the grade beam will become zero or negative. If a shear transfer betweenthe foundation and the assumed grade beams results, the analysis and design must be followed by a gradebeam design to ensure that the resulting shear (G) is satisfactorily dissipated into the grade beam andthe other structural elements.

The applied vertical loading (P), the seismic moment (M), and the shear (V) from the shear wall arecalculated elsewhere and are entered herein (see Example 32.3) as input. They act at midlength of theshear wall at the top of the foundation. This design considers the vertical loading and the momentcomponents of the shear wall. The shear component (V) is resisted through friction at the bottom ofthe foundation, axial loading in the adjoining grade beams, and the connection of the foundation to theslab on grade, as well as by any passive soil pressure that may develop. In common cases, foundationand grade beam sizes, through other considerations, prove to be adequate for V; however, for isolatedfoundations this may not be the case. If required, this design section is followed by a check for the shearcomponent V.

One type of typical interior foundation is treated in Example 32.3. Numerous variations are possibledepending on the existence of and location at which a grade beam ties into the foundation. The rela-tionships developed embrace most of the common cases. If a foundation geometry does not fall withinthe scope of this work and cannot be modeled conservatively through the method treated herein, specialanalysis and design are required. In nonsymmetrical cases, different values for the shear transfer force(G) result, depending on the direction of the applied seismic-bending moment. In such conditions, thevalue yielding the larger shear transfer is calculated and given.

Horizontal, AV s

f jds

u

s

= = × × ×1 5 203 45 1000 12

31

. .

,, ..

.

920 0 923 3450 351

0 0007

2

× ×=

=

in.

Minimum, As ×× × = < ∴

=

11 625 12 0 1 0 351

0 351 11 6

2 2. . .

. / .

in in OK

ρn 225 12 0 00252 0 002× = >. .



32.3.4.2 Geotechnical Relationships

32.3.4.2.1 Soil PressureThe soil pressure is:

(32.24)

where PD is the total (DL + LL).

FIGURE 32.10 Shear wall foundation: (a) elevation, shear wall and footing; (b) plan; (c) free body diagram of thestructural system at limit state.

Shear wall

Footing

Grade beam

f

d h

l e

L

k

(a)

Grade

beam Shear wall

B

b

L/4L/4

L

P

(b)

(c)

f 1/2 1/2 e

V M

Grade

beam

dg

hg

G

w

L/43L/4

G

sP

LBSBPd= ≤

0 251 33

..



32.3.4.2.2 Soil Pressure RatioThe soil stress ratio is:

(32.25)

32.3.4.2.3 Shear Transfer to Grade Beam (G)(See Figure 32.10.) Based on the structural model adopted at the limit state, shear transfer (G) to thegrade beams occurs if the shear-wall footing is not capable, through its geometry and the existing gravityloadings, to resist the overturning moment (M). The magnitude of the shear G depends also on thedirection of bending moment M. The larger of the two values is considered for design:

(32.26)

Factored average soil bearing (W) = 4P/BL (32.27)

32.3.5 Nomenclature

b = width of grade beam.B = width of foundation pad and its tips.d = design depth of footing.dg = design depth of grade beam.e = distance from tip of shear wall to tip of footing at bearing end.f = distance from tip of shear wall to tip of footing at uplift end.g = distance from tip of shear wall to point of action of shear force G.G = factored shear force developed between the grade beam and foundation.h = dimensional depth of footing.hg = dimensional depth of grade beam.j = distance from tip of shear wall to point of action of shear force G.k = width of footing at midlength of shear wall.l = length of shear wall.L = effective length of foundation (equal to l + e + f).M = factored moment at midlength of shear wall (equal to Ms/0.7).Ms = unfactored applied seismic moment.P = factored gravity load equal to (0.9 – 0.2SDS)Pd.Pa = unfactored gravity loading from the shear wall.Pd = total axial load on footing (equal to Pa + Pf).Pf = total weight of footing.PL = unfactored live load from shear walls = unfactored calculated soil pressure.SBP = allowable soil bearing pressure.SSR = soil stress ratio (equal to calculated/allowable).V = factored applied seismic shear.Vs = unfactored applied seismic shear.W = factored calculated soil pressure on soil.

Example 32.3. Shear-Wall Footing Design(Refer to Figure 32.10 and Figure 32.11). From the soils report, SBP = 3.0 kips/ft2. From lateral analysis,Ms = 9800 kip-ft, Pa = 100 kips, PL = 0 kips, Vs = 300 kips, and SDS = 1.0. The properties are (calculationsbased on design IBC 2006):

fc′ = 3000 psi.fy = 60 psi.

SSRs

SBP= ≤

1 331

.

GL

M PL e f= − + −

10 375 0 5. . ( )



e = 6 ft.f = 6 ft.l = 36 ft.L = l + e + f = 48 ft.

The estimated weight of the footing is:

From Equation 32.24:

FIGURE 32.11 Reinforcement designation: (a) elevation, and (b) plan. Note: The connection between the gradebeam and the foundation is modeled as hinged in the analysis. It is not necessary to design for a moment across thissection.

f l e

Shear wall1

2

4

3

Foundation

Development length

or f/6, whichever is larger

Extend grade beam

rebar 4'-0" into foundation.

Grade beam

Development length

or e/6, whichever is larger

(a)

(b)

24" min.

5 top & bottom

P

P P P

f

d a f

=

= + = + =

60

100 60 160

kips

kips kips kipss

kips) kipsP P P

MM

d L

s

= − −( ) =

=

( . . ) (0 9 0 2 160 112

00 7

9800

0 714 000

. .,= =kip-ft

kip-ft

BP

L SBPd

min. . . ( .

= ( ) = ( )0 25 1 33

160

0 25 48 1 3

kips

ft 33 3 040 1

×=

. ). in.



Assume B = 48 in.:

Assume dg = 26.5 in.; hg = dg + 3.5 in. = 26.5 in. + 3.5 in.; therefore, hg = 30 in.From Equation 32.27:

Reinforcement requirements of foundation:

See Figure 32.11a, rebar 2D 1:

32.4 Seismic Retrofit of Existing Buildings

32.4.1 Introduction

Historically, the seismic retrofit of existing concrete structures has been executed by introducing concreteshear walls, new steel, or concrete bracing elements or by strengthening existing lateral-force-resistingmembers. Recently, new methods such as base isolation and wrapping columns using steel jackets or fiberfabric with epoxy resin have been introduced. The method and the economy of the seismic retrofit dependon the characteristics of the structure. The most critical stage in the retrofit of a concrete structure is thepreliminary work for the development of the retrofit scheme. During this phase, the structural componentsof the structure, the economy, the various retrofit schemes, the timing of the work, and the possibility ofloss of occupancy are all investigated so the appropriate seismic retrofit option may be chosen.

32.4.2 Structure Weakness

Concrete structures observed to suffer the most in the aftermath of major seismic events have exhibitedone or more of the following deficiencies:

• Suspect load path or, as is occasionally the case, interrupted load path• Lack of compatibility between the vertical elements in the structure• An inadequate lateral-load-resisting system

sP

LBd= = =

0 25

160

0 25 48 43 33

. . ( (.

kips

ft) ft)kips//ft

kips/ft

kips/

2

2

1 33

3 33

1 33 3 0SSR

s

SBP= =

.

.

. ( . fft(OK)

20 833 1 0

). .= <

WP

BL= = =4 4 112

4 482 33

( )

( (.

ft) ft)kips/ft2

GL

M PL P e f

G

= − + −

=

10 375 0 5

1

4814 000

. . ( )

,ft

kip--ft kips) ft)

kips

− +

=

0 375 112 48 0

249 67

. ( (

.G

M GfBfh f

u = + × = +12

0 152

249 67 6 43

. ( . )( ) ( )kips ft ft (( )( ) .

.

6 3 0 156

2

1530 4

ft ft kcfft

kip-ft

× ×

=M

A

u

SREQQ= 11 68. in.2



For a structure to respond adequately to the applied seismic loads, there must exist a continuous andadequate load path from the point of application of the seismic force to the foundation of the structure.Inadequately designed or detailed connections along the load path can and will lead to local or overallfailure, regardless of how well the various components of the lateral-force-resisting system are designedand detailed. The issue of deformation compatibility can be seen very clearly in a structure with flexiblevertical lateral-force-resisting elements such as moment-resisting frames. Such frames experience signif-icant horizontal displacements. It is this earthquake-imposed deformation that can cause some or all ofthe lateral and vertical carrying systems to fail if they do not have the ability to allow such movement.As building codes evolve on the basis of lessons learned from various seismic events worldwide, higherdesign loads with a more advanced level of detailing for ductile behavior (not widely practiced before)are demanded. Structures designed according to codes as late as 1967 may be inadequate, based on currentstandards. Efforts to retrofit such structures to meet current governing codes can be very extensive.Toward achieving our present objectives of ensuring life safety during major seismic events and minimalstructural damage during frequently occurring earthquakes, the next two sections address two criticalobjectives in the seismic retrofit process.

32.4.3 Creation of Adequate Load Path

The structural engineer chooses the load path to support the lateral load from the point of load applicationto the foundation or soil. The load path or lateral-load-resisting system is then analyzed and designedfor the corresponding load actions. All components of the system and their connections are verified, andadjustments are made to ensure adequate strength and ductility. In concrete structures, such load pathsare achieved by adding new shear walls or by strengthening existing ones. It is not surprising, therefore,to observe that the chosen load path is different from the original system of the structure. Compatibilityof the various vertical structural elements of the structure must be investigated to ensure that the selectedload path can be activated.

32.4.4 Establish Deformation Compatibility

As discussed earlier, establishing deformation compatibility is essential to ensuring that all structuralelements necessary for stability and load transfer have adequate ductility and the ability to redistributeloading to safely withstand the deformations imposed upon them in response to seismic loads. In parkingstructures where split-level frames are common, post-earthquake investigations and studies have shownthat most of the distress was due to column-shear failure in short columns. Measures for the mitigationof column-shear failure vary between existing and new structures. The options introduced in the followingsections may be considered for each of the construction types.

32.4.4.1 Retrofit Construction

Retrofitting the column implies one of several options. The first is removing the column and replacingit using an adequate section with close tie spacing. A second option is jacketing the column so its shearcapacity can be increased; this can be accomplished by placing vertical and hoop reinforcement aroundthe existing column and by the application of gunite. Another option is to place a two-piece steel jacketand weld it on site. The gap between the existing column and the jacket is then grouted. Epoxy resin andfiber wrapping is another method that is very effective for round or oval columns because the structuralcontribution of the wrapping is developed through hoop stresses in the wrapping.

32.4.4.2 New Construction

In new construction, short columns can be designed and detailed as a continuous part of the structureto withstand the higher shear forces, or they can be detailed for moment release at their connections tothe beam, as shown in Figure 32.12.



32.4.5 Establish Adequate Lateral-Load-Resisting System

It is not possible to achieve our goal of ensuring life safety during major seismic events and minimalstructural damage during frequently occurring earthquakes just by ensuring that the structure has anadequate vertical lateral-force-resisting system. It is imperative that the seismic force be properly collectedat the roof and each floor and properly transferred into the vertical lateral-force-resisting system. Thus,the horizontal concrete diaphragms should be analyzed and strengthened as necessary so this step canbe accomplished. The existing vertical resisting system is then strengthened by retrofitting the existingelements or by introducing new elements to supplement the existing capacity. Finally, the existing footingshould be investigated and new footings and grade beams should be added where required.

FIGURE 32.12 Slip joint at top of short columns.

22" × 22" × 1/2"

Neoprene

Duro 70

6 e

qu

al s

pac

es

@ 2

" o

.c.

3"φ Foam

6"

2"

2"

2'-

0"

2"

typ

ical

1# 11×4'–6"

centered in

column

Second and

third ramps

4 e

qu

al s

pac

es

36

"

Second and

third floors

36

"

4 e

qu

al s

pac

es

Note:

For tie sizes and

spacing, see

schedule, typical

1/2" exp. joint material

Ramp-on-grade

FTG

. do

we

l lap

See

co

lum

n

sch

ed

ule

S.O.G.

5"

CLR

. Std. HK.

(12" min.)

Dowels to match

size and spacing of

vertical reinforcement



32.4.5.1 Horizontal Diaphragms

In structures constructed prior to 1970, it is very likely that little attention was given to ensuring thatthe story force could be adequately transferred into the vertical lateral-force-resisting system. As part ofthe seismic retrofit of the building, methods of ensuring that the diaphragm does not fail should bedevised. This can be achieved by introducing chord and drag elements at the floor soffit. Attaching thinsteel plates onto the concrete soffit using epoxy resin is a method that can cause little disturbance to thefunction of the structure yet have very positive results. The connection of the diaphragm to the verticallateral system should be closely examined. The introduction of steel angles bolted to both the floor soffitand the vertical lateral-force-resisting system is often done with satisfactory results. For diaphragms wherea load path into the existing vertical lateral-force-resisting system cannot be reasonably achieved, thelayout of the vertical lateral-load-resisting system should be studied. It may be imperative that new verticalmembers be introduced to allow the establishment of adequate load path.

32.4.5.2 Vertical Load-Resisting System

Existing concrete buildings are most likely to have one of three structural lateral systems:

• Space frame system• Building frame system• Bearing wall system

The level of strengthening required to achieve our goal of ensuring public safety and minimal structuraldamage no doubt differs from one structure to another; however, older buildings with space framesgenerally require more effort for establishing an adequate vertical lateral-force-resisting system. Thefollowing options are some of the available methods for strengthening the vertical lateral-force-resistingsystems.

32.4.5.2.1 Introduction of New Concrete/Masonry Shear WallsThis is a method frequently used for retrofitting concrete structures. Shear-wall placement is simpler, inmost cases, than adding moment-resisting frames. When the size and location of the new shear wallshave been established based on the design force, new footings are placed and connected to the variousfloor systems by way of drilling and bonding reinforcing steel dowels to the existing slab-on-grade. Wallreinforcements are then placed. Walls can then be formed and poured in place or, as is often the case inrecent years, a one-sided form can be placed and gunite applied (refer to Figure 32.13 and Figure 32.14).

32.4.5.2.2 Retrofitting of Existing WallsIn instances where the building layout or architecture offers no option for new shear wall introduction,existing walls may be thickened to the required adequate dimension (Figure 32.15). Additionally, requiredwall boundary elements at the end of the wall may be added if required, as shown in Figure 32.14. Existingshear walls to be thickened are properly prepared by roughening their surfaces to 0.25-in. amplitude.Appropriate dowels are then drilled and bonded into existing concrete. The required vertical and hori-zontal reinforcements are tied in place, and concrete is placed either conventionally by installing wallforms and pumping the concrete into place or low-slump gunite is shot in place. It is important to notethat the existing footings should be verified for their ability to transfer vertical and horizontal reactionsto the ground. It is often necessary to enlarge the existing footings at the thickened shear wall. Additionally,grade beams may be introduced to better defuse the lateral force into the ground.

32.4.5.2.3 Alternative Methods of Seismic RetrofitSo far, the discussion has been limited to the conventional methods for seismic retrofit of buildings whereconventional lateral-load-resisting systems are engineered to support the calculated seismic forces thatwill be developed in a building during severe seismic activity. On the other hand, base isolation is ameans by which the seismic response of the structure is significantly reduced by decoupling the buildingfrom its seismic forces by: (1) increasing the fundamental vibration period of the structure, or (2)dissipating the energy delivered to the building. Base isolation at the present time is far more expensive



to implement for retrofitting existing structures than conventional methods; however, structures such ashistoric landmarks and vital buildings that lack an existing load path for seismic forces and have limitedcapacity in the existing concrete diaphragm or large penetrations in the existing concrete diaphragm thatcannot be retrofitted conventionally can be successfully strengthened using base isolation. Some of theprimary advantages of the base isolation system include:

• Minimum disruption of important historic features• Minimum alteration of interior spaces• Minimum potential damage to architectural finishes during future earthquakes• Greater degree of life safety to building occupants• Significantly reduced seismic response• Significantly reduced story drift

For further information regarding base isolation, the reader is encouraged to consult Naaseh (1995).

FIGURE 32.13 New concrete wall.

(E) Slab

8"

Drill & bond #5

into (E) concrete

slab @ 12" o.c.

(N) 12" CIP wall

1 1/2" CLR.

#5 @ 18" o.c.

E.W., E.F.

Footing dowels to

match vertical

1" saw cut at

construction

joint, typical1

8"

3" CLR., typical

#5 @ 16" o.c.4'- 0"

(N) Footing

3 #5 cont.

(top & bottom)

Footing

dowel

lap 30"

(E) Slab-on-grade

#4 @ 18" o.c. E.W.

drill & dowel 8"

min. into (E) S.O.G.

(N) Slab-on-grade

match (E) thickness



FIGURE 32.14 Wall elevation.

FIGURE 32.15 Retrofit of existing concrete wall.

1/2" W.J.

End vertical reinforcement

with footing dowels to match

En

d v

ert

ica

lC

lass

BL

ap (

30

" m

in.)

pro

vid

e h

oo

ps

@ 4

" o

.c. i

nth

is z

on

e1

2"

min

.

(E) Footing Drill and epoxy end jamb

dowels and footing dowels

12" into (E) footing

(N) 12" concrete wall

Dowels

Top of S.D.G.

beyond

(N) Footing

(E) Concrete floor

8"

Drill & bond #4 @ 12" o.c.



(N) 6" thick shotcrete wall

#5 @ 16" o.c. E.W.

(E) Slab-on-grade

12

"


(E) Footing

(E) Concrete

shear wall

6"

6"8"



32.5 Seismic Analysis and Design of Bridge Structures

32.5.1 Seismic Analysis of Bridge Structures


In this section, a simple method that models a bridge as a single degree of freedom system is presented.As the bridge model becomes more complicated, however, this simple procedure becomes less accurate;thus, a multimodal dynamic analysis or time-history computer analysis is recommended. There are twobasic concepts for bridge seismic analysis. The first is that there is a relationship between the mass andstiffness of a bridge and the forces and displacements that affect the structure during an earthquake;therefore, if we can calculate the mass and the stiffness for our structure, we can obtain the earthquakeforces acting on it. The second concept is that bridges are designed to behave nonlinearly for largeearthquakes; therefore, the engineer is required to make successive estimates of an equivalent linearizedstiffness to obtain the seismic forces and displacements of the bridge.

32.5.1.2 Basics

Mass is a measure of a body’s resistance to acceleration. It requires a force of 1 Newton to accelerate 1kilogram at a rate of 1 meter per second squared. Stiffness is a measure of the resistance of a structureto displacement. It is the force (in Newtons) required to move a structure 1 meter. The boundaryconditions for the bridge must be carefully studied to determine the stiffness of the structure. Period isthe time (in seconds) required to complete one cycle of movement. A cycle is the trip from the point ofzero displacement to completion of the farthest left and right excursions of the structure and back to thepoint of zero displacement. Natural period is the time a single degree of freedom system will vibrate atin the absence of damping or other forces. Natural period (T) has the following relationship to the mass(m) and stiffness (k) of the system:

(32.28)

Frequency is the inverse of period and can be measured as the number of cycles per second (f) or thenumber of radians per second (ω) where one cycle equals 2π radians. Damping (viscous damping) is ameasure of a resistance of a structure to velocity. Bridges are underdamped structures. This means thatthe displacement of successive cycles becomes smaller. The damping coefficient (c) is the force requiredto move a structure at a speed of 1 meter per second. Critical damping (cc) is the amount of dampingthat would cause a structure to stop moving after half a cycle. Bridge engineers describe damping usingthe damping ratio (ξ) where:

(32.29)

A damping ratio of 5% is used for most bridge structures.

32.5.1.3 The Force Equation

The force equation for structural dynamics can be derived from Newton’s second law:

(32.30)

Thus, all the forces acting on a body are equal to its mass times its acceleration. When a structure is actedon by a force, Newton’s second law becomes:

p – fs – fD = mu′′ (32.31)

Tm

k= 2π

ξ = c

cc

F ma=∑



where:

fs = ku (32.32)

is the force due to the stiffness of the structure,

fD = cu′ (32.33)

is the force due to damping of the structure, and p is the external force acting on the structure (see Figure32.16). The variables u′ and u′′ are the first and second derivatives of displacement u, k is the forcerequired for a unit displacement of the structure, and c is a measure of the damping in the system.

Thus, Equation 32.31 can be rearranged as shown in Equation 32.34:

mu′′ + cu′ + ku = p(t) (32.34)

However, for earthquakes, the force is not applied at the mass but at the ground (Figure 32.17); therefore,Equation 32.34 becomes:

mu′′ + c(u′ – z′) + k(u – z) = p (32.35)

for the relative displacement:

ω = u – z (32.36)

and the equation of motion, when there is no external force p being applied, is:

mu′′ + cω′ + kω = –mz′′ (32.37)

FIGURE 32.16 Forces acting on a structure according to Newton’s second law.

Location of zero

displacement

u

m p(t)

k

Equals

u

FD

FS

m P(t)

c



In Equation 32.37, mass m, damping factor c, and stiffness k are all known. The support acceleration(z′′) can be obtained from accelerogram records of previous earthquakes. Equation 32.37 is a second-order differential equation that can be solved to obtain the relative displacement (ω), the relative velocity(ω′), and the relative acceleration (ω′′) for a bridge structure due to an earthquake.

32.5.1.4 Caltrans’ Response Spectra

Response spectra have been developed so engineers do not have to solve a differential equation repeatedlyto capture the maximum force or displacement of their structure for a given acceleration record. Refer toFigure 32.18 for an example response spectra. Response spectra are graphs of the maximum response(displacement, velocity, or acceleration) of different single degree of freedom systems for a given earthquakerecord. Thus, engineers can calculate the period of the structure from its mass and stiffness and use theappropriate 5% damped spectra to obtain the response of the structure to the earthquake. The force

FIGURE 32.17 Earthquake-induced displacements.

FIGURE 32.18 Example response spectra.

z(t)

u

c

m p(t)

k

2.0

1.0

Acc

ele

rati

on

0.50 1.0 2.0 3.0 4.0

Period



equation (32.37) showed three responses that can be obtained from a dynamic analysis: displacement,velocity, and acceleration. We can also obtain these using response spectra. The spectral displacement (Sd)and velocity (Sv) can be obtained from the spectral acceleration using the following relationship:

Sa = ωSv = ω2Sd (32.38)

Therefore,

(32.39)

Caltrans developed response spectra using five large California earthquake ground motions on rock; 28different spectra were created based on 4 soil depths and 7 peak ground accelerations (PGAs). Engineerscan obtain the earthquake forces on a bridge by picking the appropriate response spectra based on thePGA and soil depth at the bridge site and calculating the natural period of their structure. These responsespectra can be found in Caltrans (1995); however, Caltrans is moving toward using site-specific responsespectra for many bridge sites.

32.5.1.5 Nonlinear Behavior

Bridge members change stiffness during earthquakes. The stiffness of a column is reduced when theconcrete cracks in tension. It is further reduced as the steel begins to yield and plastic hinges form (Figure32.19). The axial stiffness of a bridge changes in tension and compression as expansion joints open andclose. The soil behind the abutment yields for large compressive forces and may not support tension.Engineers must consider all changes of stiffness to accurately obtain force and displacement values for abridge. Currently, the standard is to calculate cracked stiffness for bridge columns. A value of Icr = 0.5(Igross)can be used unless a moment-curvature analysis is warranted. Also, because bridge columns are designedto yield during large earthquakes, the column force obtained from the analysis is reduced by a ductilityfactor, and the columns are designed for this smaller force. Caltrans is currently using a ductility factor(µ) of about 5 for designing new columns; however, a moment-curvature analysis of columns should bedone when the ductility of a column is uncertain.

FIGURE 32.19 Nonlinear column stiffness.

V

Vu

Vy

First yielding

First cracking

∆y ∆u

∆

∆y

∆uµ =

SdSa Sa

T

T Sa= = =ω π π2 2

2

22 4( / )



32.5.1.6 Abutment Stiffness

Longitudinally, the soil behind the back wall is assumed to have a stiffness that is related to the area ofthe back wall as shown in Figure 32.20:

kL = (47,000)(W)(h) (kN/m) (32.40)

Transversely, the stiffness is considered to be two thirds effective per length of inside wing wall (assumingthe wing wall is designed to take the load), and the outside wing wall is only one third effective per wing-wall length for the resultant stiffness shown in Equation 32.41:

kT = (102,000)(b) (kN/m) (32.41)

An additional stiffness of 7000 kN/m for each pile is added in both directions; therefore, in the longitu-dinal direction:

kT = (42,000)(W)(h) + (7000)(n) (kN/m) (32.42)

In the transverse direction:

kT = (102,000)(b) + (7000)(n) (kN/m) (32.43)

More information on abutment stiffness can be obtained in Caltrans (1995). Bridge abutments are onlyeffective in compression. A gap may have to be closed on seat-type abutments before the soil stiffness isinitiated. The abutment stiffness remains linear until it reaches the ultimate strength of 370 kN/m2.

32.5.1.7 Parallel and Series Systems

A simplification that allows engineers to analyze by hand many complicated and statically indeterminatestructures is the concept of parallel and series structural systems. For a parallel system, all the elementsshare the same displacement; for a series system, they all share the same force. Also, their stiffnesses aresummed differently. By assuming a rigid superstructure or by making other simplifying assumptions,bridge structures can be analyzed as combinations of parallel and series systems. This concept is partic-ularly useful when evaluating the longitudinal displacement of the superstructure. Refer to Figure 32.21and Figure 32.22.

FIGURE 32.20 Abutment stiffness.

b (ft or m)W (ft or m)

h (

ft o

r m

)

kL = 25*W*hkips

in.= 47000*W*h kN

m

= 7000

kNm

per pilekp = 40

kipsm

per pile

kt = 178*bkips

in.= 102,000*b

kNm



32.5.1.8 Code Requirements

In bridge design, two load cases are considered. Case 1 is for 100% of the transverse force and 30% of thelongitudinal force. Case 2 is for 100% of the longitudinal force and 30% of the transverse force. Thisapproach takes care of uncertainty with regard to the earthquake direction and to account for curved andskewed bridges with members that take a vector component of both the longitudinal and transverse force.

32.5.2 Seismic Design of Bridge Structures


The following collection of guidelines is intended to aid bridge engineers in producing more seismic-resistant bridge designs.

32.5.2.2 Structural System and General Plan

Seismic demands on a structure should be considered conceptually when creating the general plan. Firstof all, designers can control column demands on superstructures in new bridges by judiciously choosingcolumn sizing, spacing, and flexibility. Second, column or frame stiffnesses must be carefully considered.Column types, shapes, sizes, and length are very important in the design process. Some example conceptsthat should be considered when establishing the general plan are as follows:

• Column stiffnesses in a frame should preferably be kept within 20% of each other.• Isolators or sliding bearings can be used at the tops of short, stiff columns adjacent to abutments.• End diaphragm abutments provide good seismic energy absorbers for short frames (i.e., short

length end frame with stiff columns) or short bridges.• Frames should not exceed 800 ft as a means of avoiding excessive expansion joint movements.• Reduce joint skew angles to control loss of seat support due to frame rotation.• Use articulated or single-span bridges in areas of suspected, but poorly defined, faulting.• Use double columns at expansion joints.

FIGURE 32.21 Parallel structural system.

FIGURE 32.22 Series structural system.

a b c

Ktotal = Ka + Kb + Kc

a b c

1

Ktotal

1

Ka

1

Kb

= +1

Kc

+



32.5.2.3 Superstructure Joint Shear

Below is a procedure and example details for determining joint shear reinforcement in box girder bentcaps. Typical flexure and shear reinforcement in bent caps shall be supplemented in the vicinity ofcolumns to resist joint shear. Also, the cap width and depth must be sized to limit the joint shear stressto 12 × (fc

i)0.5. Minimum cap width shall be 2 ft greater than the column dimension in the cap widthdirection. The joint shear reinforcement required shall be located within the width of the cap and withina length of the cap equal to (1) two times the column width, or (2) the column width plus two timesthe bent cap depth, whichever is less. The effective length of cap shall be reduced appropriately forcolumns located near the end of the cap and closer than the column width or cap depth. Following is aprocedure for determining the required reinforcement that must be provided within the specified jointshear zone; the reinforcement is uniformly distributed:

• Vertical reinforcement shall be 20% of the column steel. The quantity of vertical steel shall be acombination of cap stirrups and added bars. Added bars shall be hooked around main longitudinalcap bars. All vertical legs shall be well distributed to provide protection for both longitudinal andtransverse demand or be supplemented to produce adequate coverage.

• Horizontal reinforcement shall be stitched across the cap in intermediate layers. The reinforcementshall be hairpin shaped and confine vertical bars in the hairpin bends. The hairpins shall beequivalent in area to 10% of column steel. The hairpins shall be strategically placed in two ormore layers, depending on structure depth. Spacing shall be denser outside the column than thatused within the column.

• Side-face reinforcement shall be 10% of the main cap reinforcement.• Provide #4 J-bars at 6 in. on-center along longitudinal top deck bars for bent caps skewed greater

than 20°. The bars shall be alternately 24 in. and 30 in. long. Locate the J-bars within a width Deither side of the column centerline (D is column dimension).

• All vertical column bars shall be extended as high as practically possible without interfering withmain cap bars.

• Column spiral extension into the bent cap shall be replaced by equivalent continuous hoops. Thissubstitution facilitates placement of the various horizontal joint shear bars.

Figure 32.23 shows cap joint shear reinforcement within D distance from the column center line. Figure32.24 shows cap joint shear reinforcement beyond a distance D/2 from the column face.

FIGURE 32.23 Example cap joint shear reinforcement skew 0° to 20°.

Deck

CL Bent

#11 construction

bars total 4

#11 total 6

Section > D/2 from column face

24(typical)

#6 @ 6"o.c.

#4 Total 6

this face

Soffit



32.5.2.4 Superstructure Flexural Capacity

Bridge superstructures must be reinforced to resist longitudinal and transverse flexural demands pro-duced by column plastic hinging. Conventional bar reinforcement must be provided in the slabs andbent caps in the designated zone surrounding the column to satisfy such demands. Prestressing bent capscould be an alternative solution for transverse demands and additionally can supplement joint shearcapacity at the column. Pinning column tops in multiple column bents will reduce seismic demand onthe superstructure but will require a more expensive fixed foundation.

32.5.2.5 Vertical Accelerations

The 1994 Northridge earthquake gave evidence of acceleration levels for vertical excitations that werehigher than those recorded in the past. The flexural and joint shear reinforcement prescribed so capsand superstructures can resist column demands should be ample to provide flexural resistance to verticalacceleration demands; however, the vertical capacity of girder stirrups should be checked, and shear-friction reinforcement in the form of girder side-face reinforcement at the cap that is equal to 1.5 gravityload should be provided. Tie-downs at hinges and abutments might be required.

32.5.2.6 Column Displacement

Displacement demands will generally be determined by STRUDL analysis, although the static method issufficient for short length bridges (one or two bents). The column displacement capacity can be deter-mined using the push method and is dependent on combinations of vertical and horizontal reinforce-ment. Also, disconnecting random stiff columns from the superstructure by use of sliding bearings orisolation systems is another means of avoiding large load demands on stiff columns.

FIGURE 32.24 Example cap joint shear reinforcement skew 0° to 20°.

Deck

4" chamfer

(typical)

CL Bent

#6 @ 6" o.c.

#4 total 6

this face

Soft

1' -0" min.

(typical)“D”

3" min.

CLR. 20 #18 column

longitudinal

reinforcement

Note: Column hoop reinforcement

not shown for clarity.

#11 total 6

#11 construction

bars total 424

(typical)

Section within “D” from column CL



32.5.2.7 Flared Columns

Flared columns can create some unexpected demands on the superstructure, footings, and columns. Pastpolicy has assumed that lightly reinforced flares will fuse during severe seismic activity. Superstructures,columns, and footings have been designed to resist plastic hinging demands from the column core at thetop and bottom of the column; however, designers must consider alternative behavior. Developing eitherthe full column section at the top of column or hinging at the base of flares should be investigated. Bothconditions will significantly affect shear demands in the column and shear and moment demands insuperstructures and footings. Flexural reinforcement for caps and superstructures must be calculated ifhinging is assumed at the bases of flares.

32.5.2.8 Bent Cap Designs

The design of bent caps for nonseismic loads must be consistent with assumptions made for supports,especially with respect to column flares. If flares are expected to lose structural integrity during seismicloadings, the cap should be designed to carry all loads without benefit of the flares; however, the bridgemust be analyzed for all nonseismic load cases with the stiffness and strength of the in-place flares. Asin the case with flared columns, the designer must design the cap for double conditions if any type ofstructural damage or loss of vertical support is anticipated for other types of supports.

32.5.2.9 Footings

New footing design procedures were tested satisfactorily at the University of California, San Diego.Although only one test case was performed, results indicated that serious degradation and bridge collapsecan be avoided if standard details are employed. Details included #5 at 12 in. on-center vertical ties andcolumn bar hooks that turned outward. Designers should be cautioned that cantilevered footing sectionsshould not exceed L/d = 2.5 (where L is the cantilevered footing length from the column face, and d isthe effective depth of footing) in orthogonal directions and L/d = 30 diagonally to the footing cornerwith 70-t piles typically spaced at 3 ft with 1.5-ft edge distances. For higher capacity piles, the designermust ensure load paths through connections, vertical ties, development of flexural reinforcement atfooting edges (e.g., hooks), etc. for both tensile and compressive demands.

32.5.2.10 Pile-Design Concepts

The designer should strive to prevent damage in foundations. Piles constructed in competent soil, incombination with passive resistance provided by cap and soil interaction and drag forces, will be sufficientto keep piles in the elastic range for flexure or shear under seismic demand. Problem areas that requireguidelines include: (1) piles in soft soils or water, including P-delta effects; (2) pile head conditions,pinned (standard) or fixed (which places tremendous demands on the cap and requires more thannonstandard cap size and reinforcement); (3) pile demands for pile capacities greater than 70 t (e.g.,spacing, edge distance, vertical ties that are more dense or of larger size, flexural steel hooks at footingedges); and (4) batter piles (e.g., used in dense soils; not for use in water, soft, or loose soils; capacity incombination with vertical piles). These design concepts are not intended to be a complete list of allconditions or problems or a solution to problems. They are intended to alert designers to conditionswhere the foundation must have the strength and displacement capacity intended under all conditionsof demand.

32.6 Retrofit of Earthquake-Damaged Bridges

32.6.1 Introduction

Since the early 1970s, the California Department of Transportation (Caltrans) has undertaken a majorprogram to ensure the seismic safety of all freeway structures. With a large portion of the work beingfunded in the aftermath of the Loma Prieta earthquake in 1989, analysis techniques and research tovalidate such techniques have progressed significantly in the past five years. Early on in the Phase 2 retrofit



program, structure overstrength analysis was the primary tool for seismic vulnerability assessment. Hingesand restrainers were always evaluated but none had been examined after a significant earthquake, soknowledge of their performance was based primarily on laboratory tests and hand calculations. Foun-dation-strengthening techniques had not been field tested (by real earthquakes), and design methodswere based on modified service load tools and simplified assumptions. It was soon clear that thesemethods, although for the most part very conservative, did not always afford a true picture of the behavioror strength (resistance to collapse) of a structure and did not necessarily produce cost-effective designs.To gain a clearer picture of the performance of bridges, Caltrans engineers have been focusing on thefollowing:

• Load path and limit-state analysis, item input ground motions• Validity of global models• Displacement ductility analysis• Beam and column joint performance• Hinges and restrainers• Detailing ductile elements• Foundation performance

The purpose of this section is to highlight current thinking on these items and help identify availabletools to properly retrofit bridge structures.

32.6.2 Background

The goal of retrofitting is to increase the seismic resistance of a bridge to the point of preventing collapseand thereby avoiding loss of life. It is not practical or economical to retrofit all structures to meet thecurrent seismic design performance criteria for new structures. It is, however, our responsibility to ensurethat no structure collapses under the maximum credible event. Based on the no-collapse criteria, theprimary goal of retrofitting bridges is to ensure that the vertical-load-carrying capacity is maintained.Traditionally, this has meant protecting the ability of the column to carry vertical loads while undergoingcyclic lateral loading. Under this kind of loading, some damage is expected to occur in plastic hingeregions of the column. With 25 years of real-life experience, since the San Fernando Earthquake in 1971,we have been provided with a good picture of where damage can be expected to occur on a concretestructure under seismic loads. These areas include:

• Column plastic hinge regions• Column shear capacity• Column-to-footing and column-to-superstructure connections• Expansion joint openings and hinge restrainers• Abutment back walls and transverse shear keys• Pile-to-footing connections• Pile overload

The following discussions address the seismic analysis and design approaches for retrofitting concretebridge structures.

32.6.3 Seismic Analysis Approach

32.6.3.1 Load Path and Limit-State Analysis

Limit-state theory says, roughly, that a structure is only as good as the weakest link (or member) in thestructural system. Ensuring that plastic action occurs in a predetermined location is therefore the goal.For concrete bridges, this predetermined location is typically, and preferably, in the column. Controllingthe location of the plastic hinge allows the engineer to develop a rational estimate of the damage expectedto a structure and its ability to resist collapse. For this to happen, all members and components of a



structure must be examined to determine whether they can actually carry the forces required to forceplastic hinging to occur in the column. Testing and application of basic engineering principles to com-ponents of the structure (column superstructure joints, column–footing connections, pile cap, and pileconnections) have shown that areas of analysis and design once taken for granted as adequate could bevulnerable under extreme seismic loading conditions. Rigorous analysis of the structure may determinethat the capacity of a system may likely be controlled by connections to the column and not by thestrength of the column itself. Current analysis techniques commonly used by engineers to estimatereinforced-concrete capacity strongly suggest that many superstructures do not have the capacity to forceplastic hinging into the column. Because one objective of the retrofit is to ensure that plastic hingingdoes occur in the column, the superstructure strength and ductility have to be addressed in the retrofitdesign.

32.6.3.2 Global Behavior

Early retrofit analysis typically relied on global elastic modal models to predict moment and displacementdemands. Although this is still often a valid analysis technique, in some situations global analyses arenot the proper tools for seismic-demand prediction. These situations include but are not limited to:

• Short-period (T < 0.75 s) structures• Very complicated structures (requiring many assumptions)

Other tools that could be used in lieu of or in conjunction with global elastic models include: (1) handcalculations with single degree-of-freedom conditions, and (2) pushover analysis to determine the orderof plastic hinging in incremental collapse. Hand-calculation analysis should be limited to simple struc-tures or structures where the number of assumptions is limited. Pushover analysis can be used for bothsimple and complex structures. The value of pushover analyses is that the capacity of the structural systemis accounted for while the integrity of each element is determined. For example, if the two end framesof, say, a three-frame structure are designed with substantially more strength or stiffness than the interiorframe, a global analysis may well conclude that the interior frame has relatively low seismic demandswhen in fact it is being supported, or helped, by the stronger adjacent frames. The final result could stillbe that the system is adequate to avoid collapse; however, it is important for the engineer to have a clearidea of where vulnerabilities and strengths exist in the system. Because the goal of retrofit is to preventthe collapse and not just prevent plastic hinging, an efficient retrofit analysis technique would explicitlyestimate the system capacity at collapse and not just assume a direct correlation between plastic hingingof a single column and precollapse capacity of the system.

32.6.3.3 Displacement and Curvature Ductility Analysis

An alternative estimate of the ductility of a member (column) can be obtained using ductility analysistechniques proposed by Mander et al. (1984, 1988a,b). The implementation of this approach has beentested extensively and directed explicitly toward bridges by Priestly and Seible (1993). The predominantanalysis approach until recently has been moment overload—the application of force reduction factorsto loads calculated from a dynamic elastic multimodal response spectrum analysis (e.g., STRUDL orSAP90) assuming gross moments of inertia (Ig). This approach tends to underestimate system capacity.The displacement ductility approach focuses on the capacity side of the equation and directly addressesthe basic premise of the equal energy theory—that displacements are equal for a given load whether thestructure remains elastic or enters into the plastic state as long as the section has not blown apart(allowable confinement stresses have been exceeded). By directly calculating the plastic moment capacity(instead of factoring up the nominal moment capacity) and the displacement capacity of each member(instead of limiting displacement to a factor of column geometry without regard to the rotational capacityof the section itself), the engineer can make a more accurate estimate of the capacity of the system.Because the focus in this type of approach is on displacements, it is important to base the analysis on amembers effective moments of inertia (Ieff = Icr) instead of gross moments of inertia. Basing the dynamic



analysis on Icr instead of Ig will result in larger estimated displacement demands and smaller estimatedmoment (force) demands. More refined analysis techniques can be employed that assess the performanceof a member and estimated damage. This kind of information can be of particular interest whenattempting to estimate resistance to collapse.

32.6.3.4 Foundations

Footings typically have required extensive work to increase their capacity to a level consistent with thecolumn plastic moment. Early retrofitting techniques were often conservative (for lateral loads) byignoring the contribution of existing piles to the capacity of the system. Large-scale testing of existingpiles had not yet been done in situ, so nominal lateral pile capacities were often assumed when existingpile capacity was analyzed. Construction techniques for increasing the capacity of the footing relied oninstalling standard piles or prestressed tie-downs (tendons or rods). The technology simply had not beendeveloped to make the leap from standard, new bridge construction to efficient, cost-effective retrofitwork. Since those early days, many new technologies have come into use in the retrofit industry. Fieldtesting of pile foundations at the Cypress structure in Oakland, and the Terminal Separation in SanFrancisco have shown that the actual lateral capacity of concrete piles is much greater than was originallythought (90 vs. 40 kips/pile). Note that the assumed tensile capacity of existing piles is most often 0.Pile-to-footing connections were traditionally designed to develop vertical loads in a downward direction(compression), not upward (tension). Construction techniques for installing high-capacity piles (up to1000 kips/pile) in very confined spaces have been field tested with very promising results. Seismicmodeling now takes into account soil springs and group effects instead of simply assuming that allfootings are fixed, rigid members. Soil springs in a soft soil may increase the displacement estimate onthe column while decreasing the moment demand at the footing. The model may also predict that afooting is moving so much that the piles must be sized to limit displacement or resist larger loads thanwould otherwise be expected. Liquefaction and large ground displacements along fault rupture zonescontinue to be items that elude easy solutions.

32.6.4 Design Approaches

32.6.4.1 Retrofit Approaches

The three primary concepts used to retrofit structures are:

• Reduce loads imposed on the system.• Increase the capacity of the structural elements.• Provide a new or super element.

It is not uncommon for a retrofit design to make use of more than one of these concepts. The followingprovides some typical details and ideas that could be used to implement these concepts:

32.6.4.1.1 Column Plastic Hinge Regions and Column Shear CapacitySteel shells have been used extensively (and successfully throughout California and in Alaska) to addductility and provide confinement to concrete columns (Figure 32.25). Composite fiber wrap providesadditional confinement and ductility of concrete columns and is an idea that has been under developmentfor several years; results are starting to yield systems that are economical and structurally equivalent tothat of the steel shell (Figure 32.26). Remove and replace portions of the substructure is an option that hasbeen used where performance beyond no collapse is required. SuperBent provides an additional supportsystem.

32.6.4.1.2 Column-to-Footing Connections and FootingsAn additional top mat on footing is a very common retrofit due to the fact that top mats of reinforcementwere not used in footings until the late 1970s. The top mat adds tensile capacity to the footing (Figure32.27). A prestressed footing is sometimes used for increased performance.



FIGURE 32.25 Steel casing of column.

FIGURE 32.26 Composite fiber wrap.

FIGURE 32.27 Footing retrofit with additional top mat.

PCC column

Steel casing

Welded joint

Seal joint for grouting.

grout at 2" gap may

extend to outer face

of steel casing

2"

2"

Waterproofing

Finish grade

Gap: 2" min.,

4" max.

Epoxy resin-glass

composite

Existing PCC column

Section A-A

no scale

Section B-B

no scale

Pressurized grout

Epoxy resin-glass

composite

Existing PCC column

Footing extensionNew piles, typical

Str.

co

ncr

ete

BR

. FT

G.(1'-0")

PCC overlay

Excavate

Ground line



32.6.4.1.3 Column-to-Superstructure ConnectionsBent cap bolsters are used to increase the torsional capacity of the bent cap and the capacity of the columnand cap joint (Figure 32.28). Prestressed bent caps are used to increase the torsional capacity of the bentcap and the capacity of the column and cap joint.

32.6.4.1.4 Expansion Joint Openings and Hinge RestrainersPlace additional or replace existing restrainers. Seat extensions (typically pipe) allow for displacement.Joint displacement demands are reduced by using additional restrainers.

32.6.4.1.5 Pile-to-Footing ConnectionsAdditional piles can be used to gain greater tension and compression capacity. Prestressed tie-downsprovide additional footing tensile (only) capacity.

32.6.4.2 Summary

Many more difficulties are encountered in retrofit construction than in standard new bridge construc-tion; however, the field of bridge seismic analysis and retrofit has seen many developments over thepast several years. Probably the most significant change in assessing the capacity of a structural systemhas been the adoption of ductility analysis and the pseudo-nonlinear analysis approach of determininga plastic hinging sequence and ultimately a systematic yield mechanism. Construction techniques arequickly adapting to the specialized demands of seismic retrofit for bridges. Materials, techniques, andequipment have been developed and integrated from other industries, such as installation of high-capacity piles (adopted from the oil industry), and new materials such as carbon fiber are beingdeveloped in laboratories. The field of seismic retrofitting has developed at a tremendous pace overthe last several years. Engineers should expect additional changes as research and construction con-tinue. The techniques used on concrete structures in California have proven to be effective, under realseismic loads (such as the 1994 Northridge earthquake). For additional information on any of thesubjects addressed in this chapter, it is strongly suggested that the reader consult the referencesprovided.

FIGURE 32.28 Bent cap bolsters.

Ne

w d

rop

cap

5'-

0"

+ –2

'-0

"+ –

Exis

tin

g b

en

t ca

p

5'-0"1'- 0" 1'-0"+–Existing bent cap

31

New bolster

each side

CL Bent



32.7 Defining Terms

Base shear—The total design lateral force at the base of a structure.Bearing wall system—The structural system without a complete vertical-load-carrying frame.Building frame system—An essentially complete frame that provides support for dead, live, and snow

loads.Boundary element—Special reinforcement at edges of openings, shear walls, or diaphragms.Diaphragm—A horizontal system acting to transmit seismic forces to vertical lateral-force-resisting

systems.Dual system—A combination of shear walls or braced frames and intermediate or special moment-

resisting frames proportionally designed to resist seismic forces.Hoop—A closed tie that may be of several reinforcing elements with 135° hooks having a 6-bar diameter

(3-in. minimum) extension at each end or a continuously wound tie with a 135° hook at each endwith a 6-bar diameter extension (3-in. minimum) that engages the longitudinal reinforcement.

Moment-resisting frame—A frame where the frame members and joints are capable of resisting forcesprimarily by flexure.

Shear wall—A wall designed to resist seismic forces parallel to the plane of the wall.Story drift—The displacement of one level relative to the level above or below.Strength—The useable capacity of a structure or its structural members to resist lateral loads within the

code-allowable deformations.Structure base—That level in the structure at which the earthquake motions are considered to be imparted

to the structure.

References

Algermissen, S.T. and Perkins, D.M. 1972. A technique for seismic risk zoning, general considerationsand parameters. In Proceedings of International Conference on Microzonation, November 1, Seattle,WA, pp. 865–877.

Algermissen, S.T. and Perkins, D.M. 1976. A Probabilistic Estimate of Maximum Acceleration in Rock inContiguous United States, USGS Open File Report 76–416. U.S. Geological Survey, Washington,D.C.

ASCE. 2005. Minimum Design Loads for Buildings and Other Structures, ASCE 7-05. American Society ofCivil Engineers, Reston, VA, pp. 3, 109–135.

Blume, J.A., Newmark, N.M., and Corning, L.H. 1992. Design of Multistory Reinforced Concrete Buildingsfor Earthquake Motions. American Concrete Institute, Farmington Hills, MI.

Bolt, B.A. 1969. Duration of strong motion. In Proceedings of the Fourth World Conference on EarthquakeEngineering, January 13–18, Santiago, Chile, pp. 1304–1315.

Boore, D.M., Joyner, W.B., Oliver, A.A., and Page, R.A. 1978. Estimation of Ground Motion Parameters,USGS, Circular 795. U.S. Geological Survey, Washington, D.C.

Boore, D.M., Joyner, W.B., Oliver, A.A., and Page R.A. 1980. Peak acceleration velocity and displacementfrom strong motion records. Bull. Seism. Soc. Am., 70(1), 305–321.

Caltrans. 1995. Bridge Design Aids Manual. California Department of Transportation, Sacramento, CA.Campbell, K.W. 1997. Empirical near-source attentuation relationships for horizontal and vertical com-

ponents of peak ground acceleration, peak ground velocity, and pseuo-absolute accelerationreponse spectra. Seis. Res. Lett., 68, 154–179.

Cloud, W.K. and Perez, V. 1967. Accelerograms: Parkfield earthquake. Bull. Seism. Soc. Am., 57, 1179–1192.Conell, C.A. 1968. Engineering seismic risk analysis. Bull. Seism. Soc. Am., 58(5), 1583–1606.Cooper, T.R. 1995. Seismic analysis procedures. In Proceedings of the Third National Concrete and Masonry

Engineering Conference, June 15–17, San Francisco, CA.Donovan, N. C. 1973. Earthquake Hazards for Buildings: Building Practices for Disaster Mitigation. National

Bureau of Standards, U.S. Department of Commerce, Washington, D.C., pp. 82–111.



Esteva, L. 1969. Seismicity prediction: a Bayesian approach. In Proceedings of the Fourth World Conferenceon Earthquake Engineering, Santiago, Chile.

FEMA. 2003. NEHRP Recommended Provisions for Seismic Regulations for New Buildings and OtherStructures, FEMA 450. Federal Emergency Management Agency, Washington, D.C.

Housner, G. W. 1965. Intensity of earthquake shaking near the causative fault. In Proceedings of the ThirdWorld Conference on Earthquake Engineering, January 22–February 1, Auckland, New Zealand, pp.94–115.

ICBO. 1994. Uniform Building Code, Vol. 2. International Conference of Building Officials, Whittier, CA.ICC. 2006. 2006 International Building Code. International Code Council, Washington, D.C.Idriss, I.M. 1993. Procedures for Selecting Earthquake Ground Motions at Rock Sites, NIST GCR 93-625.

U.S. Department of Commerce, National Institute of Standards and Technology, Gaithersburg,MD.

Ingham, J. and Priestly, M.J.N. 1993. Shear Strength of Knee Joints. University of California, San Diego.McGuire, R.K. 1975. Seismic Structural Response Risk Analysis, Incorporating Peak Response Progressions

on Earthquake Magnitude and Distance, Report R74-51. Massachusetts Institute of Technology,Cambridge.

MacRae, G.A., Priestly, M.J.N., and Tao, J.R. 1993. P-Delta Design in Seismic Regions, SSRP No. 93/05.University of California, San Diego.

Mander, J.B., Priestley, M.J.N., and Park, R. 1984. Seismic Design of Bridge Piers, Research Report 84-2.Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand.

Mander, J.B., Priestley, M.J.N., and Park, R. 1988a. Theoretical stress–strain model of confined concrete.J. Struct. Eng., 114(8), 1804–1826.

Mander, J.B., Priestley, M.J.N., and Park, R. 1988b. Observed stress–strain behavior of confined concrete.J. Struct. Eng., 114(8), 1827–1849.

Milne, W.G. and Davenport, A.G. 1969. Distribution of earthquake risk in Canada. Bull. Seismol. Soc.Am., 59, 729–754.

Moehle, J.P. and Soyer, C. 1993. Behavior and Retrofit of Exterior RC Connections. University of California,Berkeley.

Naaseh, S. 1995. Seismic reftrofit of San Francisco City Hall. In Proceedings of the Third National Concreteand Masonry Engineering Conference, June 15–17, San Francisco, CA, pp. 769–795.

Naeim, F., Ed. 1989. The Seismic Design Handbook. Van Nostrand Reinhold, New York.Nawy, E.G. 2008. Reinforced Concrete: A Fundamental Approach, 6th ed. Prentice Hall, Upper Saddle

River, NJ, 934 pp.Newmark, N.M. and Hall, W.J. 1969. Seismic design criteria for nuclear reactor facilities. In Proceedings

of the Fourth World Conference on Earthquake Engineering, January 13–18, Santiago, Chile, pp. 37–50.Newmark, N.M. and Hall, W.J. 1973. Procedures and Criteria for Earthquake Resistance Design: Building

Practices for Disaster Mitigation. National Bureau of Standards, U.S. Department of Commerce,Washington, D.C., pp. 209–236.

Page, R.A., Boore, D.M., Joyner, W.B., and Caulter, H.W. 1972. Ground Motion Values for Use in SeismicDesign of the Trans-Alaska Pipeline System, USGS Circular 672. U.S. Geological Survey, Washington,D.C.

Priestly, M.J.N. and Seible, F. 1993. Full-Scale Test on the Flexural Integrity of Cap/Column Connectionswith #18 Column Bars, Report No. TR-93/01. University of California, San Diego.

Priestly, M.J.N. and Seible, F. 1994. Proof Test of Superstructure Capacity in Resisting Longitudinal SeismicAttack for the Terminal Separation Replacement. University of California, San Diego.

Priestly, M.J.N. et al. 1993. Proof Test of Circular Column Footing Designed to Current Caltrans RetrofitStandards: Tests for Rectangular Column Also Performed. University of California, San Diego.

Sabetta, F. and Pugliese, A. 1987. Attenuation of peak horizontal acceleration and velocity from Italianstrong-motion records. Bull. Seism. Soc. Am., 77, 1491–1513.

Sabetta, F. and Pugliese, A. 1996. Estimation of response spectra and simulation of nonstationary earth-quake ground motions. Bull. Seism. Soc. Am., 86, 337–352.


SEAOC. 1996. Recommended Lateral Force Requirements and Commentary. Seismology Committee, Struc-tural Engineers Association of California, Sacramento.

Seed, H.B. and Idris, I.M. 1982. Ground Motions and Soil Liquefaction during Earthquakes. EarthquakeEngineering Research Institute, Berkeley, CA.

Seyed, M. 1993. Ductility Analysis for Seismic Retrofit of Multi-Column Bridge Structures: Santa MonicaViaduct. ASCE Publications, Reston, VA.

Thewalt, C.R. and Stojadinovic, B. 1993. Behavior of Bridge Outriggers: Summary of Test Results. Universityof California, Berkeley.

Trifunac, M.D. and Brady, A.G. 1975. A study of the duration of strong earthquake ground motion. Bull.Seism. Soc. Am., 65, 581–626.

Yamabe, K. and Kanai, K. 1988. An empirical formula on the attenuation of the maximum accelerationof earthquake motions. In Proceedings of the Ninth World Conference on Earthquake Engineering,Vol. II, pp. 337–342.

Further InformationFor further information, consult California Department of Transportation (Caltrans), Bridge DesignPractice Manual, Section 8, 1995, and Zelinski, R., Seismic Design Memo, Caltrans Seismic TechnicalSection, California Department of Transportation, Sacramento, 1995.


(a) Sunshine Skyway Bridge in Tampa, Florida. (Photograph courtesy of Portland Cement Association, Skokie, IL.)(b) Prefabricated bridge element. (Photograph courtesy of Portland Cement Association, Skokie, IL.) (c) CoronadoBridge in San Diego, California, which is 11,720 feet in length and 50 to 200 feet in height; girders are prestressedlightweight concrete. (Photograph courtesy of Steven Simpson, Inc., San Diego, CA.)

(a) (b)

(c)


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