Design of Metal Roof Deck Diaphragms for Low Rise Buildings

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.)


DeckSheetJoist

(typ )SidelapFastener

Sidelap Frame

Button punch

Frame

(typ.) Fastener(typ.)

Weld

FrameFastener(typ.) Weld

Screwor

Screw

orNail


Joist(typ.)

S

DeckSheet

S

S C d


d



(typ.)

G, EIV

COLUMN(typ.)

VERTICALX BRACING

(typ.)

w = V / L

+b

+ SFB

L/2 L/2


P S

S

0.4 S

u

u G'a

S = P / b G = S / 1

b

= / a = P ( / b) / a


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


Shear Strength3. Corner Fastener:

4. Elastic Shear Buckling:

S = min (S S S S )Sn = min (Sne, Sni, Snc, Snb )


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


Shear Stiffness


+ equations for shear strength and stiffnessf i f tfor various fasteners


Shear Stiffness

(3 spans assumed in tables)

when using the tables


http://www.cssbi.ca/


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


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


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


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


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


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'


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 )


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


Span = 6.25 => Snb = 1315 plf

Snb = 0.80 x 1315 = 1052 plf >> SnSnb 0.80 x 1315 1052 plf >> Sn


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'


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


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.)


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


= 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


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



(typ.)

Elastic

COLUMN(typ )

VERTICALX BRACING

x 1/R

(typ.)(typ.)

VeR

V = f th ti l tR of the vertical system


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)


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


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


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


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).


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


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


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


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


Alternativesolution :


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"


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 !


Using a Numerical Model (SAP2000)

Membrane Element

0.01 x ABeam(no connectors)

0.5 x Abracing (T/O)


Properties of the membrane elements:

= 7.7x10-8 kN/mm3

E = 200 kN/mm2G = 76.92 kN/mm2

t = 1.21 mm


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


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


= 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


From Numerical Simulation: T = 1.10 s


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.


Design of Metal Roof Deck Diaphragms for Low Rise Buildings

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