1SEISMIC ANALYSIS OF SEISMIC ANALYSIS OF LIGHTLIGHT--FRAMED FRAMED

MULTIMULTI--STORY RESIDENTIAL STORY RESIDENTIAL BUILDINGSBUILDINGS

Samuel Shiotani, S.E.Samuel Shiotani, S.E.Douglas Hohbach, S.E.Douglas Hohbach, S.E.Joaquim Roberts, S.E.Joaquim Roberts, S.E.

Woodworks March Woodworks March 2009 Seminar2009 Seminar

SEISMIC ANALYSIS OF SEISMIC ANALYSIS OF LIGHTLIGHT--FRAMED FRAMED

MULTIMULTI--STORY RESIDENTIAL STORY RESIDENTIAL BUILDINGSBUILDINGS

CHALLENGESCHALLENGES

Diaphragm behaviorDiaphragm behavior

ASCE 7ASCE 7--05 & 2007 CBC 05 & 2007 CBC requirementsrequirements

Deformation of Deformation of multimulti--story shear walls to story shear walls to determine appropriate determine appropriate distribution of lateral distribution of lateral forces and building driftforces and building drift

BUILDINGBUILDING GEOMETRYGEOMETRY

TYPICAL FLOOR PLANTYPICAL FLOOR PLAN

Corridor shear wallsCorridor shear wallsParty shear wallsParty shear wallsExterior shear wallsExterior shear walls

TYPICAL FEATURETYPICAL FEATURE

Light framed multiLight framed multi--story residential buildings story residential buildings often have uniformly distributed shear walls often have uniformly distributed shear walls of approximately equivalent of approximately equivalent stiffnessesstiffnesses except except at exteriorat exterior sometimes at first floorsometimes at first floor

2DIAPHRAGM ASPECT RATIODIAPHRAGM ASPECT RATIO

Shear wallsShear wallsDiaphragm aspect ratioDiaphragm aspect ratio

DIAPHRAGM ASPECT RATIODIAPHRAGM ASPECT RATIO

Shear wallsShear wallsDiaphragm aspect ratioDiaphragm aspect ratio

DIAPHRAGM BEHAVIORDIAPHRAGM BEHAVIOR

ASCE 7 Section 12.3.1 ASCE 7 Section 12.3.1 Diaphragm FlexibilityDiaphragm Flexibility

FlexibleFlexible RigidRigid SemiSemi-- rigidrigid

FLEXIBLEFLEXIBLE DIAPHRAGMDIAPHRAGM

ASCE 7 Section 12.3.1.3 ASCE 7 Section 12.3.1.3 Calculated Flexible Diaphragm ConditionCalculated Flexible Diaphragm Condition

diaphragmdiaphragm >> 2x2x shearwallshearwall CBC Section 1613.6.1 CBC Section 1613.6.1

Assumption of flexible diaphragmAssumption of flexible diaphragm Toppings < 1 inches thickToppings < 1 inches thick Shear walls satisfy drift requirementsShear walls satisfy drift requirements Wood shear walls (no mixed systems)Wood shear walls (no mixed systems)

FLEXIBLEFLEXIBLE DIAPHRAGM DIAPHRAGM CONCERNSCONCERNS

Underestimates forces distributed to the Underestimates forces distributed to the corridor walls (long walls)corridor walls (long walls)

Overestimates forces distributed to the Overestimates forces distributed to the exterior walls (short walls)exterior walls (short walls)

Computation of building drift problematicComputation of building drift problematic

RIGID DIAPHRAGMRIGID DIAPHRAGM

ASCE 7ASCE 7DD / / SWSW = 0.6 < 2 (Transverse = 0.6 < 2 (Transverse Party walls)Party walls)DD / / SWSW = 1.3 < 2 (Longitudinal = 1.3 < 2 (Longitudinal Corridor/Ext. walls)Corridor/Ext. walls)

3BENEFITS OF RIGID BENEFITS OF RIGID DIAPHRAGM ANALYSISDIAPHRAGM ANALYSIS

More accurately distribute lateral forces More accurately distribute lateral forces to corridor and party wallsto corridor and party walls

Approximate building driftApproximate building drift

Build three dimensional computer Build three dimensional computer model for analysismodel for analysis

OPEN FRONT STRUCTUREOPEN FRONT STRUCTURE

Width, WWidth, W

LengthLength, LL

OPEN FRONT STRUCTUREOPEN FRONT STRUCTURE

Per CBC 2006 Section Per CBC 2006 Section 2305.2.5 Rigid 2305.2.5 Rigid diaphragmsdiaphragms

Length, L, less than 25 feetLength, L, less than 25 feet

L/W less than 0.67L/W less than 0.67 Exception Exception where calculations show where calculations show

that diaphragm deflections can be that diaphragm deflections can be toleratedtolerated

NORTHRIDGE EARTHQUAKE NORTHRIDGE EARTHQUAKE DAMAGEDAMAGE

OPEN FRONT BUILDINGSOPEN FRONT BUILDINGS

CUREE WOODFRAME PROJECT CUREE WOODFRAME PROJECT OPEN FRONT BUILDINGSOPEN FRONT BUILDINGS

FINDINGSFINDINGS

Better building performance Better building performance will result when seismic will result when seismic forces are resisted locally forces are resisted locally rather than being rather than being redistributed to other portions redistributed to other portions of the structureof the structure

CUREE WOODFRAME PROJECT CUREE WOODFRAME PROJECT OPEN FRONT BUILDINGSOPEN FRONT BUILDINGS

FINDINGSFINDINGS

Special design attention is needed for Special design attention is needed for transverse walls resisting torsion.transverse walls resisting torsion.

Reduce Reduce torsionaltorsional response by response by providing additional capacity and providing additional capacity and stiffness in transverse and slender stiffness in transverse and slender elements.elements.

4SHEAR WALL DEFORMATIONSHEAR WALL DEFORMATION

0

200

400

600

800

1000

1200

1400

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Deflection (inches)

Forc

e (p

lf)

Double-sided 20'

ChordChordSlipSlip

SEMISEMI--RIGID DIAPHRAGMRIGID DIAPHRAGM

Always acceptable, but difficult to Always acceptable, but difficult to calculate for wood panel construction calculate for wood panel construction due to nondue to non--linear loadlinear load--deformation. deformation.

Suggest using code diaphragm Suggest using code diaphragm deflection equations, modified as deflection equations, modified as necessary for differing boundary necessary for differing boundary conditions. conditions.

Suggest using linear approximation Suggest using linear approximation calibrated to code strength values. calibrated to code strength values.

LIGHTLIGHT--FRAMED MULTIFRAMED MULTI--STORY STORY RESIDENTIAL BUILDING PLAN RESIDENTIAL BUILDING PLAN --

HypotheticalHypothetical

LIGHTLIGHT--FRAMED MULTIFRAMED MULTI--STORY STORY RESIDENTIAL BUILDING PLAN RESIDENTIAL BUILDING PLAN --

ActualActual

1997 Uniform Building Code1997 Uniform Building Code

Section 1633 Section 1633 Detailed Systems Design RequirementsDetailed Systems Design Requirements1633.2.5 Ties and continuityAll parts of a structure shall be interconnected and the connections shall be capable of transmitting the seismic force induced by the parts being connected. As a minimum, any smaller portion of the building shall be tied to the remainder of the building with elements having at least a strength to resist 0.5 CaI times the weight of the smaller portion

1997 Uniform Building Code1997 Uniform Building Code

Section 1633 Section 1633 Detailed Systems Design RequirementsDetailed Systems Design Requirements1633.2.9 Diaphragms1633.2.9 Diaphragms7. 7. In structures in Seismic Zones 3 and 4 having a plan In structures in Seismic Zones 3 and 4 having a plan

irregularity of irregularity of Type 2 in Table 16Type 2 in Table 16--M, diaphragm chords and M, diaphragm chords and drag members shall be designed considering independent drag members shall be designed considering independent movement of the projecting wings of the structure. Each of movement of the projecting wings of the structure. Each of these diaphragm elements shall be designed for the more these diaphragm elements shall be designed for the more severe of the two following assumptions:severe of the two following assumptions:Motion of the projecting wings in the same directionMotion of the projecting wings in the same directionMotion of the projecting wings in the opposing directionMotion of the projecting wings in the opposing directionException: This requirement may be deemed satisfied Exception: This requirement may be deemed satisfied if the procedures of Section 1631 in conjunction with if the procedures of Section 1631 in conjunction with a threea three--dimensional model have been used to determinedimensional model have been used to determinethe lateral seismic forces for design.the lateral seismic forces for design.

5ASCE 7ASCE 7--0505

Section 12.12 Section 12.12 Drift and DeformationDrift and Deformation

12.12.3 Building Separation12.12.3 Building Separation

All portions of the structure shall be designed and All portions of the structure shall be designed and constructed constructed to act as an integral unitto act as an integral unit in resisting seismic in resisting seismic forces unless separated structurally by a distance forces unless separated structurally by a distance sufficient to avoid damaging contact under total sufficient to avoid damaging contact under total deflection (deflection (xx) as determined in Section 12.8.6.) as determined in Section 12.8.6.

ASCE 7ASCE 7--0505

Diaphragms, Chords and CollectorsDiaphragms, Chords and Collectors

12.10.2 Collector Elements12.10.2 Collector Elements

Collector elements shall be provided that are Collector elements shall be provided that are capable of capable of transferringtransferring the seismic forces originating in other the seismic forces originating in other portions of the structure to the element providing the portions of the structure to the element providing the resistance to those forces.resistance to those forces.

ASCE 7ASCE 7--0505

Diaphragms, Chords and CollectorsDiaphragms, Chords and Collectors12.10.2.1 Collector Elements Requiring Load 12.10.2.1 Collector Elements Requiring Load Combinations with Combinations with OverstrengthOverstrength Factor for Seismic Factor for Seismic Design Categories C through FDesign Categories C through FIn structures assigned to Seismic Design Category C, D, In structures assigned to Seismic Design Category C, D, E, or F, collector elements (see Fig. 12.10E, or F, collector elements (see Fig. 12.10--1), splices, 1), splices, and their connections to resisting elements shall resist and their connections to resisting elements shall resist the load combinations with the load combinations with overstrengthoverstrength of Section of Section 12.4.3.212.4.3.2..

ExceptionException: In structures or portions thereof : In structures or portions thereof braced braced entirely by lightentirely by light--frame shear walls,frame shear walls, collector elements, collector elements, splices, and connections to resisting elements need only be splices, and connections to resisting elements need only be designed to resist forces in accordance with Section 12.10.1.1.designed to resist forces in accordance with Section 12.10.1.1.

ASCE 7ASCE 7--05 05 Table 12.3Table 12.3--1 Horizontal Structural Irregularities1 Horizontal Structural Irregularities

C, D, E, and FB, C, D, E, andFD, E, and FR, C, D, E, andF

12.7.3Table 12.6-1Section 16.2.2

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 forceresisting system.

5.

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

12.3.3.412.3.3.312.7.3Table 12.6-116.2.2

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

4.

D, E, and FD, E, and F

12.3.3.4Table 12.6-1

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 thegross enclosed diaphragm area, or changes in effective diaphragm stiffness of more than 50% from one story to the next.

3.

D, E, and FD, E, and F

12.3.3.4Table 12.6-1

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.

2.

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

12.3.3.112.3.3.412.7.312.8.4.312.12.1Table 12.6-1Section 16.2.2

Extreme 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 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.

lb.

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

12.3.3.412.8.4.312.7.312.12.1Table 12.6-1Section 16.2.2

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 than 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.

la.

Seismic Design CategoryApplication

ReferenceSection

Irregularity Type and Description

ASCE 7ASCE 7--05 05 Table 12.3Table 12.3--1 Horizontal Structural Irregularities1 Horizontal Structural Irregularities

D, E, and FD, E, and FD, E, and FD, E, and F

12.3.3.412.3.3.4Table 12.6Table 12.6--11

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

3.3.

D, E, and FD, E, and FD, E, and FD, E, and F

12.3.3.412.3.3.4Table 12.6Table 12.6--11

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

2.2.

Seismic Seismic Design Design

CategoryCategoryApplicationApplication

ReferenceReferenceSectionSectionIrregularity Type and DescriptionIrregularity Type and Description

ASCE 7ASCE 7--0505

Table 12.3Table 12.3--112.2. ReRe--entrant Corner Irregularityentrant Corner Irregularity

See 12.3.3.4 and Table 12.6See 12.3.3.4 and Table 12.6-- 1 for Seismic 1 for Seismic Categories D, E, and FCategories D, E, and F

3.3. Diaphragm Discontinuity IrregularityDiaphragm Discontinuity IrregularitySee 12.3.3.4 and Table 12.6See 12.3.3.4 and Table 12.6-- 1 for Seismic 1 for Seismic Categories D, E and FCategories D, E and F

6ASCE 7ASCE 7--0505

Section 12.3Section 12.3 Diaphragm Flexibility, Configuration Diaphragm Flexibility, Configuration Irregularities and RedundancyIrregularities and Redundancy12.3.3.4 Increase in forces Due to Irregularities for Seismic De12.3.3.4 Increase in forces Due to Irregularities for Seismic Design sign Categories D through F.Categories D through F.

For structures assigned to Seismic Design Category D, E or F andFor structures assigned to Seismic Design Category D, E or F andhaving a horizontal structural irregularity of Type 1a, 1b, 2, 3having a horizontal structural irregularity of Type 1a, 1b, 2, 3 or 4 in or 4 in Table 12.3Table 12.3--1 or a vertical structural irregularity of Type 4 in Table 1 or a vertical structural irregularity of Type 4 in Table 12.312.3--2, the 2, the design forces design forces determined from Section 12.8.1 determined from Section 12.8.1 shall be shall be increased 25 percent for connections of diaphragms to vertical increased 25 percent for connections of diaphragms to vertical elements and to collectors and for connections of collectors to elements and to collectors and for connections of collectors to the the vertical elements. vertical elements. Collectors and their connections also shall be Collectors and their connections also shall be designed for these increased forces unless they are designed fordesigned for these increased forces unless they are designed for the the load combinations with load combinations with overstrengthoverstrength factor of Section 12.4.3.2, in factor of Section 12.4.3.2, in accordance with Section 12.10.2.1.accordance with Section 12.10.2.1.

ASCE 7ASCE 7--0505

12.3.3.4 Increase in forces Due to Irregularities 12.3.3.4 Increase in forces Due to Irregularities for Seismic Design Categories D through F.for Seismic Design Categories D through F.

design forcesdesign forcesshall be increased 25 percent shall be increased 25 percent for connections of diaphragms to vertical for connections of diaphragms to vertical elements and to collectors and for connections elements and to collectors and for connections of collectors to the vertical elements. of collectors to the vertical elements.

ASCE 7ASCE 7--05 05 Table 12.6Table 12.6--1 Permitted Analytical Procedures1 Permitted Analytical Procedures

PPNPAll other structures

PPPIrregular structures withT

7LIGHTLIGHT--FRAMED MULTIFRAMED MULTI--STORY STORY RESIDENTIAL BUILDING PLAN RESIDENTIAL BUILDING PLAN

Provide uniform distribution of similar stiffness lateral force resisting elements

LIGHT-FRAMED MULTI-STORY RESIDENTIAL BUILDINGS DIAPHRAGM ANALYSIS

RECOMMENDATION

Use rigid diaphragm analysisUse rigid diaphragm analysis (use semi(use semi--rigid as necessary at large diaphragm rigid as necessary at large diaphragm

spans or anomalies)spans or anomalies)

SHEAR WALL DEFORMATIONSHEAR WALL DEFORMATION

CBC Section 2305.3.2 CBC Section 2305.3.2 SS = = 88hh33 + + hh + 0.75he+ 0.75henn + + h h ddaaEAb Gt bEAb Gt b

SHEAR WALL DEFORMATIONSHEAR WALL DEFORMATION

0

200

400

600

800

1000

1200

1400

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Deflection (inches)

Forc

e (p

lf)

Double-sided 20' Idealized Double-sided 20'

ChordChordSlipSlip

Strength Capacity(defines linear behavior)

SHEAR WALL DEFORMATIONSHEAR WALL DEFORMATION

0

200

400

600

800

1000

1200

1400

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70

Deflection (inches)

Forc

e (p

lf)

Double-sided 20' Idealized Double-sided 20'

ChordChordSlipSlip

Strength Capacity(defines linear behavior)

Double-sided w/ finishes

STACKED SHEAR WALL STACKED SHEAR WALL DEFORMATIONDEFORMATION

8MULTIMULTI--STORY SHEAR WALL STORY SHEAR WALL DEFORMATIONDEFORMATION

MULTIMULTI--STORY SHEAR WALL STORY SHEAR WALL LENGTHSLENGTHS

SEAOC Seismology (2007)SEAOC Seismology (2007) Structures depend on Structures depend on

longer shear wallslonger shear walls

SEAOC Blue Book (1999) SEAOC Blue Book (1999) Aspect ratios > 2:1 Aspect ratios > 2:1

cannot be adequately cannot be adequately predictedpredicted

H/L=2, H/L=2, L=15ft min.L=15ft min.

H=30ft

?

THREETHREE--DIMENSIONAL DIMENSIONAL MODELINGMODELING

THREETHREE--DIMENSIONAL DIMENSIONAL MODELING TECHNIQUESMODELING TECHNIQUES

ContinuousContinuous StackedStackedi i = V= ViiLLii33/3E/3EIIiiTT = = (Vh(Vhii22)(3L)(3LTT--hhii)/6E)/6EIITT

L2L3L4h2h3h4

LT

010203040506070

0 0.5 1 1.5 2 2.5 3 3.5

Deformation (inches)

Forc

e (k

ips)

Continuous Stacked

CONTINUOUS VS. STACKED CONTINUOUS VS. STACKED SHEAR WALL DEFORMATIONSHEAR WALL DEFORMATION

IIavgavg = 1,200 in= 1,200 in44

II = 10,000 in= 10,000 in44ConservativeConservative

BENEFITS OF BENEFITS OF THREETHREE--DIMENSIONAL DIMENSIONAL

MODELINGMODELING

Approximate building driftApproximate building drift

Distribute direct and Distribute direct and torsionaltorsional shear forcesshear forces

Stiffness of nonStiffness of non--full height shear walls full height shear walls incorporated correctlyincorporated correctly

93D MODEL 3D MODEL PLAN VIEWPLAN VIEW 3D MODEL 3D MODEL PLAN VIEWPLAN VIEW

AssumptionsPlywood TypePlywood ThicknessNailing PatternChord SizeHold Down

Group 1Group 2Group 3

I1I2I3

3D MODEL 3D MODEL ISOMETRIC VIEWISOMETRIC VIEW

Roof

4th flr.

2nd flr.1st flr.

3rd flr.

3D MODEL 3D MODEL ISOMETRIC VIEWISOMETRIC VIEW

3D MODEL 3D MODEL ISOMETRIC VIEWISOMETRIC VIEW

AssumptionsPlywood TypePlywood ThicknessNailing PatternChord SizeHold Down

CONCLUSIONCONCLUSION

The appropriate analysis technique for The appropriate analysis technique for lightlight--framed multiframed multi--story residential story residential buildings is rigid diaphragm analysis buildings is rigid diaphragm analysis incorporating multiincorporating multi--story shear wall story shear wall deformations via threedeformations via three--dimensional dimensional modeling. modeling.

10

HohbachHohbach-- Lewin, Inc.Lewin, Inc.Structural EngineersStructural Engineers