Ch 9 - Role of Codes and Empirical Procedures

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B , .

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• C C ( 2010)

C 2010 B C( BC) 1997.

Static Lateral Force Procedures in Building Codes BC C B 1927. , (

).

2000, B C ( BC) . BC 97 BC 2000

1991, A C 3 06 1978.

BC 97 : .

BC 97 10%

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475 . ,

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C 2010 C A

C 2010





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:( ) ;( )

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In the NSCP-2010/UBC-97 static lateral force procedure , the totalstructural base shear is determined according to seismic zones by usingcode formulas (208-4) - (208-7). The base shear in seismic zone 4 shouldbe

Simplified Approach

The Code allows a simplified static lateral-force procedure for structuresconforming to the requirements of sec. 208.4.8.1 with the following conditions:

1. buildings of any occupancy not more than three stories in height, excludingbasements that use light-frame construction;

2. other buildings not more than two stories in height excluding basements.

For the simplified approach, the base shear is determined as

The force at each level shall be calculated as





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V e = maximum elastic base shearV y = base shear corresponding to structural collapse level or yield strengthV s = base shear corresponding to the first hinge formation in the structural systemV a = allowable base shear at service load level adopted by UBC-94δ a , δ s , δ y, and δ max are the story drifts associated with the respective base shears.

Thus the response modification factor can be expressed as

General story response of a structure .

where

Rd = ductility reduction factor, denoted by V e / V y and iswell established for single-d.o.f. damped systems;

Ω 0 = V y / V s is seismic force amplification (or over-strength factor) due to structural redundancy (internal forceredistribution after first plastic hinge formation); and

Ra = V s / V a = signifies the allowable stress factor to accountfor differences in the format of material codes.

R (in the UBC 97) does not have the Ra term.

Hence, R = R w / R a



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Thus the load combination has different modification factors in UBC-94and UBC-97:

in UBC-94: l.0 E for ASD; 1.5 E for LRFD

in UBC-97: E/ 1.4 for ASD; 1.0 E for LRFD

Range of R and Ω0 Values for Basic Structural Systems

Rw vs R



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Seismic Coefficients Ca and C v

C a and C v depend on soil profile type and seismic zone.

Sec. 208.4.3.1. Soil Profile Type -

Soil profile types S A , S B , SC , SD , and S E

are defined in Table 208-2. Type S F isdefined as soils requiring site-specificevaluation.

Near-Source Factors N a , N v

Table 208-7 and 208-8 shows that, in seismic zone 4, C a and C v are determinedusing N a and N v , which are near-source factors based on the proximity of abuilding or structure to known faults with magnitudes and slip rates.

To find N a and N v , we need three seismic source types A, B, and C as givenin Table 208-4 and 208-5. The rationale for source types is that ground motion isgreater in the vicinity of a fault than some distance away, owing to rapidprogression of fault rupture. This effect depends on moment magnitude, M.Thus, type A represents the most active fault with larger M than the least activefault signified by type C.

Seismic Source TypeTable 208-6 defines the types of seismic sources. The location and type of

seismic sources to be used for design shall be based on approved geological data(See. Fig 208-2A). Type A sources shall be based on the maps of Fig. 208-2B, C,D, E or the recent mapping of active faults by the PHIVOLCS.



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Fundamental period T

The fundamental period may be determined from any one of the following methods:

Method A: For all buildings, T may be approximated using the following formula

h n = height in feet (or meters, m) above the base to story level n of thebuilding. Values of C, in ( ) are in SI units.

Method B: The fundamental period may be calculated using the following formula:

where n denotes the total number of stories; f i represents any lateral force distributed approximately in accordance with

Eqs. (208-14) and (208-15) or any other rational distribution; andwi is the seismic dead load at level i.δ i the elastic deflection, is calculated using the applied lateral forces f i .

The value of T from Method B should not be over 30% of period T from Method A in seismic zone 4 and 40% inzones 2.



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Vertical Distribution of Lateral Force

Once the base shear has been determined, base shear V is distributed over theheight of the structure as a force at each level with consideration of a straight-line mode shape.

An extra force F t is considered at the top of the building to account for greaterparticipation of higher modes in the response of longer-period structures.

The remaining portion of the total base shear, (V - F t ) , is distributed over the

height, including the roof top, by the following formula:

where w x is the weight at a particular level and h x is the height of aparticular level above the base. At each floor the force F x is located atmass center.

Story Shear and Overturning Moment

Story shear at level x, V x , is the sum of all the lateral forces at and abovethat level.

The overturning moment at a particular level, M x , is the sum of themoments of the story forces at and above that level with the followingexpression:





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If the lateral deflection at either end of a building is more than 20% greater than the

average deflection, the building is classified as torsionally irregular and theaccidental eccentricity must be amplified using the formula

whereδ avg = the average displacement at level xδ max = the maximum displacement at level x A x = the torsional amplification factor at level x



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Reliability/Redundancy Factor ρ

The seismic base shear, as determined from the preceding equations, must bemultiplied by a reliability/redundancy factor, ρ , for the design of a lateral load-resisting system. It is given by

1 ≤ −

≤

where A B = the ground floor area of the structure in square metersr max = the maximum element-story shear ratios

The element-story shear ratio, r i, at a particular level is the ratio of the shear in themost heavily loaded member to the total story shear. The maximum ratio, r max, is

defined as the largest value of r i in the lower two-thirds of the building.

Drift Limitation

The elastic deflections due to strength-level design seismic forces are calleddesign-level response displacements, ∆ S . The subscript S in ∆S stands forstrength design. The seismic forces used to determine ∆S may be calculatedusing a reliability/redundancy factor equal to 1.0. An elastic static or dynamicanalysis may be used to determine ∆S .

The maximum inelastic response is defined as

∆ M = 0.7 R∆ S

For structures with a period less than 0.7 seconds, the maximum story drift islimited to

∆ M ≤ 0.025 h (T < 0.7 seconds)

For structures with a period greater than 0.7 seconds, the story drift limit is

∆ M ≤ 0.020 h (T ≥ 0.7 seconds)

where h is the story height.



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Basic Load Combinations for Strength Design (LRFD) All materials except concrete (No one-third increase for wind or seismic).

U = 1.4 D U = 1.2 D + 1.6 L + 0.5( L r or S )U = 1.2 D + 1.6( L r or S ) + ( f 1L or 0.8 W )U = 1.2 D + 1.3 W + f 1L + 0.5( L r or S )U = 1.2 D + 1.0 E + (f 1L + f 2S )U = 0.9 D ± ( E or 1.3 W )

Basic Load Combinations for Strength Design (LRFD) Concrete Structures (No one-third increase for wind or seismic).U = 1.4 D + 1.7 LU = 0.75(1.4 D + 1.7 L + 1.7 W )U = 0.9 D + 1.3 W (2.19)U = 1.2 D + 1.0 E + f 1L + f 2S

U = 0.9 D + 1.0 E

Where E = earthquake load resulting from the combination of the horizontal

component, E h

, and the vertical component E V

;

E = E h ± E v

E h = earthquake load due to the base shear, V . E V = 0.5 C a I

= redundancy/reliability factor

Basic Load Combinations Using ASD





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Example Given . A12-story steel building located in Manila. The lateral-load-resistingsystem consists of special moment-resisting space frames (SMRFs),

interacting with eccentric braced frames (ECBs). The far ends of beams inthe ECBs are moment-connected to columns. The building has two, 12-feet-high basement levels. The shear base is at ground level.

Building height h n = Two @ 15 + 10 @ 13 = 160 ftPlan dimensions = 90 feet 210 feetFundamental period T B from a computer analysis = 2 secsSeismic zone factor Z = 0.4Near-source factor N a = 1.0Near-source factor N v = 1.0Importance factor I = 1.0Basic structural system - dual system; steel EBF with steel SMRF.Soil type - S D

Redundancy/reliability factor = 1.0





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Building Seismic Weight W .

W is calculated as the summation of story weights tributary to each floor. It

includes the weight of the floor system with an allowance for finishes,ceiling, mechanical and air conditioning duct work, weights of walls,columns, exterior cladding, and a code-required allowance of a minimumof 10 psf for partitions.

Total steel weight = 14 psf (assumed)Unit weight of 3.25lightweight concrete topping on a 3"-deep metal deck,including the weight of deck = 50 psfAllowance for finishes, partitions, and exterior cladding = 30 psfTotal seismic weight = 14 + 50 + 30 = 94 psf, use 100 psfBuilding area: floors two through roof = 12 90 210 = 226,800 ft 2

Seismic weight W = 226,800 100/1000 = 22,680 kipsAssume, for purposes of preliminary design, all floors including the roofhave the same seismic weight. Hence, seismic weight tributary to each

floor and roof: W x = W/ 12 = 22,680 / 12 = 1890 kips

Seismic Data

The building is located in seismic zone 4.Soil profile = S D (Given)

Lateral-load-resisting system is given as a dual system consisting ofSMRFs with EBFs.

The structural system is permitted in zone 4.Building height above shear base, h n = 15 + 15 + 10 @ 13 = 160 ft

Building Period T A from Method AT A = C t (h n )3/4

T A = 0.035(160) 3/4 = 1.57 secT B = 2 secs (Given)

Period T for determining the base shear must not exceed1.3 T A = 1.3 1.57 = 2.04 secs > T B = 2.0 secsTherefore, T for design = 2.0 secs



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Seismic Coefficients

Z = 0.4 (Manila, Zone 4)

I = 1 (Standard Occupancy)

R = 8.5

C a = 0.44 N a = 0.44 1 = 0.44

C v = 0.64 N v = 0.64 1 = 0.64

C t = 0.035



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Lateral Load for other floors are shown in the Table 2.11.

Oveturning moments and allowable maximum inelastic displacements(∆

M ) are shown in Table 2.11.



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Ch 9 - Role of Codes and Empirical Procedures