seismic design-concrete structures

7/30/2019 SEISMIC DESIGN-Concrete Structures

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Page 1 Professor Panos D. Kiousis

Last Update 11/10/2011

COLORADO SCHOOL OF MINESDIVISION OF ENGINEERING

CONCRETE DESIGN IIEARTHQUAKE DESIGN

1. BASICS

Sudden movement of tectonic plates on the crust of the earth results in EARTHQUAKES.Earthquakes are transmitted in the form of waves that reach many miles from the epicenter.

The maps in Figures ASCE 7-98 - 9.4.1.1 (a) and (b) in the appendix show MAXIMUMCONSIDERED GROUND MOTION for the contiguous 48 states. The mapped values in (a)represent the expected peak acceleration of a single DOF system with a natural period equal to0.2 sec and damping equal to 5% of critical damping. It is known as the 0.2 sec spectral responseacceleration SS (subscript s for short period). Similarly, the mapped values in (b) represent the

expected peak acceleration of a single DOF system with natural period equal to 1.0 sec anddamping equal to 5% of critical damping. It is known as the 1.0 sec spectral responseacceleration S1 (subscript 1 for 1.0 second period)

Ss and S1 are used together to establish the loading criteria for seismic design.

They represent earthquake ground motion with a likelihood of exceedance of 2 percent in 50years, or a return period of about 2500 years.

A typical design response spectrum, characteristic of a region is presented here.

Figure 1: Design Response Spectrum


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Inertia effects are demonstrated in Figure 2

Historically, in North America, as well as most of the world, seismic design emphasizes the effects

of the horizontal ground motion: Because this is the larger component, and

Because a structure is typically much stiffer vertically than horizontally.

An earthquake signal is quite complex (Figure 3). The intensity of an earthquake is described interms of ground acceleration as a fraction of g. For example, the intensity of an earthquake canbe 0.2g or 20% of g.

What is important? Peak acceleration, as well as frequency characteristics and duration.

Figure 2: Demonstration of inertia effects

Figure 3: Accelerogram of the Northridge Earthquake (1994)


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North American practice requires that structures be designed for only a fraction of the forcesassociated with those displacements. This is because structures dissipate significant energy asthe materials yield and behave inelastically.

An additional explanation is shown in Figure 4 which is the basic definition of "Performance Based

Design" for earthquake resisting structures.

This figure demonstrates the concept of designing economically for a specific performancerequirement.

The main goal of such design is to construct buildings that will withstand moderate earthquakeswithout damage and severe earthquakes without collapse.

The closer the frequency of the ground motion is to one of the natural frequencies of a structure,the greater the likelihood of the structure experiencing resonance, resulting in increaseddisplacement and damage.

Earthquake response depends strongly on the geometric properties of the structure, andespecially height: Tall buildings respond more to long-period (low-frequency) ground motion,while short buildings respond more strongly to short-period (high frequency) ground motion .

Figure 4: Performance Design Concept


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Figure 5 shows the shapes for the principal modes of vibration of a three-story frame structure.The relative contribution of each mode to the lateral displacement of the structure depends on thefrequency characteristics of the ground motion. Typically, the first mode provides the greatestcontribution to lateral displacement. The taller the structure the more susceptible it is to theeffects of higher modes of vibration, which are generally additive to the effects of the lower modesand tend to have the greatest influence on the upper stories. The first few periods for examples of

some typical structures are presented in Table 1.

Table 1: Vibration Characteristics of buildings with story stiffness (N/m) 5000 times its mass (kg).

Number of Stories Natural Periods in seconds

1 0.09

2 0.143, 0.055

3 0.2, 0.071, 0.049

4 0.256, 0.09, 0.058, 0.0475 0.312, 0.107,0.068, 0.052, 0.046

10 0.594, 0.2, 0.122, 0.089, 0.071,

Structural configuration is also important. Structures with a discontinuity in stiffness or geometrycan be subjected to high displacements or forces. Figure 6 demonstrates a structure where thebottom floor is soft. In such case, the tendency is to concentrate the displacements in the softstory, with an increased potential of failure.

Figure 5: Three story structure and its modes of vibration

Figure 6: Soft first story


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The results of such design are demonstrated in Figure 7. The corner column, with low amounts oftransverse reinforcement could not provide the required ductility (soft story - large deformations)and failed. The inner columns, with significantly larger confinement did better. However, thetransverse reinforcement did not extend in the joint and resulted in early formation of hinges andfailure there.

As has been discussed in the past, thestiffer members pick up a greaterproportion of the load. We can use suchtendencies to our advantage when wecombine frames with shear walls.However, we have to be careful in less

obvious cases. For example, when stiffermembers such as masonry infill walls arenot considered in the design, the effectscan be at times undesirable.

Finally, the need to provide adequateseparation between structures cannot beemphasized enough as is demonstrated inFigure 8.

Figure 7: Soft floor failure

Figure 8: Damage due to proximity


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2. GROUND MOTION

2.1 Maximum Considered Earthquake Ground Motion is represented by the mapped spectralresponse acceleration at short periods, SS, and at 1 second, S1, obtained from the correspondingmaps in the appendix.

2.2 Site Class is defined based on soil strength characteristics as follows:

A Hard rock with measured shear wave velocity, > 5,000 ft/sec (1500 m/s)B Rock with 2,500 ft/sec < 5,000 ft/sec (760 m/s < 1500 m/s)C Very dense soil and soft rock with 1,200 ft/sec < 2,500 ft/sec (360 m/s < 760 m/s) or

with either> 50 or> 2,000 psf (100 kPa).D Stiff soil with 600 ft/sec 1,200 ft/sec (180 m/s 360 m/s) or with either 15 50

or 1,000 psf2,000 psf (50 kPa 100 kPa)

E A soil profile with < 600 ft/sec (180 m/s) or with either < 15 < 1,000 psf or any profilewith more than 10 ft (3 m) of soft clay defined as soil with PI > 20, w 40 percent, and 10 ft [3 m] of peat and/or highly organic clay whereH = thickness of soil)

3. Very high plasticity clays (H > 25 ft [8 m] with PI > 75)4. Very thick soft/medium stiff clays (H > 120 ft [36 m])

When the soil properties are not known in sufficient detail to determine the Site Class, SiteClass D shall be used. Site Classes E or F need not be assumed unless the authority having

jurisdiction determines that Site Classes E or F could be present at the site or in the event thatSite Classes E or F are established by geotechnical data .

2.3 Adjusted Maximum Earthquake Spectral Response: The spectral coefficients SS and S1 areadjusted for site class effects as follows: (1)and (2)

where, the site coefficients and are defined in Tables 4.1.2.4a and 4.1.2.4b in the appendix. varies between 0.8 and 2.5, while varies between 0.8 and 3.5. Higher values for some sitesare possible. and increase from hard rock to thick soft clay layers and as the values ofSSand S1 decrease.

2.4 SEISMIC DESIGN CATEGORY: Each structure shall be assigned a Seismic Design


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Category. Seismic Design Categories are used in the Provisions to determine permissiblestructural systems, limitations on height and irregularity, those components of the structure thatmust be designed for seismic resistance, and the types of lateral force analysis that must beperformed.

The Seismic Design Category is based on the structural Seismic Use Group and the design

spectral response acceleration coefficients, SDS and SD1, defined as 2/3 ofSMS and SM1respectively. Each building and structure shall be assigned to the most severe Seismic DesignCategory in accordance with Table 4.2.1a or 4.2.1b, irrespective of the fundamental period ofvibration of the structure, T.

TABLE 4.2.1a Seismic Design Category Based on Short Period Response Accelerations

Value ofSDSSeismic Use Group

I II IIISDS< 0.167 A A A

0.167 SDS< 0.33 B B C

0.33 SDS< 0.50 C C D

0.50 SDS Da

Da

Da

aSeismic Use Group I and II structures located on sites with mapped maximum considered earthquake spectral responseacceleration at 1 second period, S1, equal to or greater than 0.75 shall be assigned to Seismic Design Category E and SeismicUse Group III structures located on such sites shall be assigned to Seismic Design Category F.

TABLE 4.2.1b Seismic Design Category Based on 1 Second Period Response Accelerations

Value of SD1Seismic Use Group

I II IIISD1< 0.067 A A A

0.067 SD1< 0.133 B B C

0.133 SD1< 0.20 C C D

0.20 SD1 Da

Da

Da

aSeismic Use Group I and II structures located on sites with mapped maximum considered earthquake spectralresponse acceleration at 1 second period, S1, equal to or greater than 0.75 shall be assigned to Seismic DesignCategory E and Seismic Use Group III structures located on such sites shall be assigned to Seismic DesignCategory F.

Site Limitation for Seismic Design Categories E and F: A structure assigned to SeismicDesign Category E or F shall not be sited where there is the potential for an active fault to causerupture of the ground surface at the structure.

Exception: Detached one- and two-family dwellings of light-frame construction.


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MEMBER CONSIDERATIONS

Members MUST perform in a DUCTILE manner and dissipate energy in a way that does notcompromise the strength of the structure.

To achieve this goal we must consider both structural details and the overall design.

The principal method to ensure ductility in members subjected to shear and bending is to provideconfinement in concrete. How do achieve this? Using closed hoops or spiral reinforcement toenclose the core of the beam or column.

Successful seismic design of frames requires that the elements are proportioned so that hingesare formed in locations that least compromise the overall strength.

For frames undergoing lateral displacement, joints must be designed so that the columns arestronger than the beams. This way the hinges will be formed in the beams, thus minimizing theportion of the structure that is affected by the nonlinear behavior and maintaining the overall

vertical load capacity. When hinges are formed in a beam the moments at the end of themember, which are governed by flexural strength, determine the shear that must be carried(Figure 9).

Figure 9: Creation of plastic hinges and the resulting shear


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The shear V corresponding to the flexural failure at both ends of the beam or column is given by:

(3)

Clearly, this shear must be added to the shear due to dead and live gravity loads.

For example if the beam carries a factored distributed load wu, then it creates shears equal to

that must be added to the shear of Equation (3).

Transverse reinforcement design and member resizing must then be performed as needed.Shear failure is dominated by the formation of diagonal cracks, which are very brittle, as opposedto the very ductile hinges. This of course results in substantial reduction of the energy dissipationcapacity of the member.

Extra attention must be paid to short members in frames, which may be unintentionally strong inflexure compared to shear (Figure 10).

Figure 10: Shear failure of short column


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BASIC DESIGN EQUATIONS

The design criteria for earthquake loading in USA are based on procedures developed by theBuilding Seismic Safety Council and incorporated in Minimum Design Loads for Buildings andOther Structures (SEI/ASCE).

We use the values of the Spectral Response SS and S1 to determine the spectral responseaccelerations SDS and SD1 that are used in design:

23 (4) 23 (5)

ACI 318-08 provides two loading combinations that include earthquake loads:

U = 1.2 D +1.0 E + 1.0 L + 0.2 S (ACI 318-08:9-5)U = 0.9 D + 1.0 E + 1.6 H (ACI 318-08:9-7)

IBC (Section 1605.2) also provides two cases:

U = 1.2 D + 1.0 E + (f1 L or f2S)U = 0.9 D 1.0 E

f1 = 1 for floors in places of public assembly, for live loads in excess of 100 pounds per square foot(4.79 kN/m2), and for parking garage live load, and

= 0.5 for other live loads.f2= 0.7 for roof configurations (such as saw tooth) that do not shed snow off the structure.

= 0.2 for other roof configurations.

E = QE+ 0.2 SDS D (FEMA 368 5.2.7.1-1)E = QE- 0.2 SDS D (FEMA 368 5.2.7.1-2)

Note that Equation (ACI 318-08:9.5) works with (FEMA 368 5.2.7.1-1) and describes the case thatthe effects of gravity are additive to those of the earthquake loads. Similarly, Equation (ACI 318-08:9.7) works with (FEMA 368 5.2.7.1-2) and describes the case that the effects of gravitycounteract the effects of the earthquake loads.

In the equations above,QE= effect of horizontal seismic forces = reliability factor associated with the redundancy of the system.

Forstructures in Seismic Design CategoriesA, B and C, the value ofmay be taken as 1.0.

Forstructures in Seismic Design CategoryD, shall be taken as the largest of the values ofxcalculated at each storyof the structure x in accordance with Eq. 5.2.4.2:

2 20 (FEMA 368 5.2.4.2)


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where: = the ratio of the design story shear resisted by the single element carrying the mostshear force in the story to the total story shear for a given direction of loading. For bracedframes, the value of is equal to the lateral force component in the most heavilyloaded brace element divided by the story shear. For moment frames,

shall be

taken as the maximum of the sum of the shears in any two adjacent columns in the planeof a moment frame divided by the story shear. For columns common to two bays withmoment resisting connections on opposite sides at the level under consideration, 70percent of the shear in that column may be used in the column shear summation. Forshear walls, shall be taken equal to the maximum ratio, rix, calculated as the shear ineach wall or wall pier multiplied by 10/lw(the metric coefficient is 3.3/lw), where lw is thewall or wall pier length in feet (m) divided by the story shear and where the ratio 10/lwneed not be taken greater than 1.0 for buildings of light frame construction. For dualsystems, shall be taken as the maximum value as defined above considering alllateral-load-resisting elements in the story. The lateral loads shall be distributed toelements based on relative rigidities considering the interaction of the dual system. For

dual systems, the value of need not exceed 80 percent of the value calculated above.

Ax= the floor area in square feet of the diaphragm level immediately above the story.

The value ofneed not exceed 1.5, which is permitted to be used for any structure. The value ofshall not be taken as less than 1.0.

Exception: Forstructures with lateral-force-resisting systems in any direction comprised solely ofspecial moment frames, the lateral-force-resisting system shall be configured such that the valueofcalculated in accordance with this section does not exceed 1.25.

The metric equivalent of FEMA 368 Equation (5.2.4.2) is

2

.

, where, Ax is in square

meters.

Forstructures in Seismic Design Categories E and F, the value ofshall be calculated in thesame way as in design category D.

Exception: Forstructures with lateral-force-resisting systems in any direction comprised solely ofspecial moment frames, the lateral-force-resisting system shall be configured such that the valueofcalculated in accordance with designing for category D does not exceed 1.1.


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SEISMIC LOADING

Equivalent Lateral Force Procedure.

One of the most popular methods is the equivalent lateral force procedure, which is based on thefollowing processes:

1. Calculate the Seismic Base Shear V in a given direction: (FEMA 368 5.4.1)where:Cs = The seismic response coefficient.W = The total dead loadand applicable portions of other loads as follows:

a. In areas used for storage, a minimum of 25 percent of the floor live load shall beapplicable. Floor live load in public garages and open parking structures is notapplicable.

b. Where an allowance for partition load is included in the floor load design, the actualpartition weight or a minimum weight of 10 psf (500 Pa) of floor area, whichever isgreater, shall be applicable.

c. Total operating weight of permanent equipment.d. In areas where the design flat roof snow load does not exceed 30 pounds per

square ft, the effective snow load is permitted to be taken as zero. In areas wherethe design snow load is greater than 30 pounds per square ft and where siting andload duration conditions warrant and when approved by the authority having

jurisdiction, the effective snow load is permitted to be reduced to not less than 20percent of the design snow load.

The seismic response coefficient, Cs, shall be determined as follows:

(FEMA 368 5.4.1.1-1)where:

SDS = as discussed earlier, is the design spectral response acceleration in theshort period range.

R = the response modification factor from FEMA 450 Table 4.3-1I = the occupancy importance factorfrom FEMA 368 table 1.4.

CSneed not exceed the following:

(FEMA 368 5.4.1.1-2)but shall not be taken less than: 0.1 (FEMA 368 5.4.1.1-3)nor forbuildings and structures in Seismic Categories E and F:


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0.5 (FEMA 368 5.4.1.1-4)where:

SD1 = as discussed earlier, is the design spectral response acceleration at a period of

1 second and is equal to

.

T = the fundamental period of the structure in seconds. FEMA 368 presentsmultiple acceptable methods to determine the fundamental period T. Thesemethods are listed in the Appendix of this document.

2. Distribute the Seismic Forces Vertically:

The base shear V, is distributed vertically, i.e. on the floor membranes as follows: (FEMA 368 5.4.3-1)and

(FEMA 368 5.4.3-2)

where:Cvx = vertical distribution factorV = total vertical lateral force or shear at the base of the structure (kip or kN)wiand wx = the portion of the total gravity load of the structure, W, located or assigned to

Level iorxhiand hx = the height (ft or m) from the base to Level iorxk = an exponent related to the structure period as follows:

Forstructures having a period of 0.5 seconds or less, k = 1.Forstructures having a period of 2.5 seconds or more, k = 2.Forstructures having a period between 0.5 and 2.5 seconds, k shall be 2or shall be determined by linear interpolation between 1 and 2.

3. Distribute the Story Shear Horizontally:

The seismic design story shear in any story, Vx(kip or kN), shall be determined from thefollowing equation:

(FEMA 368 5.4.4)

where Fi= the portion of the seismic base shear, V (kip or kN), induced at Level i.

The seismic design story shear, Vx(kip or kN), shall be distributed to the various verticalelements of the seismic-force-resisting system in the story under consideration based onthe relative lateral stiffnesses of the vertical resisting elements and the diaphragm.


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Torsion: The design shall include the torsional moment, Mt(kipft or kNm), resulting fromthe location of the masses.

Accidental Torsion: In addition to the torsional moment, the design also shall includeaccidental torsional moments, Mta (kipft or kNm), caused by an assumed displacement ofthe mass each way from its actual location by a distance equal to 5 percent of thedimension of the structure perpendicular to the direction of the applied forces.

Dynamic Amplification of Torsion: For structures of Seismic Design Categories C, D, E, andF, where Type 1 torsional irregularity exists as defined in FEMA 368 Table 5.2.3.2, theeffects of torsional irregularity shall be accounted for by multiplying the sum ofMtplus Mtaat each level by a torsional amplification factor,Ax, determined from the following equation:

1.2 (FEMA 368 5.4.4.3-1)

where:max = the maximum displacementat Level x (in. or mm) andavg = the average of the displacements at the extreme points of the structure

at Level x (in. or mm).

The torsional amplification factor,Ax , is not required to exceed 3.0. The more severeloading for each element shall be considered for design.

4. Calculate and Distribute Overturning Moments: The structure shall be designed to resistoverturning effects caused by the seismic forces, Fi, determined earlier. At any story, theincrement of overturning moment in the story under consideration shall be distributed to thevarious vertical force resisting elements in the same proportion as the distribution of thehorizontal shears to those elements.The overturning moments at Level x, Mx(kipft or kNm), shall be determined from thefollowing equation:

(FEMA 368 5.4.5)

where:Fi = the portion of the seismic base shear, V, induced at Level I,hiand hx = the height (ft or m) from the base to Level iorx.

The foundations of structures, except inverted pendulum-type structures, shall be permittedto be designed for three-fourths of the foundation overturning design moment, Mf(kipft orkN m), determined using Eq. 5.4.5 at the foundation-soil interface.

5. Determine Drift and P-Delta Effects: Story drifts and, where required, member forces andmoments due to P-delta effects shall be determined in accordance with this section.Determination of story drifts shall be based on the application of the design seismic forcesto a mathematical model of the physical structure. The model shall include the stiffness andstrength of all elements that are significant to the distribution of forces and deformations inthe structure and shall represent the spatial distribution of the mass and stiffness of thestructure. In addition, the model shall comply with the following:


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1. Stiffness properties of reinforced concrete and masonry elements shall consider theeffects of cracked sections and

2. For steel moment resisting frame systems, the contribution of panel zonedeformations to overall story drift shall be included.

Story Drift Determination: The design story drift, , shall be computed as the difference of

the deflections at the center of mass at the top and bottom of the story under consideration.Exception: For structures of Seismic Design Categories C, D, E and F having planirregularity Types 1a or 1b of Table 5.3.2.1, the design story drift, ), shall be computed asthe largest difference of the deflections along any of the edges of the structure at the topand bottom of the story under consideration.

The deflections of Level x, x(in. or mm), shall be determined in accordance with followingequation:

(FEMA 368 5.4.6.1)

where:Cd = the deflection amplification factor in FEMA 368 Table 5.2.2,xe = the deflections determined by an elastic analysis (in. or mm), and = the occupancy importance factor determined in accordance from FEMA 368

Table 1.4.

The elastic analysis of the seismic-force-resisting system shall be made using theprescribed horizontal seismic design forces of Equation FEMA 368 5.4.3-1.

For determining compliance with the story drift limitation from FEMA 368 Table 5.2.8, thedeflections of Level x, (in. or mm), shall be calculated as required in this section. For

purposes of this drift analysis only, it is permissible to use the computed fundamentalperiod, T, in seconds, of the structure without the upper bound limitation specified earlierwith FEMA 368 Table 5.4.2 when determining drift level seismic design forces.

Where applicable, the design story drift, (in. or mm), shall be increased by theincremental factor relating to the P-delta effects as determined in the following.

P-Delta Effects: P-delta effects on story shears and moments, the resulting member forcesand moments, and the story drifts induced by these effects are not required to beconsidered when the stability coefficient , as determined by the following equation is equalto or less than 0.10:

(FEMA 368 5.4.6.2-1)wherePx = the total vertical design load at and above Level x (kip or kN); when

calculating the vertical design load for purposes of determining P-delta, theindividual load factors need not exceed 1.0;

= the design story drift occurring simultaneously with Vx(in. or mm);Vx = the seismic shear force acting between Level x and x-1 (kip or kN);


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hsx = the story height below Level x (in. or mm); andCd = the deflection amplification factor in FEMA 368 Table 5.2.2.

The stability coefficient, , shall not exceed maxdetermined as follows:

0.5

0.25 (FEMA 368 5.4.6.2-2)

where is the ratio of shear demand to shear capacity for the story between Levels x andx-1. This ratio is permitted to be conservatively taken as 1.0.

When the stability coefficient, , is greater than 0.10 but less than or equal to max, theincremental drifts and element forces shall be computed including P-Delta effects. Toobtain the story drift for including the P-delta effects, the design story drift shall bemultiplied by 1.0/(1 -).

When is greater than max, the structure is potentially unstable and shall be redesigned.


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APPENDIX


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Page 18 Professor Panos D. KiousisLast Update 11/10/2011

Figure ASCE 7-98 - 9.4.1.1 (a): Maximum Considered Earthquake Ground Motion for Contermsec Spectral Response Acceleration (5% of Critical Damping), Site Class B.


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Figure ASCE 7-98 - 9.4.1.1 (b): Maximum Considered Earthquake Ground Motion for Contermsec Spectral Response Acceleration (5% of Critical Damping), Site Class B.


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FEMA 368 Table 1.4: Occupancy Importance Factors

Seismic Use Group I

I 1.0

II 1.25

III 1.5

FEMA 368 DEFINITIONS OF SEISMIC USE GROUPS.

1.3 SEISMIC USE GROUPS: All structures shall be assigned to one of the Seismic Use Groups described in Sec 1.3.1 through 1.3.3.

1.3.1 Seismic Use Group III: Seismic Use Group III structures are those having essential facilities that are required for post-earthquake

recovery and those containing substantial quantities of hazardous substances including:

1. Fire, rescue, and police stations

2. Hospitals

3. Designated medical facilities having emergency treatment facilities

4. Designated emergency preparedness centers

5. Designated emergency operation centers

6. Designated emergency shelters

7. Power generating stations or other utilities required as emergency back-up facilities for Seismic Use Group III facilities

8. Emergency vehicle garages and emergency aircraft hangars

9. Designated communication centers

10. Aviation control towers and air traffic control centers

11. Structures containing sufficient quantities of toxic or explosive substances deemed to be hazardous to the public

12. Water treatment facilities required to maintain water pressure for fire suppression.

1.3.2 Seismic Use Group II: Seismic Use Group II structures are those that have a substantial public hazard due to occupancy or use

including:

1. Covered structures whose primary occupancy is public assembly with a capacity greater than 300 persons

2. Educational structures through the 12th grade with a capacity greater than 250 persons

3. Day care centers with a capacity greater than 150 persons

4. Medical facilities with greater than 50 resident incapacitated patients not otherwise designated a Seismic Use Group III structure

5. Jails and detention facilities

6. All structures with a capacity greater than 5,000 persons

7. Power generating stations and other public utility facilities not included in Seismic Use Group III and required for continued

operation

8. Water treatment facilities required for primary treatment and disinfection for potable water

9. Waste water treatment facilities required for primary treatment

1.3.3 Seismic Use Group I: Seismic Use Group I structures are those not assigned to Seismic Use Groups III or II.

1.3.4 Multiple Use: Structures having multiple uses shall be assigned the classification of the use having the highest Seismic Use Group

except in structures having two or more portions that are structurally separated in accordance with Sec. 5.2.8, each portion shall be

separately classified. Where a structurally separated portion of a structure provides access to, egress from, or shares life safety

components with another portion having a higher Seismic Use Group, the lower portion shall be assigned the same rating as the higher.

1.3.5 Seismic Use Group III Structure Access Protection : Where operational access to a Seismic Use Group III structure is required

through an adjacent structure, the adjacent structure shall conform to the requirements for Seismic Use Group III structures. Where

operational access is less than 10 ft (3 m) from an interior lot line or less than 10 ft (3 m) from another structure, access protection from

potential falling debris shall be provided by the owner of the Seismic Use Group III structure.


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TABLE FEMA 368 4.1.2.4a Values ofFaas a Function of Site Class and Mapped Short-PeriodMaximum Considered Earthquake Spectral Acceleration

Site Class Mapped Maximum Considered Earthquake Spectral Response.Acceleration at Short Periods

SS 0.25 SS= 0.50 SS= 0.75 SS= 1.00 SS 1.25

A 0.8 0.8 0.8 0.8 0.8

B 1.0 1.0 1.0 1.0 1.0

C 1.2 1.2 1.1 1.0 1.0

D 1.6 1.4 1.2 1.1 1.0

E 2.5 1.7 1.2 0.9 0.9

F a a a a a

NOTE: Use straight line interpolation for intermediate values ofSS.aSite-specific geotechnical investigation and dynamic site response analyses shall be performed. Exception: For

structures with periods of vibration equal to or less than 0.5 second, values of Fa for liquefiable soils may be assumedequal to the values for the Site Class determined without regard to liquefaction in Step 3 of Sec. 4.1.2.2.

TABLE FEMA 368 4.1.2.4b Values ofFvas a Function of Site Class and Mapped 1 Second PeriodMaximum Considered Earthquake Spectral Acceleration

Site Class Mapped Maximum Considered Earthquake Spectral ResponseAcceleration at 1 Second Periods

S1 0.1 S1= 0.2 S1= 0.3 S1= 0.4 S10.5

A 0.8 0.8 0.8 0.8 0.8

B 1.0 1.0 1.0 1.0 1.0

C 1.7 1.6 1.5 1.4 1.3

D2.4 2.0 1.8 1.6 1.5

E 3.5 3.2 2.8 2.4 2.4

F a a a a a

NOTE: Use straight line interpolation for intermediate values ofS1.aSite-specific geotechnical investigation and dynamic site response analyses shall be performed. Exception: For structures

with periods of vibration equal to or less than 0.5 second, values of Fv for liquefiable soils may be assumed equal to thevalues for the Site Class determined without regard to liquefaction in Step 3 of Sec. 4.1.2.2.


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Table FEMA 450 4.3-1 Design Coefficients and Factors for Basic Seismic-Force-R

ACI 318 Sec. 21.1

ACI 318 Sec. 21.1


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ACI 318 Sec. 21.5

ACI 318 Sec. 21.2

ACI 318 Sec. 21.3


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.


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5.4.2 Period Determination: The fundamental period of the building, T, in the direction underconsideration shall be established using the structural properties and deformational characteristicsof the resisting elements in a properly substantiated analysis. The fundamental period, T, socalculated, shall not exceed the product of the coefficient for the upper limit on calculated period,Cu, from Table 5.4.4 and the approximate fundamental period, Ta, calculated in accordance withSec. 5.3.3.1. The approximate period formulae of Sec. 5.3.3.1 is permitted to be used directly as

an alternative to performing an analysis to determine the fundamental period of the building, T.

TABLE FEMA 368 5.4.2 Coefficient for Upper Limit on Calculated Period

Design SpectralResponse Acceleration at 1 Second, SD1

Coefficient Cu

Greater than or equal to 0.4 1.40.3 1.40.2 1.50.15 1.60.1 1.7

Less than or equal to 0.05 1.7

5.4.2.1 Approximate Fundamental Period: The approximate fundamental period, Ta, inseconds, shall be determined by the following equation: (FEMA 368 5.4.2.1-1)where: hn = the height (ft or m) above the base to the highest level of the structure, and

Values of Approximate Period Parameters Crandx

Structure Type Cr x

Moment resisting frame systems of steel in which the frames resist 100 percentof the required seismic force and are not enclosed or adjoined by more rigidcomponents that will prevent the frames from deflecting when subjected to

seismic forces.

0.028 (the metric coefficientis 0.0724)

0.8

Moment resisting frame systems of reinforced concrete in which the framesresist 100 percent of the required seismic force and are not enclosed oradjoined by more rigid components that will prevent the frames from deflectingwhen subjected to seismic forces.

0.016 (the metric coefficientis 0.0466)

0.9

Eccentrically braced steel frames 0.030v(the metric coefficientis 0.0731)

0.75

All other structural systems 0.020 (the metric coefficientis 0.0488)

0.75

Alternatively, the approximate fundamental period, Ta, in seconds, is permitted to be determinedfrom the following equation for concrete and steel moment resisting frame structures not

exceeding 12 stories in height and having a minimum storyheight of 10 ft (3 m): 0.1 (FEMA 368 5.4.2.1-2)where N = number of stories.

The approximate fundamental period, Ta, in seconds, for masonry or concrete shear wallstructures is permitted to be determined from the following equation:

0.0019 FEMA 368 5.4.2.1-3


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The metric equivalent of the above expression is

0.0062 FEMA 368 5.4.2.1-3where Cw is a coefficient related to the effective shear wall area as follows:

100

10.83

FEMA 368 5.4.2.1-4

whereAB = The base area of the structure (ft or m )Ai = The area of shear wall i (ft

2 or m2)Di = The length of shear wall i (ft or m)hi = The height of shear wall i (ft or m)N = The number of shear walls in the building effective in resisting lateral forces in the

direction under consideration.


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FEMA 368 TABLE 5.2.3.2 Plan Structural Irregularities

Irregularity Type and DescriptionFEMAReferenceSection

Seismic DesignCategoryApplication

1a

Torsional Irregularity--to be considered when

diaphragms are not flexible.Torsional irregularity shall be considered to existwhen the maximum story drift, computed includingaccidental torsion, at one end of the structuretransverse to an axis is more than1.2 times the average of the story drifts at the twoends of the structure.

5.2.6.4.35.3.5

D, E, and FC, D, E, and F

1b

Extreme Torsional Irregularity -- to beconsidered when diaphragms are not flexible.Extreme torsional irregularity shall be consideredto exist when the maximum story drift, computed

including accidental torsion, at one end of thestructure transverse to an axis is more than 1.4times the average of the story drifts at the twoends of the structure.

5.2.6.4.35.3.55.2.6.5.1

DC and DE and F

2

Re-entrant CornersPlan configurations of a structure and its lateralforce-resisting system contain re-entrant corners,where both projections of the structure beyond are-entrant corner are greater than 15 percent of theplan dimension of the structure in the givendirection.

5.2.6.4.3 D, E, and F

3

Diaphragm DiscontinuityDiaphragms with abrupt discontinuities orvariations in stiffness, including those havingcutout or open areas greater than 50 percent of thegross enclosed diaphragm area, or changes ineffective diaphragm stiffness of more than 50percent from one story to the next.

5.2.6.4.3 D, E, and F

4

Out-of-Plane OffsetsDiscontinuities in a lateral force resistance path,such as out of-plane offsets of the verticalelements.

5.2.6.4.35.2.6.2.10

D, E, and FB, C, D, E, or F

5

Nonparallel SystemsThe vertical lateral force-resisting elements are notparallel to or symmetric about the major orthogonalaxes of the lateral force-resisting system.

5.2.6.3.1 C, D, E, and F


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FEMA 368 TABLE 5.2.8 Allowable Story Drift, aa (in. or mm)

Structure Seismic Use Group

I II III

Structures, other than masonry shearwall or masonry wall frame structures,four stories or less in height withinterior walls, partitions, ceilings, andexterior wall systems that have beendesigned to accommodate the storydrifts

0.025 hsx 0.020 hsx 0.015 hsx

Masonry cantilever shear wall

structuresc

0.010 hsx 0.010 hsx 0.010 hsx

Other masonry shear wall structures 0.007 hsx 0.007 hsx 0.007 hsx

Masonry wall frame structures 0.013 hsx 0.013 hsx 0.010 hsx

All other structures 0.020 hsx 0.015 hsx 0.010 hsx

a hsx is the story height below Level x.b There shall be no drift limit for single-story structures with interior walls, partitions, ceilings,

and exterior wall systems that have been designed to accommodate the story drifts.c Structures in which the basic structural system consists of masonry shear walls designed

as vertical elements cantilevered from their base or foundation support which are soconstructed that moment transfer between shear walls (coupling) is negligible.

seismic design-concrete structures

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