5/8/2015
Credit: APA
Seismic Design of Large Wood
Panelized Roof Diaphragms
In Heavy‐Wall Buildings
Copyright Materials
This presentation has been produced by John Lawson for the exclusive use of the
American Wood Council, yet ownership remains with John Lawson. Some photos and
diagrams credited to others have different ownerships and may have copyrights in
place and have been provided here for educational purposes only. All presentation
material produced and owned by John Lawson is protected by US and International
Copyright laws. Reproduction, distribution, display and use of the presentation
without written permission of John Lawson is prohibited.
© John Lawson 2015
Disclaimer: This presentation was developed by a third party and is not funded by the
American Wood Council or the Softwood Lumber Board.
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5/8/2015
•
The American Wood Council is a
Registered Provider with The American
Institute of Architects Continuing
Education Systems (AIA/CES), Provider
#50111237.
•
Credit(s) earned on completion of this
course will be reported to AIA CES for
AIA members. Certificates of
Completion for both AIA members and
non‐AIA members are available upon
request.
•
•
This course is registered with AIA CES for
continuing professional education. As
such, it does not include content that
may be deemed or construed to be an
approval or endorsement by the AIA of
any material of construction or any
method or manner of
handling, using, distributing, or dealing
in any material or product.
Questions related to specific materials,
methods, and services will be addressed
at the conclusion of this presentation.
Course Description
This presentation will focus on the engineered design of large
wood panelized roof diaphragms in tilt‐up concrete and masonry
wall buildings, with focus on design requirements for strength,
stiffness, and proper development and resistance of wall
anchorage forces. A historical perspective of how past seismic
experience with this building type has influenced today's building
code provides a good perspective for the participant to apply the
current provisions of ASCE 7‐10, 2012 NDS and 2008 SDPWS.
Various design illustrations and examples of high load wood
structural panel diaphragms, wall anchorage, subdiaphragms,
continuity cross ties, chords and collectors will be shown.
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Polling Question
1. What is your profession?
a) Architect
b) Engineer
c) Code Official
d) Building Designer
e) Other
5
Objectives
Upon completion, participants will be better able to:
1.
2.
3.
4.
Identify the characteristics of a panelized wood roof diaphragm.
Apply requirements for wall anchorage forces including proper detailing
for distribution of these forces into the diaphragm.
Utilize subdiaphragms as a tool to create an efficient load path for wall
anchorage forces.
Design wood diaphragms and their chords and collectors for seismic
forces.
6
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Large Wood Roof Diaphragms
Subjects Covered:
•
•
•
•
Panelized Roof Structure
Wall Anchorage System
Main Diaphragm Design
Diaphragm Deformation
Photo Source: ???????????
7
Source: APA – The Engineered Wood Association
Panelized Roof Structure
8
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A Panelized Roof Structure
Subpurlin
Purlin
Girder
9
Panelized Roof Structure
Wood structural panel oriented with strength axis parallel to
supports; allows all edges to be fully blocked for maximum
diaphragm shears, and without added blocking pieces.
15/32” thick Structural I
panels are typical for basic
roof loads (no snow).
Plywood/OSB
35psf Live, 45psf Total
allowable load capacity
per IBC T. 2304.7(5)
Hanger
Subpurlin
Bracing straps
Column Cap
Hanger
Hinge
All Wood System
10
Source: Simpson Strong-Tie
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Panelized Roof Structure
11
Source: Simpson Strong-Tie
Hangers already attached to ends
12
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Panelized Roof Structure
13
©2006 APA – The Engineered Wood Association
Panelized Roof Structure
14
©2006 APA – The Engineered Wood Association
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Panelized Wood Truss System
15
Source: APA – The Engineered Wood Association
Panelized Wood Truss System
16
Source: APA – The Engineered Wood Association
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Panelized Wood I-Joist System
17
Source: APA – The Engineered Wood Association
Panelized Hybrid Roof System
18
Source: APA – The Engineered Wood Association
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Panelized Hybrid Roof System
Wood Nailers on
Steel Joist and
Joist Girders
Hybrid System
Source: Simpson Strong-Tie
19
Panelized Roof System
• Shop
o Hangers on sub-purlins
o Joist nailers (if hybrid)
• Field-Ground
o Full length purlins, subpurlins, and sheathing
assembled on the ground
• Erection
o Purlin and sub-purlins lifted
to roof as a “panel”
Photo courtesy of Wood‐Lam Structures, Inc.
20
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Panelized Hybrid Roof System
Photo courtesy of Panelized Structures, Inc.
21
Panelized Hybrid Roof System
Photo courtesy of Panelized Structures, Inc.
22
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Panelized Hybrid Roof System
23
Panelized Hybrid Roof System
Photo courtesy of Panelized Structures, Inc.
24
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Panelized Hybrid Roof System
Photo courtesy of Wood‐Lam Structures, Inc.
25
Panelized Hybrid Roof System
Photo courtesy of Panelized Structures, Inc.
26
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Panelized Roof Framing System
27
Photo courtesy of Panelized Structures, Inc.
Up to 40,000 square feet installed daily
28
Photo courtesy of Panelized Structures, Inc.
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Development of
Wall-to-Roof Anchorage
Design Provisions
29
Wall Anchorage Design
•
•
•
•
•
•
Cross‐grain Bending Issues
Wall Anchorage Design Force
Eccentricity Issues
Pilaster Issues
Continuity Ties
Subdiaphragms
30
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Cross-grain Bending
Issues
31
Wall Anchorage Design
• Background
– 1971 San Fernando Earthquake
– 1992 Landers / Big Bear Earthquakes
– 1994 Northridge Earthquake
• Cross-grain bending of wood ledgers in
pre-1973 UBC buildings.
32
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Wall Anchorage Design
•
1971 San Fernando Earthquake
33
Photo Credit: Los Angeles City Dept of Building & Safety
Wall Anchorage Design
•
1971 San Fernando Earthquake
34
Photo Source: Earthquake Engineering Research Lab, Cal Tech
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Wall Anchorage Design
•
1992 Landers Earthquake
Wall Anchorage
Improper
35
Photo Source: California Seismic Safety Commission
Wall Anchorage Design
•
1992 Landers Earthquake

Wall Anchorage
Failure
Steel deck diaphragms:
Steel decking
Masonry Block
36
Photo Source: California Seismic Safety Commission
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Wall Anchorage Design
•
1994 Northridge Earthquake
37
Photo Source: Doc Nghiem
Wall Anchorage Design
•
1994 Northridge Earthquake
– Inadequate wall anchorage
38
Photo Source: Doc Nghiem
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Wall Anchorage Design
•
1994 Northridge Earthquake
39
Photo Source: Doc Nghiem
Wall Anchorage Design
•
1994 Northridge Earthquake
40
Photo Source: Doc Nghiem
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Wall Anchorage Design
•
1994 Northridge Earthquake
41
Photo Source: EQE
Past Performance
•
2001 Nisqually Earthquake
42
Photo Credit: Cascade Crest Consulting Engineers
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Wall Anchorage Design
•
1994 Northridge Earthquake
43
Photo Credit: Cascade Crest Consulting Engineers
Wall Anchorage Design
•
1994 Northridge Earthquake
44
Photo Source: EERI
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Wall Anchorage Design
•
1994 Northridge Earthquake
Ledgers fail in
cross‐grain bending
Nails pulled through
plywood edge
45
Photo Source: Doc Nghiem
Wall Anchorage Design
Pre‐1973 UBC
46
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Wall Anchorage Design
• Since the 1970s
–
–
–
–
No wood cross-grain bending or tension allowed
Direct connection required
No use of toenails or nails in withdrawal
No use of wood diaphragm sheathing as the tension tie
- ASCE 7-10: SDC C-F
47
Wall Anchorage 1980s
Wall Anchorage (Wood Roof)
See manufacturer’s
recommendations for
embedment depth
Member width
per manufacturer’s
recommendations
48
Source: Simpson Strong-Tie
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Wall Anchorage Design
Wall Anchorage (Wood Ledger)
49
Source: SEAOC Structural / Seismic Design Manual
Wall Anchorage Design
Wall Anchorage (Wood nailer on steel ledger)
50
Source: Simpson Strong-Tie
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Wall Anchorage Design
Wall Anchorage (Purlin to wood ledger)
Pre-engineered wall tie hardware
52
Source: Simpson Strong-Tie
Polling Question
2. Which of the following can be used to provide
wall anchorage to a wood diaphragm:
a) Wood members in cross‐grain bending
b) Wood members in cross‐grain tension
c) Toenails
d) Subpurlins
e) Nails loaded in withdrawal
54
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Wall Anchorage
Design Force
55
Wall Anchorage Design
• ASCE 7-10 force levels
Fp  0.4 S DS k a I eW p
Not less than…
Sec. 12.11.2.1
Similar force levels since 1997 UBC
for SDC D+.
New for SDC B and C in ASCE 7‐10.
Fp  0.2k a I eW p
where…
k a  1.0 
Lf
100
ka need not be
greater than 2.0
– In response to past performance problems, these forces have been
factored up to maximum expected force levels
• 3 to 4 times the ground accelerations
56
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Wall Anchorage Design
120’
Ka = 2.2, Use 2.0
Fp = 0.8SDSIeWp
40’
Ka = 1.4
Fp = 0.56SDSIeWp
Lines of shear resistance
57
Wall Anchorage Design
Lines of shear resistance
Ka = 1.8
80’
Fp = 0.72SDSIeWp
58
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Wall Anchorage Design
Example Wall Force Calculation
Fp = 0.8SDSIeWp
59
Source of Illustration: WoodWorks
Wall Anchorage Design
• Wall anchorage force Example:
Fp
33’
30’
8” thick
concrete
Fp  0.8S DS I eW p
Given:
SDC = D
SDS = 1.0g
Ie = 1.0
8’‐0” anchor spacing
 332 
8"
  14,520 lbs
W p  150 pcf 8' 
12
 230  
Fp  0.81.0 g 1.0 14,520lbs   11,616 lbs
60
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Eccentricity Issues
61
Wall Anchorage Design
Wall Anchorage (Purlin to wood ledger)
Pre-engineered wall tie hardware
(both sides?)
62
Source: Simpson Strong-Tie
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5/8/2015
Wall Anchorage Design
- ASCE 7-10: SDC C-F
Ledger
Purlin or
Subpurlin
Plan
View
e
63
Wall Anchorage Design
- ASCE 7-10: SDC C-F
Moment = Tie Force x eccentricity
Purlin or
Subpurlin
M
Plan
View
T
e
Combined Axial Tension and Bending Moment
64
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Wall Anchorage Design
- ASCE 7-10: SDC C-F
Concentric Loading Desired
Source: Simpson Strong-Tie
65
Pilaster
Issues
66
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Anchorage to Pilasters
•
1994 Northridge Earthquake
67
67
Photo Source: Doc Nghiem
Anchorage to Pilasters
•
1994 Northridge Earthquake
Load focused at pilasters
68
Photo Source: Doc Nghiem
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Anchorage to Pilasters
•
1994 Northridge Earthquake
69
Photo Courtesy of EERI
Anchorage to Pilasters
• 2014 Napa Earthquake
– Inadequate pilaster anchorage
70
Photos Courtesy of Maryann Phipps
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Anchorage to Pilasters
• 2014 Napa EQ
– Pilaster anchorage
71
Photo Courtesy of Maryann Phipps
Anchorage to Pilasters
• 2014 Napa Earthquake
Masonry Building Pilaster
72
Photo Source: Abe Lynn, Degenkolb
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Anchorage to Pilasters
• 2014 Napa Earthquake
Masonry Building Pilaster
73
Photo Source: Josh Marrow
Anchorage to Pilasters
• 2014 Napa Earthquake
74
Masonry Building Pilaster
74
Photos Source: Abe Lynn, Degenkolb
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Anchorage to Pilasters
• ASCE 7-10
- Wall Anchorage at Pilasters
- ASCE 7-10: SDC C-F
75
Anchorage to Pilasters
• Pilaster’s tributary area for anchorage load
Repetitive
Roof Anchorage
Equal
Parapet
Roof
Equal
Equal
Equal
Equal
Floor
Pilaster
76
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Anchorage to Pilasters
• Wall anchorage force focused on Pilaster
Parapet
Roof
Fp
Fp  0.4k a S DS I eW p
Pilaster
Floor
77
Polling Question
3. Wall anchorage at pilasters…
a) result from a uniform wall load
b) attract more anchorage load from the wall
c) cause eccentric loading
d) are not allowed per code
e) have no effect
78
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Continuity Ties
79
Continuity Ties
80
- ASCE 7-10: SDC C-F
Photo Credit: Doc Nghiem
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Continuity Ties
• 1994 Northridge Earthquake
– Inadequate wall anchorage
The diaphragm sheathing
in tension is not an
effective continuity tie.
81
Photo Source: Doc Nghiem
Continuity Ties
•
1994 Northridge Earthquake
82
Photo Source: Doc Nghiem
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Steel Element
Issues
83
Wall Anchorage Steel Elements
•
1994 Northridge Earthquake
Net section rupture.
Limited ability to yield
Photo Source: Doc Nghiem
84
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Wall Anchorage Steel Elements
• Since the 1997 UBC
– Ductility cannot be counted on
– Steel elements are vulnerable
- ASCE 7-10: SDC C-F
85
Wall Anchorage Steel Elements
• Capacity of Wall Anchorage System
– The design forces 0.4SDSkaIeWp have been
carefully coordinated with the expected material
overstrengths of the anchorage materials.
• Steel Elements
– Steel elements need an additional 1.4 load factor
(Sec. 12.11.2.2.2)
• Wood Elements
– No additional load
factors needed for wood
elements, including
bolts, screws and nails.
86
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Continuity Ties
Typical Tie Connection
Typical Continuity Tie
87
Continuity Ties
88
Source: Simpson Strong-Tie
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Continuity Ties
90
Panelized Wood Truss System
91
Source: APA – The Engineered Wood Association
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Continuity Ties
Source of Illustration: WoodWorks
94
Continuity Ties
• Force same as wall anchorage
Fp  0.4 S DS k a I eW p
• 1.4 steel element load factor on steel joists
and steel strap connections
• Extend tie from chord to chord
95
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Continuity Ties
96
Continuity Ties
purlin
97
Source: SEAOC Structural / Seismic Design Manual
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Subdiaphragm Design
99
Subdiaphragm Design
Subdiaphragm is a portion of a larger wood
diaphragm designed to anchor and transfer
local [wall] forces to primary diaphragm
struts and the main diaphragm
Their use is permitted under
ASCE 7‐10 Sec. 12.11.2.2.1
(SDC C‐F)
100
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Subdiaphragm Design
101
Subdiaphragm Design
Subdiaphragm Typ.
Continuity Ties
102
Source of Illustration: WoodWorks
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Subdiaphragm Design
• A part of the Wall Anchorage System
– Thus same force:
Fp  0.4 S DS k a I eW p
• Aspect Ratio Limits:
– L/W = 2.5 maximum
103
Subdiaphragm Design
 The maximum length-to-width ratio of the
structural subdiaphragm shall be 2½ to 1.
(ASCE 7-10 §12.11.2.2.1)
Fp
2½
1
Subdiaphragm chords
Continuity Tie
104
Source of Illustration: WoodWorks
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Continuity Tie Connections
Continuity Tie
Connections
Source of Illustration: WoodWorks
105
Continuity Tie Connections
• Continuity Ties are a part of the Wall
Anchorage System
– Thus same force:
Fp  0.4 S DS k a I eW p
• Check minimum interconnection force:
Fp (min)  0.133S DSW
106
50
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Continuity Tie Connections
F p (min)  0.133 S DSW
Continuity Tie
Connections
107
Source of Illustration: WoodWorks
108
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Hinge Connector
Note bolt
locations in
vertical slots
Seismic Continuity Tie
Hinge Connector with tie capacity
109
Source: Simpson Strong-Tie
Evolution of Wall Anchorage Design
San Fernando Loma Prieta Landers Northridge
1.1
Seismic Coefficient (Strength)
1
0.9
Wall ties &
cross ties req’d.
No wood crossgrain
bending
0.8
0.7
Subdiaphragms
Concentrically loaded &
Special pilasters rules
Steel elements
Wood, Conc., Masonry
0.6
0.5
0.4
0.3
0.2
0.1
0
Zone 4
SDS=1.0
SD1=0.6
111
UBC/IBC Edition
Wall Anchorage Forces (Strength‐Level)
© John Lawson SE
52
5/8/2015
Polling Question
4. Which one of the following is not a special
consideration for wall anchorage?
a) 1.4x more design force at wood elements
b) Moments at eccentric connections
c) Ties continuous across building
d) Higher loads at pilasters
e) Subdiaphragms permitted
112
113
113
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Main Diaphragm Design
114
Main Diaphragm Design
North
North/South
Seismic Loading
East/West
Seismic Loading
Wood Structural Panel Diaphragm
200‐ft
9¼” Tilt‐up Concrete Walls
33’ top of wall
30’ top of roof
400‐ft
25’
TYP.
115
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Main Diaphragm Design
48’‐0”
48’‐0”
48’‐0”
48’‐0”
48’‐0”
48’‐0”
56’‐0”
50’‐0”
50’‐0”
50’‐0”
50’‐0”
56’‐0”
2x4 DF #2 subpurlins
at 24” o.c.
116
15/32” Structural I OSB
with staggered layout
9 ¼” Concrete Wall Panels, typ.
Purlins at 8‐ft o.c.
Main Diaphragm Design
•
•
•
•
•
•
Shear Nailing
Chords and Collectors
Irregularity Considerations
Diaphragm Deflections
Deformation Compatibility
Questions
117
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Shear Nailing
118
Main Diaphragm Design
Diaphragm Forces per ASCE 7‐10 Section 12.10
n
F px 
F
ix
n
w
ix
North/South
Seismic Loading
i
w px
i
FROOF
Fpx
Fp max  0.4S DS I e w px
Fp min  0.2S DS I e w px
200‐ft
33’ top of wall
30’ top of roof
400‐ft
25’
9¼” Tilt‐up Concrete Walls
TYP.
119
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Diaphragm Shear Nailing
A
J
400’
200
’
1
wEW = 0.222wp
wNS = 0.167wp
5
120
Diaphragm Shear Nailing
121
121
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Diaphragm Shear Nailing
• Diaphragm Construction (Panelized)
– 15/32” Structural I
– Fully Blocked
– Case 2 & 4 layouts
122
Diaphragm Shear Nailing
ASD values are “Nominal”
divided by 2
15/32” Struct I
w/ 10d nails
(0.148” dia)
123
Source: SDPWS courtesy of AWC
6”/6” o.c.
320plf
4”/6” o.c.
425plf
(ASD)
(ASD)
2
1
2x framing 2x framing
2½”/4” o.c.
640plf (ASD)
3
2x framing
2”/3” o.c.
820plf
(ASD)
4
3x framing
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Diaphragm Shear Nailing
ASD values are “Nominal”
divided by 2
15/32” Struct I
w/ 10d nails (0.148”)
with 4x framing
2 lines of
2½”/4” o.c.
1005plf (ASD)
2 lines of
2½”/3” o.c.
1290plf (ASD)
5
4x framing
6
4x framing
124
Source: SDPWS courtesy of AWC
1
6
5
1157 PLF
ASD
2
4
972
3
417
4
3
602
787
5
2
278
417
278
602
972
ASD
1157 PLF
1
6
125
787
Diaphragm Shear Nailing
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Diaphragm Shear Nailing
126
North/South Loads
1
10d at 6,6,12
4
10d at 2,3,12 w/ 3x framing
2
10d at 4,6,12
5
2 lines of 10d at 2½,4,12 w/ 4x framing
3
10d at 2½,4,12
6
2 lines of 10d at 2½,3,12 w/ 4x framing
Diaphragm Shear Nailing
East/West Loads Added
A
J
32’
32’
32’
32’
24’
96’
1
24’
32’
32’
32’
32’
2
3
4
5
6
20’
6
5
4
3
2
1
160’
20’
5
127
1
10d at 6,6,12
4
10d at 2,3,12 w/ 3x framing
2
10d at 4,6,12
5
2 lines of 10d at 2½,4,12 w/ 4x framing
3
10d at 2½,4,12
6
2 lines of 10d at 2½,3,12 w/ 4x framing
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Chord Design
128
Diaphragm Shear Nailing
w
L
CHORD COMPRESSION
B
CHORD TENSION
w = distributed diaphragm load
L = diaphragm span length
B = diaphragm breadth (width)
8
129
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Collector Design
130
Collector Design
48’‐0”
56’‐0”
131
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North/South Loads
Collector Design
Line of lateral resistance
Diaphragm’s unit shear diagram (plf)
Collector
Line of lateral resistance
Line of lateral resistance
v2
v1
132
North/South Loads
Collector Design
v1
v2
Collector
L
FCollector= (v1+v2)L
v2
133
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Collector Design
East/West Loads
Line of lateral resistance
Line of lateral resistance
Collector
v2
v1
Diaphragm’s unit shear diagram (plf)
134
Line of lateral resistance
Collector Design
East/West Loads
Collector
v1
v2
L
v2
FCollector= (v1+v2)L
135
64
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Irregularity Considerations
136
56’‐0”
48’‐0”
48’‐0”
48’‐0”
48’‐0”
48’‐0”
48’‐0”
56’‐0”
48’‐0”
56’‐0”
50’‐0”
50’‐0”
50’‐0”
50’‐0”
50’‐0”
Reentrant Corner Irregularity
2x4 DF #2 subpurlins
at 24” o.c.
137
15/32” Structural I OSB
with staggered layout
9 ¼” Concrete Wall Panels, typ.
Purlins at 8‐ft o.c.
65
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56’‐0”
48’‐0”
48’‐0”
48’‐0”
48’‐0”
48’‐0”
56’‐0”
48’‐0”
56’‐0”
48’‐0”
50’‐0”
50’‐0”
50’‐0”
Reentrant Corner Irregularity
50’‐0”
50’‐0”
Seismic Design Categories D, E, F
138
50’‐0”
50’‐0”
Reentrant Corner Irregularity
50’ >0.15L
56’‐0”
48’‐0”
48’‐0”
48’‐0”
48’‐0”
48’‐0”
L=296’ > 0.15L
L=400’
50’‐0”
50’‐0”
50’‐0”
L=250’
‫ ؞‬Plan Irregularity Exists
139
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Reentrant Corner Irregularity
140
Reentrant Corner Irregularity
56’‐0”
48’‐0”
48’‐0”
48’‐0”
48’‐0”
48’‐0”
56’‐0”
56’‐0”
48’‐0” Collector
50’‐0”
50’‐0”
50’‐0”
Collector
50’‐0”
50’‐0”
48’‐0”
North/South Loading
and
East/West Loading
141
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Reentrant Corner Irregularity
Anchor Bolting of ledger:
Design for 25% more shear
142
Reentrant Corner Irregularity
Diaphragm nailing not
subject to 25% increase
Collector
143
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5/8/2015
Reentrant Corner Irregularity
Diaphragm nailing not
subject to 25% increase
Bolting of nailer:
Design for 25% more shear
Collector
144
Reentrant Corner Irregularity
Emh = ΩoQE
Collector forces likely
comply with exception
per ASCE Sec. 12.10.2.1
145
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Diaphragm Deflection
146
Diaphragm Deflection
• Calculation Methods
– 2008 SDPWS
• Deflection limits
147
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Diaphragm Deflection

Bending
5vL3
0.25vL  X C


8 EAb 1000Ga
2b
Shear/Nail Slip
L = Length (ft)
b = Width (ft)
A = Area of Chord (in2)
v = Max Shear (lbs/ft)
(unfactored E or W)
(2008 SDPWS Eq. 4.2-1)
Chord Slip
E = Elastic Modulus (psi)
Ga = Apparent Shear Stiffness (k/in)
c = Chord Slip (in)
X = Distance to Nearest Support (ft)
148
Diaphragm Deflection
5wL4

384 EI
Beam Analogy:
L
b
W(unfactored)
We want accurate estimate of 
so we use Eaverage and unfactored W
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Diaphragm Deflection
Beam Analogy:
Bending:

5wL4
384 EI
L
v
v
b
W(unfactored)
We want accurate estimate of 
so we use Eaverage and unfactored W
150
Diaphragm Deflection
Derivation:
Δ
bending
Uniformly loaded beam
5wL
5( w / 12)( L  12) 4 45wL4



384 EI
384 EI
2 EI
4
Reaction 
wL
 vb
2
w
2vb
L
Convert:
L in feet
w in lbs/ft
v
is the maximum unit
diaphragm shear in lbs/ft
and b is the diaphragm
width in feet.
Substituting:
 bending 
45  2vb  L3 45vbL3

2 EI
EI
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Diaphragm Deflection
45vbL3
EI
Replace I in terms of A & b:
 bending 
b
Achord
I   I x   Ad 2 where d = “b/2”, and Ix is negligible
2
b

I   Ad 2  2 A  12   72 Ab 2
2

 bending
45vbL3
5vL3 Matches code equations


E  72 Ab 2 8 EAb
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Diaphragm Deflection
5vL3
0.25vL  X C



8 EAb 1000Ga
2b
Bending
Shear/Nail Slip
L = Length (ft)
b = Width (ft)
A = Area of Chord (in2)
v = Max Shear (lbs/ft)
(unfactored E or W)
Chord Slip
E = Elastic Modulus (psi)
Ga = Apparent Shear Stiffness (k/in)
c = Chord Slip (in)
X = Distance to Nearest Support (ft)
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Diaphragm Deflection
Shear/Nail Slip:
Deformed shape consists
of parallelograms
w
154
Diaphragm Deflection
Shear/Nail Slip: 0.25vL
1000Ga
•Ga = Apparent shear stiffness (kips/inch)
•Combines: *Shear deformation of sheathing and
*Deformation from nail slip
•Ga from SDPWS Tables 4.2A, 4.2B, 4.2C
•Ga empirically derived from tests.
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Diaphragm Deflection

Bending
5vL3
0.25vL  X C


8 EAb 1000Ga
2b
Shear/Nail Slip
L = Length (ft)
b = Width (ft)
A = Area of Chord (in2)
v = Max Shear (lbs/ft)
(unfactored E or W)
Chord Slip
E = Elastic Modulus (psi)
Ga = Apparent Shear Stiffness (k/in)
c = Chord Slip (in)
X = Distance to Nearest Support (ft)
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Diaphragm Deflection
Chord Slip:
 X
2b
C
C
Sum all tension and compression
chord slips together
Sometimes. Connections only slip in tension…
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Diaphragm Deflection
Chord Slip:
 X
C
2b
Each chord connection
slips by C
w
158
Diaphragm Deflection
For seismic only, the actual deflection
is inelastic. δmax needs to be increased.
δmax
elastic
δM =(Cd δe)/Ie
ASCE 7-10 Sec. 12.12.3
Maximum inelastic
seismic response
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Diaphragm Deflection
• Purpose of Limits
– Avoid Impact with Adjacent Structures
– Setback from Property Lines
– Maintain Structural Integrity
“Permissible deflection shall be that deflection that will
permit the diaphragm and any attached elements to
maintain their structural integrity and continue to
support their prescribed loads as determined by the
applicable building code or standard.”
2008 SDPWS Sec. 4.2.1
160
Deformation Compatibility
An Example:
Reentrant Corners
161
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Deformation Compatibility
50’‐0”
48’‐0”
50’‐0”
56’‐0”
48’‐0”
48’‐0”
48’‐0”
48’‐0”
56’‐0”
48’‐0”
50’‐0”
50’‐0”
Collector
50’‐0”
Without a collector,
roof structure will
tear from wall here
162
Deflected shape
with a collector
Deflected shape
without a collector
Deformation Compatibility
• 1992 Landers Earthquake
Wall Anchorage
Failure
Steel decking
Masonry Block
163
Photo Source: California Seismic Safety Commission
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5/8/2015
48’‐0”
56’‐0”
48’‐0”
48’‐0”
48’‐0”
48’‐0”
56’‐0”
48’‐0”
For short reentrant
corners, a strut is still
needed to force the
short wall to rock this
distance.
50’‐0”
Strut
50’‐0”
50’‐0”
50’‐0”
50’‐0”
Deformation Compatibility
164
Deformation Compatibility
Strut
Controlled rocking
requires complete
freedom of wall to rotate.
Strut should be conservatively
designed for the force
required to rock the wall
including any additional
restraint forces.
165
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Deformation Compatibility
Another Example:
Hinging of wall base out‐of‐plane
166
Deformation Compatibility
• Pilaster restraint against rotation
167
Deformation is exaggerated for illustration purposes
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Deformation Compatibility
• 2014 Napa Earthquake
– Pilaster restraint against rotation
168
Photo Courtesy of David McCormick
Deformation Compatibility
• 2014 Napa Earthquake
– Pilaster restraint against rotation
169
Photo Courtesy of David McCormick
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Deformation Compatibility
• ASCE 7-10
- Permissible Diaphragm Deflection
170
Polling Question
5. Diaphragm deflection should be considered to:
a) Determine if the system will continue to
support its loads
b) Avoid impact with adjacent structures
c) Maintain structural integrity
d) Avoid crossing property lines
e) All of the above
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Closing Comments
172
Closing Comments
• Building Code Provisions:
– A reaction to past events.
• Current Wall Anchorage Design:
– Hopefully solves code inadequacies.
– But, not tested by a design earthquake yet.
• Plenty of Old Inventory
– Failures will continue until older buildings are
retrofitted or demolished.
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Closing Comments
• 2015 Special Design Provisions
For Wind and Seismic (SDPWS)
Available as a free download from AWC
174
Questions?
• This concludes The American Institute of Architects Continuing Education
Systems Course
• For additional information on educational programs available from the
American Wood Council.
info@awc.org
www.awc.org
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84