Static Calculation Cw

Permasteelisa – Gartner Middle East L.L.C

TABLE OF CONTENTS 1

MATERIAL PROPERTIES .........................................................................................................5 1.1

Structural Aluminium Alloys........................................................................................................... 5

1.1.1

CW Frame Elements : Alloy 6063 T6 (extrusion) – ADM 2005............................................... 5

1.1.2

Bracket Elements : Alloy 6061 T6 (extrusion) – ADM 2005 .................................................... 5

1.2

Structural Steel S275..................................................................................................................... 5

1.3

Fasteners....................................................................................................................................... 5

1.3.1

Stainless Steel Bolts (ASTM F 738M Grade A2-70, M6-M20) ................................................ 5

2

GENERAL DESCRIPTION.........................................................................................................6

3

LOADS........................................................................................................................................9 3.1

Dead Load ..................................................................................................................................... 9

3.2

Barrier Loads ............................................................................................................................... 13

3.3

Wind Loads.................................................................................................................................. 13

3.4

Cable Forces due to Wind & Pretension Loads, PCF ................................................................... 13

4

GLASS......................................................................................................................................14 4.1

General Description and Dimensions.......................................................................................... 14

4.2

Allowable Stresses for Glass Analyses ....................................................................................... 14

4.3

Glass Verification for Wind Load ................................................................................................. 15

4.3.1

Analysis Results – WLsuction (3-sec) ....................................................................................... 15

4.3.2

Analysis Results – WLpressure (3-sec) ..................................................................................... 18

4.3.3

Analysis Results – Dead Load (beyond 1 year) .................................................................... 19

4.4 4.4.1 5

Glass Verification for Barrier Loads............................................................................................. 21 Analysis Results .................................................................................................................... 21 STRUCTURAL SEALANT .......................................................................................................25

5.1 5.1.1 6

General Description..................................................................................................................... 25 Structural Check .................................................................................................................... 25 MULLIONS ...............................................................................................................................26

6.1

Male and Female Mullions (inclined / vertical facades)............................................................... 26

6.1.1

Section Properties ................................................................................................................. 26

6.1.2

Analysis Results .................................................................................................................... 27

6.1.3

Structural Check .................................................................................................................... 30

7

TRANSOMS .............................................................................................................................36 7.1

Top and Bottom Transoms .......................................................................................................... 36

GAR-C-R-J-A-GN-0101-01

3


7.1.1

Section Properties ................................................................................................................. 36

7.1.2

Structural Check .................................................................................................................... 38

8

BRACKET DESIGN..................................................................................................................40 8.1

General Description..................................................................................................................... 40

8.2

Bracket Forces ............................................................................................................................ 40

8.3

Main Hook Bracket ...................................................................................................................... 41

8.3.1

Finite Element Model ............................................................................................................. 41

8.3.2


8.4

Secondary Hook Bracket............................................................................................................. 44

8.4.1


8.4.2


8.5

Slide Bracket ............................................................................................................................... 46

8.5.1


8.5.2


8.5.3

Slide Bracket Bolt Connection to Mullion............................................................................... 48

9

ANCHORAGE DESIGN ...........................................................................................................50 9.1

Channel Forces ........................................................................................................................... 50

REFERENCES .............................................................................................................................................58 APPENDIX A - ALLOWABLE STRESSES FOR 6063-T6..........................................................................59 APPENDIX B – ALLOWABLE STRESS & FACTOR OF SAFETY............................................................61 FOR ALUMINIUM ALLOY 6061-T6.............................................................................................................61 APPENDIX C – FACTOR OF SAFETY FOR METAL FASTNERS ............................................................65 APPENDIX D – ENGINEERING VALUES for PVB ....................................................................................66


4


1

MATERIAL PROPERTIES

1.1 Structural Aluminium Alloys 1.1.1 CW Frame Elements : Alloy 6063 T6 (extrusion) – ADM 2005 Minimum Mechanical Properties: Table 3.3-1M Ftu =

205

MPa

tensile ultimate strength

Fty =

170

MPa

tensile yield strength

Fcy =

170

MPa

compressive yield strength

Fsu =

130

MPa

shear ultimate strength

Fty,ALLO = min (Fty/1.65,Ftu/1.95) = 103.03 MPa

allowable tensile strength

Fcy,ALLO = Fcy/1.65

allowable compressive strength

= 103.03 MPa

1.1.2 Bracket Elements : Alloy 6061 T6 (extrusion) – ADM 2005 Minimum Mechanical Properties: Table 3.3-1M

1.2

Ftu =

260

MPa


Fty =

240

MPa


Fcy =

240

MPa

shear ultimate strength

Fsu =

165

MPa

compressive yield strength

Fty,ALLO = min (Fty/1.65,Ftu/1.95) = 133.3 MPa

allowable tensile strength

Fcy,ALLO = Fcy/1.65

allowable compressive strength

= 145.45 MPa

Structural Steel S275 E

= 200000 MPa

modulus of elasticity

Ftu

= 380 MPa


Fty

= 275 MPa


1.3 Fasteners 1.3.1 Stainless Steel Bolts (ASTM F 738M Grade A2-70, M6-M20) Rtu

= 700 MPa

tensile strength

Rty

= 450 MPa

yield strength


5


2 GENERAL DESCRIPTION The report must be read in conjunction with Gartner’s relevant drawings. Façade under study is a top-hanging unitised male-female curtain wall system. Aluminium extrusions act as panel frame elements and are supported by high-strength aluminum alloy brackets. These brackets, which allow vertical and horizontal tolerance adjustments, are fixed back to the supporting structure (concrete, steel elements). Typical module widths are 1500 mm and 1433 mm for inclined and vertical facades, respectively. As per Permasteelisa Gartner Middle East L.L.C.’s scope of work, this report covers facade spanning from G.L. 2.7 to 18.7 (for inclined), and S.5 to V (for vertical). Kindly refer to revision 01 of drawing number GAR-C-D-J-A-GN-2080. Three facade sections have been considered in the report. For calculation purposes, three sections are named as ZONE 01 (G.L. 2.7 to 4.3), ZONE 02 (G.L. 17.7 to 18.7), and ZONE 03 (G.L. 14 to 17.7). Kindly refer to figures below.

Figure 1: GAR-C-R-J-A-GN-0101-01

Inclined Facade – ZONE 01 (G.L. 2.7 to 4.3) 6


Figure 2:


Inclined Facade – ZONE 02 (G.L. 17.7 to 18.7)

7


Figure 3:


Inclined Facade – ZONE 03 (G.L. 14 to 17.7)

8


3

LOADS

3.1 Dead Load


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10



11



12


3.2 Barrier Loads The infill has been verified under barrier loads as per ASCE 7-05: Section 4.4. The following load cases have been considered: FIL1 = 0.22 kN

point load anywhere up to 1.1 m above FFL applied to the infill on a surface area not to exceed 305 mm square;

FIL2 = 0.73 kN/m

distributed line load at 1.1 m above FFL

It should be noted that the above loads have been considered not to act simultaneously with the maximum wind load.

3.3 Wind Loads The following design wind loads has been derived from RWDI Cladding Wind Load Study for Doha Convention Centre. As per Permasteelisa Gartner Middle East L.L.C.’s scope of work, the maximum recommended wind loads for cladding design are: Profiles/CW Bracket design wind load

pw = +1.0/-1.0 kPa

Glass/Sealant design wind load

pw = +1.0/-1.0 kPa

3.4 Cable Forces due to Wind & Pretension Loads, PCF The following forces have been considered in the analyses. These forces are acting on the cantilevered brackets (cable brackets) where cable supports are running through them. Cable brackets are fastened to the support frames (mullions), which consequently bear high stresses due to load transfer from these brackets. (Refer to cable analysis)

Load 1:

Dead Load + Pretension F1 = 10 kN,

Load 2:

Wind Load (pressure) F1 = 22 kN,

Load 3:

F2 = 4 kN

Wind Load (suction) F1 = 3 kN,


F2 = 9 kN

F2 = 17 kN

13


4 GLASS ASTM E 1300 – latest edition: Standard Practice for Determining Load Resistance of Glass in Buildings has been used to verify the structural adequacy of glass.

4.1 General Description and Dimensions The standard configuration of glazing system is reported below: External pane

10 mm heat strengthened

Air cavity

16 mm

Internal pane

4+4 mm heat strengthened, laminated

The maximum glass dimensions are 1500 x 4946 mm.

4.2 Allowable Stresses for Glass Analyses The allowable surface and edge stresses for each load case have been obtained in accordance to ASTM E 1300 – 09a multiplied by a load duration factor (LDF) in Table X6.1. HS,SURFACE = 46.6 MPa

Section X8.2 HS

HS,EDGE

Table X9.1 HS

= 36.5 MPa

LDF3s LDF60s

LDF>1yr

Figure 4:

Load Duration Factors

HS,3s = LDF3s* HS,SURFACE

= 46.6 MPa

Allow. surface stress for HS 3-sec load

HS,60s = LDF60s* HS,SURFACE

= 38.7 MPa

Allow. surface stress for HS 60-sec load

HS,>1yr = LDF>1yr* HS,SURFACE

= 14.5 MPa

Allow. surface stress beyond 1 year

HSe,3s = LDF3s* HS,EDGE

= 36.5 MPa

Allow. edge stress for HS 3-sec load

HSe,60s = LDF60s* HS,EDGE

= 30.3 MPa

Allow. edge stress for HS 60-sec load

HSe,>1yr = LDF>1yr* HS,EDGE

= 11.3 MPa

Allow. edge stress beyond 1 year


14


4.3 Glass Verification for Wind Load For structural verification against wind load, glass plates have been modelled using finite element software (SJ Mepla), and a non-linear approach was employed.

4.3.1 Analysis Results – WLsuction (3-sec)


15



16


sHS,max

Figure 5:

Maximum Plate Stresses (left) & Deflections (right): Case (DL+WLsuction)

Check stresses sHS,max < sHS,3s = 46.6 MPa


Æ Adequate

17


4.3.2 Analysis Results – WLpressure (3-sec)

sHS,max

Figure 6:

Maximum Plate Stresses (left) & Deflections (right): Case (DL+WLpressure)

Check stresses sHS,max < sHS,3s = 46.6 MPa GAR-C-R-J-A-GN-0101-01

Æ Adequate 18


4.3.3 Analysis Results – Dead Load (beyond 1 year)


19


sHS,max

Figure 7:

Maximum Plate Stresses (left) & Deflections (right): Case (DL+WLpressure)

Check stresses sHS,max < sHSe,>1yr = 46.6 MPa


Æ Adequate

20


4.4 Glass Verification for Barrier Loads For structural verification against barrier loads, glass plates have been modelled using finite element software (SJ Mepla), and a non-linear approach was employed.

4.4.1 Analysis Results


21



22



23


Figure 8:

Maximum Plate Stresses (left) & Deflections (right): Load Case Combination (DL+FIL1)

Figure 9:

Maximum Plate Stresses (left) & Deflections (right): Load Case Combination (DL+FIL2)

Check stresses sHS,max < sHS,60s= 38.68 MPa GAR-C-R-J-A-GN-0101-01

Æ Adequate 24


5

STRUCTURAL SEALANT

5.1 General Description Sealant Type: GE Ultra Glaze SSG 4400 or equivalent Sealant Properties: Allowed design stress in tension Vallowed for short term loads

0.14 MPa

Modulus of elasticity in tension or compression E

1.50 MPa

Figure 10:

Typical Sections

5.1.1 Structural Check Primary sealant, VB:

(as per ASTM C 1401)

VB= pw * a * 0.5 / hmc = 0.083 MPa < 0.14 MPa

Æ Adequate

Secondary sealant, VC: VC= pw * 1 * a * 0.5 / h’mc = 0.050 MPa < 0.138 MPa

where:

a

= 1.500 m

= smaller panel side

hmc =

9 mm

h’mc =

10 mm

= silicone bite (secondary)

1.0 kPa

= design wind load

(t13

= 0.661

pw = 1 =

t13

/

+

t23)

t1

= 10 mm

t2

= 4+4 = 8 mm


Æ Adequate

= silicone bite (primary)

(Section 3.3)

25


6

MULLIONS

6.1 Male and Female Mullions (inclined / vertical facades) Inclined and vertical facades share similar system design. However, the inclined facade is considered to be critical since the maximum panel dimensions are larger than that of the vertical facade. Also, forces or loads on the inclined facade are much higher and cause more critical effects on the panel’s structural elements such as frames, brackets, etc. Conservatively, the following analyses will only consider inclined facade to check the overall structural adequacy of both vertical and inclined facades.

6.1.1 Section Properties Material: Aluminium Alloy 6063 T6

ITOT = 4.903e6 mm4 Figure 11: GAR-C-R-J-A-GN-0101-01

Male [right] / Female [left] Mullions 26


Figure 12:

Note:

Mullion Stiffener (MS Plate S275)

Mullion stiffeners are only used in mullion profiles that support cable brackets.


Figure 13: Figure 14:


Load Cases: PCF, DL, WLsuction, WLpressure

27


ZONE 02

ZONE 01

ZONE 03

Figure 15:

Max. Bending Moments for Unreinforced Mullions: Worst Case - (DL+PCF+WLpressure)

ZONE 02

ZONE 01 ZONE 03

Figure 16:

Max. Bending Moments for Reinforced Mullions: Worst Case - (DL+PCF+WLpressure)


28


ZONE 02

ZONE 01 ZONE 03

Figure 17:

Max. Deflections for Unreinforced Mullions: Worst Case - (DL+PCF+WLpressure)

ZONE 02

ZONE 01

ZONE 03

Figure 18:

Max. Deflections for Reinforced Mullions: Worst Case - (DL+PCF+WLpressure)


29


The maximum bending moment for the worst load combination for unreinforced mullions is: M

= 5.93 kN-m

(Refer to Figure 15)

The moment is divided between the mullions by stiffness. Bending moment carried by the female mullion:

(Ixx,f / Ixx,tot) x M = 2.36 kN-m

Bending moment carried by the male mullion:

(Ixx,m / Ixx,tot) x M = 3.57 kN-m

Calculated deflections: L

= 4029 mm

max

= 11.79 – (0+2.54)/2 = 13.1 mm

lim

= min.(L/200,20) = 20 mm Æ Adequate

max < lim

6.1.3 Structural Check

Figure 19:


Mullion Profiles: Female (left), Male (right)

30


Female Mullion Section check - tension in beams

Section check - compression in components of beams


31



32


Male Mullion

Section check - tension in beams

Section check - compression in components of beams


33


The maximum bending moment for the worst load combination for reinforced mullions is: M

= 14.01 kN-m


The moment is divided between the mullions by stiffness. Ixx,f

= 1.955e6 mm4

Ixx,m

= 2.948e6 mm4

Ixx,steel

= 3.600e6 x [Esteel/Ealum] = 10.345e6 mm4

(aluminum equivalent)

4

Ixx,TOTAL = 15.248e6 mm

Bending moment carried by the female mullion:

MF = (Ixx,f / Ixx,TOTAL) x M

= 1.796 kN-m

Bending moment carried by the male mullion:

MM = (Ixx,m / Ixx,TOTAL) x M

= 2.709 kN-m

Bending moment carried by the steel stiffener:

Msteel = (Ixx,steel / Ixx,TOTAL) x M

= 9.505 kN-m


34


Shared bending moments carried by the male and female mullions are lower compared to that at Section 6.1.2; therefore, no further structural check is necessary.

Check bending stress capacity of stiffener (MS plate, S275) MR,steel = [Fty/nu]*Sxx,steel = 14.82 kN-m

bending stress capacity

where: Fty = 275 MPa


nu = 1.67

safety factor 2

Sxx,steel = 25*120 /4 = 90000 mm MR,steel > Msteel


3

plastic modulus

Æ Adequate

35


7 TRANSOMS 7.1 Top and Bottom Transoms 7.1.1 Section Properties Material: Aluminium Alloy 6063 T6

Figure 20:


Bottom Transom

Top Transom 36


ZONE 02

ZONE 01 ZONE 03

Figure 22: Top Transom Bending Moments & Deflections (Strong Axis): Worst Case - (DL+PCF+WLpressure)

ZONE 02

ZONE 01 ZONE 03

Figure 23: Bott. Transom Bending Moments & Deflections (Strong Axis): Critical Case - (DL+PCF+WLpressure)


37


7.1.2 Structural Check Bottom Transom For Strong axis bending Section check - tension in beams

For Weak axis bending

P = 2500*0.018*1.476*4.414*9.81*(cos 20.6o)/2*1000

1.35 kN


38


Maximum Deflection parallel to wall: max = 1.8 mm 75% = 75% (B) = 7.5 mm

where: B = 10 mm

net = B - max = 8.2 mm > 75%

Æ Adequate

Maximum Bending Moment (weak axis): M = 0.22 kN-mm

Section check - tension in beams

Check For Combined Bending fby/Fby + fbx/Fbx < 1.0

Æ Adequate

Top Transom For Strong axis bending Section check - tension in beams


39


8 BRACKET DESIGN 8.1 General Description The curtain wall bracket configuration, as shown below, is composed of high strength extruded aluminium profiles which allow horizontal and vertical tolerance adjustments. The whole bracket assembly utilizes three types of aluminium profiles, and anchor channels which are fixed to reinforced concrete structures such as beams, columns and slabs. At areas where there are no concrete structures to install these anchor channels, panel brackets are fixed to fabricated steel elements and horizontal steel members.

8.2 Bracket Forces

ZONE 02

ZONE 01

ZONE 03

Figure 24:


Support Reactions: Load Case - (DL+PCF+WLsuction)

40


ZONE 02

ZONE 01

ZONE 03

Figure 25:

Support Reactions: Load Case - (DL+PCF+WLpressure)

8.3 Main Hook Bracket Material: Aluminium Alloy 6061 T6 Bracket length = 250 mm

The bracket has been analysed using a F.E. model to determine the extent of any stress concentrations. Due to symmetry, only half of the bracket has been modelled by means of Hexa8 brick elements. Beam2 compression only beam elements have been used (with radial disposition) to simulate the contact between bolt and bracket, and also between bracket and supporting concrete structure. A non linear analysis has been carried-out.

8.3.1 Finite Element Model Critical support reactions: (Refer to Figures 24 & 25) Load Case - (DL + PCF + WLsuction)

Load Case - (DL + PCF + WLpressure)

RVn = 0.89/2 = 0.45 kN

RVp = 3.25/2 = 1.63 kN

vertical reactions

RHn = 25.67/2 = 12.84 kN

RHp = 24.26/2 = 12.13 kN

horizontal reactions


41


FHn

FVn or FVp

Figure 26:

FHp

F.E. Model, Boundary Conditions, and Loads



Brick Stresses & Displacements: Load Case - (DL+PCF+WLsuction) 42


Figure 28:

Brick Stresses & Displacements: Load Case - (DL+PCF+WLpressure)

Check for Stress The maximum Von Mises stress for the combination of dead load and wind load is: VVM = 116.83 MPa < Vall = 133.3 MPa

Æ Adequate

Check for Deflection Deflection is negligible.


43


8.4 Secondary Hook Bracket Material: Aluminium Alloy 6061 T6

The bracket has been analysed using a F.E. model to determine the extent of any stress concentrations. It has been modelled by means of Hexa8 brick elements. Compression-only beam elements have been used to simulate the contact between secondary hook and slide brackets. A non linear analysis has been carried-out.

8.4.1 Finite Element Model Critical support reactions: (Refer to Figures 24 & 25) Load Case - (DL + PCF + WLsuction)


RVn = 0.89/2 = 0.45 kN

RVp = 3.25/2 = 1.63 kN

vertical reactions

RHn = 25.67/2 = 12.84 kN

RHp = 24.26/2 = 12.13 kN


FHn

FVn or FVp

Figure 29:


FHp


44



Figure 30:

Brick Stresses & Displacements: Load Case - (DL+PCF+WLsuction)

Figure 31:


Check for Stress VVM = 125.13 MPa < Vall = 133.3 MPa

Æ Adequate

Check for Deflection: Deflection is negligible. GAR-C-R-J-A-GN-0101-01

45


8.5 Slide Bracket Material:

6061 T6 Aluminium Alloy

8.5.1 Finite Element Model The bracket has been analysed using a F.E. model to determine the extent of any stress concentrations. It has been modelled by means of Hexa8 brick elements. Compression-only beam elements have been used to simulate the contact between secondary hook and slide brackets. A non linear analysis has been carried-out. Critical support reactions: (Refer to Figures 24 & 25) Load Case - (DL + PCF + WLsuction)


RVn = 0.89/2 = 0.45 kN

RVp = 3.25/2 = 1.63 kN

vertical reactions

RHn = 25.67/2 = 12.84 kN

RHp = 24.26/2 = 12.13 kN


FHn

FVn or FVp

Figure 32:


FHp


46



Figure 33:

Brick Stresses & Displacements: Load Case - (DL+PCF+WLsuction)

Figure 34:


Check for Stress The maximum Von Mises stress for the combination of dead load and wind load is: VVM = 66.46 MPa < Vall = 133.3 MPa Check for Deflection:

Æ Adequate

Deflection is negligible.


47


8.5.3 Slide Bracket Bolt Connection to Mullion

Material: Bolt type: M10 A2/70

Critical support reactions: (Refer to Figure 24) Load Case - (DL + PCF + WLsuction) RVn = 0.89/2 = 0.45 kN

vertical reactions

RHn = 25.67/2 = 12.84 kN


Shear due to eccentricities, (x2 + y2) = 0 + 2*752 = 11250 mm2 Mtot = Fhn*(10tolerance) - Fvn*72 = 96.0 kN-mm Fh1 = Mtot*75/(x2 + y2) = 0.64 kN

Direct shear, Fh2 = Fh/3

= 4.28 kN

Fv = Fv/3

= 0.15 kN

Resultant shear, VR = [(Fh1 + Fh2)2 + Fv2]1/2 = 4.92 kN


48



49


9 ANCHORAGE DESIGN Anchor Channel / Bolt: HAC-50 F hef = 106 mm; HBC-C 4.6F, M12

9.1 Channel Forces Critical support reactions:

Load Case - (DL+ PCF +WLsuction)


V = RVn = 0.89 kN N = RHn = 25.67 kN

M = 25.67*205 + 0.89*80 = 5333.55 kN-mm Sb = (1732 + 232) / 173 = 176.1 mm T1 = M / Sb = 30.29 kN T2 = [d2/d1]*M = 4.03 kN


50



51



52



53



54



55



56



57


REFERENCES LOADS SEI/ASCE 7-05

Minimum Design Loads for Buildings and Other Structures

ALUMINIUM ALUMINIUM DESIGN MANUAL Specification guidelines for aluminium structures ASTM B209

Specification for Aluminum and Aluminum-Alloy Sheet and Plate

ASTM B221

Specification for Aluminum-Alloy Extruded Bars, Shapes and Tubes

AAMA TIR-A9-1991

Metal curtain wall fasteners

GLASS ASTM E 1300-09a

Standard Practice For Determining The Minimum Thickness And Type Of Glass Required To Resist A Specified Load

AAMA- 1984

Structural Properties Of Glass

SILICONE ASTM C 1401 - 02

Standard Guide for Structural Sealant Glazing

ASTM C 1249 - 93

Standard Guide for Secondary Seal for Sealed Insulating Glass Units for Structural Sealant Glazing Applications

STEEL ANSI/ AISC 360-05

Specification for Structural Steel Building

SOFTWARE Straus 7.1/ Strand 7.1

Finite Element Analysis System, researched and developed by G+D Computing Pty.Ltd in Australia. Address: Suite1, Level7, 541 Kent Street, Sydney, 2000. Australia. Email: [email protected]. Web: www.strand.aust.com. Fax: +61 2 9264 2066.. Tel: +61 2 9264 2977. Reference manual and User Guide.

SJ MEPLA

SJ Software GmbH Version 3.5 Address: Haarhofstr. 52, 52080 Aachen, Germany


58


APPENDIX A - ALLOWABLE STRESSES FOR 6063-T6 Aluminium Design Manual 2005 Table 2-24 ALLOWABLE STRESSES FOR BUILDING TYPE STRUCTURES 6063-T6, Extrusions and Pipe


59



60


APPENDIX B – ALLOWABLE STRESS & FACTOR OF SAFETY FOR ALUMINIUM ALLOY 6061-T6 (AS PER ALUMINIUM DESIGN MANUAL 2005)


61



62



63



64


APPENDIX C – FACTOR OF SAFETY FOR METAL FASTNERS (AS PER AAMA TIR–A9-1991)


65


APPENDIX D – ENGINEERING VALUES for PVB


66

Static Calculation Cw

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