seismic design of diaphragms...0.3 for buildings designed with buckling restrained braced frame...

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S. K. Ghosh Associates Inc.

www.skghoshassociates.com

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Seismic Design of Diaphragms

S. K. Ghosh


Palatine, IL and Aliso Viejo, CA


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2009 NEHRP Provisions

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2009 NEHRP ProvisionsPart 3 Resource Paper 10

Replace withMulti-partResource Paper

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BSSC PUC IT-6 Scope

Reexamine and refine seismic design provisions for cast-in-place concrete, precast concrete (with or without topping), metal, and wood diaphragms, focusing on objectives with regards to performance in the design earthquake.

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Multi-Part Resource Paper

Global (ASCE 7) Issues

Cast-in-Place Concrete Diaphragms

Precast Concrete Diaphragms (topped and untopped)

Steel Deck Diaphragms (topped and untopped)

Wood Diaphragms

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Global (ASCE 7) Issues

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Diaphragms, Chords, and Collectors

12.10.1.1 Diaphragm Design Forces. Floor and roof diaphragms shall be designed to resist design seismic forces from the structural analysis, but not less than the following forces:

Where

Fpx = the diaphragm design force

Fi = the design force applied to Level i

wi = the weight tributary to Level i

wpx = the weight tributary to the

diaphragm at Level x

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Diaphragms, Chords, and Collectors

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- 9 -

Diaphragm Design Forces

0

1

2

3

4

5

6

7

0 50 100 150 200

Fpx

Fx

Force (kips)

Flo

or

Lev

el

- 10 -

Diaphragm Design Force

Recommendations in PCI’s Seismic Design Manual, based on results of research:

For structures assigned to SDC B or C, if every floor diaphragm is designed for the force at the uppermost level derived from the IBC, additional load factors are not required for elastic diaphragm response under the design earthquake.

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For structures assigned to SDC D, E, or F, if lateral forces are resisted entirely by special moment frames, additional load factors are not required if every floor diaphragm is designed for the force at the uppermost level derived from ASCE 7.

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For structures assigned to SDC D, E, or F, if shear walls are part of the lateral force-resisting system, it is sufficient to apply a diaphragm load factor of 2 to the force at the uppermost level derived from ASCE 7 and to design each floor for that force.

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Diaphragm IT Contributors

Ned Cleland Mario Rodriguez

Kelly Cobeen Richard Sause

Robert Fleischman

S. K. Ghosh William Gould

Neil Hawkins Dichuan Zhang

Dominic Kelly

Tom R. Meyer

Jose Restrepo

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Diaphragm IT Products

Design Force Level Proposal for Part 1 of the 2015 NEHRP Provisions – modifies ASCE 7-10 Section 12.10 Approved for inclusion in ASCE 7-16

Design Force Level Proposal for Part 3 of the 2015 NEHRP Provisions – modifies ASCE 7-10 Section 12.10

Precast Diaphragm Design Proposal for Part 1 of the 2015 NEHRP Provisions – modifies ASCE 7-10 Section 14.2 Approved for inclusion in ASCE 7-16

Resource Paper for Part 3 of the 2015 NEHRP Provisions

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2015 NEHRP Provisions

p. 16 of Set 8

Each mode’s contribution is reduced by R( )

2

1

,n

ij j j

i

F f w φ=

=

∑( )a iS T

g R

Fj

j

j

jj

ASCE 7 Method

Fjw j

jFpj

Floor Accelerations for Diaphragm Design

and

0 2 0 4 0 4

0 5

0 5 Acceleration "Magnification" 1 0

DS e px px DS e DS

e px px e

e e

PGA. S I F / w . S I but . S

g

PGA PGA. I F / w I

g g

or . I . I

≤ ≤ ≈

→ ≤ ≤

≤ ≤

SRSS

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0

1

2

3

4

5

0 0.2 0.4 0.6 0.8 1

Peak ground acceleration (g)

Flo

or m

agni

ficat

ion

RC Frames n 5

RC Frames 5< n 10

RC Frames 10 < n 20

Walls 5 < n 10

Walls 10 < n 20

Steel Frames n 5

Steel Frames 5 < n 10

Steel Frames 10 < n 20

Steel Frames n > 20

Braced Frames n 5

Braced Frames 5 < n 10

Braced Frames 10 < n 20

Braced Frames n > 20

≤≤≤≤

≤≤≤≤

≤≤≤≤

≤≤≤≤

≤≤≤≤

≤≤≤≤≤≤≤≤

≤≤≤≤≤≤≤≤

≤≤≤≤

≤≤≤≤

7-story building

Northridge Earthquake Data

Repaired PCI building

p. 17 of Set 8

?Floor Accelerations for Diaphragm Design

ASCE 7 Method

ASCE 7 Range, I e =1

0 5 Acceleration "Magnification" 1 0e e

. I . I≤ ≤

The upper and lower limits in ASCE7 do not seem to be rational

The computation of floor acclerations based on the assumption that all modes

are equally reduced by plasticity does not seem rational

••

either

Northridge earthquake and shaketable test data

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Diaphragm Design

In 2001 Rodriguez et al. noted that inelastic response in multi-story buildings tended to cause an important reduction in floor accelerations contributed by the first mode of response but had a much lesser effect on those contributed by the higher modes of response.

They proposed the First Mode Reduced method, in which the roof acceleration could be determined by a square root sum of the squares combination in which the first mode contribution was reduced for inelasticity and the higher modes were left unreduced.

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Diaphragm Design

Fpx = Cpxwpx/Rs

≥ 0.2SDS Ie wpx

Cpx comes from Cp0, Cpi, and Cpn

Note: Cpi is not used in the 2015 NEHRP Provisions

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Diaphragm Design

2015 NEHRPProvisions

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- 21 -

Diaphragm Design

ASCE 7-16

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Diaphragm Design

Cp0 = 0.4 SDS Ie

Cpn= Γm1Ω0CS2

+ Γm2CS2

2 Cpi

Note: The lower-bound limit on Cpn is in ASCE 7-16 only, not in the 2015 NEHRP Provisions.

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Diaphragm Design

Γm1 = 1 + 0.5zS (1 – 1/n)

Γm2 = 0.9zS (1 – 1/n) 2

where zS = modal contribution coefficient modifier dependent on seismic force-resisting system.

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Diaphragm Design

Values of mode shape factor zs

0.3 for buildings designed with Buckling Restrained Braced Frame systems

0.7 for buildings designed with Moment-Resisting Frame systems

0.85 for buildings designed with Dual Systems with Special or Intermediate Moment Frames capable of resisting at least 25% of the prescribed seismic forces

1.0 for buildings designed with all other seismic force-resisting systems

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Diaphragm Design

1.0

1.1

1.2

1.3

1.4

1.5

1.6

0 5 10 15 20 25

Γm1

Eq. 3.1 zs = 1

Eq. 3.1 zs = 0.7

Wall buildings

Frame buildings

Number of levels, n

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Diaphragm Design

0.0

0.2

0.4

0.6

0.8

1.0

0 5 10 15 20 25

Γm2

Eq. 3.1 zs = 1

Eq. 3.1 zs = 0.7

Wall buildings

Frame buildings

Number of levels, n

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Diaphragm Design

Cpi is the greater of values given by:

Cpi = Cp0

Cpi = 0.9Γm1Ω0CS

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Diaphragm Design

CS = V/W or Vt/W

CS2 = minimum of:

(0.15n + 0.25) Ie SDS

Ie SDS

Ie SD1/[0.03(n-1)] for n ≥ 2 or 0 for n = 1

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Consistent Look into the Design Spectra CsR

For the “Second mode”, R = 1

CS(T2) = min(0.15n+0.25, 1)IeSDS

≤ IeSD1/ [0.03(n-1)]

n: number of levels above ground, n ≥ 2

Comparison of Results (RR for ASCE7 and Measured)

7-story bearing wall building

p. 30

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.5 1.0 1.5

Re

lati

ve h

eig

ht

Cpx / Cpo

Measured EQ4

Proposed

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Comparison of Results (RR for ASCE7 and Measured)

5-story special MRF building

p. 31

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.5 1.0 1.5

Re

lati

ve

he

igh

t

Cpx / Cpo

Measured DEN67

Proposed

Comparison of Results(RR for ASCE7 and Measured)

3-story PCI building

p. 32

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Comparison of Results(RR for ASCE7 and Measured)

NEES Wood Capstone Building (data Processed by R Hanson)

p. 33

Comparison of Results (RR for ASCE7 and Computed)

Steel BRB and special MRF buildings

p. 34

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.5 1 1.5 2

Re

lati

ve h

eig

ht

Cpx / Cpo

6 story

BRB Analysis

SMRF Analysis

BRB Proposed

SMRF Proposed

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 0.5 1 1.5 2

Re

lati

ve h

eig

ht

Cpx / Cpo

12 story

BRB Analysis

SMRF Analysis

BRB Proposed

SMRF Proposed

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35 of 15

Comparison using Updated DSDM Equations

Berk

ele

y (

SD

C E

)

Seatt

le (

SD

C D

)

Charlest

on (

SD

C D

)

Knoxvill

e (

SD

C C

)

0

0.5

1

1.5

2

2.5

1 2 3 4 5 6 7 8 9 10 11 12

0

0.5

1

1.5

2

2.5

1 2 3 4 5 6 7 8 9 10 11 12

0

0.5

1

1.5

2

2.5

1 2 3 4 5 6 7 8 9 10 11 12

0

0.5

1

1.5

2

2.5

1 2 3 4 5 6 7 8 9 10 11 12

Acc

eler

atio

n (g

)

0

0.5

1

1.5

2

2.5

1 2 3 4 5 6 7 8 9 10 11 12

0

0.5

1

1.5

2

2.5

1 2 3 4 5 6 7 8 9 10 11 12Number of Stories

RR

ΨE

ΨD

ΨR

ASCE7DSDM

Acc

eler

atio

n (g

)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 2 3 4 5 6 7 8 9 10 11 12

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 2 3 4 5 6 7 8 9 10 11 12

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 2 3 4 5 6 7 8 9 10 11 12

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 2 3 4 5 6 7 8 9 10 11 12Numer of Stories

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1 2 3 4 5 6 7 8 9 10 11 12

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6


RR

ΨE

ΨD

ΨR

ASCE7DSDM

00.20.40.60.8

11.21.41.61.8

2

1 2 3 4 5 6 7 8 9 10 11 12

00.20.40.60.8

11.21.41.61.8

2

1 2 3 4 5 6 7 8 9 10 11 12

00.20.40.60.8

11.21.41.61.8

2

1 2 3 4 5 6 7 8 9 10 11 12

00.20.40.60.8

11.21.41.61.8

2

1 2 3 4 5 6 7 8 9 10 11 12

UCSD

00.20.40.60.8

11.21.41.61.8

2

1 2 3 4 5 6 7 8 9 10 11 12

00.20.40.60.8

11.21.41.61.8

2


Acc

eler

atio

n (g

)

RR

ΨE

ΨD

ΨR

ASCE7DSDM

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1 2 3 4 5 6 7 8 9 10 11 12Numer of Stories

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1 2 3 4 5 6 7 8 9 10 11 12Numer of Stories

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1 2 3 4 5 6 7 8 9 10 11 12Numer of Stories

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1 2 3 4 5 6 7 8 9 10 11 12Numer of Stories

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1 2 3 4 5 6 7 8 9 10 11 12Numer of Stories

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7


ASCE7

Acc

eler

atio

n (g

)

RR

ΨE

ΨD

ΨR

DSDM

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Diaphragm Capacity

Why are we not seeing inadequate performance of diaphragms in seismic events?

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Inertial Forces in Diaphragms

Existing diaphragms may carry seismic inertial forces through:

(a) inherent overstrength in the floor system, including the floor plate and framing elements, that permit the transfer of higher than code design forces,

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Inertial Forces in Diaphragms

or

(b) inherent ductility or plastic redistribution qualities within the diaphragm (or at the boundaries of the diaphragm) that limit the amount of inertial forces that can develop, without significant damage or failure.

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Diaphragm Design

Flexure-controlled diaphragm: Diaphragm with a well-defined flexural yielding mechanism, which limits the force that develops in the diaphragm.

The factored shear resistance shall be greater than the shear corresponding to flexural yielding.

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Diaphragm Design

Shear-controlled diaphragm: Diaphragm that does not meet the requirements of a flexure-controlled diaphragm.

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Diaphragm Design (NEHRP Provisions)

Diaphragm System Shear Control Flexure ControlCIP Concrete 1.5 2

Precast concreteEDO 1.0 0.7BDO 1.0 1.0RDO 1.0 1.3

Untopped Steel Deck

Ductile 3.0 NA

Low ductility 2.0 NA

Topped Steel Deck

Reinforced topped Steel Deck with shear stud connection to framing

2.0 2.5

Other topped Steel Deck with structural concrete fill

1.5 2.0

Wood Typical 3.0 NA

When Rs is greater than 1, such a diaphragm should have a well-defined, ductile shear yielding mechanism which limits the force that develops in the diaphragm.

pxpx px

s

CF = w

R

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Diaphragm Design (ASCE 7-16)

Diaphragm System Shear-Controlled

Flexure-Controlled

Cast-in-place concrete designed in accordance with Section 14.2 and ACI 318

- 1.5 2

Precast concrete designed in accordance with Section 14.2.4 and ACI 318

EDO 1 0.7 0.7

BDO 2 1.0 1.0

RDO 3 1.4 1.4

Wood sheathed designed in accordance with Section 14.5 and AF&PA (now AWC) Special Design Provisions for Wind and Seismic

- 3.0 NA

1. EDO is precast concrete diaphragm Elastic Design Option.2. BDO is precast concrete diaphragm Basic Design Option.3. RDO is precast concrete diaphragm Reduced Design Option.

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Diaphragm Design Force Level Comparisons

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4-Story Perimeter Wall Precast Concrete Parking Structure (SDC C, Knoxville)

16'

10'-6"

10'-6"

10'-6"

47'-6"

204'

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4-Story Perimeter Wall Precast Concrete Parking Structure (SDC C, Knoxville)

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4-Story Interior Wall Precast Concrete Parking Structure (SDC D, Seattle)

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4-Story Interior Wall Precast Concrete Parking Structure (SDC D, Seattle)

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8-Story Precast Concrete Moment Frame Office Building

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8-Story Precast Concrete Moment Frame Office Building

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8-Story Precast Concrete Shear Wall Office Building

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8-Story Precast Concrete Shear Wall Office Building

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Steel-Framed Assembly Structure in Southern California

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Steel-Framed Office Structure in Seattle, WA

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Cast-in-Place Concrete Framed Parking Structure in Southern California

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Cast-in-Place Concrete Framed Residential Structure in Northern California

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Cast-in-Place Concrete Framed Residential Structure in Seattle, WA

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- 57 -

Cast-in-Place Concrete Framed Residential Structure in Hawaii

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Steel Framed Office Structure in Southern California

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Thank You!!

seismic design of diaphragms...0.3 for buildings designed with buckling restrained braced frame...

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