nehrp seismic design technical briefs - the...

8/2/2011

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NEHRP Seismic Design Technical Briefs

Available at....http://www.nehrp.gov/pdf/nistgcr10-917-4.pdf

8/2/2011

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Outline1. Introduction2. The Role of Diaphragms3. Diaphragm Elements4. Principles for Design of Diaphragms5. Building Analysis Guidance6. Diaphragm Analysis Guidance7. Design Guidance8. Additional Requirements9. Detailing & Constructability Issues10. References11. Notation

Scope

• Cast-in-place concrete diaphragms

• Conventionally reinforced or prestressed

• US Codes• International Building Code (2009)

• ASCE 7 (2010)

• ACI 318 (2008)

• Seismic Design Categories B – F

• For practicing structural engineers

1. Introduction

1. Introduction

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moment-resistingframe

diaphragm

transfer (podium)slab

basementwall

structural (shear) wall

gravity framing

below grade soil pressure

inclinedcolumn

gravityloads

inertialforces

Roles of diaphragms

• Stability

• Gravity loads

• Inertial forces

• Out-of-plane forces

• Inclined columns

• “Transfer” forces

• Soil loads

2. The Roles of Diaphragms

Diaphragm components

vu

Vu

(a) Plan

M

V

(b) Simple beam idealization

Mu

Vu

compression chord

tension chord

wall

diaphragm

(c) Internal moment and shear resistance

MuCu

Tu

d

3. Diaphragm Components

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Collectors (drags, struts)

(b) Collector actions(a) Plan

a

b

c

d

collector same width as wall

beff

45°

collector spread into slab

Cu,max

Tu,max

vu

a

b

c

d


Distributor (a collector in reverse)

distributor

basement wall

Cu

Tu

diaphragm


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Measured floor accelerations

Moehle and Sozen, 1980

4. Diaphragm Behavior and Design Principles

Design lateral forces

(a) Structure

w1

wn

w2

hn

h2

h1

(b) Model

Fx

(c) Forces for vertical element design

Fpx

(d) Forces fordiaphragm design

VCF vxx (ASCE 7 Eq. 12.8-11)

pxn

xi

i

n

xi

i

px w

w

F

F

(ASCE 7 Eq. 12.8-12)

pxn

xi

i

n

xi

i

px w

w

F

F

(ASCE 7 Eq. 12.10-1)

pxeDSpx wISF 2.0min, (ASCE 7 Eq. 12.10-2)

pxeDSpx wISF 4.0max, (ASCE 7 Eq. 12.10-3)

but not be less than

and need not exceed

4. Diaphragm Behavior and Design Principles5. Building Analysis Guidance

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Northridge earthquake, 19944. Diaphragm Behavior and Design Principles

The overstrength factor, o

For structures assigned to SDC C through F, collector design forces are the maximum of (a), (b), and (c):

(a) Forces resulting from application of Fx using the load combinations withoverstrength factor Ω0 of ASCE 7 Section 12.4.3.2;

(b) Forces resulting from application of Fpx using the load combinations withoverstrength factor Ω0 of ASCE 7 Section 12.4.3.2;

(c) Forces resulting from application of Fpx,min in the basic load combinationsof ASCE 7 Section 12.4.3.


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(a) Isolated frame and wall

Frame Wall Frame Wall

Diaphragm

(b) Frame and wall connectedby floor diaphragm

Transfer forces4. Diaphragm Behavior and Design Principles

mat

subterranean levels

grade level

podium diaphragm

shear wall

tower core wall

E

Elevation

Transfer forces

Large diaphragm transfer

Large diaphragm transfer

At discontinuities, model diaphragm flexibility. Stiffness modifiers commonly fall in the range 0.15 to 0.50.


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Diaphragm openings

Force couple resisting overturning

(a) Elevation

Limited diaphragm transfer capacity

Good diaphragm transfer capacity

(b) Section A

A

Basement Wall

Podium

4. Diaphragm Behavior and Design Principles

Diaphragm models:Equivalent beam model

(a) Plan

M

V


Mu

Vu

wall

diaphragm

6. Diaphragm Analysis Guidance

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Diaphragm models:Equivalent beam-on-springs model

AB

C

(a) Plan

kA kB kC

M

V



Diaphragm models:Corrected equivalent beam model

RC , kC

RA , kA RB , kB

RD , kD

(a) Plan

RA

M

V

RB


Fx, Fpx

C.R.

ei

ex

x

y


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Diaphragm models:Finite element model

CollectorWall


Idealized diaphragm load paths:

vu

Vu

(a) Plan

M

V


Mu

Vu

compression chord

tension chord

wall

diaphragm


MuCu

Tu

d

dMTC uuu

h


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Idealized diaphragm load paths:

(a) Partial plan

a

b

c

d

beff

45°

collector spread into slab

Cu,max = CD + Cv

Tu,max = TD + Tv

(c) Collector forces(b) Collector actions

Cu,max

Tu,max

vu

a

b

c

d


Partial-depth collectors6. Diaphragm Analysis Guidance

Par

tial-d

epth

co

llect

or

Secondary distributed

collector

a

c

e

g

M

V

Mu,hi

h

iVu,ad Vu,eg

d

f

b

k

jChord reinforcement

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Idealized diaphragm load paths:collector entering wall

45oCollector force transferred to these horizontal wall bars; bars added if required to resist both shear and collector force

Collector force

Typical wall reinforcement

Collector bars extend into wall a minimum of a development length, ld, and the length required to transfer force to horizontal wall bars


Idealized diaphragm load paths:openings

L

VB

VT

compression chord

tension chord

wall

T

B

l

R


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Idealized diaphragm load paths:transfer around opening

Opening

Basement wall

Wall force

Compression strutDistributor Tension tie

Develop tension tie beyond node

d

a fb e

c h g

Plan


Idealized diaphragm load paths:too-long distributors

Plan

A

B

C

D

E

F

a b

c

g

h

i

de f

j

Wall

Wall

Basement wall


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Load and resistance factors

Load combinations with overstrength factor

SLQDS EDS 2.02.02.1 0

HQDS EDS 6.12.09.0 0 (ASCE 7-10 § 12.4.3.2)

Basic load combinations

(ASCE 7-10 § 12.4.2.3)

HQDS EDS 6.12.09.0

SLQDS EDS 2.02.02.1

Orthogonal load combinations

Only required for structures assigned to SDC C through F and having nonparallel systems or plan irregularity type 5.

….but common practice considers orthogonal combination (100%/30%) for all diaphragm and collector design.

7. Design Guidance

Load and resistance factors7. Design Guidance

Resistance (strength reduction) factor for shear

(ACI 318-08 § 9.3.4)

= 0.6 unless diaphragm nominal shear strength exceeds shear corresponding to diaphragm nominal flexural strength.

and

≤ minimum value of for shear used for shear wall or frame design.

= 0.6 for diaphragm shear

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Bonded tendons OK up to 60,000 psi

Unbonded, unstressed tendons not permitted.

Tension chordsdMTC uuu

9.0 ;1

y

us f

TA

Typically placed in middle third of slab or beam thickness.

7. Design Guidance

Placement in beams of special moment frames…100%/30% ruleeffect on Mpr

Tension chordsPre-compression from unbonded tendons.

• Prestressing proportioned to resist 1.2D + 1.6Lred

• Seismic load combination is 1.2D + f1Lred + E.

• Typically, this leaves some pre-compression available for diaphragm flexure, specifically, the percentage is

1006.1

2.12.11 1

redred LDLD

f

7. Design Guidance

• This can resist a moment of M = fpcSm.

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Concentrated vs distributed tension chord reinforcement

7. Design Guidance

vu

Vu

(a) Plan

M

V


Mu

Vu

compression chord

tension chord

wall

diaphragm


MuCu

Tu

d

Concentrated vs distributed chord reinforcement

7. Design Guidance

(a) Plan

M

V


Mu

Vu


MuCu

Tu

d

vu,max > vu,avg

Vu

• Concentrate chord reinforcement within 0.25h.

• Design for vu,avg.

h

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Compression chords7. Design Guidance

Compression chord

Diaphragm Wall

Diaphragmopening

Section A-A

Fx or Fpx

7. Design Guidance

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Diaphragm shear strength7. Design Guidance

psi, 2 '

ytccvn ffAV

vu

t

Force transfer between diaphragm and vertical elements

7. Design Guidance

(b) Collectoractions

Tu,max

Cu,max

lab

lbc

lcd

(a) Shear and collector reinforcement

Collector

Collector reinforcement

Shear frictionreinforcement

Shearreinforcement

a

b

c

d

vu

Case A: Collector width = wall width

wall

Load path: Shear-friction reinforcement transfers shear vu to collectors along ab and cd and to wall along bc.

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Force transfer between diaphragm and vertical elements

7. Design Guidance

(b) Collectoractions

Tu,max

Cu,max

lab

lbc

lcd

(a) Shear and collector reinforcement

Collector

Collector reinforcement

Shear frictionreinforcement

Shearreinforcement

a

b

c

d

vu

Case A: Collector width > wall width

wall

beffLoad path: Shear-friction reinforcement transfers

shear vu to collectors along ab, bc, and cd.

Collector transfers force directly to wall ends and also through shear-friction to wall face along bc.

a

d c

b

(b) Tension transfer

Openings adjacent to vertical elements7. Design Guidance

(a) Planbasement wall below

collector/distributor

opening

d c

a b

tie reinforcement

develop in tension

(c) Compression transfer

develop in tension

d c

a b

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Re-entrant corners7. Design Guidance

Plan

wall diaphragm

ld

abc

de

bars ed hooked andlapped with bars bd

Steps and depressions7. Design Guidance

lsp

lsp

eTu

Tu

Mu = Tue

lsp lsp

lsp

eTu

Mu = Tuelsp

eTu

(a) Step

(b) Depression

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Additional requirements• Material properties

• Mechanical splices in collectors must be Type II.• Inspection

• Special inspection required.• Bracing columns to diaphragms

• Inclined columns• Bracing for other columns (nominal reinforcement sufficient, except

possibly for very tall buildings)• Effect of collector reinforcement and axial force on special

moment frame beams• Mpr

• detailing• Collector yielding at connections with walls due to wall rotation

8. Additional Requirements

Diaphragm reinforcement

• Most slabs have continuous bottom mat. Consider incorporating shear reinforcement into this mat. Construction documents should specify lap splice and development lengths as required.

• Careful coordination with PT reinforced generally required.

8. Detailing & Constructability Issues

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Collector and chord detailing

• Commonly located in middle third of slab depth.

• In SDC D, E, and F, • center to center spacing = 3db , ≥ 1.5 in.

• clear cover = 2.5db , ≥ 2 in.

• Otherwise, transverse reinforcement required.

• Study connections and intersections carefully


Collector and chord detailing

• Watch those big and long collectors


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Shear transfer

• Especially study locations where vertical elements have been cast before diaphragm concrete.


h

Construction jointw/ shear keys

Mechanical splice

PT anchor

PT tendons

Rebar

h

Conduits and embedded services

• Embedded conduit

• Nonstructural items


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