Seismic Design/UBC97 Code

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UNIFORM BUILDING CODE

UBC97 SEISMIC PROVISIONS Eng . Anas M. Fares Msc. Structural Engineering

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SOIL PROFILE CATEGORIES

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A set of six soil profile categories, SA through SF, have been incorporated. Five of these soil types are considered stable profiles representing hard rock (SA), rock (SB), very dense soil and soft rock (SC), stiff soil (SD), and soft soil (SE). Soil categories are based on the average shear wave velocity in the upper 30 m or blow count of a standard penetration test. Type SF is a soft soil profile requiring a site-specific evaluation. The default profile is SD, probably the most common soil profile in most of California. UBC97 does not use soil profiles directly in the base shear equations. Instead, SA, SB, SC, SD, SE, or SF are used in combination with the seismic zone factor Z, and the near-source factors Na and Nv, to determine the site-dependent coefficients Ca and Cv. Ca and Cv define ground motion response within the acceleration and velocity-controlled range of the response spectrum.

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UBS97 DESIGN RESPONSE SPECTRUM Ca and Cv define ground motion response within the acceleration and velocity-controlled range of the response spectrum.

2.5Ca

CONTROL PERIODS Ts = Cv /2.5Ca To = 0.2Ts

Cv /T Ca

To

Ts

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RESPONSE MODIFICATION FACTOR: R

Building a structure to respond 100% elastically in a large-magnitude earthquake would not be economical. Therefore, the prescribed design lateral strengths are considerably lower than needed to maintain a structure in the elastic range. This reduced design strength level results in nonlinear behavior and energy absorption at displacements in excess of initial yield.

Strength reductions due to nonlinear behavior are influenced by: a) the maximum allowable displacement ductility demand, b) the fundamental period of the system, and c) the soil-profile type. Strength reductions from the elastic strength are accomplished by using a response modification factor, R.

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RESPONSE MODIFICATION FACTOR: R

The response modification factor, R, represents the inherent overstrength and global ductility capacity of structural components. Ductility can be defined as a measure of the ability of a structural system to deform in the plastic range prior to failure. Ductile performance is important because seismic energy is dissipated through yielding of the structural components, and because it permits considerable displacements during intense earthquakes without risk to the structure's integrity and occupants’ life safety.

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RESPONSE MODIFICATION FACTOR: R

 Reductions in design forces due to inherent overstrength increase the lateral strength of the structure from the design strength to the strength that is associated with the formation of the first plastic hinge.  Reductions in design forces due to global ductility capacity increase the lateral strength of the structure from the strength that can be identified with the formation of the first plastic hinge to the strength associated with the formation of a mechanism.

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RESPONSE MODIFICATION FACTOR: R

 Because all structures are designed for strengths less than would be needed in a completely elastic structure, the value of the response modification factor (R) always exceeds 1.0.  Lightly damped structures constructed of brittle materials are assigned low values of R because they cannot support deformation in excess of initial yield.  Highly damped structures constructed of ductile materials are assigned higher values of R.

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RESPONSE MODIFICATION FACTOR: R

 The level of reduction specified in the UBC97 seismic provisions is essentially based on the analysis of the historical performance of various structural systems in strong earthquakes.  The structure response modification factor is determined from the type of the structural system used in structural design, as defined in Table 16-N and for nonbuilding structures in Table 16-P.  Systems with higher ductility (e.g., steel moment-resisting frames) have higher R values associated with better seismic performance expectations.

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RESPONSE MODIFICATION FACTOR: R Idealized Force-Displacement

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RESPONSE MODIFICATION FACTOR: R Idealized Relationship between Base Shear and Drift

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UBS97 DESIGN RESPONSE SPECTRUM

2.5Ca

CONTROL PERIODS Ts = Cv /2.5Ca To = 0.2Ts

Cv /T

Ca

To

Ts UBC97-Anas M.Fares -

UBC97 SEC. 1630.2 STATIC FORCE PROCEDURE

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DESIGN BASE SHEAR, V

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The strength level design base shear is given by the formula

V

Cv I W RT

[UBC (Eq. 30.4)]

where T = fundamental period of the structure in the direction under consideration

I = seismic importance factor Cv = a numerical coefficient dependent on the soil conditions at the site and the seismicity of the region, (UBC Table 16-R) W = seismic dead load

R = a factor that accounts for the ductility and overstrength of the structural system, (UBC Table 16-N) Z = seismic zone factor, (UBC Table 16-I). Note that Z does not directly appear in the base shear formula. It does, however, affect the seismic coefficients Ca and Cv . UBC97-Anas M.Fares

DESIGN BASE SHEAR, V The strength level design base given by the formula

Cv I V W RT

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[UBC (Eq. 30.4)]

is subject to three limits: 1) The design base shear need not exceed V 

2) It cannot be less than V  0.11Ca IW

2.5Ca I W R

[UBC Eq. (30.5)]

[UBC Eq. (30.6)]

3) In seismic zone 4, It cannot be less than V 

0.8Z N v I W R

[UBC Eq. (30.7)]

where Ca = a seismic coefficient dependent on site soil conditions and on regional seismicity. Nv = near-source factor that depends on the proximity to and activity of known faults near the structure. Faults are identified by seismic source type, which reflects the slip rate and potential magnitude of earthquake generated by the fault. The near-source factor, Nv, is also used in determining the seismic coefficient Cv for buildings located in seismic zone 4. UBC97-Anas M.Fares

SEISMIC ZONE FACTOR, Z

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Five seismic zones—numbered 1, 2A, 2B, 3, and 4—are defined. The zone for a particular site is determined from a seismic zone map [UBC (FIGURE 16-2)]. The map accounts for the geographical variations in the expected levels of earthquake ground shaking, and gives an estimated peak horizontal acceleration on rock having a 10% chance of being exceeded in a 50-year period. The numerical values of Z are

Zone

1

2A

2B

3

4

Z

0.075

0.15

0.2

0.3

0.4

[UBC (Table 16-I)] The value of the seismic zone coefficient Z can be considered the peak ground acceleration in percentage of gravity. For example, Z = 0.4 indicates a peak ground acceleration of 0.4g equal to 40% of gravity.

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SEISMIC ZONE FACTOR, Z

UBC97 Seismic Zone Map of the United States. For areas outside of the United States, see Appendix Chapter 16 of UBC97. The map is based on a 10% probability of exceedence in 50 years.

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SEISMIC IMPORTANCE FACTOR, I

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OCCUPANCY CATEGORY

1. 2. 3. 4. 5.

Essential facilities I = 1.25 Hazardous facilities I = 1.25 Special occupancy structures I = 1.0 Standard occupancy structures I = 1.0 Miscellaneous structures I = 1.0

[UBC (Table 16-K)]

 In seismic design, the importance factor I is used to increase the margin of safety against collapse.  Essential structures are those that must remain operative immediately following an earthquake such as emergency treatment areas and fire stations.  Hazardous facilities include those housing toxic or explosive substances.  Examples of special occupancy structures are those not classified as essential or hazardous, and required for continuous operation.  Standard occupancy structures such as office buildings, hotels, and residences

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Table 16-K Occupancy Category

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Occupancy or Function of Structure

Seismic Importance Factor I

Hospitals; Fire/Police Stations; Emergency Shelters

1.25

Dangerous Toxic or Explosive Substances

1.25

3. Special occupancy structures

Public Assembly; Schools; Day-Care Centers; Nurseries; Nursing Homes; Jails

1.00

4. Standard occupancy structures

Hotels; Apartments; Dwellings; Wholesale/Retail; Office Bldgs

1.00

5. Miscellaneous structures

Factories; Private Garages; Carports/Sheds

1.00

Occupancy Category

1. Essential facilities 2. Hazardous facilities

Seismic Importance Factor, I Used to amplify design forces as a means of controlling damage and producing “enhanced” performance in Occupancy Categories 1 and 2

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BUILDING PERIOD, T

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The building period T may be determined by analysis or by using empirical formulas. It is denoted TA if determined by empirical formulas, and TB if determined by analysis.

The following single empirical formula may be used for all framing systems:

TA  Ct  hn 

3/ 4

Lateral Force Resisting System

[UBC Eq. (30.8)]

Ct (hn in m)

Ct (hn in ft)

Steel Moment Frames

0.0853

0.035

Concrete Moment Frames

0.0731

0.030

Eccentrically Braced Steel Frames

0.0731

0.030

All other buildings

0.0488

0.020

hn= height above the base to level that is uppermost in the main portion of the structure.

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BUILDING PERIOD, T

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Ct for structures with Concrete or Masonry Shear Walls :

Ct 

0.0743 Ac

Ac= combined effective area, in m2, of the shear walls in the first story of the structure. The value of Ac shall be determined from the following formula: 2   De   Ac   Ae 0.2       hn  

[UBC Eq. (30.9)]

Ae= minimum cross-sectional area in any horizontal plane in the 1st story, in m2 of a shear wall. De= length, in m, of a shear wall in the first story in the direction parallel to the applied forces. The value of De /hn ≤ 0.9. UBC97-Anas M.Fares

BUILDING PERIOD, T

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Rayleigh’s Formula: Single-degree-of-freedom system.

TB  2

m W  2 k gF

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BUILDING PERIOD, T

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Rayleigh’s Formula: Multi-degree-of-freedom system.

1 TB  2 g

2 W   ii

1  W112  W2 22  W3 32  W4 42   2   F  g F   F   F   F   ii 2 2 3 3 4 4  1 1  UBC97-Anas M.Fares

BUILDING PERIOD, T

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Period TB, determined more accurately using Rayleigh’s formula or a computer analysis, that can be used in calculating the base shear has certain limitations.

In seismic zone 4

TB  1.3TA

In seismic zones 1, 2A, 2B, and 3

TB  1.4TA

This provision is included to eliminate the possibility of using an excessively long period to justify an unreasonably low base shear. This limitation does not apply when checking drifts

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STRUCTURAL SYSTEM COEFFICIENT , R

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The coefficient R shown in UBC Table 16-N is a measure of ductility and overstrength of a structural system, based primarily on performance of similar systems in past earthquakes. A higher value of R has the effect of reducing the design base shear. For example, for a steel special moment-resisting frame, the factor has a value of 8.5, whereas for ordinary moment-resisting frame, the value is 4.5. This reflects the fact that a special moment-resisting frame performs better during an earthquake.

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Bearing Wall System

Moment-Resisting Frame System

Building Frame System

Dual System

Undefined System

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STRUCTURAL SYSTEM COEFFICIENT , R

Basic structural system

Dual Systems (frame resists at least 25% of seismic shear)

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Lateral-force-resisting system description

R

Ωo

Height limit for seismic zones 3 and 4

Concrete Shear Walls With Concrete SMRF

8.5

2.8

N.L.

Concrete Shear Walls With Concrete IMRF

6.5

2.8

N.P.

N.L.—no limit N.P.—not permitted. 1633.2.7 Concrete frames. Concrete frames required by design to be part of the lateralforce-resisting system shall conform to the following: 1. In Seismic Zones 3 and 4 they shall be special moment resisting frames. 2. In Seismic Zone 2 they shall, as a minimum, be intermediate moment-resisting frames.

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SEISMIC DEAD LOAD, W The total seismic load W represents the total mass of the building and includes the weights of structural slabs, beams, columns, and walls; and nonstructural components. When partition locations are subject to change (as in office buildings), a uniform distributed dead load of at least 0.48kN/m2 of floor area is used in calculating W. In storage areas and warehouses, 25% of the design live load is included in the seismic weight W. In areas of heavy snow, a load of 1.44 kN/m2 should be used where the snow load is greater than 1.44 kN/m2. However, it may be reduced to as little as 0.36 kN/m2 when approved by building officials. The rationale for including a portion of the snow load in heavy snow areas is the fact that in these areas, a significant amount of ice can build up and remain on roofs In addition to determining the overall weight W, it is necessary to evaluate tributary weight Wx at each floor for both vertical and horizontal distribution of loads. Therefore, the calculations for W must be done in an orderly tabular form so that overall weights as well as tributary weights can be properly accounted for. UBC97-Anas M.Fares

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SEISMIC DEAD LOAD, W

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1997 UBC 1630.1.1 Effective Seismic Weight

V = CSW W = total dead load + …… • Warehouses………………..…………..25% live • Buildings with partitions……………….0.48 kN/m2 • Design snow load > 1.44 kN/m2………… ≥ 25% design snow load ** • Permanent equipment…………………100% dead ** UBC leaves this up to local jurisdictions

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SEISMIC DEAD LOAD, W

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Note: Floor weight WD includes floor structure, ceiling, mechanical equipment, and an allowance for partitions. Story weight for calculation of lateral forces Wx = Walls + Floor + Equipment = WA + WB + WC + WD + Wequip UBC97-Anas M.Fares

SEISMIC COEFFICIENTS Cv AND Ca

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 The seismic coefficients Cv and Ca, given in UBC Tables 16-R and 16-Q, are site-dependent ground motion coefficients that define the seismic response throughout the spectral range. They are measures of expected ground acceleration at a site.  The coefficients, and hence the expected ground accelerations, are dependent on the seismic zone and soil profile type. They therefore reflect regional seismicity and soil conditions at the site.  Additionally, in seismic zone 4, they also depend on the seismic source type and near-source factors Na and Nv .  For a given earthquake, a building on soft soil types such as SC or SD experiences a greater force than if the same building were located on rock, type SA or SB. This is addressed in the UBC through the Ca and Cv coefficients, which are calibrated to soil type SB with a value of unity.  Instead of a single coefficient, two coefficients, Ca and Cv, are used to distinguish the response characteristics of short-period and long-period buildings. Long-period buildings are more affected by soft soils than shortperiod buildings. UBC97-Anas M.Fares

SEISMIC COEFFICIENTS Cv AND Ca

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[UBC (Table 16-R)]

UBC97-Anas M.Fares

SEISMIC COEFFICIENTS Cv AND Ca

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[UBC (Table 16-Q)]

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SOIL PROFILE TYPES

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 The soil profile types labeled SA through SF [UBC (Table 16-J)] represent the effect of soil conditions on ground motion.

 Seismic ground motion can be amplified by site geology and soil characteristics.  The value of Z, given in the seismic zone map, is for the rock, type SB soil. Therefore, except for hard rock, type SA soil, the value of Z increases for soil types SC, SD, SE, and SF. 

When soil properties are not known, type SD must be used.

 SE need not be assumed unless the building official determines that soil type SE is present or it is established by geotechnical data.

UBC97-Anas M.Fares

SOIL PROFILE TYPES

[UBC (Table 16-J)]

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Seismic Source Type A, B, and C

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 The seismic source types labeled A, B, or C [UBC (Table 16-U)] are used to identify earthquake potential and activity of faults in the immediate vicinity of the structure.  They are defined in terms of the slip rate of the fault and the maximum magnitude of earthquake that may be generated at the fault.  The highest seismic risk is posed by seismic source type A, which is defined by a maximum moment magnitude of 7.0 or greater and a slip rate of 5 mm/year or greater.  Type A signifies active faults such as the San Andreas capable of producing large magnitude events. Most faults in California are classified as type B, while those outside of California, not capable of producing large magnitude events, are classified as inactive, type C faults.

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Seismic Source Type A, B, and C

[UBC (Table 16-U)]

When determining the seismic source type, it is crucial that both maximum moment magnitude potential (M) and slip rate (SR) conditions be satisfied concurrently. In California, the majority of faults fall into the type B seismic source classification. The San Andreas Fault is one notable exception, receiving a type A seismic source classification. Most faults outside California are type C seismic source. UBC97-Anas M.Fares

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NEAR SOURCE FACTORS Na and Nv

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► in seismic zone 4 where large-magnitude earthquakes are expected, particularly severe damage to structures is likely to happen when structures are built very near or directly on the top of active faults. The ground acceleration that these structures experience may be up to twice the acceleration that more distant structures experience. ►UBC97 has adopted two near-source factors, Na and Nv to take into consideration this impact in seismic zone 4. These amplification factors are acceleration- (for short-period structures) and velocity- (for large-period structures) controlled factors. Near source effects are greater for long-period structures (i.e., Nv larger than Na).

►The near-source factors Na and Nv are given in [UBC (Tables 16-S and 16.T)]. In seismic zone 4, they are used in conjunction with the proximity of the building or structure to known faults to determine the seismic coefficients Ca and Cv. ►The purpose of Na and Nv is to increase the soil-modified ground motion parameters, Ca and Cv , when there are active faults capable of generating largemagnitude earthquakes within 15 kilometers of a seismic zone 4 site. UBC97-Anas M.Fares

NEAR SOURCE FACTORS Na and Nv

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10 km

Surface Projection of a Fault Plane The shortest distance to a seismic source is the minimum distance between the site and the area defined by the vertical projection of the source on the surface (i.e., surface projection of fault plane) UBC97-Anas M.Fares

NEAR SOURCE FACTORS Na and Nv

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[UBC (Table 16-S)] a

The near-source factor may be based on the linear interpolation of values for distances other than those shown in the table. b

The location and type of seismic sources to be used for design shall be established based on approved geotechnical data (e.g., most recent mapping of active faults by the U.S. Geological Survey or the California Division of Mines and Geology). c

The closest distance to seismic source shall be taken as the minimum distance between the site and the area described by the vertical projection of the source on the surface (i.e., surface projection of fault plane). The surface projection need not include portions of the source at depths of 10 km or greater. The largest value of the nearsource factor considering all sources shall be used for design. UBC97-Anas M.Fares

NEAR SOURCE FACTORS Na and Nv

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[UBC (Table 16-T)]

For example: For seismic source type B at a distance to the fault of less than 2km, Na = 1.3. This is then used to determine the seismic coefficient Ca. Similarly, Nv = 1.6 for seismic source type B at a distance less than 2 km. This is then used to determine Cv .

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DISTRIBUTION OF LATERAL FORCE Fx

(a) Loading Diagram

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(b) Cumulative Diagram

Vertical Distribution of Story Shears UBC97-Anas M.Fares

DISTRIBUTION OF LATERAL FORCE Fx

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The base shear V is distributed over the height of the structure as a force at each level Fi, plus an extra force Ft at the top: n

V  Ft   Fi i 1

The extra force at the top is

Ft  0.07TV  0.25V

if

T  0.7sec

Ft  0

if

T  0.7sec

Ft accounts for the greater participation of the higher-mode responses of longer-period structures. The remaining portion of the total base shear (V – Ft) is distributed over the height, including the top, by the formula

Fx

V  Ft  wx hx    n

wh i 1

i i

where w is the weight at a particular level, and h is the height of that level above the shear base. For equal story heights and weights, the distribution of the story forces is linearly, increasing toward the top. Any significant variation from this triangular distribution indicates an irregular UBC97-Anas M.Fares structure.

STORY SHEAR Vx AND OVERTURNING MOMENT Mx

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The story shear at level x is the sum of all the story forces at and above that level: n

Vx  Ft   Fi ix

The overturning moment at a particular level Mx is the sum of the moments of the story forces above, about that level. Hence n

M x  Ft  hn  hx    Fi  hi  hx  ix

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TORSION

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Accidental torsion that occurs due to uncertainties in the building’s mass and stiffness distribution must be added to the calculated eccentricity. This is done by adding a torsional moment at each floor equal to the story force multiplied by 5% of the floor dimension, perpendicular to the direction of the force. This procedure is equivalent to moving the center of mass by 5% of the plan dimension, in a direction perpendicular to the force.

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TORSION

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If the lateral deflection at either end of a building is greater than 20% of the average deflection, the building is classified as torsionally irregular and the accidental eccentricity must be amplified using the formula

2

  max  Ax     3.0 1.2 avg  where

δmax = maximum displacement at level x δavg = average displacement at level x Ax = the torsional amplification factor at level x

 avg  max

 max  1.2   avg

Torsional shears may be subtracted from direct shears if the torsional shear is reduced by the effects of accidental torsion. However, torsional shears that are increased by the effects of accidental torsion must be added to direct shears. UBC97-Anas M.Fares

RELIABILITY / REDUNDANCY FACTOR: ρ

Redundancy is an important characteristic of a structure, providing multiple paths of resistance (i.e., load paths). Higher redundancy in a structure implies better reliability. Inelastic action of a structure during a major seismic event can cause part of the structure to fail. For structures expected to experience severe inelastic demands, the lateral load-resisting system of the structure should be made as redundant as possible so that loads can be distributed to other lateral-force-resisting elements. The redundancy factor provides for multiple load paths for resisting earthquake forces. More redundancy means better reliability because there is increased opportunity for inelastic deformations. It takes into account the number of lateral-force-resisting elements, plan area of building, and distribution of forces to the lateral-force-resisting elements. UBC97-Anas M.Fares

RELIABILITY / REDUNDANCY FACTOR: ρ

Observation of the structural performance in Northridge, Kobe, and other large earthquakes has shown that structures with adequately redundant systems perform better than do structures with few lateral load-resisting elements. For this reason, the reliability/redundancy factor has been introduced to persuade engineers to design more highly redundant structures. In certain situations, it may be difficult to achieve a redundant design. In those cases, the magnitude of the inelastic response and the ductility demand should be reduced by increasing earthquake design loads by way of the ρ factor. The reliability/redundancy factor is applied in the load combination equations rather than in the base shear equation because stiffness and drift control requirements are not directly influenced.

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RELIABILITY / REDUNDANCY FACTOR: ρ

The reliability/redundancy factor, ρ, is applied as an increase in horizontal seismic forces associated with the base shear [UBC-97 Sec.1630.1.1]. The reliability/redundancy factor, ρ, effectively reduces the response modification factor, R, based on the extent of structural redundancy inherent in the design configuration of the structure and its lateralforce-resisting system.

In addition to the number and distribution of vertical elements of the lateral-force-resisting system, the size of the ground floor area of the structure determines the value of ρ. The reliability/redundancy factor (ρ) value varies between 1.0 and 1.5.

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RELIABILITY / REDUNDANCY FACTOR: ρ

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The seismic base shear, as determined from the preceding equations, must be multiplied by a reliability/redundancy factor, ρ, for the design of a lateral loadresisting system. It is given by 6.1 1   2  1.5 rmax AB

where

AB = ground floor area of the structure in m2 rmax = maximum element-story shear ratio

The element-story shear ratio, ri, at a particular level is the ratio of the shear in the most heavily loaded member to the total story shear. The maximum ratio, rmax, is defined as the largest value of ri in the lower two-thirds of the building. UBC97-Anas M.Fares

RELIABILITY / REDUNDANCY FACTOR: ρ

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For special moment-resisting frames, except when used in dual systems, shall not exceed 1.25. The number of bays of special moment-resisting frames shall be increased to reduce ρ, such that is less than or equal to 1.25. When calculating drift, or when the structure is located in Seismic Zone 0, 1 or 2, ρ shall be taken equal to 1. For shear wall buildings, r depends on floor area of the building, number of shear walls resisting the story shear, and the length of shear walls. For moment frames, it depends on the floor area of the building and the number of columns. For dual systems, r is evaluated by calculating rmax for the portion of the story shear carried by moment frames. rmax for the portion of the story shear carried by shear walls. ρ using the ρmax value in steps 1 and 2, and multiplying it by 0.8.

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RELIABILITY / REDUNDANCY FACTOR: ρ

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For shear walls, ri shall be taken as the maximum value of the product of the wall shear multiplied by 3.05/lw and divided by the total story shear, where lw is the length of the wall in m. For moment frames, ri shall be taken as the maximum of the sum of the shears in any two adjacent columns in a moment frame bay divided by the story shear. For columns common to two bays with moment-resisting connections on opposite sides at Level i in the direction under consideration, 70 percent of the shear in that column may be used in the column shear summation. For dual systems, ri shall be taken as the maximum value of ri as defined above considering all lateral-load-resisting elements. The lateral loads shall be distributed to elements based on relative rigidities considering the interaction of the dual system. For dual systems, the value of ρ need not exceed 80 percent of the value calculated above.

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DRIFT LIMITATIONS

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S

The drifts corresponding to the design seismic forces

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DRIFT LIMITATIONS

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1997 UBC 1630.9 Story Drift Determination (Δ) Lateral displacement of one level relative to the next level above or below δs,x = Total Drift Eh

Δs,x = Story Drift Δs,x = δs,x - δs,x-1

δs,x-1

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DRIFT LIMITATIONS

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The elastic deflections due to strength-level design seismic forces are called designlevel response displacements, ΔS. The subscript S in ΔS stands for strength design. To determine ΔS: The seismic forces is calculated using a reliability/redundancy factor equal to 1.0 Ignore the previously mentioned limitations on the period used in the calculation of base shear. An elastic static or dynamic analysis may be used to determine ΔS. The Maximum Inelastic Response is defined as

 M  0.7 R S where R is the structural system coefficient defined earlier. The subscript M in ΔM signifies that we are calculating a maximum value for the deflection due to seismic response that includes inelastic behavior. UBC97-Anas M.Fares

DRIFT LIMITATIONS

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→ Deflection control is specified in terms of the story drift defined as the lateral displacement of one level relative to the level below. The story drift is determined from the maximum inelastic response, ΔM. → The calculated displacement must include the effects of both translation and torsion. Hence, drift must be checked in the plane of the lateral-load-resisting elements, generally at the building corners. → Effects of P-Δ must be included in the calculation of ΔM unless it is shown by calculation that the effects are insignificant. Maximum story drift ΔM is limited to

 M  0.020h

if

T  0.7sec

 M  0.025h

if

T  0.7sec

where h is the story height. UBC97-Anas M.Fares

DRIFT LIMITATIONS

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Strength design load combinations, as given by the following equations, are used in the determination of ΔS.

1.2 D  1.0 E  0.5L 0.9 D  1.0 E

For reinforced concrete buildings, it is mandatory to use cracked section properties, Icr to compute displacements. Typical values are given below. Walls Icr = 0.7 Ig Beams Icr = 0.35 Ig Columns Icr = 0.5 Ig to 0.7 Ig The designer is referred to Table 6.5, Federal Emergency Management Agency (FEMA) Publication 356, for additional stiffness values.

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Table 6-5 FEMA 356 Effective Stiffness Values

Aw : gross area of web

UBC97-Anas M.Fares

DRIFT LIMITATIONS 1997 UBC 1630.10 Story Drift Limitation

Story drift corresponding to the design seismic forces Δs,x = δs,x - δs,x-1 Maximum story drift due to inelastic seismic response ΔM,x = 0.7 R Δs,x ≤ Δa

Allowable Story Drift (Δa )

Δa= 0.020 hsx Δa= 0.025 hsx

for for

T ≥ 0.7 sec. T < 0.7 sec.

hsx = Story height below level x

UBC97-Anas M.Fares

DEFORMATION COMPATIBILITY

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Deformation Compatibility: achieve parity in seismic performance of structural framing elements and their connections that are not required by design to be part of lateral-force-resisting systems but are nonetheless subjected to the deformations resulting from seismic forces, with those required by design.

For structural framing elements and connections that are not part of lateral-forceresisting systems, UBC97 requires design and detailing to be adequate to maintain support of design gravity loads (dead plus live) when subjected to the expected deformations caused by seismic forces.

Designing for deformation compatibility consists of: • Establishing deformation demands. • Assessing individual elements and their connections for their capacity to deform.

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DEFORMATION COMPATIBILITY

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When computing expected deformations for structural framing elements and connections that are not part of lateral-force-resisting systems, UBC97 requires the following:  P-Δ effects on such elements should be considered.  Expected deformations should be the greater of the maximum inelastic response displacement (ΔM) considering P-Δ effects or the deformation caused by story drift =0.0025h (story height).  The stiffening effect of such elements should be neglected.  The forces induced by the expected deformation may be considered as ultimate or factored forces.  For elements constructed with concrete or masonry, the presumed flexural and shear stiffness properties should not exceed one-half of the gross section properties unless a rational cracked-section analysis is performed.  Additional deformations that may result from foundation flexibility and diaphragm deflections should be considered. UBC97-Anas M.Fares

DEFORMATION COMPATIBILITY

62

Column deformation for use in compatibility considerations. Deformation of column = building deflection ΔB + diaphragm deflection ΔD. UBC97-Anas M.Fares

DEFORMATION COMPATIBILITY

63

Deformation compatibility consideration of foundation flexibility. UBC97-Anas M.Fares

LOAD COMBINATIONS

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Basic Load Combinations: Concrete Structures LRFD (Load Resistance Factor Design), Strength Design. where U1= 1.4D U2= 1.2D+1.6L+0.5(Lr or S) U3=1.2D+1.6(Lr or S)+(f1L or 0.8W) U4= 1.2D+1.3W+f1 L+0.5(Lr or S) U5= 1.2D+1.0E+(f1 L+ f2 S) U6  0.9D  (1.0 E or 1.3W)

E   Eh  Ev Ev  0.5Ca I D

U = ultimate load resulting from load combinations D = dead load L = live load W = load due to wind pressure S = snow load E = earthquake load resulting from the combination of the horizontal component, Eh, (Eh = earthquake load due to the base shear, V) and the vertical component EV f1 = 1.0 for floors in public assembly live loads in excess of 4.79 kN/m2 garage live load f1 = 0.5 for other live loads. f2 = 0.7 for roof configurations (such as saw tooth) that do not shed snow off the structure. f2 = 0.2 for other roof configurations. ρ = redundancy/reliability factor UBC97-Anas M.Fares

LOAD COMBINATIONS

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Seismic Strength Design Load Combinations U5= 1.2D+1.0E+(f1 L+ f2 S)

Equation (12-5)

U6  0.9D

Equation (12-6)

 (1.0 E or 1.3W)

E   Eh  0.5Ca I D  1

in Seismic Zones 1 and 2

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LOAD COMBINATIONS

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Special Seismic Load Combinations Nonuniform ductility in structural systems due to vertical discontinuities LRFD (Load Resistance Factor Design), Strength Design. Diaphragm transfers shear from discontinuous shear wall

Shear walls Transfer girder Shear wall

Columns support discontinuous wall

Cantilever girder supports column above Column supports discontinuous wall

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LOAD COMBINATIONS

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Special Seismic Load Combinations Nonuniform ductility in structural systems due to vertical discontinuities LRFD (Load Resistance Factor Design), Strength Design.

U  1.2 D  f1L  1.0 Em U  0.9 D  1.0 Em Em  o Eh Em : Estimated maximum earthquake force that can be developed in the structure Ωo : Seismic force amplification factor that is required to account for structural overstrength. Ωo shall be taken from Table 16-N.

These combinations are intended to cover conditions where uniform ductility in the structural system is lacking due to vertical discontinuities. UBC97-Anas M.Fares

SUMMARY FORMAT

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Terms to Calculate Earthquake Loads Z SA, SB, SC, SD, SE, or SF

Seismic Zone Factor Soil Profile Types

Na, Nv

Near-Source Factors (Zone 4 only)

Ca, Cv

Seismic Coefficients (Seismic Zone & Soil Type)

R

Response Modification Factor

V

Base Shear

ρ

Redundancy Factor

E

Earthquake Load UBC97-Anas M.Fares

STATIC VS. DYNAMIC ANALYSIS

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UBC97-Anas M.Fares

SUMMARY FORMAT

Vmax

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Vmin  0.11Ca IW  2.5Ca I Cv I  WV W  max  R RT [Zone 4 only] V  0.8ZN v I W min  R

Ca = acceleration-based seismic coefficient Cv = velocity-based seismic coefficient Ca and Cv are given in terms of: 1. Seismic zone factor, Z. 2. Soil profile type, SA through SF. 3. Near-source factors, Na and Nv for zone 4. The seismic zone factor, Z, has the following values: Z = 0.4 for zone 4 0.3 for zone 3 0.2 for zone 2B 0.15 for zone 2A 0.075 for zone 1 0.0 for zone 0 UBC97-Anas M.Fares

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I = importance factor = 1.25 for essential and hazardous facilities 1.0 for special and standard occupancy R = Response modification factor: numerical coefficient representative of the inherent overstrength and global ductility capacity of the lateral force-resisting systems

T = elastic fundamental period of vibration, in seconds, of the structure in the direction under consideration. The period T is commonly noted as TA when determined by approximate methods, and TB when determined by more accurate methods such as dynamic analysis. TA may be determined by TA = 0.0853(hn)3/4 for steel moment-resisting frames 0.0731(hn)3/4 for reinforced concrete moment frames and eccentrically braced frames 0.0488(hn)3/4 for all other buildings

1.3TA for zone 4, if not T = TA TB   1.4TA for zones 1, 2A, 2B, and 3, if not T = TA

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SUMMARY FORMAT

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Na = near-source factor used in the determination of Ca in seismic zone 4, related to the proximity of the building to known faults with maximum moment magnitude and slip rates (UBC Tables 16-S and 16-U) Nv = near-source factor used in the determination of Cv in seismic zone 4, related to the proximity of the building to known faults with maximum moment magnitude and slip rates (UBC Tables 16-T and 16-U) SA, SB, SC, SD, SE, and SF = soil profile types (UBC Table 16-J) where SA = hard rock SB = soft rock, normally found in California SC = very dense soil and soft rock SD = stiff soil profile SE = soft soil profile SF = soil profile requiring site-specific evaluation (This category include soils vulnerable to potential failure under seismic loading, peats, organic clays, very high-plasticity clays, and very thick soft-to-medium stiff clays with depths in excess of 37 m) UBC97-Anas M.Fares