design of metal roof deck diaphragms for low-rise steel buildings

7/22/2019 Design of Metal Roof Deck Diaphragms for Low-Rise Steel Buildings

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for Low-Rise Steel Buildings

Robert Tremblaycole Polytechnique, Montral, Canada

North American Steel Construction Conference

Orlando, Florida

May 12, 2010


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Plan

SDI Method

Example 1 (US) Example 2 (Canada) & Modelling

onc us onsMay12 ED69A

www.aisc.org/conferencepdh

R. Tremblay, Ecole Polytechnique of Montreal 2

May13 WE86S


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1. Background Information

ROOF JOISTS(typ.)ROOF BEAMS

(typ.)ruc uraSystem

COLUMNVERTICALX BRACING.(typ.)



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DeckSheetJoist Sidelap

Sidelap Frame

Button punch

.(typ.)

Weld

Fastener(typ.) Weld

Screw

ScrewNail



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Joist(typ.)

S

DeckSheet

S

S C d



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(typ.)

G, EIV

COLUMN(typ.)

VERTICALX BRACING

(typ.)

w = V / L

b

SFB

L/2 L/2



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P S

S

0.4 S

u

u G'

a

S = P / b G = S /

1

b

= / a = P ( / b) / a



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2. SDI Method

http://www.sdi.org/ http://www.cssbi.ca/R. Tremblay, Ecole Polytechnique of Montreal 10


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Shear Strength

Qf Qf Qf Qf Qf Qf Qf

1. Edge Panel:

Pn

Fe FeFp Fp w/2

xpxe

Fe = 2 Q x / wF = 2 Q x / w

f e

f

L

Qf QfQs Qs QsQf Qf

2. Intermediate Panel:

P w/LnP w/Ln

e1

Fe2

e1

Fe2

p1

Fp2

p1

Fp2

xp1xe1xp2xe2

w/2

Qf QfQs Qs QsQf

L

Qf



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Shear Strength

3. Corner Fastener:

4. Elastic Shear Buckling:

n ne, ni, nc, nb



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Shear Stiffness



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+ equations for shear strength and stiffness

or var ous as eners



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Shear Stiffness

(3 spans assumed in tables)

when using the tables



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http://www.cssbi.ca/



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http://www.canamgroup.ws

http://www.us.hilti.com

http://www.vulcraft.com

. .

http://www.wheelingcorrugating.com/R. Tremblay, Ecole Polytechnique of Montreal 25


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3. Example 1 (U.S.)

Joists @ 75''o/cX-Bracing1.5'' steel deck

' "- Boston, MA

00'-0"

5

- SCBF- R=6, Cd=5.0

@

25'-0"=1

& O=2.0- Seismic

10 @ 20'-0" = 200'-0"

1

Truss (typ.)

loads resisted

by diaphragmA K

Roof dead load = 21 psfWeight of walls = 5 psfRoof snow load = 35 psf

1s

L

Site Class D = 0.30 g ; = 0.07g = 6 s

S S

T

& X-braces



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Design Assumptions 0"5

Design parallel

@25'-0"=100'

X-Bracing10 @ 20'-0" = 200'-0"

A K

1

Rigid diaphragm

=> torsion

Occupancy Category II

=> = Regular structure

E uivalent Lateral

hn = 22 ft & CBF0.75

Force Procedure

a lies

a

. .

V based on amplified period

Wind loads neglected

u a . . .

(to be verified)



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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

CRCM0.46 V

R= 6.0 & I= 1.0''

0.02 V

= s = . = = . h

Include torsional effects -1K

0.2

0.3

/Cs

BostonSa(Elastic)

Cs(CBF - R= 6.0)

22'

41.3O

11.0

.0 K

0.0

0.1Sa(g

)

25'

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Period, T (s)

T/C brace system



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Tension-compression bracing required for SCBF

Use ASTM A500, gr. C square HSS (Fy= 50 ksi)

Pu16.6K/2/cos(41.3o) = 11.0K (negl. gravity loads)

b/t< 0.64(E/Fy)0.5 = 15.4 (AISC 341-05)

0.5. y -

with L = (252 + 222)0.5 x 12 = 400 in.,

= -. ,

but KL/r< 200 permitted if columns designed



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ARyFy = (1.4)(50)(1.89) = 132K,

but not greater than the brace force than can

be transferred to the brace by the system

e.g., oun a on over urn ng up .

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



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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

overstrength (0Eh) or forces corresponding toieldin in braces!! 0.02 V

0.54 VK

V

CRCM0.46 V

.

0.02 V

100'10'



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Diaphragm designed for Su= 166 plf:

1 1/2 wide rib (WR) roof deck (Canam P3606):

span = 75; sheet length = 225

Hilti X-ENP-19 L15 frame fasteners

layout & 2 sidelap connectors/span (SDI 3rd ed.):

S = 354 lf & G= 14.3 k/inDeckSheetJoist

(typ.)

SidelapFastener(typ.)

FrameFastener(typ.)



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. n . n .K1 = 0.304 ft



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Span = 6.25 => Snb = 1315 plf

= = >>



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870

K1 = 0.304 ft

3.78 + (0.3)1072 + (3)(0.304)(6.25)

6.25

870K2 = 870 k/in

K4 = 3.78G = 14.3 k/in

=3.78 + 51.5 + 5.70

Dxx = 1072 ft

Check with spreadsheet:

= 548 plf

= 14.7 k/in



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Collectors designed for Pu= 8.30K:

(SDC B: no need to design for overstrength)

K4.15c)

KK

22'

16.6 /100' = 0.166 kip/ft- .

- 8.30

25' (typ.)

0.02 V

0.54 V

V

CRCM0.46 V

= .

0.02 V

100'10'



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Chords designed for Pu= 7.9K :

a) c)

K

CR

DeckSheetJoist

(typ.)


PLAN

15.7 / 200' = 0.0785 kip/ftK

.Fastener(typ.)

K

K

K

0.0785 kip/ft

6.3

-1.6-7.9

b) d)

7.7K

22'

2030.8 / 200' = 0.154 kip/ftK

- 7.7K

PLAN ELEVATION (LONG WALL)

.

Pu= (154 plf)(200)2/ 8 / 100 = 7.7K

Select W8x10, A = 2.96 in2



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Check and diaphragm flexibility:

w = V / L

bSteel Deck

Chord (typ.)

+ SFB

.

V

L/2 L/2X Bracing

(typ.)Collector

(typ.)



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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)L = 200 ft

SECTION "A"

S= .b = 100 ftG = 14.3 k/in



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dB D . . . . .Less than 2% drift limit (5.28 forhn = 22)

0.63 > 2 x 0.11 = 0.22 => Flexible diaphragm

=> Out-of-plane X-braces

dont resist V

0.55 VK= 16.9

V = 30.8

CRCM0.45 V

''



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Verification of the Building Period

M WT 2 2

K g V

= =

w =

For flexible diaphragms (ASCE-41):

DB

( )( )

+ = +

B DB D

0.78W WT 2 0.10 0.080 , in inches

g V VT = CuTa

W = 593k 0.02

0.04

.

V/W Computed T

Under V = 30.8k, B = 0.11 & D = 0.63

+ 0.5

0.0 0.5 1.0 1.5 2.0

Period, T (s)

0.00

. . . . .= 1.09 s



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(typ.)

Elastic

COLUMNVERTICAL

X BRACING

x 1/R

.(typ.)

VeV = o e ver ca sys em


K4.15


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KK

K16.6 /100' = 0.166 kip/ft- 4.15

- 8.30

22'

25' (typ.)

Collector Collector

RoofDiaphragm

BracingMembers(Inelastic)

Columns

VV

K

KK K117 /100' = 1.17 kip/ft

29.3

- 29.3- 58.5CollectorElements

BracingConnections

Anchor Bolts& Foundations

K22'

25' (typ.)

13223.8



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4. Design Example 2 (Canada)

76.0 m

Seismic Loads

Site: Montreal Site Class C .6m

Vertical Bracing:

Tension-Only (T/O) Bracing

45

o . , d .

Roof snow loads: Ss = 2.48 kPa

Building Height : 8.6 m

Design along N-S direction


Steel Deck


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Joists(typ.)

Steel Deck38 mm Deep3 Spans Min.

Tension-OnlyX-Bracing (typ.)

G

45600

6@

7600=

W460x52 (typ.)

A

1 11


Membrane


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450 + Insulation+ Gypsum board+ Steel deck

18 600

500

+ Joists/Beams+ Electr./Mech.= 1.23 kN/m

2

Precast pre-insulatedpanels : 4.94 kN/m

2

76.0 m

45.6m

300

10 000

WRoof= (45.6)(76.0) [ 1.23 kPa + (0.25)(2.48 kPa) ] = 6410 kN

[mm]

Walls . . . .

W = 6410 + 3620 = 10 030 kN


V S(T) I W / (R R )


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V = S(T) IEW / (Ro Rd)

Ta = 2 x 0.025 x 8.6 = 0.43 s (to be verified)S = 0.422

E .R

o= 1.3

Rd= 3.0

V = [(0.422) (1.0) (10030) ] / [ (1.3) (3.0)] = 1080 kN

Accidental eccentricity= 0.1 x 76.0 m = 7.6 m

Note: Contribution of the

.

vertical bracing parallelto the direction ofloading is neglected

1080 kN 648 kNCM

7.6 m

ex e ap ragm .


D i f th V ti l B i


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Design of the Vertical Bracing

648 kN

= 48.5 deg.

8.6 m

X en T/O : Tf= 489 kN

HSS ASTM A500 gr. C

F = 345 MPa

3 requirements :

r yKL/r < 200 , with K = 0.5 and L = Lc-c- 500 mm 11 000 mmbo/t < 330/Fy0.5si KL/r < 100

y. s r =

& linear interpolation if 100 < KL/r < 200R. Tremblay, Ecole Polytechnique of Montreal 51


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HSS 102x102x4.8 :

= mmTr= 506 kN > Tf(= 489 kN)

KL/r = 5500 / 39.4 = 140 < 200 OK

b/t = (102 4 x 4.30) / 4.3 = 19.7 < 19.8 OK


Diaphragm Design


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Diaphragm Design

Expected strength of bracing members& expected horizontal shear in diaphragm, Vu

= =u y y y

1/1.34

T AR F ,o R 1.1

V /2u= +

=

.u y y y y y

y y

.

R FKL

CCTT uu uu

r E

HSS 102x102x4.8 : RyFy= 385 MPaT

u

= 628 kNCu= 176 kN

u= u+ u cos = w o e u ng >> V = 1080kNR. Tremblay, Ecole Polytechnique of Montreal 53


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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

CCTT uu uu

V /2u

Joist Spacing : 1900 mm

19 mm Welds & No. 10 ScrewsR. Tremblay, Ecole Polytechnique of Montreal 54

Select t = 1 21 mm


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Select t = 1.21 mm

e s onscrews at 150 mm o/c

qr

= 24.8 kN/m > 23.4 kN/m

G = 24.3 kN/mm



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Alternative

solution :


Lateral Deformations


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Lateral Deformations

w = 1080 kN / 76.0 m= 14.2 kN/m

w = V / L

B = 21.1 mm (Bracing) + bSF

F= 5 wL4/(384 EI)L/2

B

L/2

I = 2 x 6440 (45 600/2)

= 6.70 x 1012mm4

HSSConnectors F .

= 2 L = 76 000 mm

W460x52A = 6640 mm2

S= 9.3 mm

b = 45 600 mm

G = 24.3 kN/mmSECTION "A"


Ch k I t St D ift


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Check Inter-Storey Drift:

= Elastic= 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 !


Using a Numerical Model (SAP2000)


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Using a Numerical Model (SAP2000)

Membrane

Element

0.01 x ABeam(no connectors)

0.5 x Abracing (T/O)



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Modification of the stiffness of the membrane elements:


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Axial Stiffness Modification:Kx(f11) & Ky(f22)Modifier = 0.001(deck axial

stiffness neglected)

Shear Stiffness Modification:G (f12)

G = 24.3 kN/mm

= 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:


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Modification of the seismic mass:

w = 1.23 kN/m2+ (0.25)(2.48 kPa) = 1.85 kN/m2

= 1.85x10- kN/mm

w = x t= 7.7x10-8x 1.21= 9.317x10-8kN/mm2

o er = . x - . x -= 19.9



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B .= 4.3 mm

S= 9.5 mm

Total= 34.9 mmx 50

x 200R. Tremblay, Ecole Polytechnique of Montreal 63

Modification of the stiffness of membrane elements:


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Modifier Kx(f11) = 1219 / 914= 1.333

DeckSheetJoist

(typ.)


Modifier Ky(f22) = 0.001

FrameFastene(typ.)

Total= 33.5 mmR. Tremblay, Ecole Polytechnique of Montreal 64

Verification of the Building Period


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g

M WT 2 2

= =

w = V / L

For flexible diaphragms (ASCE-41):

DB

( )( )

+ = +

B DB D

0.78W WT 2 0.004 0.0031 , in mm

For the example building (Section 2) :

W = 10 030 kNUnder V = 1080 kN, B = 21.1 mm & D = 15.2 mm

T [ (10 030 / 1080) (0.004x21.1 + 0.0031x15.2) ]0.5

= 1.11 s R. Tremblay, Ecole Polytechnique of Montreal 65

LDiaphragm


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Diaphragm'

B b

,

BracingBents (K )

B D

B D

2

T 2K K g

=

B D 3 2with : K L EI L G'b=

+

For the sample building (Section 2) :

KB = 1080 kN / 21.1 mm = 51.1 kN/mm

= = 12 4 . , .

L = 76 000 mm, b = 45 600 mmK = 97.0 kN/mm

=> T 1.10 s


From Numerical Simulation: T = 1.10 s


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NBCC 2005:


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Ta = 0.025 hn = 0.025 (8.6 m) = 0.215 sbut T = 2 x Ta = 0.43 s permitted if verifiedby dynamic analysis

0.8

0.6

a, . - .

T = 2 Ta, CNB

= 0.43 s - S = 0.42

0.2

0.4g

T = Tcalc= 1.10 s - S = 0.13

0 0.4 0.8 1.2 1.6 2

T (s)

0

=S(T) Mv IE W

RdRo


Numerical modelling useful for more complex structures:


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. Lachapelle, Lainco Inc. / R. Tremblay, Ecole Polytechnique of Montreal 69


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1

4

2

3

. Lachapelle, Lainco Inc. / R. Tremblay, Ecole Polytechnique of Montreal 70

Conclusions


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Conclusions

SDI method is a comprehensive approach to

assess s ear s reng an s ness proper es o

metal roof deck diaphragms.

e sm c es gn orces can e re uce y a ng

advantage of the diaphragm flexibility on the

building period, but realistic (conservative)period estimates are needed.

Capacity design approach needed to prevent

inelastic response in the diaphragms, includingchords and collectors.


design of metal roof deck diaphragms for low-rise steel buildings

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