pci/nsf/cpf part 2: 1 of 30 nees/eeri webinar april 23 2012 outline introduce pci/nsf/cpf dsdm...

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April 23 2012PCI/NSF/CPFPART 2:1 of 30

OutlineOutline

Introduce PCI/NSF/CPF DSDM Research Effort Review Key Behaviors of Precast

Diaphragms and Design Philosophy Adopted Summarize DSDM Research Project Findings Present Precast Diaphragm Design

Procedure Cover Precast Diaphragm Design Example Discuss Codification Efforts

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Precast Concrete Diaphragm Seismic Design Procedure

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Design Procedure

Applicabilityo Seismic design of precast concrete diaphragms with and without topping slabs

Design Methodology Summary

Objectiveo Provide adequate strength and deformability of connectors between precast

diaphragm segments

MethodoAmplify code forces Fp by a factor

oAmplify shear forces by an overstrength factor

oSelect appropriate diaphragm reinforcing based on deformation capacity

oCheck gravity column drifts using factors Cd,dia and Cr,dia

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Design Procedure

Step 1: Determine the diaphragm seismic baseline design force as per ASCE 7-05

Design Steps

Step 2: Determine diaphragm seismic demand level (Low, Moderate, and High).

Step 3: Select diaphragm design option (Elastic, Basic and Reduced).

Step 4: Determine the required diaphragm reinforcement classification (LDE, MDE and HDE).

Step 9: Select specific diaphragm reinforcement type and determine properties.

Step 10: Strength design of diaphragm reinforcement at joints between precast elements.

Step 5: Determine the diaphragm force amplification factor ()

Step 6: Determine the diaphragm shear overstrength factor ().Step 7: Determine the amplified diaphragm design force.

Step 8: Determine the diaphragm internal forces (in-plane shear, axial and moment).

Step 11: Determine the diaphragm stiffness: effective elastic (Eeff ) and shear modulus (Geff)

Step 12: Check the diaphragm-induced gravity column drift

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Design ProcedureStep 1: Baseline design force

Step 1: Determine the diaphragm seismic baseline design force as per ASCE 7-05

(1) Determine design spectral acceleration from hazard maps as per ASCE 7 Section 11.4

(2) Determine SDC from seismic use groups as per ASCE 7-11.6

(3) Calculate the controlling seismic response coefficient Cs as determined in accordance with ASCE 7-12.8.1. Use structure fundamental period T as determined in accordance with ASCE 7-12.8.2

(4) Calculate the vertical distribution factor Cvc, at each floor level in accordance with ASCE 7-12.8.3

(5) Calculate the lateral seismic design force Fx at each floor level as per ASCE 7 Section 12.8.3

(6) Calculate maximum diaphragm design acceleration, Cdia, max

Cdia,max= max (Fx / wx) (Eqn.1)

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Design ProcedureStep 1: Baseline design force (con’t)

Calculate Baseline Diaphragm Force at each level x, FDx

FDx = x Cdia,max wx (Eqn. 2)

where wx = the portion of the total structure weight (w) located at Level x,

x is the diaphragm force vertical distribution factor:

Multistory buildings: x See Appendix 1 of PART 1.

Parking garage : x=1.0 top floor, x=0.68 other floors

Shear Wall

0

1

2

3

4

5

6

7

8

9

10

0 0.2 0.4 0.6 0.8 1 1.2

x factor: Shear Walls

# of stories

x

Appendix 1: Diaphragm Force Vertical Distribution

1.00 10

0.70 1.00 9

0.40 0.70 1.00 8

0.50 0.40 0.70 1.00 7

0.60 0.52 0.40 0.70 1.00 6

0.70 0.64 0.55 0.40 0.70 1.00 5

0.80 0.76 0.70 0.60 0.80 0.70 1.00 4

0.90 0.88 0.85 0.80 0.90 0.85 0.70 1.00 3

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1

10987654321

Total Number of StoriesStory Number

1.00 10

0.70 1.00 9

0.40 0.70 1.00 8

0.50 0.40 0.70 1.00 7

0.60 0.52 0.40 0.70 1.00 6

0.70 0.64 0.55 0.40 0.70 1.00 5

0.80 0.76 0.70 0.60 0.80 0.70 1.00 4

0.90 0.88 0.85 0.80 0.90 0.85 0.70 1.00 3

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 2

1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1

10987654321

Total Number of StoriesStory Number

Shear Wall

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0

1

2

3

4

0 0.2 0.4 0.6 0.8 1

Design: w/Ramp

0

1

2

3

4

0 0.2 0.4 0.6 0.8 1

Design: w/o Ramp

Design ProcedureCommentary Step 1: Baseline design force

Comparison to Analytical Results: Maximum Diaphragm Force Profile (MCE)

Taller Structures

0

1

2

3

4

5

6

7

8

0 0.2 0.4 0.6 0.8 1F/Fmax

Sto

ry

Analytical Results: SWAnalytical Results: MF

x distribution: SW

x distribution: MF0

1

2

3

4

5

6

7

8

0 0.2 0.4 0.6 0.8 1F/Fmax

Story Shear wall structure

Moment frame structureMulti-linear design for SWMulti-linear design for MFConservative Design

Low-rise and Parking Structures

0

1

2

3

4

0 0.2 0.4 0.6 0.8 1F/Fmax

Sto

ry

Analysis: w/ RampAnalysis: w/o Ramp

Exterior wall + Lite wall

Interior wall + Lite wall

Perimeter wall

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If AR>2.5 and diaphragm seismic demand falls in Low, it shall be moved from Low to Moderate.

Design ProcedureStep 2: Demand Level

Step 2: Determine diaphragm seismic demand level

(1) Three diaphragm seismic demand levels are defined as: Low, Moderate, and High

(2) Diaphragm demand level is based on seismic design category (SDC), number of stories and diaphragm span as follows:

For SDC B and C: Low

For SDC D and E: See Fig. 1

If AR<1.5 and diaphragm seismic demand falls in Low, it can be moved from High to Moderate

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Design ProcedureCommentary Step 2: Demand Level (con’t)

BDO Max Joint Opening Demands in MCE

Effect of Diaphragm Aspect Ratio

0

0.1

0.2

0.3

0 1 2 3 4

ARd( i

n)

High

Moderate

Low

0

0.1

0.2

0.3

0 1 2 3 4

L=60'

0

0.1

0.2

0.3

0 1 2 3 4

L=180'

Low Moderate High

0

1

2

3

4

5

6

7

8

0 30 60 90 120 150 180 210 240Diaphragm Span (ft)

Num

ber

of S

tori

es

0

1

2

3

4

5

6

7

8

0 30 60 90 120 150 180 210 240Diaphragm Span (ft)

Num

ber of story

d<0.1 0.1<d<0.2 d>0.2

High (AR>1.5)

Moderate

Low(AR<2.5)

0

1

2

3

4

5

6

7

8

0 30 60 90 120 150 180 210 240

0

1

2

3

4

5

6

7

8

0 30 60 90 120 150 180 210 240

0

1

2

3

4

5

6

7

8

0 30 60 90 120 150 180 210 240

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Design ProcedureStep 2: Demand Level (con’t)

(1) Diaphragm span on a floor level is defined as the larger value of: - maximum interior distance between two LFRS elements - twice the exterior distance between the outer LFRS element and the building free edge

Le Le Lm

d1

d2

d1

a

Span = max (Lm, 2Le, 2d1, d2) AR = max (Lm/a, 2Le/a)

Chord reinforcement

Design for VQ/I (see 3.1.C of PART3)

Lm

d1

d2

d1

Span = max (Lm, 2d1, d2)

AR = Lm/d1

Chord reinforcement

Design for combined M, N and V (see 3.1.C of PART3)

(2) Diaphragm aspect ratio (AR) is calculated using the floor diaphragm dimension perpendicular to (sub)diaphragm span associated with the pair of adjacent chord lines.

Commentary Step 2

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Comments:The Elastic Design Option (EDO):

targets elastic diaphragm behavior in the MCE. uses a diaphragm force amplification factor E. allows the use of low deformability reinforcement (LDE).

Design ProcedureStep 3: Design Option

Step 3: Select diaphragm design option

Three diaphragm design options are defined as: Elastic, Basic and Reduced



The Basic Design Option (BDO): targets elastic diaphragm design in the DBE.uses a diaphragm force amplification factor D.requires the use of moderate deformability reinforcement (MDE).



The Basic Design Option (BDO): targets elastic diaphragm design in the DBE.uses a diaphragm force amplification factor D.requires the use of moderate deformability reinforcement (MDE).

A Reduced (Force) Design Option (RDO):permits diaphragm yielding in the DBEuses a diaphragm force amplification factor R.requires the use of high deformability reinforcement (HDE).targets MCE deformation demands within allowable HDE deformation limits.

Increased Deformation Capacity but Lower Design Force

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Design Option

Diaphragm Seismic Demand Level

Low Moderate High

Elastic Recommended With Penalty* Not Allowed

Basic Alternative Recommended With Penalty*

Reduced Alternative Alternative Recommended

Design Procedure

Table 1. Diaphragm design option

Step 3: Design Option (con’t)

Diaphragm design option is based on diaphragm seismic demand level

*15% Design Force Increase

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Design ProcedureCommentary Step 3: Design Option

0

0.1

0.2

0.3

0 100 200 300

Length (ft)

d(i

n)

0

0.05

0.1

0.15

0.2

0.25

0.3

0 100 200 300

Length (ft)

d (i

n)

n=6n=4n=2

0

0.1

0.2

0.3

0 100 200 300

increase designstrength by 15%

0

0.1

0.2

0.3

0 100 200 300

HighModerateLow

Design Force Penalty determined through analytical results (MCE response):• BDO Designs for High Diaphragm Seismic

Demand

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Design ProcedureStep 4: Reinforcement Classification

• High deformability element (HDE):

• Moderate deformability element (MDE):

• Low deformability element (LDE):

Step 4: Determine required Diaphragm Reinforcement Classification

Three Classifications:

Comments: Classification of diaphragm reinforcement determined through cyclic testing protocols

in the Precast Diaphragm Reinforcement Qualification Procedure (See PART 2)

In meeting the required maximum deformation capacity using the above testing protocols, the required cumulative inelastic deformation capacity is also met.

An element demonstrating a reliable and stable maximum joint opening deformation capacity:

of greater than 0.6”

of between 0.3” and 0.6”

not meeting others (< 0.3”)

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Design OptionDiaphragm Reinforcement Classification

Low Moderate High

Elastic Recommended Allowable Allowable

Basic Not allowed Recommended Allowable

Reduced Not allowed Not allowed Recommended

Design Procedure

The required diaphragm reinforcement classification is based on diaphragm design option, see Table 2

Step 4: Reinforcement Classification (con’t)

Table 2. Required diaphragm reinforcement classification

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Design ProcedureStep 5: Force Amplification Factor

Step 5: Determine diaphragm force amplification factor ()

where n is the total number of stories in building, L is diaphragm span in ft as defined in Step 2 AR is diaphragm aspect ratio (0.25 ≤ AR ≤ 4.0).

(L/60-AR) not to be taken larger than 2.0 nor less than -2.0.

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0

200

400

600

800

1000

1200

1400

1600

0 0.2 0.4 0.6

d (in)

T (k)

0

200

400

600

800

1000

1200

1400

1600

0 0.2 0.4 0.6

0

200

400

600

800

1000

1200

1400

1600

0 0.2 0.4 0.6

Local

E – Diaphragm force amplification factor used in the EDO. Calibrated to produce elastic diaphragm response in the MCE.

Design Procedure

GlobalLDE MDE HDE

Commentary Step 5: Force Amplification



D – Diaphragm force amplification factor used in the BDO. Calibrated to produce elastic diaphragm response in the DBE.D produces MCE deformation demand not exceeding MDE allowable, 0.2”


D – Diaphragm force amplification factor used in the BDO. Calibrated to produce elastic diaphragm response in the DBE.D produces MCE deformation demand not exceeding MDE allowable, 0.2”

R – Diaphragm force amplification factor used in the RDO. Calibrated to produce MCE deformation not exceeding HDE allowable, 0.4”

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10

D (in)

Fpx (k)

EDO-2.66

MCEDBEd = 0.6"Yield0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10

BDO-1.93

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10

RDO-1.39

HDE

Test

Req.

MDE

Test

Req.

Mean response from suite of spectrum compatible earthquakes

SDC E n=6 SWL= 240’

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Design ProcedureCommentary Step 5: Force Amplification

Comments: Design equation is greater than or equal to 90% of mean data. The data is the mean of the maximum response from 5 ground motions.

The design equations (design procedure Eqns. 3-5) are curve fits of the analytical results (e.g. those shown on the pushover curves).

1.5

2

2.5

3

3.5

0 1 2 3 4 5

AR

E

1

1.5

2

2.5

3

0 1 2 3 4 5

AR

D

N=2N=4N=6

1

1.2

1.4

1.6

1.8

2

0 1 2 3 4 5

AR

R

1.5

2

2.5

3

3.5

0 1 2 3 4 5

1

1.5

2

2.5

3

0 1 2 3 4 5

1

1.2

1.4

1.6

1.8

2

0 1 2 3 4 5

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Design ProcedureStep 6: Shear Overstrength Factor

Step 6: Determine diaphragm shear overstrength factor (v):

where AR is diaphragm aspect ratio: 0.25 ≤ AR ≤ 4.0

(1) For elastic design option, v = vE: 0.1vE (Eqn. 6)

(2) For basic design option, v = vB:

7.142.1 13.0 ARvB (Eqn. 7)

(3) For reduced design option, v = vR:

46.292.1 18.0 ARvR (Eqn. 8)

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

0 1 2 3 4 5

AR

B

N=2N=4N=6

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

0 1 2 3 4 5

AR

R

N=2

N=4

N=6Commentary Step 6: The overstrength factors equations are similarly based on the statistical data from the analytical earthquake simulations.

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Design ProcedureStep 7: Diaphragm Design Force

Berkeley (SDC E)

It should be noted that other rationally-based expressions are being proposed for design force increase for all diaphragms in general.

FMR Method (Restrepo and Rodriguez 2007)

Amplify the baseline diaphragm force obtained from Eqn. 2 by the diaphragm force amplification factor obtained from Eqn. 3-5:

Step 7: Determine diaphragm design force

FDia,x= FDx (Eqn. 9)

The precast diaphragm design procedure presented here can be aligned to work with these factors.

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Design ProcedureStep 8: Diaphragm Internal Forces

The internal force demands (Nu, Vu, Mu) at all potential critical joints in the diaphragm must be determined based on application the amplified diaphragm design force.

Step 8: Determine diaphragm internal forces

1. Semi-rigid diaphragm model: The internal forces at critical sections can be extracted from a structural analysis model of the building incorporating semi-rigid modeling of the floor and roof diaphragms.

Comments:• The diaphragm is to be evaluated for the

effects of seismic loading in each orthogonal direction individually.

• The diaphragm effective elastic moduli, Eeff

and Geff , can be estimated as 25%~35% of the uncracked concrete E and G for the semi-rigid diaphragm model.

• These estimated values shall be verified in Step 12 after sizing the diaphragm reinforcement.

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Diaphragm Design Example

Nlite

Nbeam

w=(Fpx/3)/L

Vbeam

VSW VSW

LLbeam

L'Lbeam

Nbeam

Vbeam

d

x

Parking flat under transverse loading

Joint Axial Force

0

50

100

150

200

250

0 100 200 300x (ft)

N (

kips

)

Top floor

Other floors

Joint Shear Force

-200

-150

-100

-50

0

50

100

150

200

0 100 200 300

x (ft)

V (

kips

)

Top floor

Other floors

Joint Moment

-2000

-1000

0

1000

2000

3000

4000

5000

6000

7000

0 100 200 300

x (ft)M

omen

t (k-

ft)

Top floor

Other floors

Step 8: Diaphragm Internal Forces (con’t)

2. Analysis using free-body diagrams: Determine internal forces at all potential critical sections in the diaphragm by taking the applied amplified diaphragm forces and reactions on the diaphragm and evaluate appropriate free-bodies at each critical section using the principles of statics.

N V

M

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Design ProcedureCommentary Step 8: Internal Forces

Rational Methods: As an alternative to the two options, rational methods such as the strut-and-tie method or the panel and stringer method can be used.

Strut-and-Tie Panel and Stringer

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Design ProcedureStep 9: Diaphragm Reinforcement

• See Prequalified Precast Diaphragm Reinforcement in PART 2 to determine the classification and look up the properties of commonly-used existing diaphragm reinforcement.

2) Establish diaphragm reinforcement properties required for design including:(a) Elastic stiffness in tension and shear: kt, kv

(b) Yield strength in tension and shear: tn , vn

1) Select diaphragm reinforcement type based on required Diaphragm Reinforcement Classification.

0.121.68216.8HDE0.60.04354.21260Ductile mesh Gr.1018

0.124.2382HDE0.70.0568601234Pour strip chord Gr.60

0.124.2382MDE0.30.071601018Dry chord w/ flat plate Gr. 60

0.124.2382LDE0.10.071601018Dry chord Gr.60

[in][ksi][ksi/in][in][in][ksi][ksi/in]

dvyvn /Akv /AClassificationdtudtytn /Akt /A

ShearTension

2A-1a. Reinforcing Bar

0.121.68216.8HDE0.60.04354.21260Ductile mesh Gr.1018

0.124.2382HDE0.70.0568601234Pour strip chord Gr.60

0.124.2382MDE0.30.071601018Dry chord w/ flat plate Gr. 60

0.124.2382LDE0.10.071601018Dry chord Gr.60

[in][ksi][ksi/in][in][in][ksi][ksi/in]

dvyvn /Akv /AClassificationdtudtytn /Akt /A

ShearTension

2A-1a. Reinforcing Bar

0.0517.1372MDE0.30.04110.22300Angled bar (#3)

0.118.1181HDE0.60.0439209Hairpin (#4)

0.08218.1226HDE0.60.0663.155JVI

[in][kips][k/in][in][in][kips][k/in]

dvyvnkvClassificationdtudtytnkt

ShearTension

2A-1b. Connectors

0.0517.1372MDE0.30.04110.22300Angled bar (#3)

0.118.1181HDE0.60.0439209Hairpin (#4)

0.08218.1226HDE0.60.0663.155JVI

[in][kips][k/in][in][in][kips][k/in]

dvyvnkvClassificationdtudtytnkt

ShearTension

2A-1b. Connectors

Prequalified to a Classification Level

Needed properties in tension and shear for design

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Design ProcedureStep 9: Diaphragm Reinforcement (con’t)

• Use the cyclic testing protocols and qualification backbones in the Precast Diaphragm Reinforcement Qualification Procedure to classify and determine properties of new diaphragm reinforcement.

P

2 3

Ke

PbP1

P2

1

15%P2

b 2aa

2

2a

3

1

a

b

P2a

ExperimentalEnvelope

Backbone

Tmax

0.75Tmax

D

Monotonic response

Force

Displacement

Applied Tension/Compression

Displacement

Note, D=Reference Deformation

1.0D

0

Tension Displacement

10 20 30 Cycle #

[email protected]"

Monotonically Increasing Displacement

Incr

ease

in in

crem

ents

of

2.0D

unt

il f

ailu

reShear Displacement

Compensation to provide zero shear

[email protected]@0.5D [email protected] [email protected]

[email protected]@2.0D

[email protected]

[email protected]

[email protected]

2.0D

3.0D

4.0D

5.0D

6.0D

7.0D

8.0D

Applied Tension/Compression Displacement

Compression Force

Deform in Compression until Force Equals Preceding Cycle Tension Force

Comments:• The Precast Diaphragm Reinforcement Qualification Procedure is found in PART 2.

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Design Procedure

Diaphragm reinforcement must possess sufficient strength (Nn, Vn, Mn) at joints between precast elements to resist the diaphragm internal forces.

Step 10: Design the diaphragm reinforcement to resist the diaphragm internal forces.

Step 10: Diaphragm Strength Design

Comments: The interpretation of nominal flexural strength (Mn) depends on the design option selected.

For Elastic Design Option (EDO): yn MM (Eqn. 34a)

For Basic Design Option (BDO): )(2

1pyn MMM (Eqn. 34b)

For Reduced Design Option (RDO): pn MM (Eqn. 34c)

The following interaction formula is used for diaphragm reinforcement design:

where f = 0.9 and v = 0.85

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Design ProcedureCommentary Step 10: Strength Design

Comments:

A rational method has been developed for the diaphragm strength calculation. This method is embedded in a design aid program in PART 3 of the Seismic Design Methodology Document for Precast Concrete Diaphragms.

d

d0

b

s’ s

s

s

s

s

s

s0

s0

s

s

s

s

s

s

s0

s0

s

s

s

s

s

s

s0

s0

N.A.

C

Tchord

Tconn

1

c/3

cb

Cconc

Ttopping

2/3(

d-c)

2/3(

d-s 0-

c)

cc0

V

M

d0

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Design ProcedureStep 11: Diaphragm Stiffness

Step 11: Determine the diaphragm effective elastic modulus (Eeff ) and shear modulus (Geff)

Comments: The rational method used to estimate diaphragm strength also produces effective stiffness parameters Eeff and Geff (See PART 3). The average value produced for the differently reinforced diaphragm joints can be used.

If using a semi-rigid diaphragm structural analysis model, the calculated Eeff and Geff shall be checked with respect to the values estimated in Step 8, and the analysis repeated if necessary.

DLFRS,i

ddia,i

Ddia,i

LFRSDiaphragm

col,iLFRS, i

LFRS

Gravity column

Diaphragm

h

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Design ProcedureStep 12: Drift Check

Step 12: Check the diaphragm induced gravity column drift

(1) Determine the diaphragm elastic deformation (d dia, el) under design force (FDia):

- Semi-rigid diaphragm model: Extract the maximum diaphragm deformation from the static analysis performed in Step 8 using the calculated Eeff and Geff

- Free-body Method: Obtain the maximum diaphragm deformation based on classical methods using the M, V diagrams obtained in Step 8 using the calculated Eeff and Geff

(2) Determine the diaphragm inelastic deformation by applying the deformation amplifier (Cd,dia) to elastic diaphragm deformation (d dia, el):

d dia = Cd,dia d dia, el (Eqn. 11)

where for EDO: Cd,dia = 1.0 CDC1 = 0.05

for BDO: Cd,dia = 1.5 CDC1 = 0.08

for RDO: Cd,dia = 2.9 CDC1 = 0.10

and CD is the diaphragm drift P-D multiplier,

where C1 is a the design option factor shown above

)4/)(240/(1 1 ARLCC D

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Design ProcedureStep 12: Drift Check (con’t)

(3) Determine the diaphragm induced gravity column drift by introducing a diaphragm drift reduction factor (Cr,dia) to the diaphragm inelastic deformation (d dia)

dia = d diaCr,dia h (Eqn. 12)

where h is the floor-to-floor height and Cr,dia is calculated from:

(4) Check the diaphragm induced gravity column drift with design limit:

- If dia ≤ 0.01 OK

- If dia > 0.01 then check dia + LFRS

where LFRS is the LFRS story drift determined per ASCE 7, 12.8.6:

If dia + LFRS ≤ 0.04 OK

For EDO: 0.4 ≤ Cr,dia = 1.1 1– 0.13AR ≤ 1.0 (Eqn. 13)

For BDO: 0.4 ≤ Cr,dia = 1.08 – 0.11AR ≤ 1.0 (Eqn. 14)

For RDO: 0.4 ≤ Cr,dia = 1.00 – 0.11AR ≤ 1.0 (Eqn.

15)

and AR is diaphragm aspect ratio as limited by Step 6.

If dia + LFRS > 0.04, then redesign the diaphragm to increase diaphragm stiffness (via diaphragm reinforcement or span)

pci/nsf/cpf part 2: 1 of 30 nees/eeri webinar april 23 2012 outline introduce pci/nsf/cpf dsdm...

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