By: R. Terry Malone, PE, SE - WoodWorks€¦ · • Wood Engineering and Construction...
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Transcript of By: R. Terry Malone, PE, SE - WoodWorks€¦ · • Wood Engineering and Construction...
-
Presented by:
By: R. Terry Malone, PE, SE
Senior Technical Director
Architectural & Engineering
Solutions
Presentation updated to 2012 IBC, ASCE 7-10
2008 SDPWS
Copyright McGraw-Hill, ICC
Presentation Based On:
Offset Diaphragms
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“The Wood Products Council” is a Registered Provider with The American Institute of Architects Continuing Education Systems (AIA/CES), Provider #G516.
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 ofhandling, 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.
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Course Description
Lateral force resisting systems in today’s structures are much more
complex than they were several decades ago, incorporating multiple
horizontal and vertical offsets in the diaphragms, multiple
irregularities, and fewer lateral resisting elements. This two part
presentation will provide a brief review of a method used to
analyzed these complex structures. In part 1, topics will include
code requirements, how to recognize diaphragm irregularities and
discontinuities, how shears are distributed through complex
diaphragms, a method of analysis used to solve the transfer of
forces across areas of discontinuity, and the analysis of flexible
wood sheathed or untopped steel decking diaphragms with
horizontal offsets.
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Learning Objectives• Basic Information
Discuss boundary elements, complete lateral resisting load
path requirements and related code sections.
• Examine Common Types of Discontinuities
Examine common types of discontinuities and irregularities
and discuss how to establish complete lateral load paths
across areas of discontinuity.
• Discuss an Analytical Method of Analysis
Review an analytical method used for solving complex
diaphragms and shear walls (Diekmann Method) using
“Transfer Diaphragms” and the “Visual Shear Transfer
Method.”
• Offset Diaphragms-Examples
Review the analysis of flexible offset diaphragms for loading in
the transverse direction.
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Presentation Assumptions
Assumptions:
• Loads to diaphragms and shear walls
• Strength level or allowable stress design
• Wind or seismic forces.
• The loads are already factored for the appropriate load combination.
Code and Standards:
• ASCE 7-10 “Minimum Design Loads for Buildings and Other Structures”
• 2012 IBC
• 2008 SDPWS-”Special Design Provisions for Wind and Seismic”
Analysis and Design references:
• The Analysis of Irregular Shaped Structures: Diaphragms and Shear Walls-
Malone, Rice
• Woodworks-The Analysis of Irregular Shaped Diaphragms
• Design of Wood Structures- Breyer, Fridley, Pollock, Cobeen
• SEAOC Seismic Design Manual, Volume 2
• Wood Engineering and Construction Handbook-Faherty, Williamson
• Guide to the Design of Diaphragms, Chords and Collectors-NCSEA
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Evolution to Complex Buildings
• Simple structures Complex structures
• The method of analysis is: Required for all construction types.
Straight forward and simple to use. “Based on simple statics!”
• Today’s presentation focuses on:• Continuous load paths across areas of discontinuities.
• Flexible wood sheathed or un-topped steel deck diaphragms.
Wood diaphragms are well suited for these shapes as they can be
easily adapted to the building shape and are cost effective.
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http://www.woodworks.org/education-publications/research-papers/#
Complete Example with narrative and calculations
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Marselle Condominiums 5 stories of wood over 6 stories concrete
Structural Engineer engineer: Yu & Trochalakis, PLLC (podium) 2 above grade
Photographer: Matt Todd Photographer
Mid-rise Multi-family
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Dis
co
nti
nu
ou
s c
ho
rds
Tra
ns
ve
rse
Cant.
Mid-rise Multi-family
SWSWSWSW
SWSWSWSWSW
SW
Lds. Discontinuous strutsLongitudinal
Lds.
No exterior
Shear walls
Flexible, semi-rigid, or rigid???
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Harrington Recovery CenterStructural engineer: Pujara Wirth Torke, Inc.Photographer: Curtis Walz
Offsets in the diaphragm
and walls
Vertically offset
Diaphragms?
Openings in
diaphragm
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• Boundary Elements
• Complete Load Paths
• Method of Analysis
Basic Information
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SW
Struts, Collectors, and Chords- (my) Terminology
W ( plf)
Chord
Chord
Chord
Str
ut
Diaphragm
support
Co
llecto
rSW
Collector
ChordC
ho
rd/C
ollecto
r
Chord
Str
ut
TD1
Chord
Ch
ord
/Co
llecto
r
SW
Discontinuous
diaphragm
chord
SW
Strut- receives shears from one side only*.
Collector- receives shears from both sides.
Chord-perpendicular to the applied load and
receives axial tension and compression
forces.
*[ Drag struts and collectors are synonymous in ASCE7]
SW
Diaphragm
support
T
C Chord
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Diaphragm 1 Diaphragm 2
Diaphragm 2
Boundary (typical)
Chord
Chord
Co
llecto
r
Str
ut
Str
ut
Chord
Str
ut
Fundamental Principles:A shear wall is a location where
diaphragm forces are resisted
(supported), and therefore defines
a diaphragm boundary location.
Note: Interior shear walls
without a collector or a
complete alternate load path
are NOT ALLOWED!
Diaphragm Boundary Elements
SW
1
SW
2
SW
3
Note: All edges of a diaphragm shall be supported by a boundary
element.
Diaphragm 1
Boundary (typical)
• Diaphragm Boundary Elements:
• Chords, drag struts, collectors, Shear walls,
frames
• Boundary member locations:
• Diaphragm and shear wall perimeters
• Interior openings
• Areas of discontinuities
• Re-entrant corners.
• Diaphragm and shear wall sheathing shall not be used
to splice boundary elements.
• Collector elements shall be provided that are capable of
transferring forces originating in other portions of the
structure to the element providing resistance to those
forces.
Required for
Seismic and
wind
1 2
B
3
C
A
-
Loads
Co
llecto
r
Collector
Diaphragm 1 Diaphragm 2S
tru
t
Chord Chord
Str
ut
Str
ut
Diaphragm 2
Boundary
Diaphragm 1
boundary
Re-entrant corner
Tearing will occur if collectors
are not installed at re-entrant corner.
1 2
A
B
3
C
Deflection
if no tie
Deflected curve if proper tie
Deflected curve if no tie
SW1
SW2SW3
SW4
Chord
Chord
Boundary Elements “L” Shaped Buildings-Transverse Loading
Deflection
if tie
Diaph.
Boundary
(Longitudinal
loading)
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• Boundary Elements
• Complete Load Paths
• Method of Analysis
Basic Information
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Strut/chord
Open
3
4
5
21
F
E
D
C
B
6 9 107 8
Strut/chord
Str
ut
Str
ut
(typ
.)
Strut
chord
Strut chord
Strut /chord
Str
ut
Strut/chord
Strut/chord
SW
1
SW5
SW2
SW3
SW6
SW4
Str
ut
MR
F1
Multiple
offset
diaphragm
Offset
strut
Support Support
Co
llecto
r
Collector
Collector
(typ.)
Collector
(typ.)
Collector
(typ.)
Co
llecto
r (t
yp
.)
A
Complete Continuous Lateral Load Paths
Analysis: ASCE7-10 Sections:• 1.3.1.3.1-Design shall be based on a rational analysis
• 12.10.1-At diaphragm discontinuities such as openings and re-entrant
corners, the design shall assure that the dissipation or transfer of edge
(chord) forces combined with other forces in the diaphragm is within shear
and tension capacity of the diaphragm.What does
this mean?
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Strut/chord
Open
3
4
5
21
F
E
D
C
B
6 9 107 8
Strut/chord
Str
ut
Str
ut
(typ
.)
Strut
chord
Strut chord
Strut /chord
Str
ut
Strut/chord
Strut/chord
SW
1
SW5
SW2
SW3
SW6
SW4
Str
ut
MR
F1
Support Support
Co
llecto
r
Collector
Collector
(typ.)
Collector
(typ.)
Collector
(typ.)
Discontinuous
diaphragm
chord/strut
Discontinuous
diaphragm
chord
Discont.
diaph.
chord
Discont.
diaphragm
chord
Discont.
diaphragm
chord
Co
llecto
r (t
yp
.)
A
Complete Continuous Lateral Load Paths
ASCE7-10 Section 1.4-Complete load paths are required including members and their splice connections
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Strut/chord
Open
3
4
5
21
F
E
D
C
B
6 9 107 8
Strut/chord
Str
ut
Str
ut
(typ
.)
Strut
chord
Strut chord
Strut /chord
Str
ut
Strut/chord
Strut/chord
SW
1
SW5
SW2
SW3
SW6
SW4
Str
ut
MR
F1
Offset shear walls
and struts
Support Support
Co
llecto
r
Collector
Collector
(typ.)
Collector
(typ.)
Collector
(typ.)
Offset shear
walls
Co
llecto
r (t
yp
.)
A
Complete Continuous Lateral Load Paths
ASCE7-10 Section 1.4-Complete load paths are required including member and their splice connections
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Strut/chord
Open
3
4
5
21
F
E
D
C
B
6 9 107 8
Strut/chord
Str
ut
Str
ut
(typ
.)
Strut
chord
Strut chord
Strut /chord
Str
ut
Strut/chord
Strut/chord
SW
1
SW5
SW2
SW3
SW6
SW4
Str
ut
MR
F1
Opening
in diaph.
Support Support
Co
llecto
r
Collector
Collector
(typ.)
Collector
(typ.)
Collector
(typ.)
Co
llecto
r (t
yp
.)
Vertical
offset in
diaphragm
A
Complete Continuous Lateral Load Paths
Design: • IBC 2305.1.1-Openings in shear panels that materially effect their strength shall be fully
detailed on the plans and shall have their edges adequately reinforced to transfer all
shear stresses.
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• Boundary Elements
• Complete Load Paths
• Method of Analysis
Basic Information
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Method of AnalysisThe Visual Shear Transfer Method
+ -
+
Positive
Direction
+ -
Transverse Direction (shown)
Lds.
Shears Applied to Sheathing Elements
FY
FX
+M
Symbol for 1 ft x 1 ft
square piece of sheathing
in static equilibrium (typ.)
+
+ -
Shears Transferred Into Boundary Elements
Unit shear transferred from the sheathing
element into the boundary element (plf)
Unit shear acting on sheathing element (plf)
-
+
-
+-
+ -
-+
Basic Shear DiagramPositive diaph.shear elements
Pos.
Neg.
Diaphragm shear transferred
into boundary element (typ.)
Strut in
tension
Resisting
wall
shears
Resisting
wall
shears
Resisting
wall
shears
Strut in
Compr.
Strut in
comp.
Strut in
tension
SW 2
SW 1
SW 3
Diaphragm
C.L.
Strut Forces Strut Forces
T
C
T
T
C
C
1 2
A
B
Negative diaph.
shear elements
(-)
(+)
(+)
(+)
(-)
(-)
(-)
+ -
Positive sign
convention
Maximum
moment
1 ft. x 1 ft. square sheathing
element symbol at any location
in the diaphragm.
Shear Distribution Into a Simple DiaphragmThe Visual Shear Transfer Method
Support Support
SW
SW
All edges of a diaphragm shall be supported by a boundary element (chord, strut, collector) or
other vertical lateral force resisting element (shear wall, frame).
w=uniform load
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Introduction to Transfer Diaphragms
and Transfer AreasC
ollecto
r
T Collector
(support)
(support)
Chord
Chord
TD1
TD Ratio=4:1
Maximum Co
llecto
r
T
Framing members, blocking, and connections shall extend
into the diaphragm a sufficient distance to develop the force
transferred into the diaphragm.
Transfer Diaphragm
• sub-diaphragm
• Transfers local forces out to primary
chords/struts of the main diaphragm.
What does
this
mean?
-
SW
SW
Diaph.
C.L.
W ( plf)
Longitudinal Collector
Diaphragm chord
Discontinuous
diaphragm
chord
1 2
A
B
3
CDiaphragm chord
Dra
g s
tru
t
Diaphragm
support
Diaphragm
support
Transfer Diaphragm Members and Elements
4
Transfer
Area
Diaphragm chord
• The length of the collector is often
determined by dividing the collector
force by the diaphragm nailing capacity.
(Wrong!)
• The collector is often checked for
tension only. (Wrong!) Compression
is rarely checked.
Typical callout
CMST14 tie strap x 10’-0” with (xx) 10d
nails over 2x flat blocking. Lap 2-8”
onto wall.
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Transfer Mechanism
1 2
B
3
C
T C
Main
chord
Main
chord
B
C
A
2 3
Disrupted
chord
Resis
tin
g
forc
es
Transfer area without transverse collectors
Transfer using beam concept
Transfer
Diaphragm
( Beam)
Transfer
area
Disrupted
chord
Support
Support
Collector
Rotation
of section
This force must be
transferred out to
the main chords.
A complete load
path is required.
Collector must extend
the full depth of the
transfer diaphragm
NOTE:
SW
Collector
Full depthChord
Ch
ord
/Co
llecto
r
Str
ut
TD1
Ch
ord
/Co
llecto
r
SW
Discontinuous
diaphragm
chord
SW
Resis
tin
g
forc
es
-
SW
Co
llecto
r
T T
+
-
Analogous to a beam with a
concentrated Load.
Chord force at
discontinuity
Subtract
from basic
shears
Add to basic
diaphragm
shears
1
A
B
2
C
Collector
(TD support)
(TD support)
Chord
TD1
Basic Shear Diagram at transfer diaphragm
-75 plf
+250 plf
+300
plf +225 +225
plf plf
vnet=+300+(250)= +550 plf
vnet =+225–(75)= +150 plf
3
TD depthTra
nsfe
r d
iap
hra
gm
len
gth
+
, Shear =VC
DTD DTD
, Shear = VA
DTD
vnet=+300-(75)= +225 plf
vnet =+225 +(250)
= +475 plf
Transfer Diaphragm Shears
ab
VA=
VC=
LT
D
T(b)LTD
T(a)
LTD
LT
D
Basic ProcedureMethod by Edward F. Diekmann
+500
plf
Main
chord
Main
chord
Disrupted
chord
Basic diaph.
shear TD shears
vnet= 300 + (250) = 550 plf
Net shear
The transfer diaph.
aspect Ratio should
be similar to the
main diaphragm.
No outside force
is changing the
basic diaphragm
shear in this area
No outside force
is changing the
basic diaphragm
shear in this area
T
C
Co
llecto
r
-
+ +
+ +
+225 plf +150 plf
+550 plf +475 plf
Resulting net shear
diagram on collector
325 plf 325 plf
Net direction
of shears acting
on collector
Shear Distribution Into The Collector
Direction of shear
transferred into
collector
Collector
• Collector force=area of shear diagram
Shear left=+550-225= +325 plf
2
• Place the net diaphragm shear
on each side of the collector
• Sum shears on collector (based upon
direction of shears transferred onto
collector).
Fcollector=(325+325)(Lcollector)Dir. of force
on collector
B
2 3
Net shear
Note: The net shears
will not always be
equal.
Lcollector
• Place the transfer shears on each side
of the collector
Shear right=+475-150=+325 plf
-
TD1
Support
Support
Discont.
Chord / strutF
ab
A
C
B
21Transfer
Diaph. depth
Tra
nsfe
r D
iap
h.
len
gth
L
aFRA
)(
L
L
bFRC
)(
Transfer
Diaphragm
Analogous to a simple span
beam with a concentrated load
TD1
Support
Support
Discont.
Chord / strutF
A
C
B
21
Transfer
Diaph. depth
Tra
nsfe
r D
iap
h.
len
gth
b
LFRB
)(
L
b
aFRA
)(
Transfer
Diaphragm
Analogous to a propped cantilever beam
with a concentrated load
Simple Span Transfer Diaphragm
Collector Chord, strut
or shear wall
Chord, strut
or shear wallChord, strut
or shear wall
Chord, strut
or shear wall
F
F
RB
RA
RC
RA
Propped Cantilever Transfer Diaphragm
ab
Simple Span and Propped Cantilever Transfer Diaphragms
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Diaphragms with Horizontal Offsets
-
SW 1
SW 2
Diaph.
C.L.
25’ 20’
15
’
w=200 plf
Diaph. chord Collector
Co
llecto
r
TD
ch
ord
s
Diaph. chord
80’
35’
50’
Discontinuous
diaphragm chord
1 2
A
B
3
C
Co
llecto
r
TD
ch
ord
s
Support
Support
TD1
+ -
Sign Convention
4
Diaph. chord
F2B
RL lb
200 plf
25’
F2A
Free body for F2B
1 2
A
B
∑M=0
35’
M2B ft.-lb
F2B lb
Support RL lb
RR lb
Example 1-Diaphragm with Horizontal End OffsetTransverse Loading
V2 l
b
V3 l
b
A/R=2.5:1
Support
-
SW 1
SW 2
Diaph.
C.L.
25’ 20’
15’
80’
V=Basic shear
- TD shear plf
F2B
v= DTD
Vcplf
VA lb
VC lb
v= Net shear> 2x
Basic shear
v2R plf v2L plf
v1 plf
v3 plf
1 2
A
B
3
C
Basic shear diagram
Net TD shears (basic shear +/- transfer diaph. shears)
No net change Net change
occurs in TDNo net change
35’
Transfer Diaphragm and Net Diaphragm Shear
+ -
Sign Convention
4
15’
35’
RL lb
RR lb
(Net shear)
Po
s.
Neg
.
v4 plf
TD
sh
ear
dia
gra
m
F2B
v= DTD
VAplf
-
SW 1
SW 2
Diaph.
C.L.
25’ 20’
15’
F3C
FCL
C
T F2B
T
F2A
1 2
A
B
3
C
F2B
+v2
-v3x1’
x2’+F lb-F lb
Longitudinal Chord Force Diagrams
0 plf
+ -
Sign Convention4
17.5’
v1 v2L
Support
Support
0 plf
FCL
F2B
F3A
-
SW 1
25’ 20’
15
’F=6000 lb
F=6000 lb
(this is not an insignificant force.)
F3B
F3B
T C
1 2
A
B
3
C
Transverse Collector Force Diagrams
+ -
Sign Convention
Net shear Net shear
-
Diaphragm Nailing Callouts
10d
@ 4
/6/1
2 B
1
2 3Transfer area Boundary
(High shear area)
Transfer diaphragm
Boundary (Typ.)
Boundary locations
Diaphragm boundary
357.2
plf
320 p
lf
285 p
lf
214.3
plf
42.9
plf
37.1
plf
70 p
lf
214.3 plf
357.1 plf
70 plf Basic shear diagram
150 plf
10d
@ 6
/6/1
2 B
10d
@ 6
/12 U
B
Case I
10d @ 4/6/12 B
10d
@ 6
/12 U
B
Case I
10d
@ 6
/12 U
B
Case I
Check the shear capacity of the
nailing along the collector
Callout all nailing on drawings:
• Standard diaphragm nailing
• Boundary nailing
• Collector nailing
x4x3x1 x2 Special nailing along
collectors
Sum of shears to collector or
highest boundary nailing-
greater of
-
SW 1
1
2
A
3
C
4
SW 2
B
Win
do
w w
all
Horizontal offset
in chord/strut
F=20 kips
Strut/chord
Strut/chord
Actual Project
C.L.
diaphragm
• No calculations
• No collector
100’
100’
200’
-
NOTE:
v max=1864 plf
F=7626 lb
v=304 plf
F=25230 lb
F=6991 lbF=7454 lb F=7512 lb
v max=1748 plf
F=25278 lb @
c.l. diaphragm
(calc’d=22500 lb)
F=24905 lb
v=328 plfv=244 plfv=504 plf
v=997 plf v=588 plfv=390 plf
v=997 plf
(designed)
• Diaphragm designed as a simple rectangular diaphragm, no offset,
using only a spreadsheet.
• Checked only diaphragm shear and chord force (maximum depth,
not offset depth).
• No collectors, connection designs or details at re-entrant corners.
• Forces on trusses at collectors were not called out on drawing.
Actual Project
Steel decking
Diaphragm
Shears
Critical
connections
Transfer diaphragms
and collectors are
required
4 ft. offset
45 ft.
95 ft.
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QUESTIONS?This concludes The American Institute of Architects Continuing Education Systems Course
Part 1- Offset Diaphragms
R. Terry Malone, P.E., S.E.
Senior Technical Director
WoodWorks.org
Contact Information:
Events/Presentation Archives (slide handouts)-free
Paper:
http://www.woodworks.org/education-publications/research-papers/#
