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Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 1
Seismic Design of Precast
Concrete Structures
S. K. Ghosh
S. K. Ghosh Associates Inc.
Palatine, IL and Aliso Viejo, CA
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 2
2015 NEHRP Provisions
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 3
Two Diaphragm-Related
Developments
FEMA P-1050, the 2015 NEHRP Provisions
includes two significant new items related to the
seismic design of precast diaphragms.
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 4
Two Aspects to Seismic Design
Seismic design is an exercise in tradeoff
between
Strength and
Inelastic deformability
Inelastic deformability is directly related to
design and detailing
Inelastic Required
Deformability Strength
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 5
New Items in the 2015 NEHRP
Provisions
Design Force Level Provision in Part 1 – modifies
ASCE 7-10 Section 12.10 Section 12.10.3 in ASCE
7-16
Design Force Level Provision in Part 3 – modifies
ASCE 7-10 Section 12.10
Precast Diaphragm Design Provision in Part 1 –
modifies ASCE 7-10 Section 14.2.4 Section 14.2.4
in ASCE 7-16
Resource Paper in Part 3
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 6
Alternative ASCE 7-16 Force Level
for Seismic Design of Diaphragms
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 7
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
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 8
Diaphragm Design Forces
0
1
2
3
4
5
6
7
0 50 100 150 200
Fpx
Fx
Force (kips)
Flo
or
Lev
el
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 9 p. 9 of Set 8
Each mode’s contribution is reduced by R
2
1
,n
i
j j j
i
F f w
a iS T
g R
Fj
j
j
j j
ASCE 7 Method
Fj wj
j Fpj
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
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 10
0
1
2
3
4
5
0 0.2 0.4 0.6 0.8 1
Peak ground acceleration (g)
Flo
or
mag
nif
icati
on
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. 10 of Set 8
? Floor Accelerations for Diaphragm Design
ASCE 7 Method
ASCE 7 Range, Ie =1
05 Acceleration "Magnification" 10e 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
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 11
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.
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 12
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
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 13
Diaphragm Design
2015 NEHRP
Provisions
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 14
Diaphragm Design
ASCE 7-16
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 15
Diaphragm Design
Cp0 = 0.4 SDS Ie
Cpn= m10CS2
+ m2CS22
≥ Cpi
Note: The lower-bound limit on Cpn is in ASCE
7-16 only, not in the 2015 NEHRP Provisions.
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 16
Diaphragm Design
• m1 = 1 + 0.5zS (1 – 1/N)
• m2 = 0.9zS (1 – 1/N) 2
where zS = modal contribution coefficient
modifier dependent on seismic force-resisting
system.
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 17
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
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 18
Diaphragm Design
1.0
1.1
1.2
1.3
1.4
1.5
1.6
0 5 10 15 20 25
Γm1
Number of levels, ne
Eq. 3.1 zs = 1
Eq. 3.1 zs = 0.7
Wall buildings
Frame buildings
Number of levels, n
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 19
Diaphragm Design
0.0
0.2
0.4
0.6
0.8
1.0
0 5 10 15 20 25
Γm2
Number of levels, ne
Eq. 3.1 zs = 1
Eq. 3.1 zs = 0.7
Wall buildings
Frame buildings
Number of levels, n
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 20
Diaphragm Design
Cpi is the greater of values given by:
Cpi = 0.8Cp0
Cpi = 0.9 m10CS
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 21
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
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 22
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
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 23
Diaphragm Capacity
Why have we not been seeing inadequate
performance of diaphragms in seismic events?
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 24
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,
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 25
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.
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 26
Diaphragm Force Reduction
Factor, Rs
Elastic diaphragm design force level divided by
a diaphragm force reduction factor, Rs, to
account for overstrength, ductility, or both.
Reduction factors are different for flexure-
controlled and shear-controlled diaphragms.
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 27
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.
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 28
Diaphragm Design
Shear-controlled diaphragm: Diaphragm
that does not meet the requirements of a
flexure-controlled diaphragm.
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 29
Diaphragm Design (NEHRP
Provisions)
Diaphragm System Shear Control Flexure Control
CIP Concrete 1.5 2
Precast concrete
EDO 1.0 0.7
BDO 1.0 1.0
RDO 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.
px
px px
s
CF = w
R
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 30
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.
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 31
Transfer Diaphragms
ASCE 7-10 Section 12.10.1.1, 4th paragraph
Where the diaphragm is required to transfer design seismic
forces 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 changes in relative
lateral stiffness in the vertical elements, these forces shall be
added to those determined from Eq. 12.10-1. The redundancy
factor, ρ, applies to the design of diaphragms in structures
assigned to Seismic Design Category D, E, or F. 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.
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 32
Transfer Diaphragms
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 33
Transfer Diaphragms
ASCE 7-16 Section 12.10.1.1, 4th paragraph
All diaphragms shall be designed for the inertial forces
determined from Eq. 12.10-1 through 12.10-3 and for all
applicable transfer forces. For structures having a horizontal
structural irregularity of Type 4 in Table 12.3-1, the transfer
forces from the vertical seismic force-resisting elements above
the diaphragm to other vertical seismic force-resisting elements
below the diaphragm shall be increased by the overstrength
factor of Section 12.4.3 prior to being added to the diaphragm
inertial forces. For structures having other horizontal or vertical
structural irregularities of the types indicated in Section 12.3.3.4,
the requirements of that section shall apply.
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 34
Transfer Diaphragms
12.10.3.3 Transfer Forces in Diaphragms
All diaphragms shall be designed for the inertial forces
determined from Eq. 12.10.3-1 and 12.10.3-2 and for all
applicable transfer forces. For structures having a horizontal
structural irregularity of Type 4 in Table 12.3-1, the transfer
forces from the vertical seismic force-resisting elements above
the diaphragm to other vertical seismic force-resisting elements
below the diaphragm shall be increased by the overstrength
factor of Section 12.4.3 prior to being added to the diaphragm
inertial forces. For structures having other horizontal or vertical
structural irregularities of the types indicated in Section 12.3.3.4,
the requirements of that section shall apply.
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 35
Transfer Diaphragms
ASCE 7-16 Section 12.10.1.1, 4th paragraph
ASCE 7-16 Section 12.10.3.3,
Exception: One- and two-family dwellings of light
frame construction shall be permitted to use Ω0 = 1.0.
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 36
Collectors
12.10.3.4 Collectors - Seismic Design Categories C
through F
In structures assigned to Seismic Design Category C, D, E, or
F, collectors and their connections including connections to
vertical elements shall be designed to resist 1.5 times the
diaphragm inertial forces from Section 12.10.3.2 plus 1.5
times the design transfer forces.
EXCEPTION: 1. Any transfer force increased by the
overstrength factor of Section 12.4.3 need not be further
amplified by 1.5.
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 37
Diaphragm Design Force Level
Comparisons
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 38
4-Story Perimeter Wall Precast Concrete
Parking Structure (SDC C, Knoxville)
16'
10'-6"
10'-6"
10'-6"
47'-6"
204'
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 39
4-Story Perimeter Wall Precast Concrete
Parking Structure (SDC C, Knoxville)
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 40
4-Story Interior Wall Precast Concrete
Parking Structure (SDC D, Seattle)
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 41
4-Story Interior Wall Precast Concrete
Parking Structure (SDC D, Seattle)
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 42
8-Story Precast Concrete Moment Frame
Office Building
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 43
8-Story Precast Concrete Moment Frame
Office Building
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 44
8-Story Precast Concrete Shear Wall Office
Building
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 45
8-Story Precast Concrete Shear Wall Office
Building
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 46
Precast Concrete Diaphragm
Design
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 47
Diaphragm Design Options
Elastic Design Option (EDO)
Basic Design Option (BDO)
Reduced Design Option (RDO)
Diaphragm remains elastic in DBE and
MCE
Highest diaphragm design force
Connections can include LDE, MDE
and HDE
Diaphragm remains elastic in DBE but Not Necessarily in MCE
Lower diaphragm design force than
EDO
Connections can include MDE and
HDE
Some Diaphragm yielding in DBE,
significant in MCE
Lowest diaphragm design force
Connections must be High Deformation Elements (HDE)
Shear overstrength factor is needed
No shear overstrength needed since elastic
design
Shear overstrength factor is needed
SEAOH 2015 (C. Naito)
Deformation Category
Ten
sion F
OR
CE
LDE – Low Deformability Element
MDE – Moderate Deformability Element
HDE – High Deformability Element
OPENING DISPLACEMENT
LDE MDE HDE
48
7.5 mm
(0.3 in.) 15 mm
(0.6 in.)
SEAOH 2015 (C. Naito)
Diaphragm Seismic Design Level (DSDL)
• Step 1B: Determine Diaphragm Seismic Design Level (DSDL)
0
1
2
3
4
5
6
7
8
0 50 100 150 200
Nu
mb
er o
f S
tori
es,
n
Diaphragm Span, L [ft]
DSDL: Low
DSDL:
Moderate
DSDL: High
Seismic Design
Category
B or C D, E or F Diaphragm
Seismic Design Level:
LOW
IS DSDL LOW &
AR>2.5? Diaphragm Seismic
Design Level: MODERATE
Diaphragm Seismic
Design Level: HIGH
DSDL Moderate
IS DSDL HIGH & AR<1.5?
YES
YES
NO
NO
49
SEAOH 2015 (C. Naito)
Seismic Design Option
• Step 2A: Determine Diaphragm Design Option
Diaphragm Seismic
Design Level: LOW
Diaphragm Seismic
Design Level: MODERATE
Diaphragm Seismic
Design Level: HIGH
Design Option Diaphragm Seismic Demand level
Low Moderate High
Elastic Recommended With Penalty* Not Allowed
Basic Alternative Recommended With Penalty*
Reduced Alternative Alternative Recommended
Penalty* = Diaphragm design force shall be increased by 15%.
Choose Design Option: Elastic / Basic / Reduced
50
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 51
Precast Concrete
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 52
FEMA P-1051 Chapter 6 Overview
• Introduction
• Alternative ASCE 7-16 Force Level for
Seismic Design of Diaphragms
• Step-by-Step Determination of Traditional
Diaphragm Seismic Design Force
• Step-by-Step Determination of Alternative
Diaphragm Seismic Design Force
• Diaphragm Design Force Level Comparisons
• Connector Qualification Protocol
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 53
Precast Concrete
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 54
Requirements for Precast Concrete
Systems: Design Examples
• The examples in Section 11.1 illustrate the design of untopped
and topped precast concrete floor and roof diaphragms of three
five-story masonry buildings (SDC B, C, D)
• The example in Section 11.2 illustrates the design of an
intermediate precast concrete shear wall building in a region of
low or moderate seismicity. The precast concrete walls in this
example resist the seismic forces for a three-story office
building.
• The example in Section 11.3 illustrates the design of a special
precast concrete shear wall for a single-story industrial
warehouse building.
• The example in Section 11.4 is a partial example for the design
of a special moment frame constructed using precast concrete
per ACI 318 Section 18.9.
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 55
FEMA P-1051 Chapter 11 Overview
11.1
HORIZONTAL DIAPHRAGMS
11.1.1
Untopped Precast Concrete Units for Five-Story Masonry Buildings Assigned to Seismic Design Categories B and C
11.1.2
Topped Precast Concrete Units for Five-Story Masonry Building Assigned to Seismic Design Category D
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 56
11.1.1 Untopped Precast Concrete
Units for Five-Story Masonry
Buldings Assigned to SDC B and C
This example illustrates floor and roof
diaphragm design for five-story masonry
buildings in SDC B and in SDC C on soft rock.
The example in Section 13.2 provides design
parameters used. The floors and roofs of these
buildings are made of untopped 8-inch-thick
hollow-core precast, prestressed concrete
plank.
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 57
11.1 Horizontal Diaphragms
Hollow core plank floor plan for diaphragm examples
6'-0"
6'-
8"
Prestressed
hollow core
slabs
40'-0" 24'-0" 24'-0" 24'-0" 40'-0"
4'-0"
14'-
0"
24'-
0"
24'-
0"
24'-
0"
152'-0"
72'-
0"
8" concrete
masonry wall
A B C D E F
4
3
2
1
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 58
11.1 Horizontal Diaphragms
Building Elevation
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 59
This example illustrates floor and roof
diaphragm design using topped precast units in
the five-story masonry building when it is
assigned to SDC D. The topping thickness
exceeds the minimum of 2 in. The topping is
lightweight (115 pcf) concrete with f'c of 4,000
psi and is to act compositely with the 8-in.-thick
hollow-core precast, prestressed concrete
plank. Design parameters are provided in
Section 13.2.
11.1.2 Topped Precast Concrete Units for Five-Story Masonry Building Assigned to SDC D
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 60
FEMA P-1051 Chapter 11 Overview
11.2
THREE-STORY OFFICE BUILDING
WITH INTERMEDIATE PRECAST
CONCRETE SHEAR WALLS
11.3
ONE-STORY PRECAST SHEAR WALL
BUILDING
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 61
11.2 Three-story Office Building
with Intermediate Concrete
Shear Walls
This example illustrates the seismic design of
intermediate precast concrete shear walls.
These walls can be used up to any height in
SDCs B and C but are limited to 40 ft for SDCs
D, E, and F. An increase in structural height to
45 ft is permitted for “single story storage
warehouse facilities.”
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 62
11.2 Three-Story Office Building
with Intermediate Precast Concrete
Shear Walls
25'-0"25'-0"25'-0"25'-0"25'-0"25'-0"
150'-0"
40
'-0"
40
'-0"
40
'-0"
12
0'-
0"
15
'-0"
8'-0"
26 IT 28precast
beams
18" DT roof and floor
slabs (10 DT 18)
8" precast
shear walls
8'-
0"
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 63
11.3 One-Story Precast Shear Wall
Building
• This example illustrates the design of a precast
concrete shear wall for a single-story building
assigned to a high seismic design category.
• The precast concrete building is a single-story
industrial warehouse building (Risk Category II) on
Site Class C soils.
• The precast wall panels used in this building are
typical DT wall panels.
• Walls are designed using intermediate precast
structural walls.
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 64
11.3 One-Story Precast Shear Wall
Building 15 DT at 8'-0" = 120'-0"
48'-
0"
48'-
0"
12 D
T a
t 8'-
0"
= 9
6'-
0"
Steel tube
columns
Joist girder
(typical)
24
LH
03
at 4
'-0"
o.c
.
24L
H0
3at
4'-
0"
o.c
.
3 DT at 8'-0" =
24'-0"
16'-0"
O.H.
door
5 DT at 8'-0" = 40'-0" 3 DT at 8'-0" =
24'-0"
16'-0"
O.H.
door
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 65
FEMA P-1051 Chapter 11 Overview
11.4
SPECIAL MOMENT FRAMES
CONSTRUCTED USING PRECAST
CONCRETE
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 66
Precast Concrete
Instructional Slides developed by S. K. Ghosh, PhD
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 67
Precast Concrete
Instructional Slides developed by S. K. Ghosh, PhD,
Instructional Material Complementing FEMA 1052, Design Examples Diaphragms Analysis - 68
Questions
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