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8/2/2011
1
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
3. Diaphragm Components
Distributor (a collector in reverse)
distributor
basement wall
Cu
Tu
diaphragm
3. Diaphragm Components
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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.
4. Diaphragm Behavior and Design Principles5. Building Analysis Guidance
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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.
4. Diaphragm Behavior and Design Principles5. Building Analysis Guidance
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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
(b) Simple beam idealization
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
(b) Simple beam idealization
6. Diaphragm Analysis Guidance
Diaphragm models:Corrected equivalent beam model
RC , kC
RA , kA RB , kB
RD , kD
(a) Plan
RA
M
V
RB
(b) Simple beam idealization
Fx, Fpx
C.R.
ei
ex
x
y
6. Diaphragm Analysis Guidance
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Diaphragm models:Finite element model
CollectorWall
6. Diaphragm Analysis Guidance
Idealized diaphragm load paths:
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
dMTC uuu
h
6. Diaphragm Analysis Guidance
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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
6. Diaphragm Analysis Guidance
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
6. Diaphragm Analysis Guidance
Idealized diaphragm load paths:openings
L
VB
VT
compression chord
tension chord
wall
T
B
l
R
6. Diaphragm Analysis Guidance
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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
6. Diaphragm Analysis Guidance
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
6. Diaphragm Analysis Guidance
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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
(b) Simple beam idealization
Mu
Vu
compression chord
tension chord
wall
diaphragm
(c) Internal moment and shear resistance
MuCu
Tu
d
Concentrated vs distributed chord reinforcement
7. Design Guidance
(a) Plan
M
V
(b) Simple beam idealization
Mu
Vu
(c) Internal moment and shear resistance
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
8. Detailing & Constructability Issues
Collector and chord detailing
• Watch those big and long collectors
8. Detailing & Constructability Issues
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Shear transfer
• Especially study locations where vertical elements have been cast before diaphragm concrete.
8. Detailing & Constructability Issues
h
Construction jointw/ shear keys
Mechanical splice
PT anchor
PT tendons
Rebar
h
Conduits and embedded services
• Embedded conduit
• Nonstructural items
8. Detailing & Constructability Issues
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