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metal roof deck diaphragms design guide and presentation. Structural diaphragms. Civil engineering material
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Design of Metal Roof Deck DiaphragmsDesign of Metal Roof Deck Diaphragmsfor Low-Rise Steel Buildings
Robert Tremblaycole Polytechnique, Montral, Canada
North American Steel Construction ConferenceOrlando, Florida
May 12, 2010
Plan
Background InformationBackground Information
SDI Method
Example 1 (US)
Example 2 (Canada) & Modelling
C l i ConclusionsMay12 ED69A
www.aisc.org/conferencepdh
R. Tremblay, Ecole Polytechnique of Montreal 2
May13 WE86S
1. Background Information
ROOF JOISTS(typ.) ROOF BEAMS
St t l (typ.)
V
StructuralSystem
COLUMN(typ )
VERTICALX BRACING
V
(typ.)(typ.)
R. Tremblay, Ecole Polytechnique of Montreal 3
DeckSheetJoist
(typ )SidelapFastener
Sidelap Frame
Button punch
Frame
(typ.) Fastener(typ.)
Weld
FrameFastener(typ.) Weld
Screwor
Screw
orNail
R. Tremblay, Ecole Polytechnique of Montreal 4
Joist(typ.)
S
DeckSheet
S
S C d
R. Tremblay, Ecole Polytechnique of Montreal 5
d
R. Tremblay, Ecole Polytechnique of Montreal 6
ROOF JOISTS(typ.) ROOF BEAMS
(typ.)
G, EIV
COLUMN(typ.)
VERTICALX BRACING
(typ.)
w = V / L
+b
+ SFB
L/2 L/2
R. Tremblay, Ecole Polytechnique of Montreal 7
P S
S
0.4 S
u
u G'a
S = P / b G = S / 1
b
= / a = P ( / b) / a
R. Tremblay, Ecole Polytechnique of Montreal 8
R. Tremblay, Ecole Polytechnique of Montreal 9
2. SDI Method
http://www.sdi.org/ http://www.cssbi.ca/R. Tremblay, Ecole Polytechnique of Montreal 10
Shear Strength
Qf Qf Qf Qf Qf Qf Qf
1. Edge Panel:
Pn
Fe FeFp Fp w/2xpxe
Fe = 2 Q x / wF = 2 Q x / w
f e
p f p
L
p f p
Qf QfQs Qs QsQf QfF FF F
2. Intermediate Panel:
P w/LnP w/Ln
Fe1
Fe2
Fe1
Fe2
Fp1
Fp2
Fp1
Fp2
xp1xe1xp2xe2
w/2
Qf QfQs Qs QsQfL
Qf
R. Tremblay, Ecole Polytechnique of Montreal 11
Shear Strength3. Corner Fastener:
4. Elastic Shear Buckling:
S = min (S S S S )Sn = min (Sne, Sni, Snc, Snb )
R. Tremblay, Ecole Polytechnique of Montreal 12
R. Tremblay, Ecole Polytechnique of Montreal 13
Shear Stiffness
P ( /b)
SDI Procedure :PS
Su
G =P (a/b)
S + C + d0.4 Su
1G'
a
S = P / b = / a
G = S / = P ( / b) /
a
b
S C d
R. Tremblay, Ecole Polytechnique of Montreal 14
Shear Stiffness
R. Tremblay, Ecole Polytechnique of Montreal 15
R. Tremblay, Ecole Polytechnique of Montreal 16
+ equations for shear strength and stiffnessf i f tfor various fasteners
R. Tremblay, Ecole Polytechnique of Montreal 17
R. Tremblay, Ecole Polytechnique of Montreal 18
R. Tremblay, Ecole Polytechnique of Montreal 19
Shear Stiffness
(3 spans assumed in tables)
when using the tables
R. Tremblay, Ecole Polytechnique of Montreal 20
R. Tremblay, Ecole Polytechnique of Montreal 21
R. Tremblay, Ecole Polytechnique of Montreal 22
R. Tremblay, Ecole Polytechnique of Montreal 23
http://www.cssbi.ca/
R. Tremblay, Ecole Polytechnique of Montreal 24
http://www.canamgroup.ws
http://www.us.hilti.com
http://www cssbi ca/
http://www.vulcraft.com
http://www.cssbi.ca/
http://www.wheelingcorrugating.com/R. Tremblay, Ecole Polytechnique of Montreal 25
3. Example 1 (U.S.)
Joists @ 75''o/cX-Bracing
(typ.)1.5'' steel deck
(sheets 25'-0" long)- Boston, MA@(typ.) (sheets 25 -0 long)
0
0
'
-
0
"
5 - SCBF- R=6, Cd=5.0
4
@
2
5
'
-
0
"
=
1
& O=2.0- Seismic
10 @ 20'-0" = 200'-0"
4
1
Truss (typ.)
loads resistedby diaphragm
A KRoof dead load = 21 psfWeight of walls = 5 psfRoof snow load = 35 psf
1sL
Site Class D = 0.30 g ; = 0.07g = 6 s
S ST
& X-braces
R. Tremblay, Ecole Polytechnique of Montreal 26
Design Assumptions
-
0
"
5
Design parallelto short walls
g
4
@
2
5
'
-
0
"
=
1
0
0
'
-
to short walls
X-Bracing 10 @ 20'-0" = 200'-0"
4
A K
1
Rigid diaphragm=> torsion
Occupancy Category II
=> Importance Factor, I = 1.0 Regular structure
Equivalent Lateral
Importance Factor, I 1.0
hn = 22 ft & CBF=> T = 0 02 (22) 0.75 = 0 20 sq
Force Procedure applies
=> Ta = 0.02 (22) 0.75 = 0.20 s V based on amplified period
=> C T = 1 6(0 20) = 0 32 spp
Wind loads neglected=> CuTa = 1.6(0.20) = 0.32 s
(to be verified)R. Tremblay, Ecole Polytechnique of Montreal 27
W = 593K0.02 V
Assume T = 1.6 x Ta = 0.32 s
= 1.0 (SDC B)0.54 V
K
K
= 16.6
V = 30.8
CRCM 0.46 V
R = 6.0 & I = 1.0
=> C = 0 052 => V = 30 8K (E ) 100'10'0.02 V
=> Cs = 0.052 => V = 30.8K (Eh)
Include torsional effects-11
K
K
10010
0.2
0.3
/
C
s
BostonSa (Elastic)Cs (CBF - R = 6.0)
22'
41.3O
11.0
11.0 KK
0.0
0.1
S
a
(
g
)
25'
/C0.0 0.5 1.0 1.5 2.0 2.5 3.0Period, T (s)
T/C brace system
R. Tremblay, Ecole Polytechnique of Montreal 28
Bracing members: Tension-compression bracing required for SCBF
Bracing members:
Use ASTM A500, gr. C square HSS (Fy = 50 ksi)
Pu 16.6K/2/cos(41.3o) = 11.0K (negl. gravity loads)
b/t < 0.64(E/Fy)0.5 = 15.4 (AISC 341-05)
KL/r < 4 0(E/F )0.5 = 96 (AISC 341 05) KL/r < 4.0(E/Fy)0.5 = 96 (AISC 341-05)with L = (252 + 222)0.5 x 12 = 400 in.,K = 0 5 (X-bracing)K = 0.5 (X-bracing),but KL/r < 200 permitted if columns designedfor the brace expected yield tensile capacityfor the brace expected yield tensile capacity
R. Tremblay, Ecole Polytechnique of Montreal 29
Select HSS 3x3x3/16: (tdes = 0.174)
Ag = 1.89 in2
b/t = (3.0-3x0.174)/0.174 = 14.2 < 15.4 OK
KL/r = (0 5)(400)/1 14 = 175 < 200 OK (but > 96) KL/r = (0.5)(400)/1.14 = 175 < 200 OK (but > 96)
cPn = 13.9K > 11.0K OK16.6K
22'11
.0
-11.0 KK Check Pu = 11.0K with gravity loads once
25'
41.3Ogravity loads once columns are designed
25
R. Tremblay, Ecole Polytechnique of Montreal 30
Tension capacity of brace connections: Tension capacity of brace connections:
ARyFy = (1.4)(50)(1.89) = 132K,but not greater than the brace force than canbe transferred to the brace by the system( f d ti t i lift)(e.g., foundation overturning uplift).
Note: brace force corresponding to 0Eh(0 = 2.0) does not apply
Compression capacity of brace connections:1.1RyPn = (1.1)(1.4)(13.9/0.9) = 23.8K
R. Tremblay, Ecole Polytechnique of Montreal 31
Diaphragm (incl. collectors & chords): Diaphragm and collector elements on short walls
designed for 16.6K/100 = 166 plf.
Currently, ASCE 7 & AISC do not require design of these elements for load combinations withthese elements for load combinations with overstrength (0Eh) or forces corresponding to yielding in braces!! 0.02 Vyielding in braces!!
0.54 VK= 16 6
V
CRCM 0.46 VK= 16.6
0.02 V
100' 10'
R. Tremblay, Ecole Polytechnique of Montreal 32
Diaphragm designed for Su = 166 plf: 1 1/2 wide rib (WR) roof deck (Canam P3606): span = 75; sheet length = 225 #10 screw sidelap connectors #10 screw sidelap connectors Hilti X-ENP-19 L15 frame fasteners
Select 22 ga. (0.0295) deck with 36/4 fastenerSelect 22 ga. (0.0295 ) deck with 36/4 fastener layout & 2 sidelap connectors/span (SDI 3rd ed.):
Sn = 354 plf & G = 14.3 k/inSn 354 plf & G 14.3 k/inDeckSheetJoist
(typ.)SidelapFastener(typ.)
FrameFastener(typ.)( y )
R. Tremblay, Ecole Polytechnique of Montreal 33
Span = 6 25 => S = 545 plf S = 0 65 x 520 = 354 plfSpan = 6.25 => Sn = 545 plf. Sn = 0.65 x 520 = 354 plfK1 = 0.304 ft
R. Tremblay, Ecole Polytechnique of Montreal 34
Span = 6.25 => Snb = 1315 plf
Snb = 0.80 x 1315 = 1052 plf >> SnSnb 0.80 x 1315 1052 plf >> Sn
R. Tremblay, Ecole Polytechnique of Montreal 35
R. Tremblay, Ecole Polytechnique of Montreal 36
R. Tremblay, Ecole Polytechnique of Montreal 37
G =870
K1 = 0.304 ft
/
G =3.78 + (0.3)1072 + (3)(0.304)(6.25)
6.25
G 870K2 = 870 k/in
K4 = 3.78G = 14.3 k/in
G = 8703.78 + 51.5 + 5.70
Dxx = 1072 ft
Check with spreadsheet:
= 548 plf
= 14.7 k/inR. Tremblay, Ecole Polytechnique of Montreal 38
Collectors designed for Pu = 8.30K:(SDC B: no need to design for overstrength)
K
K
4.15
4 15
c)K
KK
22'
16.6 /100' = 0.166 kip/ft- 4.15
- 8.30
25' (typ.)
0.02 V
0.54 VK16 6
V
CRCM 0.46 VK= 16.6
0.02 V
100' 10'
R. Tremblay, Ecole Polytechnique of Montreal 39
Chords designed for Pu = 7.9K :a) c)
KV = 30 8
CR
CM
DeckSheet
Frame
Joist(typ.)
SidelapFastener(typ.)
PLAN15.7 / 200' = 0.0785 kip/ftK
V = 30.8CMFrameFastener(typ.)
K
KK
0.0785 kip/ft
6.3
-1.6-7.9
b) d)
K
7.7K
22'
20(typ )30.8 / 200' = 0.154 kip/ft
K
- 7.7K
PLAN ELEVATION (LONG WALL)(typ.)
Pu = (154 plf)(200)2 / 8 / 100 = 7.7K
Select W8x10, A = 2.96 in2
R. Tremblay, Ecole Polytechnique of Montreal 40
Check and diaphragm flexibility:w = V / L
bSteel DeckUnits (typ.)
Chord (typ.)
+ SFB
Units (typ.)
Vertical
V
L/2 L/2Vertical
X Bracing(typ.)
Collector(typ.)
R. Tremblay, Ecole Polytechnique of Montreal 41
w = V / L
w = 30.8k / 200 ft= 154 plf
b
B = 0.11 (Bracing) + SF
B
F = 5 wL4/(384 EI)I = 2 x 2.96 (12 x 50)2Connectors
L/2 L/2
( )= 2.13 x 106 in4
F = 0.089W8x10A = 2.96 in2(HSS)
S = wL2/(8 Gb) 0 54L = 200 ft
SECTION "A"
S = 0.54b = 100 ftG = 14.3 k/in
R. Tremblay, Ecole Polytechnique of Montreal 42
= C ( + ) / I = 5 0 (0 11 + 0 63) / 1 0 = 3 7 = Cd(B + D) / I = 5.0 (0.11 + 0.63) / 1.0 = 3.7Less than 2% drift limit (5.28 for hn = 22)
0.63 > 2 x 0.11 = 0.22 => Flexible diaphragm=> Out-of-plane X-braces
dont resist V
K
0.55 VK
K
= 16.9
V = 30.8
CRCM 0.45 V
100'10' 100 10
R. Tremblay, Ecole Polytechnique of Montreal 43
Verification of the Building PeriodV / L
M WT 2 2K g V
= =
w = V / L
For flexible diaphragms (ASCE-41): D
B
( ) ( ) + = + B D B D0.78W WT 2 0.10 0.080 , in inchesg V V0 06
T = CuTa
W = 593k 0.020.04
0.06
V
/
W
Computed T
Under V = 30.8k, B = 0.11 & D = 0.63T [ (593 / 30.8) (0.004 x 0.11 + 0.0031 x 0.63) ]0.5
0.0 0.5 1.0 1.5 2.0Period, T (s)
0.00
T [ (593 / 30.8) (0.004 x 0.11 + 0.0031 x 0.63) ]= 1.09 s
R. Tremblay, Ecole Polytechnique of Montreal 44
ROOF JOISTS(typ.) ROOF BEAMS
(typ.)
Elastic
COLUMN(typ )
VERTICALX BRACING
x 1/R
(typ.)(typ.)
VeR
V = f th ti l tR of the vertical system
R. Tremblay, Ecole Polytechnique of Montreal 45
KKKK16.6 /100' = 0.166 kip/ft
4.15
- 4.15- 8.30
22'
25' (typ.)Collector Collector
RoofDiaphragm
BracingMembers(Inelastic)
Columns
VV
K
KK K
K
117 /100' = 1.17 kip/ft
29.3
- 29.3- 58.5
23 8
CollectorElements
BracingConnections
Anchor Bolts& Foundations
Collector Collector
ELEVATION (END WALL)
KK
22'
25' (typ.)
13223.8
ELEVATION (END WALL)
R. Tremblay, Ecole Polytechnique of Montreal 46
4. Design Example 2 (Canada)
76.0 m
NSeismic Loads
Site: Montreal, Site Class C
N
5
.
6
m
,Vertical Bracing:
Tension-Only (T/O) BracingType MD: R = 1 3 R = 3 0
4
5
Type MD: Ro = 1.3, Rd = 3.0 Roof snow loads: Ss = 2.48 kPaBuilding Height : 8.6 mDesign along N-S direction
R. Tremblay, Ecole Polytechnique of Montreal 47
Joists(typ.)
Steel Deck38 mm Deep3 Spans Min.
Tension-OnlyX-Bracing (typ.)
G
4
5
6
0
0
6
@
7
6
0
0
=
4
W460x52 (typ.)
10 @ 7600 = 76 000
A
10 @ 7600 = 76 000
1 11
R. Tremblay, Ecole Polytechnique of Montreal 48
450Membrane+ Insulation+ Gypsum board+ Steel deck
18 600500
+ Joists/Beams+ Electr./Mech.= 1.23 kN/m2
Precast pre-insulatedpanels : 4.94 kN/m2
76.0 m
4
5
.
6
m
300
10 000
WRoof = (45.6)(76.0) [ 1.23 kPa + (0.25)(2.48 kPa) ] = 6410 kNW = 2 (76 0) [ (9 1)2/2/8 6 ][ 4 94 kPa ] = 3620 kN
[mm]
WWalls = 2 (76.0) [ (9.1)2/2/8.6 ][ 4.94 kPa ] = 3620 kNW = 6410 + 3620 = 10 030 kN
R. Tremblay, Ecole Polytechnique of Montreal 49
V = S(T) IE W / (Ro Rd)
Ta = 2 x 0.025 x 8.6 = 0.43 s (to be verified)S = 0.422I = 1 0IE = 1.0 Ro = 1.3 Rd = 3.0
V = [(0.422) (1.0) (10030) ] / [ (1.3) (3.0)] = 1080 kN
76 0 m Accidental eccentricity = 0.1 x 76.0 m = 7.6 mNote: Contribution of the
76.0 m
vertical bracing parallel to the direction of loading is neglected (fl ibl di h )
1080 kN 648 kNCM
7.6 m
(flexible diaphragm).
R. Tremblay, Ecole Polytechnique of Montreal 50
Design of the Vertical Bracing
648 kN
= 48.5 deg.
8.6 m
X en T/O : Tf = 489 kNHSS ASTM A500 gr. CFy = 345 MPay 3 5 a
T = A F > Tf3 requirements :
Tr = A Fy > TfKL/r < 200 , with K = 0.5 and L = Lc-c - 500 mm 11 000 mmbo/t < 330/Fy0.5 si KL/r < 100
425/F 0 5 i KL/ 200425/Fy0.5 si KL/r = 200& linear interpolation if 100 < KL/r < 200
R. Tremblay, Ecole Polytechnique of Montreal 51
HSS 102x102x4.8 :A 1630 2A = 1630 mm2
Tr = 506 kN > Tf (= 489 kN)KL/r = 5500 / 39.4 = 140 < 200 OKb/t = (102 4 x 4.30) / 4.3 = 19.7 < 19.8 OK
R. Tremblay, Ecole Polytechnique of Montreal 52
Diaphragm Design
Expected strength of bracing members& expected horizontal shear in diaphragm, Vu
( )= =
u y y y
1/1.342 68
T AR F ,o R 1.1
C 1 2 AR F / 1 AR F V /2u( )= + =
2.68u y y y y y
y yy 2
C 1.2 AR F / 1 AR F
R FKL
CC TT uu uuy 2r E
HSS 102x102x4.8 : RyFy = 385 MPaTu = 628 kNCu = 176 kN
V 4 (C + T ) ( ) 2130 kN ( h l b ildi )Vu = 4 (Cu + Tu) (cos ) = 2130 kN (whole building)>> V = 1080kN
R. Tremblay, Ecole Polytechnique of Montreal 53
Vu = 4 (Cu + Tu) (cos ) = 2130 kN (whole building)
Design shear flow:
< V with RoRd = 1.3 = 3240 kN OK
qf = (2130 kN / 2) / 45.6 m = 23.4 kN/mqf
CC TT uu uu
V /2u
Canam P3606 Steel Deck :Canam P3606 Steel Deck : Joist Spacing : 1900 mm
19 mm Welds & No. 10 ScrewsR. Tremblay, Ecole Polytechnique of Montreal 54
Select t = 1.21 mmW ld 36/9Welds on 36/9screws at 150 mm o/c
qr = 24.8 kN/m > 23.4 kN/mG = 24.3 kN/mm
R. Tremblay, Ecole Polytechnique of Montreal 55
Alternativesolution :
R. Tremblay, Ecole Polytechnique of Montreal 56
Lateral Deformations
w = 1080 kN / 76.0 m= 14.2 kN/m
w = V / L
B = 21.1 mm (Bracing) + b
SF
F = 5 wL4/(384 EI)2
L/2
B
L/2
I = 2 x 6440 (45 600/2)2
= 6.70 x 1012 mm4
= 4 6 mmHSSConnectors F = 4.6 mm
S = wL2/(8 Gb)L = 76 000 mmW460x52A = 6640 mm2
S wL /(8 G b)S = 9.3 mmb = 45 600 mmG = 24.3 kN/mmSECTION "A"
R. Tremblay, Ecole Polytechnique of Montreal 57
Check Inter-Storey Drift:
Under E : Expected = RoRdElasticUnder E : Expected RoRdElasticElastic = 21.1 + 4.6 + 9.3 = 35.0 mm
Expected = (1.3)(3.0)(35.0) = 137 mm = 0.016 hs< 0.025 hs => OK !
R. Tremblay, Ecole Polytechnique of Montreal 58
Using a Numerical Model (SAP2000)
Membrane Element
0.01 x ABeam(no connectors)
0.5 x Abracing (T/O)
R. Tremblay, Ecole Polytechnique of Montreal 59
Properties of the membrane elements:
= 7.7x10-8 kN/mm3
E = 200 kN/mm2G = 76.92 kN/mm2
t = 1.21 mm
R. Tremblay, Ecole Polytechnique of Montreal 60
Modification of the stiffness of the membrane elements:
Axial Stiffness Modification:Kx (f11) & Ky (f22)Modifier = 0.001od e 0 00(deck axialstiffness neglected)
Shear Stiffness Modification:G (f12)
G = 24.3 kN/mm
G = G x tG = G x t= 76.92 x 1.21= 93.07 kN/mm
Modifier = 24.3 / 93.07= 0.261
R. Tremblay, Ecole Polytechnique of Montreal 61
Modification of the seismic mass:
w = 1.23 kN/m2 + (0.25)(2.48 kPa) = 1.85 kN/m26 / 2= 1.85x10-6 kN/mm2
w = x t= 7.7x10-8 x 1.21= 9.317x10-8 kN/mm2
Modifier = 1 85x10-6 / 9 317x10-8Modifier = 1.85x10-6 / 9.317x10-8= 19.9
R. Tremblay, Ecole Polytechnique of Montreal 62
= 21 1 mmB = 21.1 mm
F = 4.3 mmF 4.3 mm
S = 9.5 mmTotal = 34.9 mmx 50
x 200R. Tremblay, Ecole Polytechnique of Montreal 63
Modification of the stiffness of membrane elements:
Modifier Kx (f11) = 1219 / 914= 1.333
DeckSheetJoist
(typ.)SidelapFastener(typ.)
Modifier Ky (f22) = 0.001 FrameFastene(typ.)
Total = 33.5 mmR. Tremblay, Ecole Polytechnique of Montreal 64
Verification of the Building Period
M WT 2 2K g V
= = w = V / L
K g V
For flexible diaphragms (ASCE-41): D
B
( ) ( ) + = + B D B D0.78W WT 2 0.004 0.0031 , in mmg V Vg V VFor the example building (Section 2) :
W = 10 030 kNUnder V = 1080 kN, B = 21.1 mm & D = 15.2 mmT [ (10 030 / 1080) (0.004x21.1 + 0.0031x15.2) ]0.5
= 1.11 sR. Tremblay, Ecole Polytechnique of Montreal 65
LDiaphragm
(EI G') ( )K K W+B
D b
(EI, G )
BracingBents (K )
( )B DB D
2
K K WT 2K K g
+=
BD D 3 2with : K L EI L G'b
= +
For the sample building (Section 2) :
KB = 1080 kN / 21.1 mm = 51.1 kN/mmG = 24 3 kN/mm I = 6 70 x 1012 mm4G = 24.3 kN/mm, I = 6.70 x 10 mmL = 76 000 mm, b = 45 600 mmKD = 97.0 kN/mmD=> T 1.10 s
R. Tremblay, Ecole Polytechnique of Montreal 66
From Numerical Simulation: T = 1.10 s
R. Tremblay, Ecole Polytechnique of Montreal 67
NBCC 2005:
Ta = 0.025 hn = 0.025 (8.6 m) = 0.215 sbut T = 2 x Ta = 0.43 s permitted if verified by dynamic analysis
0.8 T CNB = 0 215 s S = 0 67
0 4
0.6
S ( )
Ta, CNB = 0.215 s - S = 0.67
T = 2 Ta, CNB = 0.43 s - S = 0.42
0.2
0.4S (g)
T = Tcalc = 1.10 s - S = 0.13
0 0.4 0.8 1.2 1.6 2T (s)
0
V =S(T) Mv IE W( ) V
Rd RoR. Tremblay, Ecole Polytechnique of Montreal 68
Numerical modelling useful for more complex structures:
. Lachapelle, Lainco Inc. / R. Tremblay, Ecole Polytechnique of Montreal 69
1
42
3
. Lachapelle, Lainco Inc. / R. Tremblay, Ecole Polytechnique of Montreal 70
Conclusions
SDI method is a comprehensive approach to h t th d tiff ti fassess shear strength and stiffness properties of
metal roof deck diaphragms.
S i i d i f b d d b t ki Seismic design forces can be reduced by taking advantage of the diaphragm flexibility on the building period, but realistic (conservative) g ( )period estimates are needed.
Capacity design approach needed to prevent inelastic response in the diaphragms, including chords and collectors.
R. Tremblay, Ecole Polytechnique of Montreal 71