Static Calculation Cw

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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 = 103.03 MPa allowable compressive strength

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

Minimum Mechanical Properties: Table 3.3-1M

Ftu= 260 MPa tensile ultimate strength

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 = 145.45 MPa allowable compressive strength

1.2 Structural Steel S275

E = 200000 MPa modulus of elasticity

Ftu = 380 MPa tensile ultimate strength

1.3 Fasteners

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

Rtu = 700 MPa tensile strength

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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.

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3 LOADS

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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, P

CF

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, F2 = 9 kN

Load 2: Wind Load (pressure) F1 = 22 kN, F2 = 4 kN

Load 3: Wind Load (suction) F1 = 3 kN, F2 = 17 kN

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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 = 36.5 MPa Table X9.1 HS

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

LDF>1yr LDF3s LDF60s

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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.

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Figure 5: Maximum Plate Stresses (left) & Deflections (right): Case (DL+WLsuction)

Check stresses

sHS,max < sHS,3s = 46.6 MPa Æ Adequate

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4.3.2 Analysis

Results – WL

pressure

(3-sec)

Figure 6: Maximum Plate Stresses (left) & Deflections (right): Case (DL+WLpressure)

Check stresses

sHS,max < sHS,3s = 46.6 MPa Æ Adequate

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Figure 7: Maximum Plate Stresses (left) & Deflections (right): Case (DL+WLpressure)

Check stresses

sHS,max < sHSe,>1yr = 46.6 MPa Æ Adequate

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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

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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

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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 Æ Adequate

where: a = 1.500 m = smaller panel side hmc = 9 mm = silicone bite (primary)

h’mc = 10 mm = silicone bite (secondary)

pw = 1.0 kPa = design wind load (Section 3.3)

1 = t1 3 / (t1 3 + t2 3 ) = 0.661 t1 = 10 mm t2 = 4+4 = 8 mm

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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

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Figure 12: Mullion Stiffener (MS Plate S275)

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

6.1.2 Analysis

Results

Figure 13:

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Figure 15: Max. Bending Moments for Unreinforced Mullions: Worst Case - (DL+PCF+WLpressure)

Figure 16: Max. Bending Moments for Reinforced Mullions: Worst Case - (DL+PCF+WLpressure)

ZONE 03 ZONE 02 ZONE 01 ZONE 03 ZONE 02 ZONE 01

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Figure 17: Max. Deflections for Unreinforced Mullions: Worst Case - (DL+PCF+WLpressure)

Figure 18: Max. Deflections for Reinforced Mullions: Worst Case - (DL+PCF+WLpressure)

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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

max < lim Æ Adequate

6.1.3 Structural

Check

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Female Mullion

Section check - tension in beams

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Male Mullion

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

M = 14.01 kN-m (Refer to Figure 16)

The moment is divided between the mullions by stiffness. Ixx,f = 1.955e6 mm

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Ixx,m = 2.948e6 mm 4

Ixx,steel = 3.600e6 x [Esteel/Ealum] = 10.345e6 mm 4

(aluminum equivalent) Ixx,TOTAL = 15.248e6 mm

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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

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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 tensile yield strength

nu = 1.67 safety factor

Sxx,steel = 25*1202/4 = 90000 mm3 plastic modulus

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7 TRANSOMS

7.1 Top and Bottom Transoms

7.1.1 Section

Properties

Figure 20: Bottom Transom

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

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

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7.1.2 Structural

Check

Bottom Transom

For Strong axis bending

For Weak axis bending

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

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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

Check For Combined Bending

fby/Fby + fbx/Fbx < 1.0 Æ Adequate

Top Transom

For Strong axis bending

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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

Figure 24: Support Reactions: Load Case - (DL+PCF+WLsuction)

ZONE 03

ZONE 02

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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

ZONE 03

ZONE 02

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Figure 26: F.E. Model, Boundary Conditions, and Loads

8.3.2 Analysis

Results

Figure 27: Brick Stresses & Displacements: Load Case - (DL+PCF+WLsuction)

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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.

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8.4 Secondary Hook Bracket

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

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8.4.2 Analysis

Results

Check for Stress

VVM = 125.13 MPa < Vall = 133.3 MPa Æ Adequate

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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.

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8.5.2 Analysis

Results

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 Æ Adequate

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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 horizontal reactions

Shear due to eccentricities, (x2 + y2) = 0 + 2*752 = 11250 mm2 Mtot = Fhn*(10tolerance) - Fvn*72 = 96.0 kN-mm Fh1 = Mtot*75/(x 2 + y2) = 0.64 kN Direct shear, Fh2 = Fh/3 = 4.28 kN Fv = Fv/3 = 0.15 kN Resultant shear, VR = [(Fh1 + Fh2) 2 + Fv 2 ]1/2 = 4.92 kN

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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) (Refer to Figure 24)

V = RVn = 0.89 kN N = RHn = 25.67 kN M = 25.67*205 + 0.89*80 = 5333.55 kN-mm Sb = (173 2 + 232) / 173 = 176.1 mm T1 = M / Sb = 30.29 kN T2 = [d2/d1]*M = 4.03 kN

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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

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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

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APPENDIX B – ALLOWABLE STRESS & FACTOR OF SAFETY

FOR ALUMINIUM ALLOY 6061-T6

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APPENDIX C – FACTOR OF SAFETY FOR METAL FASTNERS

(AS PER AAMA TIR–A9-1991)

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Static Calculation Cw

TABLE OF CONTENTS

1 MATERIAL PROPERTIES

1.1 Structural Aluminium Alloys

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

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

1.2 Structural Steel S275

1.3 Fasteners

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

2 GENERAL DESCRIPTION

3 LOADS

3.2 Barrier Loads

3.3 Wind Loads

3.4 Cable Forces due to Wind & Pretension Loads, P

4 GLASS

4.1 General Description and Dimensions

4.2 Allowable Stresses for Glass Analyses

4.3 Glass Verification for Wind Load

4.3.2 Analysis

Results – WL

(3-sec)

4.4 Glass Verification for Barrier Loads

4.4.1 Analysis

Results

5 STRUCTURAL SEALANT

5.1 General Description

5.1.1 Structural

Check

6 MULLIONS

6.1 Male and Female Mullions (inclined / vertical facades)

6.1.1 Section

Properties

6.1.2 Analysis

Results

6.1.3 Structural

Check

7 TRANSOMS

7.1 Top and Bottom Transoms

7.1.1 Section

Properties

7.1.2 Structural

Check

8 BRACKET DESIGN

8.1 General Description

8.2 Bracket Forces

8.3 Main Hook Bracket

8.3.1 Finite Element Model

8.3.2 Analysis

Results

8.4 Secondary Hook Bracket

8.4.1 Finite Element Model

8.4.2 Analysis

Results

8.5 Slide Bracket

8.5.1 Finite Element Model

8.5.2 Analysis

Results

8.5.3 Slide Bracket Bolt Connection to Mullion

9 ANCHORAGE DESIGN

9.1 Channel Forces

REFERENCES

APPENDIX A - ALLOWABLE STRESSES FOR 6063-T6

APPENDIX B – ALLOWABLE STRESS & FACTOR OF SAFETY

FOR ALUMINIUM ALLOY 6061-T6

APPENDIX C – FACTOR OF SAFETY FOR METAL FASTNERS

(AS PER AAMA TIR–A9-1991)