Hollow Core Diaphragm Design PDF

6/17/2020
H OLLOW C ORE D IAPHRAGM D ESIGN

DIAPHRAGM DESIGN BASED ON ASCE 7‐10
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Speaker
Dr. Ned Cleland
President
Blue Ridge Design, Inc.
Winchester, VA
H OLLOW C ORE D IAPHRAGM D ESIGN

DIAPHRAGM DESIGN BASED ON ASCE 7‐10
GENERAL DESIGN CRITERIA

• 2015 IBC (references ASCE 7-10)
• ASCE 7-10 (rigid vs. flexible diaphragms, diaphragm design forces)
• ACI 318-14 (design and detailing) primary. No exceptions to the
design and detailing provisions of this document is made in the IBC
or ASCE 7.
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HOLLOW CORE DIA PHRA G M DESIG N
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ASCE 7-10 12.8.4 HORIZONTAL

DISTRIBUTION OF FORCES
• Rigid diaphragms
• Seismic story shear is to be distributed to vertical elements of
the seismic force-resisting system based on the relative lateral
stiffnesses of those elements
• Flexible diaphragms
• Seismic story shear is to be distributed to vertical elements of
the seismic force-resisting system based on tributary areas
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RIGID VS. FLEXIBLE DIAPHRAGMS

w
Stiffness K K K
Flexible 0.25wL 0.50wL 0.25wL
Rigid 0.33wL 0.33wL 0.33wL
L/2 L/2
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DIAPHRAGM:
RIGID OR FLEXIBLE?
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ASCE 7-10 12.3 FLEXIBLE, RIGID

DIAPHRAGMS
Prescriptive Approach
&
Calculation Approach
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ASCE 7-10 12.3.1.1 DEFINITION FOR

FLEXIBLE DIAPHRAGM (PRESCRIPTIVE)
12.3.1.1 Flexible Diaphragm Condition. Diaphragms
constructed of untopped steel decking or wood
structural panels are permitted to be idealized as
flexible if any of the following conditions exist:
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FLEXIBLE DIAPHRAGM (PRESCRIPTIVE)
12.3.1.1 Flexible Diaphragm Condition.
a. In structures where the vertical elements are steel
braced frames; steel and concrete composite braced
frames; or concrete, masonry, steel, or steel and concrete
composite shear walls.
b. In one- and two-family dwellings.
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DEFINITION FOR FLEXIBLE

DIAPHRAGM (PRESCRIPTIVE)
ASCE 7-10 12.3.1.1 Flexible Diaphragm Condition.
c. In structures of light-frame construction where all of the following
conditions are met:
1. Topping of concrete or similar materials is not placed over wood
structural panel diaphragms except for nonstructural topping no greater
than 1 1/2 in. thick.
2. Each line of vertical elements of the seismic force-resisting system
complies with the allowable story drift of Table 12.12-1.
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DEFINITION FOR RIGID DIAPHRAGM

(PRESCRIPTIVE)
ASCE 7-10 12.3.1.2 Rigid Diaphragm Condition.
Diaphragms of concrete slabs or concrete-filled metal deck with

span-to-depth ratios of 3 or less in structures that have no
horizontal irregularities are permitted to be idealized as rigid.
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Is any of the following true?
1- & 2-family dwelling of light- Vertical elements one of the following:
frame construction •Steel braced frames
Structure of light-frame
•Composite steel and concrete braced frames
construction where conditions in
•Concrete, masonry, steel or composite shear walls
Y Section
12.3.1.1c.1,2 are met
Is diaphragm wood N Y Assume Flexible

START
structural panels or See Next Slide

untopped steel decking? Assume Rigid
N
Y
N Is diaphragm Is span-to-depth ratio ≤ 3 and
• Concrete slab? Y no horizontal irregularities?
• Concrete filled metal deck? PCI.ORG
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FLEXIBLE DIAPHRAGMS (CALCULATION)
ASCE 7-10 12.3.1.3 Calculated Flexible Diaphragm
Condition. Diaphragms … are permitted to be idealized as
flexible where the computed maximum in-plane deflection of
the diaphragm under lateral load is more than two times the
average story drift of adjoining vertical elements of the seismic
force –resisting system of the associated story under equivalent
tributary lateral load as shown in Fig. 12.3-1.
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ASCE 7-10 FIGURE 12.3-1

RIGID VS. FLEXIBLE DIAPHRAGM
Is MDD > 2 (ADVE)?
De
MAXIMUM DIAPHRAGM
SEISMIC LOADING DEFLECTION (MDD)
AVERAGE DRIFT OF
VERTICAL ELEMENT
S (ADVE)
Y N
Assume Flexible Assume Rigid

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ASCE 7-10 12.3.1 Diaphragm Flexibility
The structural analysis shall consider the relative stiffnesses of

diaphragms and the vertical elements of the seismic force-resisting
system. Unless a diaphragm can be idealized as either flexible or rigid in
accordance with Sections 12.3.1.1, 12.3.1.2, or 12.3.1.3, the structural
analysis shall explicitly include consideration of the stiffness of the
diaphragm (i.e., semirigid modeling assumption).
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2015 IBC 1604.4 Analysis.
. . . A diaphragm is rigid for the purpose of distribution of story shear and

torsional moment when the lateral deformation of the diaphragm is less
than or equal to two times the average story drift. Except where
diaphragms are flexible, or are permitted to be analyzed as flexible, Where
required by ASCE 7, provisions shall be made for the increased forces
induced on resisting elements of the structural system resulting from
torsion due to eccentricity between the center of application of the lateral
forces and the center of rigidity of the lateral force-resisting system.
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ASCE 7-10 SECTION 12.10

DIAPHRAGMS, CHORDS AND
COLLECTORS
12.10.1 Diaphragm Design Forces
12.10.2 Collector Elements
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DIAPHRAGM DESIGN FORCES

ASCE 7-10 Eq. 12.10-1
12.10‐1
Where
Fpx = diaphragm design force
Fi = the design force applied at level I
wi = the weight tributary to Level I
wpx = the weight tributary to the diaphragm at Level x
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ASCE 7-10 Eq.12.10-2 – minimum threshold
ASCE 7-10 Eq.12.10-3 – maximum threshold
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DIAPHRAGMS, CHORDS, AND COLLECTORS
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7
Floor Level
6 Fpx
Fx
5
0
0 20 40 60 80 100 120 140 160 180
Force (kips)
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FLOOR ACCELERATIONS FOR DIAPHRAGM

DESIGN: ASCE 7 METHOD
Fj
wj Fj j j
Fpj j
j
SRSS
2 Each mode’s contribution is reduced by R

n
 S a T i  
Fj  i 1
 f w j , j

i
  g R 
and
PGA
0 .2 S D S I e  F p x / w p x  0 .4 S D S I e
but  0 .4 S D S
g
PGA PGA
 0 .5 Ie  Fp x / w p x  Ie
g g
o r 0 .5 I e  A c c e le r a tio n " M a g n ific a tio n "  1 .0 I e PCI.ORG
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FLOOR ACCELERATIONS FOR DIAPHRAGM

DESIGN: ASCE 7 METHOD
5
0 .5 I e  A c c e le r a tio n " M a g n ific a tio n "  1 .0 I e
Northridge Earthquake Data

Northridge earthquake and shaketable test data
RC Frames n  5
?
RC Frames 5< n 10
4 RC Frames 10 < n 20
Floor magnification
Walls 5 < n 10

Walls 10 < n  20
3 Steel Frames n 5
Steel Frames 5 < n 10
Steel Frames 10 < n  20
2
Steel Frames n > 20
Braced Frames n  5
1 Braced Frames 5 < n  10
ASCE 7 Range, Ie =1 Braced Frames 10 < n  20
Braced Frames n > 20
0
0 0.2 0.4 0.6 0.8 1 7-story building
Peak ground acceleration (g) Repaired PCI building
 T h e u p p e r a n d lo w e r lim its in A S C E 7 d o n o t s e e m to b e r a tio n a l

 T h e c o m p u ta tio n o f flo o r a c c le r a tio n s b a s e d o n th e a s s u m p tio n th a t a ll m o d e s
a r e e q u a lly r e d u c e d b y p la s tic ity d o e s n o t s e e m r a tio n a l e ith e r
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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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TRANSFER FORCES
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TRANSFER FORCES
ASCE 7-10 12.10.1.1
Where the diaphragm is required to transfer design seismic force from

the vertical resisting elements above the diaphragm to other vertical
resisting elements below the diaphragm due to offsets in the placement
of the elements or to changes in relative lateral stiffness in the vertical
elements, these forces shall be added to those determined from Eq.
12.10-1.
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TRANSFER FORCES
ASCE 7-10 12.10.1.1
The redundancy factor, ρ, applies to the design of diaphragms in

structures assigned to Seismic Design Category D, E, or F. ……..
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TRANSFER FORCES
ASCE 7-10 12.10.1.1
………For inertial forces calculated

in accordance with Eq. 12.10-1, the
redundancy factor shall equal 1.0.
For transfer forces, the redundancy
factor, ρ, shall be the same as that
used for the structure.
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TRANSFER FORCES
ASCE 7-10 12.10.1.1 • 12.3.3.4 Increase in Forces
Due to Irregularities for
For structures having horizontal or Seismic Design Categories D
vertical structural irregularities of through F.
the types indicated in Section
12.3.3.4, the requirements of that
section shall also apply.
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TRANSFER FORCES
A horizontal irregularity of Type 4 exists “where there is a
discontinuity in a lateral force-resistance path, such as an out-
of-plane offset of at least one of the vertical elements, as
shown before.
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TRANSFER FORCES
This irregularity points to Section 12.3.3.3 for SDC
B, C, D, E and F and requires “structural elements
supporting discontinuous walls . . . shall be designed
to resist the seismic load effects including
overstrength factor of Section 12.4.3.”
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TRANSFER FORCES
“The connections of such discontinuous walls or
frames to the supporting members shall be
adequate to transmit the forces for which the
discontinuous walls or fames were required to be
designed.”
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TRANSFER FORCES
This situation can happen in a
bearing-wall building with hollow
core floors where walls for the upper
floors are eliminated to create large
open space on the 1st level by
bearing those walls on columns so
that the diaphragm must transfer the
in-plane forces to walls at the ends
of space. This might be a hotel
lobby.
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TRANSFER FORCES
• Does this configuration with a transfer diaphragm constitute
a “structural element supporting discontinuous walls”
(horizontally) and therefore require the application of the
overstrength factor to the transfer force applied to the
diaphragm?
• The commentary says, “Such offsets impose vertical and
lateral load effects on horizontal elements that are difficult to
provide for adequately.”
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TRANSFER FORCES
The commentary to Section 12.3.3.3 states that “The purpose
of requiring elements … that support discontinuous walls or
frames to be designed to resist seismic load effects including
overstrength is to protect the gravity load-carrying system
against possible overloads caused by overstrength of the
seismic force-resisting system.”
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TRANSFER FORCES
This section does not address loads for the
diaphragm. The transfer force becomes a collector
force subject only to the overstrength factor for SDC
C, D, E and F
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SEISMIC LOAD EFFECTS INCLUDING

OVERSTRENGTH FACTOR
A: Collector Elements 12.10.2.1 (SDC C-F)
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SEISMIC LOAD EFFECTS INCLUDING

OVERSTRENGTH FACTOR
A:
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ASCE 7-10 SECTION 12.10.2.1

DESIGN OF COLLECTOR ELEMENTS
Ω0QE : QE calculated using V
Collector Governing
from Section 12.8 or 12.9
Design Force
QE calculated
MAXIMUM Ω0QE : QE calculated using Fpx NEED NOT using Fpx,max
OF from Eq. (12.10‐1) EXCEED from Eq. (12.10‐
3)
QE : QE calculated using Fpx,min
from Eq. (12.10‐2)
In addition, transfer forces as described in Section 12.10.1.1, if present, need to be

considered
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CONCRETE DIAPHRAGMS –
ACI 318-14 PROVISIONS
A reinforced concrete slab acting as a structural diaphragm
must satisfy all applicable ACI 318 requirements for a one-way
or a two-way non-prestressed or prestressed slab as well as
all applicable requirements of the new Chapter 12,
Diaphragms.
If diaphragm is part of a building assigned to SDC D, E, or F, it

must also satisfy all applicable requirements of 18.12.
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DIAPHRAGMS
One‐Way Slabs Acting as Diaphragms
Minimum Non‐prestressed: 7.3.1
thickness
Prestressed: 24.2
Calculated deflections within limits
Shrinkage and Non‐prestressed: 24.4.1, 24.4.3.1
temperature Normal to flexural reinforcement.
reinforcement For Gr. 60 reinforcement: 0.0018Ag
Spacing ≤ min. {5h, 18 in.}
Prestressed: 24.4.4.1,7.6.4.2
Continue to Next Slide
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DIAPHRAGMS
One‐Way Slabs Acting as Diaphragms
Non‐prestressed: 7.7.2.3, 7.6.1.1
Flexural
As, min: as given by 7.6.1.1
reinforcement
Prestressed: 21.2.2, 7.6.2.1, 24.3
Crack control Non‐prestressed: 24.3.2, 24.3.3
Prestressed: 7.6.2.3
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DIAPHRAGMS
Two-Way Slabs Acting as Diaphragms
Minimum thickness Non-prestressed: 8.3.1
Prestressed: 24.2
Calculated deflections within limits
Shrinkage and 24.4 does not apply, EXCEPT that it is required by

temperature 8.6.1.1
reinforcement

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DIAPHRAGMS
Two-Way Slabs Acting as Diaphragms
Flexural Non-prestressed:
reinforcement 7.7.2.3
8.6, 8.7, 8.5.2.2
Area of reinforcement in each direction ≥ that given by 8.6.1.1
Spacing at critical sections ≤ 2h
Other details including 8.7.4
Note: important structural integrity requirements, 8.7.4.2.1, 8.7.4.2.2
Prestressed: 21.2.2, 8.6.2.2, 8.6.2.3
Crack control Prestressed: 8.6.2.3, 8.7.5.3
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DIAPHRAGMS IN BUILDINGS ASSIGNED TO

SDC D, E, OR F 18.12 Structural Diaphragms and Trusses
18.12.1 Scope
Refers to legally adopted general

28.12.2 Design forces
building code
18.12.3 Seismic load path
18.12.4 Cast-in-place composite-topping slab diaphragms
18.12.5 Cast-in-place topping slab diaphragms

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SDC D, E, OR F
18.12 Structural Diaphragms and Trusses
18.12.6 Minimum thickness of 2 in. for concrete slabs and

diaphragms composite topping slabs serving as
structural diaphragms.
Min. reinforcement ratio shall comply 2-½ in. for topping slabs acting as
with 24.4 structural diaphragms without relying
Except for P/T slabs, reinforcement on composite action.
spacing in each way ≤ 18 in. 18.12.7 Reinforcement
Other requirements including
important ones for collector
elements. Nonlinear strain distribution
18.12.8 Flexural strength requirement of 22.2.1.2 does not
apply.
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SDC D, E, OR F
18.12 Structural Diaphragms and Trusses
18.12.9.1: Vn of structural
18.12.9 Shear strength diaphragms.
18.12.9.2: Upper limit on Vn of
structural diaphragms.
18.12.9.3, 18.12.9.4 : Vn Above joints
Refers to 26.5.6 Construction, between precast elements in
contraction, and isolation joints and noncomposite and composite cast-
18.12.10 Construction joints
Table 22.9.4.2 condition (b) in-place topping slab diaphragms
requirements for clean interface, free (shear-friction-strength).
of laitance, intentionally roughened.
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18.12 - DIAPHRAGMS
Complete rewrite in ACI 318-08. Key technical
changes…
• 18.12.3: Identify seismic load path
• 18.12.8: Flexural design generalized
• 18.12.9.1: Shear strength of topping slab
diaphragms
• 18.12.9.3: Shear friction reinforcement over joints
in precast elements
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18.12– STRUCTURAL DIAPHRAGMS &

TRUSSES 18.12.1– SCOPE
• Floor and roof slabs acting as
structural diaphragms
• Structures assigned to SDC D, E,
or F
• Collector elements and trusses
forming part of the seismic force-
resisting system
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18.12.2 – DESIGN FORCES

• Obtained from legally adopted general building code
• For collector elements, earthquake forces amplified
by Ω0
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18.12.3.1 – SEISMIC LOAD PATH

All diaphragms and their connections shall be proportioned
and detailed to provide for a complete transfer of forces to
collector elements and to the vertical elements of the seismic
force-resisting system.
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18.12.3.2 – SEISMIC LOAD PATH

Elements of a structural diaphragm system that are subjected
primarily to axial forces and used to transfer diaphragm shear or
flexural forces around openings or other discontinuities, shall
comply with the requirements for collectors in 21.11.7.5 and
21.11.7.6.
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18.12.4 – CIP COMPOSITE-TOPPING

SLAB DIAPHRAGMS
18.12.4 — Cast-in-place composite-
topping slab diaphragms . . . the
topping slab is reinforced and the
surface of the previously hardened
concrete on which the topping slab is
placed is clean, free of laitance, and
intentionally roughened.
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18.12.4 – CIP COMPOSITE-TOPPING

SLAB DIAPHRAGMS
Although Table 12.9.4.2 requires joint roughness for shear friction to
be to an amplitude of ¼ in., the amplitude of “intentional roughness” is
not defined in 18.12.4.1 that governs cast-in-place composite topping
slabs.
Les Martin used to say that the intent was originally “not intentionally
made smooth” when arguing that machine-cast hollow core would
provide sufficient roughness for composite behavior. This issue has
been the subject of a number of research studies.
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18.12.5 – CIP TOPPING SLAB

DIAPHRAGMS
18.12.5 — Cast-in-place topping

slab diaphragms . . . the cast-in-
place topping acting alone is
proportioned and detailed to resist
the design earthquake forces.
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18.12.6 – MINIMUM THICKNESS

REQUIREMENTS
18.12.6 — Minimum thickness of
diaphragms
Concrete slabs and composite topping slabs

serving as structural diaphragms: 2 in.
Topping slabs placed over precast floor or

roof elements, acting as structural
diaphragms and not relying on composite
action with the precast elements: 2-1/2 in.
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24.4, 25.2 – REINFORCING STEEL

REQUIREMENTS
Shrinkage and temperature reinforcement is required in one way slabs perpendicular to the direction of
bending and is the minimum required also in the direction of the span in one-way slabs (7.6.1.1, 7.7.2.3)
and in both directions in two-way slabs (8.6.1.1). Minimum reinforcement ratio is dependent on the grade
of reinforcement used:
Maximum spacing for deformed bars is five times slab thickness not to exceed 18 in.
Specified yield strength, fy, shall be reached in tension
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7.6.4.2, 24.4.4.1, 18.12.7 – REINFORCING

STEEL REQUIREMENTS
• When prestressing tendons are used :
• Minimum compressive stress in concrete will be 100 psi on gross section after losses (24.4.4.1)
• Maximum spacing of tendons is 6 ft (7.6.4.2.1)
• When spacing exceeds 54 in., additional shrinkage and temperature steel shall be provided
between tendons at the slab edge for a distance equal to the tendon spacing (7.6.4.2.2)
• Bonded tendons used as reinforcement to resist collector forces or diaphragm shear or flexural
tension shall not exceed 60 ksi stress due to design earthquake forces (18.12.7.2)
• Type 2 splices are required where mechanical splices transfer diaphragm forces to vertical elements of
the seismic force- resisting system (125% yield strength, 100% tensile strength). (18.12.7.4)
• Collector elements with compressive stresses exceeding 0.2fc′ at any section shall have transverse
reinforcement satisfying 18.10.6.4(e) shear wall boundary element transverse reinforcement] over the
length of the element. The specified transverse reinforcement is permitted to be discontinued at a
section where the calculated compressive stress is less than 0.15fc′ (18.12.7.5)
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18.12.7 – REINFORCING STEEL

REQUIREMENTS
18.12.7.1 — . . . Where welded wire reinforcement is used as the
distributed reinforcement to resist shear in topping slabs placed over
precast floor and roof elements, the wires parallel to the span of the
precast elements shall be spaced not less than 10 in. on center.
Reinforcement provided for shear strength shall be continuous and
shall be distributed uniformly across the shear plane.
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R18.12.7 – REINFORCING STEEL

REQUIREMENTS
R18.12.7.1 — . . . The minimum spacing requirement for welded wire
reinforcement in topping slabs on precast floor systems is to avoid fracture of the
distributed reinforcement during an earthquake.
Cracks in the topping slab open immediately above the joint between the flanges
of adjacent precast members, and the wires crossing those cracks are restrained
by the transverse wires.
Therefore, all the deformation associated with cracking should be accommodated

in a distance not greater than the spacing of the transverse wires.
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REQUIREMENTS
R18.12.7.1 — . . . The minimum spacing requirements do not apply to
diaphragms reinforced with individual bars, because strains are distributed over a
longer length.
7.7.2.3 – Maximum spacing s of deformed reinforcement shall be the lesser of 3h

and 18 in.
24.4.3.3 - The spacing of deformed shrinkage and temperature reinforcement

shall not exceed the lesser of 5h and 18 in.
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REQUIREMENTS
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18.12.7.6 – REINFORCING STEEL

REQUIREMENTS
18.12.7.6 — Longitudinal reinforcement for collector elements at splices and
anchorage zones shall have either:
(a) A minimum center-to-center spacing of three longitudinal bar diameters, but

not less than 1-1/2 in., and a minimum concrete clear cover of two and one-
half longitudinal bar diameters, but not less than 2 in.; or
(b) Transverse reinforcement as required by 9.6.3.3, except as required in

18.12.7.5.
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18.12.7.6 – REINFORCING STEEL

REQUIREMENTS
18.12.7.6 Longitudinal reinforcement detailing for collector elements at
splices and anchorage zones shall satisfy (a) or (b):
(a) Center-to-center spacing of at least three longitudinal bar diameters, but

not less than 1-1/2 in., and concrete clear cover of at least two and one-
half longitudinal bar diameters, but not less than 2 in.
(b) Area of transverse reinforcement, providing Av at least the greater of

0.75√f’c(bws/fyt) and 50bws/fyt, except as required in 18.12.7.5.
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18.12.8 – FLEXURAL STRENGTH
• Flexural Design of Diaphragms Based on Linear Strain

Distribution
• Nonlinear Strain Distribution can be Ignored
• Effect of Openings to be Considered
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18.12.9.1 – SHEAR STRENGTH

For cast in place slabs, nominal shear strength Vn shall not exceed:
Vn = ACV(2l√f’c + ρtfy) ACI Equation 18.12.9.1
ACV is the thickness times the length of the diaphragm and

corresponds to the gross area of the effective deep beam that forms
the diaphragm.
The reinforcement should be placed perpendicular to the span of the

diaphragm.
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18.12.9.1 – SHEAR STRENGTH

For cast-in-place topping slab diaphragms on precast floor or roof
members, Acv shall be computed using the thickness of topping slab
only for noncomposite topping slab diaphragms and the combined
thickness of cast-in-place and precast elements for composite topping
slab diaphragms.
For composite topping slab
diaphragms, the value of fc′ used
to determine Vn shall not exceed the
smaller of fc′ for the precast members
and fc′ for the topping slab.
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SHEAR STRENGTH
Starting with ACI 318-99 and continued in ACI 318-14: For cast in place
topping slabs, both composite and non-composite, placed on precast
concrete elements, the nominal shear strength Vn shall not exceed:
Vn = AVffy  ACI Equation 18.12.9.3
Neglects the contribution of the concrete due to construction practice
causing shrinkage cracks under service loads.
In addition, nominal shear strength shall not exceed 8ACV√f’c (not given an
ACI equation number)
PCI.ORG
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SHEAR STRENGTH
Avf is total area of shear friction reinforcement within topping slab,

including both distributed and boundary reinforcement, that is oriented
perpendicular to joints in the precast system and coefficient of friction,
μ, is 1.0λ. At least one half of Avf is required to be uniformly distributed
along the length of the potential shear plane. Area of distributed
reinforcement in topping slab needs to satisfy 7.6.1.1 in each direction.
PCI.ORG
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SHEAR STRENGTH
• The shear strength of the chord reinforcement can be

included in the total shear strength calculation.
• Not more than half can be concentrated at the ends.
• How should shear strength be proportioned between web

and chord?
PCI.ORG
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SHEAR STRENGTH
• If a free-body is cut along a joint, both web and chord

reinforcement cross the plane. As a shear friction
evaluation, all demand on the steel is tension.
• Forces may be distributed to the reinforcement based on

the total area of steel, but the chord reinforcing area may be
much larger because of the required chord tension.
PCI.ORG
76
SHEAR STRENGTH
• How much of the tension strength must be discounted
because it is assigned for shear resistance?
• Is the limit based on the proportional area, or based on the

limit imposed that half must be carried by the web
reinforcement?
• The contribution of chord reinforcement to shear strength is

not limited by its primary chord tension demand.
PCI.ORG
77
HOLLOW CORE SLAB SYSTEMS
PCI.ORG
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PCI.ORG
79
DIAPHRAGM ACTION WITH HOLLOW

CORE SLABS
• Lateral force-resisting distribution
• Structural integrity
• Elements of Diaphragm
• Longitudinal Joints
• Transverse Joints
• Boundary elements
• Topped vs. Untopped
PCI.ORG
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LATERAL FORCE-RESISTING
DISTRIBUTION
• Rigid Diaphragms
• Flexible Diaphragms
PCI.ORG
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LATERAL FORCE-RESISTING
DISTRIBUTION
PCI.ORG
82
STRUCTURAL INTEGRITY
• Minimum tie forces
• Minimum wall bracing forces
PCI.ORG
83
STRUCTURAL INTEGRITY
PCI.ORG
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ELEMENTS OF A DIAPHRAGM
• Boundary Element
• Chord
• Collector or Drag Strut
• Longitudinal Joint
• Transverse Joint
PCI.ORG
85
PCI.ORG
86
LONGITUDINAL JOINTS
• Grouted shear keys

• Vertical load transfer
• Horizontal shear transfer
• Grouted reinforcement for ties
PCI.ORG
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LONGITUDINAL JOINTS
The grouted keyways between slabs do have the capacity to transfer
longitudinal shear from one slab to the next.
Using a shear stress of 80 psi, the useable (design) strength for

longitudinal shear is: φVn = φ(0.08)hnet Lj φ =0.75
When the grout strength is exceeded or ductile behavior is required, shear

friction principles may be used to design reinforcement to be placed per-
pendicular to the longitudinal joints. This reinforcement may be placed in the
transverse joints at the slab ends rather than being distributed along the
length of the joints.
PCI.ORG
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LONGITUDINAL JOINTS
PCI.ORG
89
TRANSVERSE JOINTS
• Reinforcement in the transverse joints may provide the shear friction
reinforcement for shear in the longitudinal joints.
• The transverse joint may also have to act as part of a drag strut with
axial tension or compression to carry diaphragm loads to the lateral
force-resisting elements.
• A transverse joint may also be part of the chord member where
flexural tension is resisted.
• An interior transverse joint disrupts the web of the horizontal beam
where horizontal shear would have to be transferred to maintain the
full effective depth of the diaphragm.
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TRANSVERSE JOINTS
• Chord tension is resisted by reinforcement that provides flexural
strength to the diaphragm.
• It is suggested that the effective depth of the reinforcement from the
compression edge of the diaphragm be limited to 0.8 times the depth
of the diaphragm.
• Because diaphragms tend to act as tied arches rather than beams,
tension in the chord reinforcement does not go to zero at the ends of
the diaphragm. The chord reinforcement must be anchored at the
ends of the diaphragm where standard hooks at the ends of the
chords will suffice.
PCI.ORG
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BOUNDARY JOINTS
• For anchorage at a transverse boundary element, the bars may be grouted into the
keyways or into hollow core slab cores where the top of the core is cut away.
Concrete is then used to fill the cores for the length of the bar embedment.
• It is not clear when anchorage of the connector bars in keyways is sufficient and
when the connector bars should be placed in hollow core slab cores. There is a
concern that as the boundary element and keyway crack, anchorage for a connector
bar in a keyway may be lost.
• Deformations and reversible loading in a seismic event would suggest that anchoring
connector bars in hollow core slab cores would be preferable in more intense seismic
situations. In keeping with code philosophy, it is suggested that bars be anchored in
hollow core slab cores in structures assigned to SDC C and higher.
PCI.ORG
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BOUNDARY JOINTS
• Edge member
• Chord
• Collector
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TOPPED VS. UNTOPPED

• When a composite structural topping is provided, it should have a minimum thickness of 2 in.
to 2 ½ in.
• The topping can be designed as a non-composite diaphragm without consideration of the
hollow core slabs.
• When the topping provides the strength and the stiffness for the diaphragm but the
connections are made in the hollow core slabs, shear stresses will be present at the interface
of the topping and the hollow core slabs. These stresses will generally be well distributed
throughout the interface, but may be more highly localized near the connections.
• The primary benefits of a composite structural topping are to increase stiffness and to allow
easier continuous ties in plans with irregular shapes or large openings. However, in seismic
areas, the additional topping weight increases the seismic design forces. Topped diaphragms
may be a necessity in buildings assigned to high SDC, and with plan irregularities or large
diaphragm span-to-depth ratios.
• Untopped hollow core slab diaphragms may be sufficient when the diaphragm force system is
straightforward and the in-plane diaphragm deflections are acceptable.
PCI.ORG
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TOPPED HOLLOW CORE
• 18.12.4 cast-in-place composite topping slab

diaphragms
• 18.12.5 cast-in-place non-composite diaphragms
PCI.ORG
95
COMPOSITE TOPPING DIAPHRAGM

• Composite design for gravity loads
• Effects of camber
• Topping thickness at ends and at midspan
• Topping following camber
• Control joints
• Bond of topping to hollow core
• 80 psi limit (Table 16.4.4.2, both intentionally roughened and
not intentionally roughened)
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HOLLOW CORE DIAPHRAGM DESIGN

EXAMPLE
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BUILDING DATA
• 6 stories without parapet
• Risk Category II
• 14 ft floor-to-floor
• Dead Loads
• Weight of 8-in. hollow core slabs = 53.5 psf
• Weight of partitions and mechanical equipment = 20 psf
• Weight of precast concrete framing system = 32 psf
• Weight of exterior wall system (average) = 35 psf
PCI.ORG
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WIND DESIGN PER ASCE 7-10
• Basic Wind Speed 130 mph
• Building is rigid in both directions
• Roof height h = 84 ft
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Table 4.9.1 Calculation of velocity pressures, qz, along height of building

PCI.ORG
100
Table 4.9.2 Wind forces in the North-South and East-West directions
PCI.ORG
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WIND FORCES
ALONG STORY
HEIGHT
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RIGID DIAPHRAGM DISTRIBUTION

TO WALLS
• 30 ft end walls – 59.1 kips
• 20 ft center wall – 17.5 kips
• Location of maximum moment @

87.1 ft from left support.
• Maximum moment = 2577 ft-kips

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CHORD FORCES
Using perimeter beams as chords
𝑀
𝑁𝑢
𝜙𝑑
44.7 kips
. .
where d is taken as 0.8 times the depth of the diaphragm
PCI.ORG
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CHORD DESIGN
Connect beams to columns for this force plus forces due to
volume change and gravity loads.
The chord must continue through the center wall.
𝑁 44.7
𝐴 0.75 in.
𝑓 60
Use 2- #6 bars
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CONNECTION OF DIAPHRAGM WEB TO

CHORDS
Chord tension transferred to diaphragm web in shear
𝑀 2577
𝑉 40.3 kips
𝑑 0.8 80
Distribute over length from zero moment to maximum moment
40.3
𝑉 0.46 kip/ft
87.1
Negative wind pressure connection: pressure & suction
381 lb/ft
PCI.ORG
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TRANSVERSE JOINT FORCES
• Shear friction for the shear with bars placed in keyways

perpendicular to the transverse joint
• With keyways at 3 ft on center:
𝑁 𝑉 3 0.381 3 0.46
𝐴
𝜙𝑓 𝜙𝑓 𝜇 0.9 60 0.75 60 1.4
0.043 in. /keyway
PCI.ORG
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LONGITUDINAL SHEAR (PARALLEL TO

LONGITUDINAL JOINTS)
Maximum longitudinal joint shear is at the first joint from the 30 ft shear wall
Center bay connections made directly to shear walls – center bay joint length only
𝑉 59.1 kip
𝜙𝑉 𝜙 0.08 ℎ 𝑙 0.75 0.08 8 2 20 12 86.4 kip
Transverse shear-friction reinforcement in transverse joints at ends

𝑉 59.1
𝐴 1.3 in. / 2 transverse joints
𝜙𝑓 𝜇 0.75 60 1.0
1 #8 bar in each transverse joint
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SHEAR CONNECTION TO 30-FT WALL

Shear-friction reinforcement for Vu30 = 1.3 in.2
Negative wind pressure not concurrent with shear
Structural integrity ties will control out-of-plane force
𝑁 0.3 20 6 kip for bay

𝑁 6
𝐴 0.11 in.
𝜙𝑓 0.9 60
Use six (6) #5 bars near hollow core slab ends

PCI.ORG
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SHEAR AT CENTER 20-FT WALL
𝑉 8.75 kips on each side of wall

𝑉 8.75
𝐴 0.19 in. 2
𝜙𝑓 𝜇 0.75 60 1.0
Use two #3 bars located near hollow core slab ends or use mechanical
connections
PCI.ORG
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LOAD APPLIED PERPENDICULAR TO

HOLLOW CORE SPANS (EW DIRECTION)
• The maximum load in the EW wind direction occurs at floor level 5
(from Table 4.9.2): F5 = 45.7 kips
• The corresponding uniformly distributed wind load is: W = 45.7/80 =

0.571 kip/ft
• Shear distribution to 30-ft walls is: V30 = 45.7/2 = 22.9 kips
• Maximum moment = 0.571 (80)2 /8 = 457 ft-kips

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CHORD FORCES
𝑁 3.2 kips, where d is 0.8 times diaphragm depth

. .
𝑁 3.2
𝐴 0.053 in.
𝑓 60
#3 bars across transverse joints are adequate for chord force
PCI.ORG
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LONGITUDINAL SHEAR (SHEAR

PARALLEL TO LONGITUDINAL
JOINTS)
• Vuh = Mu / d where d is taken as 0.8 times the diaphragm depth
2.9 kips
.
will not control when compared to 59.1 kips applied in the NS direction
PCI.ORG
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SHEAR CONNECTION TO WALLS
• Using shear friction reinforcement: Vu = 22.9 kips/30-ft wall = 0.76 kip/ft
• With bars in keyways at 3 ft on center:
.
𝐴 0.036 in. per keyway
. .
Use a #3 bar in every other keyway
PCI.ORG
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SHEAR IN TRANSVERSE JOINT
𝑉 22.9 0.571 30 5.77 kips
𝑉 5.77
𝐴 0.13 in.
𝜙𝑓 𝜇 0.75 60 1.0
A #3 bar at every second keyway will be adequate
PCI.ORG
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PCI.ORG
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PCI.ORG
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SDC B SEISMIC DESIGN
• For seismic design, it is assumed that the building, with zip code
02110, is located in Boston, Mass.
• Risk category: II
• Importance factor: Ie = 1.0
• Site class: D
• Seismic design category: The mapped spectral accelerations at
this site (based on its latitude and longitude or postal address),
corresponding to 0.2-second and 1-second periods, are: Ss =
0.217g and S1 = 0.069g
PCI.ORG
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ACCORDING TO ASCE 7-10 TABLES 11.6-1

AND 11.6-2, THE BUILDING IS ASSIGNED TO
SDC B.
Site coefficients (from ASCE 7-10 Tables 11.4-1 and 11.4-2): Fa = 1.6,
Fv = 2.4
SMS = FaSs = 1.6(0.217g) = 0.35g
SM1 = FvS1 = 2.4(0.069g) = 0.17g
SDS = 𝑆 0.23
SD1 = 𝑆 0.11
PCI.ORG
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SEISMIC WEIGHT
• The building weight attributable to a typical floor is:
• 𝑤𝑖=80(200)[0.0535 (ℎ𝑜𝑙𝑙𝑜𝑤 𝑐𝑜𝑟𝑒)+0.020 (𝑝𝑎𝑟𝑡𝑖𝑡𝑖𝑜𝑛𝑠)+0.032 (𝑝𝑟𝑒𝑐𝑎𝑠𝑡

𝑓𝑟𝑎𝑚𝑖𝑛𝑔)]+14(0.035)(200+80)(2)(𝑒𝑥𝑡𝑒𝑟𝑖𝑜𝑟 𝑤𝑎𝑙𝑙𝑠)=1962 kips
• For the roof:
• 𝑤𝑟𝑜𝑜𝑓=80(200)((0.0535+0.020+0.032)+7(0.035)(200+80)(2)=1825 kips
• The total weight is 𝑊=5(1962)+1825=11,635 kips

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BASE SHEAR
The approximate building period is: 𝑇 𝐶ℎ 0.02(84)0.75 = 0.55 sec
V = CsW
𝑆 0.23
𝐶 0.046 where 𝑅
𝑅 5.0
𝐼
5 for a building frame system with ordinary reinforced concrete shear walls
.
𝐶 0.040 governs
. .
V = 0.040(11,635) = 465 kips

PCI.ORG
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VERTICAL DISTRIBUTION
𝐹 𝐶 𝑉
𝑤 ℎ
𝐶
∑ 𝑤
𝑘 1.03 𝑓𝑜𝑟 𝑇 0.55 𝑠𝑒𝑐
PCI.ORG
122

∑ 𝐹
𝐹 𝑤
∑ 𝑤
The forces need not exceed

0.4𝑆 𝐼 𝑤 0.4 0.23 1.0 1962 181 kips
(168 kips for the roof diaphragm)
The forces must not be less than

0.2𝑆 𝐼 𝑤 90 kips
Thus, the design lateral force for the roof diaphragm is 𝐹

128 kips
PCI.ORG
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SEISMIC FORCE VS. STORY HEIGHT
PCI.ORG
124
MODIFICATIONS IN 7TH EDITION OF PCI

DESIGN HANDBOOK
• In 7th edition of the PCI Design Handbook, low and moderate SDC (B and C) are grouped
together.
• No amplification of the code-specified seismic design force is considered necessary if the

design force at the uppermost level is used for every floor diaphragm.
• Same will apply also to structures assigned to high SDC (D, E, F) if lateral forces are
resisted entirely by special moment frames.
• For SDC D, E, and F structures where shear walls are part of the seismic force-resisting
system, a multiplier of 2 applies to the roof-level diaphragm design force; this amplified
force is then to be kept constant down the height of the building.
PCI.ORG
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DIAPHRAGM DESIGN FORCE ACTING

PARALLEL TO HOLLOW CORE SPANS (NS
DIRECTION)
• The equivalent uniformly distributed lateral load is wu = 128/200 =
0.64 kip/ft
• Using a rigid diaphragm, the shear distribution to the walls is:

30-ft walls: Vu30 = 55.7 kips
20-ft wall: Vu20 = 16.5 kips
PCI.ORG
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DIAPHRAGM EQUILIBRIUM
• Maximum moment at 87.1 ft. from

left
• Maximum moment = 2426 ft-kips
PCI.ORG
127
CHORD FORCES WITH PERIMETER

BOUNDARY ELEMENT
PCI.ORG
128
CONNECTION OF DIAPHRAGM TO WEB

• Take d as 0.8 times the diaphragm depth
𝑉 37.9 kips
.
• Distribute over length from zero moment to maximum moment

.
𝑉 0.44 kip/ft
.
• Additionally, this connection must resist the outward force from the
exterior wall system. Per section 12.11 of ASCE 7-10, the design force
for wall anchorage Nu should be the greater of the following:
0.4𝑆 𝑘 𝐼 𝑤 0.4 0.23 1.0 1.0 0.035 x 14 =0.045 kip/ft
0.2𝑤 0.2 0.035x14 =0.098 kip/ft
PCI.ORG
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At the transverse joint, the same shear parallel to the transverse joint as
at the chord must be transferred. However, the tension should consider
the inertial force from the weight of the exterior bay, which is the largest of
the following:
PCI.ORG
130

PARALLEL TO LONGITUDINAL JOINTS)
• The maximum longitudinal shear is at the
first joint away from the 30-ft wall.
• Provide shear friction reinforcement in the

two transverse joints and the two boundary
elements for shear resistance.
• Conservatively consider 5% minimum

eccentricity being resisted only by end walls.
PCI.ORG
131

• Note that in the seismic calculation, this shear friction reinforcement was distributed over
four joints as opposed to two joints in the wind calculation.
• In the seismic detailing, a collector is provided so the shear can be distributed over the full
width of the building and the outside bays are available for the shear transfer. No collector
was used in the wind calculation so this shear had to be resisted in the center bay only.
• Shear friction reinforcement is provided at the outside edges of the outer bays. The chord
reinforcement is also located at the outside edges. It has been considered the practice to
consider these effects as additive since both cause tension in the reinforcement. This may
be conservative.
PCI.ORG
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6/17/2020

• ACI 318-14, Sec. 22.9.4.6 requires the area of reinforcement required to resist a net
tension to be added to the area of reinforcement required for shear friction crossing the
assumed plane.
• The commentary to this section states: “Where moment acts on a shear plane, the flexural
compression and tension forces are in equilibrium and do not change the resultant
compression Avffy acting across the shear plan or the shear-friction resistance”
• Since the chord in the hollow core diaphragm acts more as the tension in a tied arch, it is
conservatively chosen to treat these effects as additive.
PCI.ORG
133

At first joint
𝑀 55.7 3 3 0.64 /2 164 ft-kips In transverse joints,

𝑉 𝑁
𝐴 𝐴 0.35 𝑖𝑛.
𝜙𝑓 𝜇 𝜙𝑓
Use two #5 bars.
164
𝐴 0.35 0.4 𝑖𝑛.
0.9 0.8 80 60
Four #6 bars OK
PCI.ORG
134
LONGITUDINAL SHEAR (SHEAR PARALLEL

TO LONGITUDINAL JOINTS)
Shear connection to 30-ft wall:
Transfer shear to wall and collector element
62.1
𝑉 0.78 𝑘𝑖𝑝/𝑓𝑡
80
𝑉
𝐴
𝜙𝑓 𝜇
0.78
𝐴 0.017 𝑖𝑛. /𝑓𝑡
0.75 60 1.0
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Use #4 hairpins at 8 ft on center Special Note: In SDC B,
amplification of the collector design
(Fig. 4.9.3 detail D) force is not required. It is included
here only to demonstrate the
Collector element reinforcement procedure.
80 30 𝑁 Ω 𝑁 2.5 19.5 48.8 𝑘𝑖𝑝𝑠

𝑁 0.78 19.5 𝑘𝑖𝑝𝑠
2
48.8
𝐴 0.9 𝑖𝑛.
0.9 60
Use two #7 bars

PCI.ORG
136

Shear connection at 20-ft wall
𝑉 8.3 𝑘𝑖𝑝𝑠
0.104
𝐴 0.002 𝑖𝑛. /𝑓𝑡
over building width 0.75 60 1.0
8.3 Use #4 bars at 8 ft on center.

𝑉 0.104 𝑘𝑖𝑝 /𝑓𝑡
80
𝑉
𝐴
𝜙𝑓 𝜇
PCI.ORG
137

Collector element reinforcement
80 20
𝑁 0.104 2 6.2 𝑘𝑖𝑝𝑠
2
𝑁 Ω 𝑁 2.5 6.2 15.5 𝑘𝑖𝑝𝑠
15.5
𝐴 0.29 𝑖𝑛.
0.9 60
Use #4 bars (Fig. 4.9.3 detail E)

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CALCULATION OF DIAPHRAGM
DEFLECTION
• Idealize diaphragm section as a transformed section
• Solve for the neutral axis depth
• Calculate Icr about the neutral axis
• For a rigid diaphragm, deflection can be calculated as uniform

load deflection between end walls less the effect of the center wall
as a concentrated force.
PCI.ORG
139
DIAPHRAGM DESIGN FORCE ACTING

PERPENDICULAR TO HOLLOW CORE SLABS
(EW DIRECTION)
• Equivalent uniformly distributed lateral load is 1.6 kips/ft

• Moment = 1280 ft-kips
• Chord force Mu/ϕd = 1280/(0.9)(0.8)(200) = 8.9 kips
• As = 8.9/60 = 0.15 in.2
The #3 bars across transverse joints at 3 ft. on center are adequate.
PCI.ORG
140
ADDITIONAL DETAILS
• Longitudinal shear will not control because it is much smaller than the
longitudinal shear caused by the diaphragm design force acting in the
orthogonal direction
• Shear connection to walls with 5% eccentricity = 0.35 kip/ft. #3 bars at 3 ft

on center in grouted key is adequate.
• Collector reinforcement: N = (200-30)(0.35)/2 = 29.8 kips

Nu = ΩoN = 2.5(29.8) = 74.5 kips
As = 74.5/(0.9)(60) = 1.38 in.2 > (4) #4 bars
Use (4) #6 bars

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SHEAR IN TRANSVERSE JOINT

• Shear force resisted by one EW wall considering 5% eccentricity = 70.4 kips.
• Shear force at transverse joint = 70.4-1.6(30) = 22.4 kips
• In center bay, wp = 200(0.0535+0202+0.032) + 14 (0.035)(2) = 22.1 kip/ft
• Use the largest of:
• 0.4SDSkaIewp =0.4(0.23)(1.0)(1.0)(22.1) = 2.0 kips/ft
• 20% of wp = 0.2(22.1) = 4.4 kips/ft (controls)
• Vu = 4.4(20)(0.55) = 48.4 kips per transverse joint = 48.4/200 = 0.24 kip/ft
shear
• Controlled by NS direction parallel to hollow core slabs at 0.44 kip/ft
PCI.ORG
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PCI.ORG
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THANK YO U !
145
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6/17/2020

H OLLOW C ORE D IAPHRAGM D ESIGN

• AIA HSW Credit ( 1.0 LU)

The Precast/Prestressed Concrete Institute (PCI) is a

H OLLOW C ORE D IAPHRAGM D ESIGN

GENERAL DESIGN CRITERIA

ASCE 7-10 12.8.4 HORIZONTAL

RIGID VS. FLEXIBLE DIAPHRAGMS

Flexible 0.25wL 0.50wL 0.25wL

Rigid 0.33wL 0.33wL 0.33wL

ASCE 7-10 12.3 FLEXIBLE, RIGID

ASCE 7-10 12.3.1.1 DEFINITION FOR

ASCE 7-10 12.3.1.1 DEFINITION FOR

DEFINITION FOR FLEXIBLE

DEFINITION FOR RIGID DIAPHRAGM

Diaphragms of concrete slabs or concrete-filled metal deck with

RIGID VS. FLEXIBLE DIAPHRAGMS

Is diaphragm wood N Y Assume Flexible

structural panels or See Next Slide

ASCE 7-10 12.3.1.3 DEFINITION FOR

ASCE 7-10 FIGURE 12.3-1

Assume Flexible Assume Rigid

RIGID VS. FLEXIBLE DIAPHRAGMS

The structural analysis shall consider the relative stiffnesses of

RIGID VS. FLEXIBLE DIAPHRAGMS

. . . A diaphragm is rigid for the purpose of distribution of story shear and

ASCE 7-10 SECTION 12.10

12.10.1 Diaphragm Design Forces

12.10.2 Collector Elements

DIAPHRAGM DESIGN FORCES

DIAPHRAGM DESIGN FORCES

ASCE 7-10 Eq.12.10-3 – maximum threshold

DIAPHRAGMS, CHORDS, AND COLLECTORS

DIAPHRAGM DESIGN FORCES

FLOOR ACCELERATIONS FOR DIAPHRAGM

2 Each mode’s contribution is reduced by R

FLOOR ACCELERATIONS FOR DIAPHRAGM

Northridge Earthquake Data

Walls 5 < n 10

 T h e u p p e r a n d lo w e r lim its in A S C E 7 d o n o t s e e m to b e r a tio n a l

DIAPHRAGM DESIGN FORCE

For structures assigned to SDC B or C, if every

DIAPHRAGM DESIGN FORCE

For structures assigned to SDC D, E, or F, if lateral

DIAPHRAGM DESIGN FORCE

For structures assigned to SDC D, E, or F, if shear

Where the diaphragm is required to transfer design seismic force from

The redundancy factor, ρ, applies to the design of diaphragms in

………For inertial forces calculated

SEISMIC LOAD EFFECTS INCLUDING

SEISMIC LOAD EFFECTS INCLUDING

ASCE 7-10 SECTION 12.10.2.1

In addition, transfer forces as described in Section 12.10.1.1, if present, need to be

If diaphragm is part of a building assigned to SDC D, E, or F, it

Minimum thickness Non-prestressed: 8.3.1

Shrinkage and 24.4 does not apply, EXCEPT that it is required by

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Prestressed: 21.2.2, 8.6.2.2, 8.6.2.3