Seismic Design of Low-Rise Steel Buildings with Metal Roof Deck Diaphragms: Canadian Seismic

Seismic Design of Low-Rise Steel Buildings with Metal Roof Deck Diaphragms: Canadian Seismic Provisions and Building Period Robert Tremblay Ecole Polytechnique, Montreal, Canada Colin Rogers McGill University, Montreal, Canada st tuto Mexicano e ca o de la a Co Construcciรณn st ucc รณ e en Acero ce o Instituto X Symposio Internacionale, Queretaro, Qpro. Mexico March 2009

Plan 1. Background Information 2. Seismic Design of a Simple Building 3. Influence of Diaphragm Flexibility on Building Period 4. Conclusions

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

2

1

1. Background Information Structural System

ROOF BEAMS (typ.)

ROOF JOISTS (typ.)

V VERTICAL X BRACING (typ.)

COLUMN (typ.)

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

3

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

4

2

Sidelap Deck Sheet

Joist (typ.)

Sidelap Fastener (typ.)

Frame

Button punch Weld

Frame Fastener (typ.)

Weld Screw or Nail

Screw

Joist (typ.)

q

Deck Sheet

q

γ

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

5

ROOF JOISTS (typ.)

ROOF BEAMS (typ.)

G’, EI

V VERTICAL X BRACING (typ.)

COLUMN (typ.)

w=V/L

b

ΔB

Δ F +Δ S

L/2

L/2 R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

6

3

1500 kN Actuator

Frame

Pin (typ.)

3658 mm

Specimen

Hor. Reaction Vert. Reaction (typ.)

6096 mm

Δ

Joist (typ.)

q

V

qu

a

0.4 qu

G' 1

b

q=V/b γ=Δ/a

γ G’ = q / γ = V (a / b) / Δ

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

7

Design Codes and Handbook National Building Code of Canada CSA-S16 Standard Design of Steel Structures

CISC Handbook of Steel Construction

CSSBI Steel Deck Diaphragms

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

8

4

NBCC 2005:

S(Ta) Mv IE W

V=

Rd Ro

Mv : Higher modes

1.0 0.8

S (g)

Ta : Design period

NBCC 2005 Site Class C (very dense soil)

0.6

Vancouver Montreal

0.4

IE : Importance factor W : Seismic weight

0.2

Rd : Ductility Ro : Overstrength

0.0 0.0

1.0

2.0

Period (s)

3.0

4.0

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

V=

9

S(Ta) Mv IE W Rd Ro S computed with Ta : – Ta = 0.085 hn0.75 (Steel moment-resisting frames) – Ta = 0.025 hn

(Braced steel frames)

– Ta = 0.05 hn0.75

(Shear walls and other structures)

or: Ta = T from dynamic analysis, but not greater than 1 5 x empirical (MRFs) or 2.0 1.5 2 0 x empirical (others)

W = Dead load + 0.25 x Roof snow load + 0.60 x Storage load R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

10

5

V Ve V=

S(Ta) Mv IE W Rd Ro

RdVy

Vy RoVf

Vf

Δ

Δe

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

V= System

S(Ta) Mv IE W Rd Ro Rd

Ro

RdRo

Moment Resisting Frames D MD LD

5.0 3.5 2.0

1.5 1.5 1.3

7.5 5.3 2.6

Concentrically braced frames

MD LD

3.0 2.0

1.5 1.3

4.5 2.6

y braced Eccentrically frames

D

4.0

1.5

6.0

Plate walls

D LD -

5.0 2.0

1.6 1.5

8.0 3.0

1.5

1.3

2.0

Conventional constr.

11

Cat.

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

12

6

NBCC 2005

CSA-S16-05

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

Capacity Design ROOF BEAMS (typ.)

V VERTICAL X BRACING (typ.)

V=

ROOF JOISTS (typ.)

COLUMN (typ.)

Perimeter members

13

Ve RoRd

Brace connections Foundations

V

V Roof Diaphragm

Bracing

Anchor rods

members

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

14

7

Why adopting capacity design for diaphragms?

• The system will behave as intended (inelastic response in the vertical elements) • Diaphragm integrity is maintained to ensure proper force transfer to the vertical elements • Damage to the diaphragm can lead to failure of roof framing members carrying gravity loads.

• Damage to the diaphragm can be difficult to detect and repair • Lack of quality control to ensure proper diaphragm construction R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

15

2. Seismic Design of a Simple Building 1. Geometry / Seismic Loads 2. Design of the Vertical Bracing 3. Diaphragm Design 4. Drift Estimates 5. Axial Loads in Perimeter Members

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

16

8

2.1 Geometry / Seismic Loads 76.0 m

45.6 m

N

Site: Montreal, Site Class C Vertical Bracing: g Tension Only (T/O) Bracing Type MD: Ro = 1.3, Rd = 3.0 Roof snow loads: Ss = 2.48 kPa Building Height : 8.6 m Design along N-S direction R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

Contreventement en X tension seulement (typ.)

Tablier métallique.

38 mm prof.

3 portées min.

A

6 @ 7600 = 45 600

G

Poutrelles (typ.).

17

Poutre W460x52 (typ.)

10 @ 7600 = 76 000 1

11

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

18

9

Membrane + Insulation + Gypsum board + Steel deck + Joists/Beams + Electr./Mech.

2 = 1.23 kN/m

450

500 18 600

Precast pre-insulated 2 panels : 4.94 kN/m

45.6 m

76.0 m

10 000 300 [mm]

WRoof = (45.6)(76.0) [ 1.23 kPa + (0.25)(2.48 kPa) ] = 6410 kN WWalls = 2 (76.0) [ (9.1)2/2/8.6 ][ 4.94 kPa ] = 3620 kN W = 6410 + 3620 = 10 030 kN R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

19

V = S(T) IE W / (Ro Rd) Ta = 2 x 0.025 x 8.6 = 0.43 s (to be verified) S = 0.422 IE = 1.0 Ro = 1 1.3 3 Rd = 3.0

V = [(0.422) (1.0) (10030) ] / [ (1.3) (3.0)] = 1080 kN 76.0 m

CM 7.6 m

1080 kN

648 kN

Accidental eccentricity = 0.1 x 76.0 m = 7.6 m Note: Contribution of the vertical bracing parallel to the direction of loading is neglected (flexible diaphragm).

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

20

10

2.2 Design of the Vertical Bracing 648 kN

8.6 m θ

θ = 48.5 deg.

X en T/S : Tf = 489 kN HSS ASTM A500 gr. C Fy = 345 MPa 3 requirements : Tr = φ A Fy > Tf KL/r < 200 , with K = 0.5 and L = Lc-c - 500 mm ≈ 11 000 mm bo/t < 330/Fy0.5 si KL/r < 100 425/Fy0.5 si KL/r = 200 & linear interpolation if 100 < KL/r < 200 R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

21

HSS 102x102x4.8 : A = 1630 mm2 Tr = 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

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

22

11

2.3 Diaphragm Design Expected strength of bracing members & expected horizontal shear in diaphragm, Vu Tu = AR yFy ,où R y = 1.1

(

Cu = 1.2 AR yFy / 1 + λ2.68 y λy =

)

1/1.34

≤ AR yFy

Vu /2

KL R yFy r π2E Tu

HSS SS 102x102x4.8 :

Cu

Tu

Cu

RyFy = 385 MPa Tu = 628 kN Cu = 176 kN

Vu = 4 (Cu + Tu) (cos θ) = 2130 kN (whole building) >> V = 1080kN R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

23

Vu = 4 (Cu + Tu) (cos θ) = 2130 kN (whole building) < V with RoRd = 1.3 = 3240 kN OK Design shear flow: qf = ((2130 kN / 2)) / 45.6 m = 23.4 kN/m q

f

Cu

Tu

Tu

Cu

Vu /2

Canam P3606 Steel Deck : Joist Spacing : 1900 mm 19 mm Welds & No. 10 Screws R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

24

12

Select t = 1.21 mm Welds on 36/9 screws at 150 mm o/c qr = 24.8 24 8 kN/m > 23 23.4 4 kN/m Gâ&#x20AC;&#x2122; = 24.3 kN/mm

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

25

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

26

Alternative solution :

13

2.4 Lateral Deformations w=V/L

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

ΔB

Δ F+Δ S

L/2

ΔF = 5 wL4/(384 EI) I = 2 x 6440 (45 600/2)2 = 6.70 x 1012 mm4 ΔF = 4.6 mm

L/2

HSS Connectors W460x52 A = 6640 mm2

SECTION "A"

ΔB = 21.1 mm (Bracing)

L = 76 000 mm b = 45 600 mm G’ = 24.3 kN/mm

ΔS = wL2/(8 G’b) ΔS = 9.3 mm

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

27

Check Inter-Storey Drift: Under E :

ΔExpected = RoRdΔElastic

ΔElastic = 21.1 + 4.6 + 9.3 = 35.0 mm ΔExpected = (1.3)(3.0)(35.0) = 137 mm = 0.016 hs < 0.025 hs => OK !

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

28

14

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 & C.A. Rogers, McGill University

29

Properties of the membrane elements: Îł = 7.7x10-8 kN/mm3 E = 200 kN/mm2 G = 76.92 kN/mm2 t = 1.21 mm

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

30

15

Modification of the stiffness of the membrane elements: Axial Stiffness Modification: Kx (f11) & Ky (f22) Modifier = 0.001 (deck axial stiffness neglected) Shear Stiffness Modification: G’ (f12) G’ = 24.3 kN/mm G’ = 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 & C.A. Rogers, McGill University

31

Modification of the seismic mass: w = 1.23 kN/m2 + (0.25)(2.48 kPa) = 1.85 kN/m2 = 1.85x10-6 kN/mm2 w=γxt = 7.7x10-8 x 1.21 = 9.317x10-8 kN/mm2 Modifier = 1.85x10-6 / 9.317x10-8 = 19.9

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

32

16

ΔB = 21.1 mm ΔF = 4.3 mm ΔS = 9.5 mm x 50

ΔTotal = 34.9 mm

x 200 R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

33

Modification of the stiffness of membrane elements: Modifier Kx (f11) = 1219 / 914 = 1.333 Modifier Ky (f22) = 0.001

Joist (typ.)

Deck Sheet

Sidelap Fastener (typ.)

Frame Fastene (typ.)

ΔTotal = 33.5 mm R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

34

17

2.5 Axial Loads in Perimeter Members N-S Beams: (collectors)

2130 kN / 2 / 45.6 m = 23.4 kN/m

2130 kN / 76.0 m = 28.06 kN/m

PLAN 355

117 -239

-61 - 416

23.4 kN/m

Tu

Cu

-355

Tu

Cu

1065 kN R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

35

Tmax

E-W Beams: (chords) C max

2130 kN / 76.0 m = 28.06 kN/m

PLAN

Cmax = Tmax = (28.06 kN/m)(76.0 m)2 / 8 / 45.6 m = 444 kN

Note: E-W seismic loads also induce axial loads in E-W & N-S beams.

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

36

18

3. Influence of Diaphragm Flexibility on Building Period 1 Background 1.

B k d IInformation f i 2. Field Test Programs 3. Laboratory Test Programs

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

37

3.1 Background Information w=V/L

T = 2π

M WΔ = 2π K g V

For flexible diaphragms (ASCE-41):

T ≈ 2π

W ( ΔB + 0.78ΔD ) = g V

ΔB

ΔD

W ( 0.004 ΔB + 0.0031ΔD ) , Δ en mm V

For the example building (Section 2) :

W = 10 030 kN Sous V = 1080 kN, ΔB = 21.1 mm & ΔD = 15.2 mm T ≈ [ (10 030 / 1080) (0.004x21.1 + 0.0031x15.2) ]0.5 = 1.11 s R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

38

19

L Diaphragm (EI, G') Bracing Bents (KB)

ΔB

T = 2π

ΔD

( KB + KD ) W KBKD

b

with : KD =

g

π2 L3 π2EI + L G'b

For the sample building (Section 2) :

KB = 1080 kN / 21.1 mm = 51.1 kN/mm G’ = 24.3 kN/mm, I = 6.70 x 1012 mm4 L = 76 000 mm, b = 45 600 mm KD = 97.0 kN/mm => T ≈ 1.10 s R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

39

From Numerical Simulation: T = 1.10 s

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

40

20

NBCC 2005: Ta = 0.025 hn = 0.025 (8.6 m) = 0.215 s but T = 2 x Ta = 0.43 s permitted if verified y dynamic y analysis y by 0.8

Ta, CNB = 0.215 s - S = 0.67

0.6

T = 2 Ta, CNB = 0.43 s - S = 0.42 S (g)

0.4

T = T calc = 1.10 1 10 s - S = 0.13 0 13

02 0.2 0 0

0.4

0.8

1.2

1.6

2

T (s)

V=

S(T) Mv IE W Rd Ro

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

41

Parametric Study: Site: Vancouver, BC and Montreal, QC Building area : 600 to 4200 m2 Aspect ratio: L/b = 1.0 to 2.5 Building height: hn = 4.8 4 8 to 10.8 10 8 m Bracing type: T/C & T/O SFRS type: Rd = 3.0 (MD), 2.0 (LD) and 1.5 (CC) 1.2

T (Long span)

T (Short span)

0.8

Vancouver

0 05 hn 0.05

0.4

0.025 hn

0.0

Perio od (s)

Perio od (s)

1.2

0.8

Vancouver

0 05 hn 0.05

0.4

0.025 hn

0.0 0

4

8

Building Height, hn (m)

12

0

4

8

12

Building Height, hn (m) Computed T R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

42

21

A = 600 to 4200 m2 L/b = 1.0 to 2.5 hn = 4.8 to 10.8 m T/O Bracing Rd = 2.0 ((Type yp LD)) 40

40

T/O - TYPE LD Vancouver S/(RdRo) 2/3 S(0.2s)/(RdRo) Ta < 0.05 hn Ta = T

20

T/O - TYPE LD Montreal

30

V/W (%)

30

V/W (%)

NBCC: Ta = 0.025 hn < 0.05 hn

S/(RdRo) 2/3 of S(0.2 s)/(RdRo) Ta < 0.05 hn Ta = T

20 10

10

0

0 0.0

0.5

1.0

1.5

Period (s)

2.0

2.5

0.0

0.5

1.0

1.5

Period (s)

2.0

2.5

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

43

3.2 Field Test Programs

University of British Columbia

University of Sherbrooke

Ambient vibration testing (2003-04): Natural frequencies Mode shapes Damping R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

44

22

Test Set-up (University of Sherbrooke)

Portable equipment y measurements Velocity Multiple setups of 6 transducers: 2 reference transducers (x and y) 4 roving sensors 5-10 minutes / setup R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

45

Typical measurements (University of Sherbrooke)

Mode 1

Mode 2

Mode 3

f = 2,3 23H Hz

f = 3,7 37H Hz

f = 4,1 41H Hz

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

46

23

T (s)

Ambient vibration results:

1.0

0.5

T (s)

1.0

Ta

0.0

0.5

0.0 0.0

2.0

4.0

6.0

8.0

hn (m)

10.0

12.0

20

40

60

80

100

120

140

Diaphragm Span, L (m)

.

T = 0.001 5.75 L2 + 1.25 L hn b 1.2

T (Long span)

T (Short span)

0.8

Vancouver

0.05 hn

0.4

0.025 hn

0.0

Perriod (s)

Perriod (s)

1.2

0.8

Vancouver

0.05 hn

0.4

0.025 hn

0.0 0

4

8

Building Height, hn (m)

12

0

4

8

12

Building Height, hn (m) Computed T Lamarche (2005) R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

47

Possible reasons for the observed mismatch: 1. Contribution of non structural roof components to in-plane diaphragm stiffness 2. Amplitude of ambient vibrations too low to trigger slippage of deck and mobilize connection flexibility y 3. Warping restrained at the sheet ends

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

48

24

Influence of non structural roof components 17.5 (45) 15.0 (43) 12.5 S (kN/m)

(39) 10.0 7.5

(41)

5.0 Roofing S-N Bare Steel S-N Bare Steel End Lap BP-W Bare Steel End Lap S-N

2.5 0.0 0

5

10

γ (x10-3 rad)

15

20

Test on 22 gauge 38 mm deep steel deck G’ increased by 26-45%

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

49

30 25

q (kN/m)

20 15 10 25 mm Fibreboard 16 mm Gypsum G B Board d S/N 0.91 mm Steel Deck (305 mm o/c) B/P 0.91 mm Steel Deck (305 mm o/c)

5 0 0

5

10

γ (mrad)

15

20

Mastrogiuseppe, S., Rogers, C.A., Tremblay, R. and Nedisan, C.D. 2006. Influence of NonStructural Components on Roof Diaphragm Stiffness and Fundamental Periods of Single-Storey Steel Buildings. J of Constructional Steel Research, 64, 2, 214-227.

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

50

25

G'BS+GB / G'BS

1.5 1.4 1.3 1.2 1.1 1.0 0

10

20

30

40

30

40

G'BS (kN/mm)

G'BS+G GB (kN/mm)

40

Computed Gâ&#x20AC;&#x2122; with and without roofing

30

20

10

0 0

10

20

G'BS (kN/mm) R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

Average = 0.98

TB BS+GB / TBS

Average = 0.99 1.00

1.00

0.95

0.95

0.90

0.90

Vancouver

Montreal 0.85

0.85 0.2

0.4

0.6

0.8

1.0

1.2

0.0

1.4

0.4

0.8

1.2

1.6

2.0

1.6

2.0

T BS (s)

TBS (s) 0.15

0.15

TBS - TBS S+GB (s)

51

Vancouver

Montreal

0.10

0.10

0.05

0.05

0.00

0.00 0.2

0.4

0.6

0.8

T BS (s)

1.0

1.2

1.4

0.0

0.4

0.8

1.2

TBS (s)

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

52

26

Low amplitude in ambient vibration testing & warping restraint Δ

q

V

SDI Procedure :

qu

a

0.4 qu

G’ =

G' 1

b

γ

V (a/b)

ΔS + ΔC + ΔW

G’ = q / γ = V (a / b) / Δ

q=V/b γ=Δ/a

ΔS

ΔC

ΔW

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

53

Too low amplitude in ambient vibration testing q

Steel joist (typ.)

qu

Deck panel

Side-lap fastener (typ.)

Frame fastener (typ.)

0.4 qu

G' G 1

γ

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

54

27

Restrained warping SDI method mostly based on single sheet tests Warping deformations in opposite directions In overlaping joints

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

55

Recent ambient vibration test results compared with ith 3D SAP2000 Analysis (2007)

•

Building: 71 m x (91 (91.5 5 + 21) m x 6 6.8 8m

•

NBCC: Ta = 0.05 hn = 0.34 s

•

Ambient vibration: T1 = 0.39 s

Tremblay, R., Nedisan, C., Lamarche, C.-P., and Rogers, C. 2008. Periods of Vibration of a Low-Rise Building with a Flexible Steel Roof Deck Diaphragm. Proc. 5th International Conference on Thin-Walled Structures, Brisbane, Australia, 615-622.

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

56

28

5

21 000

N

14

91 500 11 500

6 @ 10 000 = 60 000

2 @ 10 000 = 20 000 254

Vertical Bracing (typ.)

C7

Steel joist (typ.)

C8

J

Button Punch @ 150 o/c

10 000

1

Button Punch @ 600 o/c

H

C2

8 820

Mezzanine EL. 13 405

3265

F

Slab 38+65

C5

27 420

C4

5 @ 10 500 = 52 500

Steel Deck 0.91 x 38 x 914 (typ.)

C3

C1 C6

A Steel Deck 0.76 x 38 x 914 Button punch @ 150 o/c Welds @ 300 o/c

Steel Deck 0.76 x 38 x 914 Button punch @ 300 o/c Welds @ 300 o/c (except otherwise noted)

Button Punch @ 150 o/c

C10

C9

Button Punch @ 150 o/c Frame welds @ 150 o/c

Button Punch @ 150 o/c

Elevations: TOS = 17 000 Column Base PL = 9725

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

C7

57

C8

C2

HSS127x127x4.8

HSS 127x127x6.4

C3

C5

C4

HSS 89x89x6.4

HSS 127x127x4.8 C2 & C5@C9

C1

HSS127x127x4.8 C3

C1 & C10

C4

C6 C10

C9

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

58

29

Case

Description

1 2 2.1 2.2 2.3 2.4 3 3.1 3.2 4 4.1 4.2 Test

Basic model Influence of end member fixity 1 + fixed column bases 2.1 + fix ended W-shape beams (strong axis) 2.2 + fix ended joists (weak axis) and tie joists (strong axis) 2.3 + fixed brace ends Influence of perimeter members and walls 2 + infinite in-plane stiffness for the interior masonry wall on gridline 5 3.1 + infinite in-plane stiffness for all exterior walls Influence of roof diaphragm shear stiffness 3 + infinitely stiff steel deck connectors 4.1 + warping prevented at overlapping deck sheet end laps Measured values

TN-S (s) 1.11

TE-W (s) 1.00

0.98 0.97 0.80 0.79

0.83 0.72 0.70 0.70

0.78 0.74

0.70 0.52

0.67 0.34 0.39

0.47 0.23 0.30

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

59

3.3 Test Program Polytechnique/McGill (2007-2010) 12 @ 1751.6 = 21 020 6400

7310

W360x39

â&#x20AC;˘ Restrained warping

1000 kN Dynamic Actuator (typ.)

W360x39 with HSS 101.6x101.6x4.8 Shear Connectors (typ.)

8 @ 914 = 7310

â&#x20AC;˘ Amplitude of vibration

7310

450mm Joists (typ.)

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

60

30

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

61

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

62

31

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

63

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

64

32

Dynamic Testing Protocol

q qu

SS2 SS1

0.4 qu

G' Sine Sweep

γ

12 @ 1751.6 = 21 020

Various displacement time histories with increasing amplitude dynamically applied with actuators at the two ends (frame mounted on rockers)

6400

7310

W360x39

7310

1000 kN Dynamic Actuator (typ.)

W360x39 with HSS 101.6x101.6x4.8 Shear Connectors (typ.)

8 @ 914 = 7 7310

1

450mm Joists (typ.)

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

65

Phase I Tests (2007) • 0.76 mm deck sheets with endlaps: 7007 mm

G’ =

1 ΔS + ΔC + ΔW

7007 mm

=

1 0.0229 + 0.0271 + 0.1873

7007 mm

= 4.20 kN/mm

• 0.76 mm deck sheets without endlaps: 21 020 mm

1 G’ = ΔS + ΔC + ΔW

1 = 0.0229 + 0.0282 + 0.0453

= 10.4 kN/mm

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

66

33

Variation of the specimen period with loading amplitude: G’ = 4.20 kN/mm – Tpredicted = 0.18 s

Fundamental Period (s)

0.25

0.20

0.15

G’ = 10.2 kN/mm – Tpredicted = 0.11 s

0.10

White Noise Tests

0.05

Without End Laps With End Laps

0.00 0.00

0.05

0.10

0.15

0.20

RMS Absolute Acceleration at L/2 (g)

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

67

4. Conclusions • Metal roof deck diaphragms suitable for seismic resistance • Capacity design for roof diaphragms, collectors and chords in Canadian seismic provisions • Fl Flexibility ibilit off rooff diaphragm di h can lengthen the building period but further studies needed before it can be implemented in design R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

68

34

Acknowledgements • Graduate Students C. Nedisan, C.-P. Lamarche, S. Mastroguiseppe, J. Franquet and R. Massarelli • Technical staff at École Polytechnique • Research groups at U. of Sherbrooke and UBC • Financial support from NSERC, FQRNT & CFI and the industry (WSB, Vancouver steel deck diaphragm committee, CSSBI, SDI, CWB, Hilti, ITW Buildex, SSEF, Canam Group, RJC, Sofab and Acier Leroux)

R. Tremblay, Ecole Polytechnique of Montreal & C.A. Rogers, McGill University

69

35