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1 STRUCTURAL CALCULATIONS Using MASTERSERIES POWERPAD Project Name: BARZAN CAMP STEEL STRUCTURE AT SPORT HALL AT ROOF FLOOR SLAB IN CLUBHAUSE V01 STRUCTURAL ENGINEERS ALWADI STEEL ST17-GATE 98 IND. AREA DOHA-QATAR Tel: (+974) 4600982 Fax: (+974) 4505194 PROJECT NO: 325 NOVEMBER 2010

1-Sport Hall at Roof Floor Slab (15!12!2010)v01

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Page 1: 1-Sport Hall at Roof Floor Slab (15!12!2010)v01

1

SSTTRRUUCCTTUURRAALL CCAALLCCUULLAATTIIOONNSS Using

MASTERSERIES POWERPAD

Project Name: BARZAN CAMP

STEEL STRUCTURE AT SPORT HALL AT ROOF FLOOR SLAB IN CLUBHAUSE

V01

SSTTRRUUCCTTUURRAALL EENNGGIINNEEEERRSS

AALLWWAADDII SSTTEEEELL ST17-GATE 98

IND. AREA

DOHA-QATAR

Tel: (+974) 4600982 Fax: (+974) 4505194

PPRROOJJEECCTT NNOO:: 332255

NOVEMBER 2010

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ST17-Gate98

IND. AREA

DOHA-QATAR

Job ref : Job Ref

Sheet : 2

Made By : TAMER MOHAMMED

Date : 06/04/2010

Checked : HANY AHMED HASSAN

Approved : HANY AHMED HASSAN

2

1. MATERIAL SPECIFICATIONS:-

- Concrete characteristic strength = 35 MPa

- Steel Section is steel 43, its yield strength = 275 MPa

- Connection Bolts between Steel Elements are high strength bolts grade 8.8

- Expansion Bolts between Steel Elements and Concrete are HSA16

- Welding electrode with yield strength (E7018) = 460 MPa

- Welding electrode with ultimate strength = 520 MPa

2. CODES-

- Q.C.S.2007.

-Design of Steel sections and connections according to British Standard 5950-1-

2000.

- Loadings are applied as per BS-6399 V1,2.

-All tolerances as per B.S-5950-2000 code.

3. SOFT WARES:-

-MASTER SERIES 2010.

-PROFIS.

- LIMCON.

-CFS V06.

4. DESIGN CRITERIA:

- Concrete Slab Thickness = 100 mm.

- Live Load on Roof Slab = 150 Kg/m2.

- Live Load on First Floor = 250 kg/m2.

- Own weight of steel members calculate automatic.

- Super Dead Load at Roof Floor (Collateral + Finishing +Metal Deck) =

400 Kg/m2.

- Super Dead Load at First Floor (Collateral + Finishing +Metal Deck) =

250 Kg/m2.

- Wall load at Roof Floor (200 mm thick concrete wall- 5.00 m Height) =

0.20X25X5 = 25 Kn/m.

- Wind Speed 45 m/Sec (3Second) = 25m/Sec (mean Hourly).

- Bottom Chord of Truss Member is connecting together with Lateral

Support Spacing not more 4.00 m.

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Job ref : Job Ref

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Date : 06/04/2010

Checked : HANY AHMED HASSAN

Approved : HANY AHMED HASSAN

3

5. Loading Cases and Load Combination

Load Group Labels Load Group UT Unity Load Factor (All Cases) Load Group D0 Dead Load (Columns Self Weight) Load Group D1 Super Imposed Dead Load Load Group L0 Live Load Load Group L1 Live Load Load Group W1 Wind Direction 0 Degrees from X Axis (Fetches 225 to 315 Degrees) Load Group A1 Dead Load (Self Weight) Load Group G1 Construction Load

Load Case 001 : Ultimate Limit State (Final Stage) Load Combination + 1.00 UT + 1.40 D0 + 1.40 D1 + 1.60 L1 + 1.40 A1

Load Case 002 : Ultimate Limit State (Construction Stage) Load Combination + 1.00 UT + 1.40 D0 + 1.60 L0 + 1.40 A1 + 1.60 G1

Load Case 003 : Live Load (Serviceability) Load Combination + 1.00 UT + 1.00 L1

Load Case 004 : Super Imposed Load (Serviceability) Load Combination + 1.00 UT + 1.00 D1

Load Case 005 : Dead Load - Selfweight (Serviceability) Load Combination + 1.00 UT + 1.00 D0 + 1.00 A1

Load Case 006 : Dead plus Live (Ultimate) Load Combination + 1.00 UT + 1.40 D1 + 1.60 L1 + 1.40 A1

Load Case 007 : Live Only (Serviceability) Load Combination + 1.00 UT + 1.00 L1

Load Case 008 : Dead plus Wind (1.0 D0 + 1.0 A1 + 1.0 D1 + 1.4 W1) (a=5) Load Combination + 1.00 UT + 1.00 D0 + 1.00 D1 + 1.40 W1 + 1.00 A1

Load Case 009 : Dead plus Wind (1.4 D0 + 1.4 A1 + 1.4 D1 + 1.4 W1) (a=5) Load Combination + 1.00 UT + 1.40 D0 + 1.40 D1 + 1.40 W1 + 1.40 A1

Load Case 010 : Dead plus Live plus Wind (1.20D0+1.20A1+1.20D1+1.2 L1+1.2 W1) (a=5) Load Combination + 1.00 UT + 1.20 D0 + 1.20 D1 + 1.20 L1 + 1.20 W1 + 1.20 A1

Load Case 011 : Dead plus Wind (1.0 D0 + 1.0 A1 + 1.0 D1 + 1.0 W1) (a=5) Load Combination + 1.00 UT + 1.00 D0 + 1.00 D1 + 1.00 W1 + 1.00 A1

Load Case 012 : Dead plus Live plus Wind (1.00D0+1.00A1+1.00D1+0.8 L1+0.8 W1) (a=5) Load Combination + 1.00 UT + 1.00 D0 + 1.00 D1 + 0.80 L1 + 0.80 W1 + 1.00 A1

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Job ref : Job Ref

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Made By : TAMER MOHAMMED

Date : 06/04/2010

Checked : HANY AHMED HASSAN

Approved : HANY AHMED HASSAN

4

6. Wind Load on Floor.

Wind Loading to BS 6399 - Part 2

Results for User Defined Site - Altitude 50 m

Wind Reference 1

Using the Standard Method

Site Basic Data Location and Base wind speed BREVe3 site data for SD320379 - Base wind speed, Vb 25 m/s Altitude and Obstructions Site altitude 50 m - Shelter effect from obstructions is not included Seasonal factor, Ss Season length is All year - Seasonal factor, Ss 1.000 Annual risk and probability factor Design annual risk 0.02 - Probability factor, Sp 1.000 Topographic Increments Site altitude only - Topography not significant - assumed to be flat Heights (m) Heights above ground 2, Diagonals 5 Direction Factors - Using unity direction Factors Direction (°N) 0 30 60 90 120 150 180 210 240 270 300 33 Direction factor, Sd 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

Standard Method Site description Site is in country, nearest distance to sea = 1.00km.

Height Above Ground = 2.0 m - Ve 37.0 m/s - q 841.2 N/m² He 2.000 a 5.0 Sa 1.050, Sb 1.411 Ca 1.000

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MASTERFRAME WIND PRESSURE VALUES Dynamic Pressure Values, q (N/m²) for a = 5 Wind Direction to X Axis 0 90 q (N/m²) for H = 2 841.2 841.2

7. Wind Load.

Wind Load On Roof - (Roof Plan) - Plan View

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8. Dead and Live Load.

Frame Geometry - (Roof Plan) - Plan View

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9. Wall Load.

Wall Load On Roof - (Roof Plan) - Plan View

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10. FRAME GEOMETRY.

PLAN VIEW

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Truss Section At Axe B

Truss Section At Axe C to U

Truss Section At Axe V to W

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11. Nodal Deflection.

Load Case 004 : Super Imposed Load (Serviceability)

Deflected Shape - (Grid Line : B - B) - Front View

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Load Case 004 : Super Imposed Load (Serviceability)

Deflected Shape - (Grid Line : F - F) - Front View

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Load Case 004 : Super Imposed Load (Serviceability)

Deflected Shape - (Grid Line : W - W) - Front View

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12. - Support Reaction.

Frame Geometry - (Grid Line : B - B) - Front View

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Frame Geometry - (Grid Line : F - F) - Front View

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Frame Geometry - (Grid Line : W - W) - Front View

Member Forces Ultimate (Maximum Values)

Mem

ber

No.

Node

End1

End2

Axial

Force

(kN)

Torque

Moment

(kN.m)

Shear Force

(kN)

Bending Moment

(kN.m)

Maximum Moment

(kN.m @ m)

Maximum

Deflection

(mm @ m) x-x y-y x-x y-y x-x y-y

AXE B

41 221.00T 0.05 473.69 0.00 0.00 0.02 94.50 0.12 49.24

44 221.00T -0.05 471.27 0.00 94.50 0.02 @ 0.200 @ 4.100 @ 10.637

73 386.41T -0.05 -307.91 0.00 62.00 0.11 94.50 0.12 49.24

74 386.41T 0.05 -312.04 0.00 0.00 0.11 @ 0.200 @ 4.100 @ 10.637

AXE F

143 21.90C 0.00 256.05 0.00 0.00 0.01 52.23 50.24

148 21.90C 0.00 251.95 0.00 50.80 0.01 @ 22.800 @ 11.615

194 21.90C -0.01 -259.10 0.00 52.23 -0.01 52.23 50.24

196 21.90C 0.01 -263.21 0.00 0.00 -0.01 @ 22.800 @ 11.615

AXEW

539 102.72T -0.07 400.84 0.00 0.00 -0.03 79.76 -0.14 48.53

544 102.72T 0.07 396.72 0.00 79.76 -0.03 @ 0.200 @ 4.100 @ 10.810

574 318.58T 0.06 -283.20 0.00 57.06 -0.11 79.76 -0.14 48.53

576 318.58T -0.06 -287.33 0.00 0.00 -0.11 @ 0.200 @ 4.100 @ 10.810

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13. – MEMBER FORCE .

Envelope (Ultimate Cases)

Frame Geometry - (Grid Line : B - B) - Front View

Maximum and Minimum Axial Force (kN) - Compression Positive

Envelope (Ultimate Cases)

Frame Geometry - (Grid Line : F - F) - Front View

Maximum and Minimum Axial Force (kN) - Compression Positive

Envelope (Ultimate Cases)

Frame Geometry - (Grid Line : W - W) - Front View

Maximum and Minimum Axial Force (kN) - Compression Positive

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Envelope (Ultimate Cases)

Bending Moment Envelope (Ultimate Cases) (Major Axis) - (Grid Line : B - B) - Front View

Bending Moment Values (kN.m)

Envelope (Ultimate Cases)

Bending Moment Envelope (Ultimate Cases) (Major Axis) - (Grid Line : F - F) - Front View

Bending Moment Values (kN.m)

Envelope (Ultimate Cases)

Bending Moment Envelope (Ultimate Cases) (Major Axis) - (Grid Line : W - W) - Front View

Bending Moment Values (kN.m)

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14. - DESIGN OF TRUSS MEMBERES.

14.1. - DESIGN OF TOP CORD BEAM AT AXE B.

AXIAL WITH MOMENTS (MEMBER)

Top

Members 16-17, 19, 21-23, 25-26, 28, 30, 33, 35, 37, 39-40, 42 and 44 (N.41-N.74) @ Level 3 in Load Case 1

Member Loading and Member Forces Loading Combination : 1 UT + 1.4 D0 + 1.4 D1 + 1.6 L1 + 1.4 A1

D1 UDLY -004.000 ( kN/m )

L1 UDLY -001.500 ( kN/m )

A1 UDLY -002.400 ( kN/m )

D1 D 078.500 ( kN/m³)

Member Forces in Load Case 1 and Maximum Deflection from Load Case 12

Mem

ber

No.

Node

End1

End2

Axial

Force

(kN)

Torque

Moment

(kN.m)

Shear Force

(kN)

Bending Moment

(kN.m)

Maximum Moment

(kN.m @ m)

Maximum

Deflection

(mm @ m) x-x y-y x-x y-y x-x y-y

41 221.00T 0.05 473.69 0.00 0.00 0.02 94.50 0.12 32.83

74 386.41T 0.05 -312.04 0.00 0.00 0.11 @ 0.200 @ 4.100 @ 10.618

Classification and Properties (BS 5950: 2000) Section (54.13 kg/m) 406x178 UB 54 [Grade 43] Class = Fn(b/T,d/t,py,F,Mx,My) 8.15, 46.81, 275, 693.55, 94.49, 0.12 (Axial: Non-Slender) SemiComp Effective Properties Area=68.95 cm², Sxx=1018.38(1054.6) cm³, Syy=178.3 cm³ Auto Design Load Cases 1-2, 6 and 8-10

Local Capacity Check Fvx/Pvx 471.27 / 511.503 = 0.921 High Shear x = (2Fvx/Pvx-1)² (2 x 471.27 / 511.503 - 1)² = 0.71 Sxx = Fn(Sxx, Avx, x) 1018.38, 31, 0.71 796.806 cm³

Mcx = py.Sxx1.2 py.Zxx 275 x 796.811.2 x 275 x 782.5 = 219.122 kN.m

Fvy/Pvy 0 / 575.268 = 0 Low Shear Mcy = py.Syy1.2 py.Zyy 275 x 178.31.2 x 275 x 115.26 = 38.036 kN.m

Pz = Ag.py 68.95 x 275 = 1896.125 kN n = F/Pz 693.548 / 1896.125 = 0.366 OK F/Ag.py+Mx/Mcx+My/Mcy 693.548 / 1896.125 + 94.447 / 219.122 + 0.019 / 38.036 = 0.797 OK

Compression Resistance Pc λx = Lex/rxx 100x1x1/16.48 = 6.1 OK Pcx = Area.pcx 68.95x275/10 = 1896.125 kN Table 24 a

Lateral Buckling Check Mb Mb = Mc Fully Restrained 217.745 kN.m

Simplified Approach py.Zx 275x779.16 214.269 kN.m py.Zy 275x115.26 31.697 kN.m F/Pc+mx.Mx/py.Zx+my.My/py.Zy 693.548/1896.125+0.63x94.5/214.3+0.815x0/31.7 0.644 OK

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F/Pcy+mLT.MLT/Mb+my.My/py.Zy 693.548/1896.125+0.44x0/217.7+0.815x0/31.7 0.366 OK

More Exact Approach Max=Mcx/(1+.5F/Pcx) 217.7/(1+.5x693.5/1896.1) 184.08 kN.m May=Mcy/(1+F/Pcy) 38/(1+693.5/1896.1) 27.849 kN.m F/Pcx+mx.Mx/Max+.5myx.My/Mcy 693.5/1896.1+0.63x94.5/184.1+.5x0.8x0.1/38 0.691 OK F/Pcy+mLT.MLT/Mb+my.My/May 693.5/1896.1+0.44x0/217.7+0.8x0/27.8 0.366 OK Max=Mcx(1-F/Pcx)/(1+.5F/Pcx) 217.7(1-693.5/1896.1)/(1+.5x693.5/1896.1) 116.749 kN.m May=Mcy(1-F/Pcy)/(1+F/Pcy) 38(1-693.5/1896.1)/(1+693.5/1896.1) 17.663 kN.m m.Mx/Max+m.My/May 116.749+0.815x0.019/17.663 0.001 OK

Deflection Check - Load Case 12 δ Span/360 32.83 23000 / 360 32.83 mm OK

14.2. - DESIGN OF TOP CORD BEAM AT AXE F.

AXIAL WITH MOMENTS (MEMBER)

Top

Members 105, 109, 112, 117, 121, 125, 132, 137, 140, 144, 146, 148 and 150-151 (F1-F2) @ Level 3 in Load Case 1

Member Loading and Member Forces Loading Combination : 1 UT + 1.4 D0 + 1.4 D1 + 1.6 L1 + 1.4 A1

D1 UDLY -007.000 ( kN/m )

L1 UDLY -002.626 ( kN/m )

A1 UDLY -004.200 ( kN/m )

D1 D 078.500 ( kN/m³)

Member Forces in Load Case 1 and Maximum Deflection from Load Case 12

Mem

ber

No.

Node

End1

End2

Axial

Force

(kN)

Torque

Moment

(kN.m)

Shear Force

(kN)

Bending Moment

(kN.m)

Maximum Moment

(kN.m @ m)

Maximum

Deflection

(mm @ m) x-x y-y x-x y-y x-x y-y

143 6.15T 0.00 256.05 0.00 0.00 0.00 52.23 31.93

196 6.15T 0.01 -263.21 0.00 0.00 0.00 @ 22.800 @ 11.653

Classification and Properties (BS 5950: 2000) Section (46.03 kg/m) 406x140 UB 46 [Grade 43] Class = Fn(b/T,d/t,py,F,Mx,My) 6.35, 53, 275, 736.9, 52.23, 0 (Axial: Non-Slender) SemiComp Effective Properties Area=58.64 cm², Sxx=808.17(887.6) cm³, Syy=118.1 cm³ Auto Design Load Cases 1-2, 6 and 8-10

Local Capacity Check Fvx/Pvx 259.109 / 452.39 = 0.573 Low Shear Mcx = py.Sxx1.2 py.Zxx 275 x 808.171.2 x 275 x 778.17 = 222.248 kN.m

Pz = Ag.py 58.64 x 275 = 1612.6 kN n = F/Pz 736.899 / 1612.6 = 0.457 OK F/Ag.py+Mx/Mcx+My/Mcy 736.899 / 1612.6 + 52.23 / 222.248 + 0 = 0.692 OK

Compression Resistance Pc λx = Lex/rxx 100x1x1/16.36 = 6.1 OK Pcx = Area.pcx 58.64x275/10 = 1612.600 kN Table 24 a

Lateral Buckling Check Mb Mb = Mc Fully Restrained 222.248 kN.m

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Simplified Approach py.Zx 275x778.17 213.997 kN.m F/Pc+mx.Mx/py.Zx 736.899/1612.6+0.492x52.2/214 0.577 OK F/Pcy+mLT.MLT/Mb 736.899/1612.6+0.487x52.2/222.2 0.571 OK

More Exact Approach Max=Mcx/(1+.5F/Pcx) 222.2/(1+.5x736.9/1612.6) 180.913 kN.m F/Pcx+mx.Mx/Max 736.9/1612.6+0.492x52.2/180.9 0.599 OK F/Pcy+mLT.MLT/Mb 736.9/1612.6+0.487x52.2/222.2 0.571 OK

Deflection Check - Load Case 12 δ Span/360 31.93 23000 / 360 31.93 mm OK

14.3. - DESIGN OF TOP CORD BEAM AT AXE W.

AXIAL WITH MOMENTS (MEMBER)

Top

Members 462, 466, 471, 473-475, 477-478, 480, 482, 485, 487, 489 and 491-494 (W1-W2) @ Level 3 in Load Case 1

Member Loading and Member Forces Loading Combination : 1 UT + 1.4 D0 + 1.4 D1 + 1.6 L1 + 1.4 A1

D1 UDLY -007.000 ( kN/m )

L1 UDLY -002.625 ( kN/m )

A1 UDLY -004.200 ( kN/m )

D1 D 078.500 ( kN/m³)

Member Forces in Load Case 1 and Maximum Deflection from Load Case 12

Mem

ber

No.

Node

End1

End2

Axial

Force

(kN)

Torque

Moment

(kN.m)

Shear Force

(kN)

Bending Moment

(kN.m)

Maximum Moment

(kN.m @ m)

Maximum

Deflection

(mm @ m) x-x y-y x-x y-y x-x y-y

539 102.72T -0.07 400.84 0.00 0.00 -0.03 79.76 -0.14 32.02

576 318.58T -0.06 -287.33 0.00 0.00 -0.11 @ 0.200 @ 4.100 @ 10.810

Classification and Properties (BS 5950: 2000) Section (54.13 kg/m) 406x178 UB 54 [Grade 43] Class = Fn(b/T,d/t,py,F,Mx,My) 8.15, 46.81, 275, 607.23, 79.75, 0.13 (Axial: Non-Slender) SemiComp Effective Properties Area=68.95 cm², Sxx=1044.16(1054.6) cm³, Syy=178.3 cm³ Auto Design Load Cases 1-2, 6 and 8-10

Local Capacity Check Fvx/Pvx 396.72 / 511.503 = 0.776 High Shear x = (2Fvx/Pvx-1)² (2 x 396.72 / 511.503 - 1)² = 0.304

Sxx = Fn(Sxx, Avx, x) 1044.16, 31, 0.304 949.368 cm³

Mcx = py.Sxx1.2 py.Zxx 275 x 949.371.2 x 275 x 867.01 = 261.076 kN.m Fvy/Pvy 0.002 / 575.268 = 0 Low Shear Mcy = py.Syy1.2 py.Zyy 275 x 178.31.2 x 275 x 115.26 = 38.036 kN.m

Pz = Ag.py 68.95 x 275 = 1896.125 kN n = F/Pz 607.229 / 1896.125 = 0.320 OK F/Ag.py+Mx/Mcx+My/Mcy 607.229 / 1896.125 + 79.714 / 261.076 + 0.028 / 38.036 = 0.626 OK

Compression Resistance Pc λx = Lex/rxx 100x1x1/16.48 = 6.1 OK Pcx = Area.pcx 68.95x275/10 = 1896.125 kN Table 24 a

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Lateral Buckling Check Mb Mb = Mc Fully Restrained 259.529 kN.m

Simplified Approach py.Zx 275x863.26 237.397 kN.m py.Zy 275x115.26 31.697 kN.m F/Pc+mx.Mx/py.Zx+my.My/py.Zy 607.229/1896.125+0.562x79.8/237.4+0.8x0/31.7 0.510 OK F/Pcy+mLT.MLT/Mb+my.My/py.Zy 607.229/1896.125+0.44x0/259.5+0.8x0/31.7 0.321 OK

More Exact Approach Max=Mcx/(1+.5F/Pcx) 259.5/(1+.5x607.2/1896.1) 223.708 kN.m May=Mcy/(1+F/Pcy) 38/(1+607.2/1896.1) 28.81 kN.m F/Pcx+mx.Mx/Max+.5myx.My/Mcy 607.2/1896.1+0.562x79.8/223.7+.5x0.8x0.1/38 0.522 OK F/Pcy+mLT.MLT/Mb+my.My/May 607.2/1896.1+0.44x0/259.5+0.8x0/28.8 0.321 OK Max=Mcx(1-F/Pcx)/(1+.5F/Pcx) 259.5(1-607.2/1896.1)/(1+.5x607.2/1896.1) 152.066 kN.m May=Mcy(1-F/Pcy)/(1+F/Pcy) 38(1-607.2/1896.1)/(1+607.2/1896.1) 19.583 kN.m m.Mx/Max+m.My/May 152.066+0.8x0.029/19.583 0.001 OK

Deflection Check - Load Case 12 δ Span/360 32.02 23000 / 360 32.02 mm OK

14.4. - DESIGN OF BOTTOM CORD BEAM AT AXE B.

AXIAL WITH MOMENTS (MEMBER)

Bott Chord

Members 18, 20, 24, 27, 29, 31-32, 34, 36 and 38 (N.45-N.68) @ Level 2

Between 15.200 and 19.000 m, in Load Case 9

Member Loading and Member Forces Loading Combination : 1 UT + 1.4 D0 + 1.4 D1 + 1.4 W1 + 1.4 A1

D1 D 078.500 ( kN/m³)

Member Forces in Load Case 9 and Maximum Deflection from Load Case 12

Mem

ber

No.

Node

End1

End2

Axial

Force

(kN)

Torque

Moment

(kN.m)

Shear Force

(kN)

Bending Moment

(kN.m)

Maximum Moment

(kN.m @ m)

Maximum

Deflection

(mm @ m) x-x y-y x-x y-y x-x y-y

45 395.00T 0.00 20.21 0.00 -15.34 0.00 22.39 0.00 24.23

68 238.73T 0.00 -11.75 0.00 -11.37 0.00 @ 1.916 @ 0.000 @ 8.797

Classification and Properties (BS 5950: 2000) Section (39.06 kg/m) 356x127 UB 39 [Grade 43] Class = Fn(b/T,d/t,py,F,Mx,My) 5.89, 47.21, 275, 0, 22.38, 0.01 (Axial: Non-Slender) Plastic Auto Design Load Cases 1-2, 6 and 8-10

Local Capacity Check Fvx/Pvx 11.255 / 384.853 = 0.029 Low Shear Mcx = py.Sxx1.2 py.Zxx 275 x 658.51.2 x 275 x 575.8 = 181.088 kN.m Pz =Ae.py 49.76x275 = 1368.4 kN

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n = F/Pz -910.448 / 1368.4 = 0.665 OK Srx = Fn(Sxx, n) 658.5, 0.665 288.75 cm³ Mrx = Srx.py 288.75 x 275 79.407 kN.m Sry = Fn(Syy, n) 89.1, 0.665 72.52 cm³ Mry = Sry.py 72.52 x 275 18.893 kN.m (Mx/Mrx)Z1+(My/Mry)Z2 (1.06/79.407)²+(0.001/18.893)1= 0.665 OK

Equivalent Uniform Moment Factors mLT, mx, my and myx mLT=0.2+(.15M2+.5M3+.15M4)/Mmax 0.2+(.15x10+.5x10+.15x1)/10 0.44 0.864 Table 18

my=0.2+(.1M2+.6M3+.1M4)/Mmax 0.2+(.1x0+.6x0+.1x0)/0 .8x0/0 0.9 Table 26 mx=0.2+(.1M2+.6M3+.1M4)/Mmax 0.2+(.1x17+.6x10+.1x11)/22 .8x19/22 0.69 Table 26

myx=0.2+(.1M2+.6M3+.1M4)/Mmax 0.2+(.1x0+.6x0+.1x0)/0 .8x0/0 0.8 Table 26

Lateral Buckling Check Mb Le = 1.00 L 1 x 3.8 = 3.8 m λ = Le/ryy 3.8 / 2.69 141.26 OK v = Fn (x,Le,ryy,λ) 35.137, 3.8, 2.69, 141.26 0.862 Table 19 λLT= u.v.λ.βW 0.873 x 0.862 x 141.26 1 106.39

pb = Fn (py,λLT) 275, 106.39 114.45 N/mm² Table 16 Mb = Sxx.pb Mc 658.5 x 114.45 181.088 = 75.368 kN.m

Simplified Approach py.Zx 275x575.8 158.345 kN.m py.Zy 275x57.25 15.744 kN.m F/Pc+mx.Mx/py.Zx+my.My/py.Zy 0+0.69x22.4/158.3+0.9x0/15.7 0.098 OK F/Pcy+mLT.MLT/Mb+my.My/py.Zy 0+0.864x10.1/75.4+0.9x0/15.7 0.116 OK

More Exact Approach Max=Mcx/(1+.5F/Pcx) 181.1/(1+.5x0/487.9) 181.088 kN.m May=Mcy/(1+F/Pcy) 18.9/(1+0/410.6) 18.893 kN.m F/Pcx+mx.Mx/Max+.5myx.My/Mcy 0/487.9+0.69x22.4/181.1+.5x0.8x0/18.9 0.085 OK F/Pcy+mLT.MLT/Mb+my.My/May 0/410.6+0.864x10.1/75.4+0.9x0/18.9 0.116 OK Max=Mcx(1-F/Pcx)/(1+.5F/Pcx) 181.1(1-0/487.9)/(1+.5x0/487.9) 181.088 kN.m May=Mcy(1-F/Pcy)/(1+F/Pcy) 18.9(1-0/410.6)/(1+0/410.6) 18.893 kN.m m.Mx/Max+m.My/May 0.864x10.121/181.088+0.9x0.003/18.893 0.048 OK

Deflection Check - Load Case 12 δ Span/360 24.23 19166 / 360 24.23 mm OK

14.5. - DESIGN OF BOTTOM CORD BEAM AT AXE F.

AXIAL WITH MOMENTS (MEMBER)

Bott Chord

Members 111, 114, 119, 123, 128, 135-136, 139, 141 and 143 (N.150-N.186) @ Level 2

Between 0.000 and 3.800 m, in Load Case 1

Member Loading and Member Forces Loading Combination : 1 UT + 1.4 D0 + 1.4 D1 + 1.6 L1 + 1.4 A1

D1 D 078.500 ( kN/m³)

Member Forces in Load Case 1 and Maximum Deflection from Load Case 12

Mem

ber

Node

End1

Axial

Force

Torque

Moment

Shear Force

(kN)

Bending Moment

(kN.m)

Maximum Moment

(kN.m @ m)

Maximum

Deflection

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No. End2 (kN) (kN.m) x-x y-y x-x y-y x-x y-y (mm @ m)

150 236.28T 0.00 10.39 0.00 -8.62 0.00 12.16 0.00 23.90

186 243.46T 0.00 -10.76 0.00 -8.94 0.00 @ 11.327 @ 0.000 @ 9.698

Classification and Properties (BS 5950: 2000) Section (33.0 kg/m) 305x102 UB 33 [Grade 43] Class = Fn(b/T,d/t,py,F,Mx,My) 4.74, 41.8, 275, 0, 12.17, 0.01 (Axial: Non-Slender) Plastic Auto Design Load Cases 1-2, 6 and 8-10

Local Capacity Check Fvx/Pvx 9.924 / 340.53 = 0.029 Low Shear Mcx = py.Sxx1.2 py.Zxx 275 x 480.81.2 x 275 x 415.87 = 132.22 kN.m

Pz =Ae.py 41.82x275 = 1150.05 kN n = F/Pz -726.119 / 1150.05 = 0.631 OK Srx = Fn(Sxx, n) 480.8, 0.631 235.22 cm³ Mrx = Srx.py 235.22 x 275 64.686 kN.m Sry = Fn(Syy, n) 60, 0.631 51.42 cm³ Mry = Sry.py 51.42 x 275 12.57 kN.m (Mx/Mrx)Z1+(My/Mry)Z2 (1.776/64.686)²+(0.001/12.57)1= 0.631 OK

Equivalent Uniform Moment Factors mLT, mx, my and myx mLT=0.2+(.15M2+.5M3+.15M4)/Mmax 0.2+(.15x1+.5x10+.15x10)/10 0.44 0.857 Table 18

my=0.2+(.1M2+.6M3+.1M4)/Mmax 0.2+(.1x0+.6x0+.1x0)/0 .8x0/0 0.667 Table 26 mx=0.2+(.1M2+.6M3+.1M4)/Mmax 0.2+(.1x10+.6x11+.1x10)/12 .8x12/12 0.933 Table 26

myx=0.2+(.1M2+.6M3+.1M4)/Mmax 0.2+(.1x0+.6x0+.1x0)/0 .8x0/0 0.92 Table 26

Lateral Buckling Check Mb Le = 1.00 L 1 x 3.8 = 3.8 m λ = Le/ryy 3.8 / 2.16 175.93 OK v = Fn (x,Le,ryy,λ) 31.63, 3.8, 2.16, 175.93 0.792 Table 19 λLT= u.v.λ.βW 0.868 x 0.792 x 175.93 1 120.88

pb = Fn (py,λLT) 275, 120.88 94.52 N/mm² Table 16 Mb = Sxx.pb Mc 480.8 x 94.52 132.22 = 45.446 kN.m

Simplified Approach py.Zx 275x415.87 114.364 kN.m py.Zy 275x38.09 10.475 kN.m F/Pc+mx.Mx/py.Zx+my.My/py.Zy 0+0.933x12.2/114.4+0.667x0/10.5 0.099 OK F/Pcy+mLT.MLT/Mb+my.My/py.Zy 0+0.857x10.5/45.4+0.667x0/10.5 0.197 OK

More Exact Approach Max=Mcx/(1+.5F/Pcx) 132.2/(1+.5x0/320.4) 132.22 kN.m May=Mcy/(1+F/Pcy) 12.6/(1+0/234.5) 12.57 kN.m F/Pcx+mx.Mx/Max+.5myx.My/Mcy 0/320.4+0.933x12.2/132.2+.5x0.9x0/12.6 0.086 OK F/Pcy+mLT.MLT/Mb+my.My/May 0/234.5+0.857x10.5/45.4+0.7x0/12.6 0.197 OK Max=Mcx(1-F/Pcx)/(1+.5F/Pcx) 132.2(1-0/320.4)/(1+.5x0/320.4) 132.22 kN.m May=Mcy(1-F/Pcy)/(1+F/Pcy) 12.6(1-0/234.5)/(1+0/234.5) 12.57 kN.m m.Mx/Max+m.My/May 0.857x10.455/132.22+0.667x0.002/12.57 0.068 OK

Deflection Check - Load Case 12 δ Span/360 23.9 19166 / 360 23.9 mm OK

14.6. - DESIGN OF BOTTOM CORD BEAM AT AXE W.

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AXIAL WITH MOMENTS (MEMBER)

Bott Chord

Members 468, 472, 476, 479, 481, 483-484, 486, 488 and 490 (N.546-N.571) @ Level 2

Between 0.000 and 3.800 m, in Load Case 9

Member Loading and Member Forces Loading Combination : 1 UT + 1.4 D0 + 1.4 D1 + 1.4 W1 + 1.4 A1

D1 D 078.500 ( kN/m³)

Member Forces in Load Case 9 and Maximum Deflection from Load Case 12

Mem

ber

No.

Node

End1

End2

Axial

Force

(kN)

Torque

Moment

(kN.m)

Shear Force

(kN)

Bending Moment

(kN.m)

Maximum Moment

(kN.m @ m)

Maximum

Deflection

(mm @ m) x-x y-y x-x y-y x-x y-y

546 308.50T 0.00 11.18 0.00 -7.90 0.00 12.68 0.00 23.48

571 210.14T 0.00 -7.68 0.00 -6.78 0.00 @ 1.916 @ 0.000 @ 8.989

Classification and Properties (BS 5950: 2000) Section (33.0 kg/m) 305x102 UB 33 [Grade 43] Class = Fn(b/T,d/t,py,F,Mx,My) 4.74, 41.8, 275, 0, 12.67, 0.01 (Axial: Non-Slender) Plastic Auto Design Load Cases 1-2, 6 and 8-10

Local Capacity Check Fvx/Pvx 10.776 / 340.53 = 0.032 Low Shear Mcx = py.Sxx1.2 py.Zxx 275 x 480.81.2 x 275 x 415.87 = 132.22 kN.m

Pz =Ae.py 41.82x275 = 1150.05 kN n = F/Pz -747.698 / 1150.05 = 0.650 OK Srx = Fn(Sxx, n) 480.8, 0.65 223.53 cm³ Mrx = Srx.py 223.53 x 275 61.471 kN.m Sry = Fn(Syy, n) 60, 0.65 50.13 cm³ Mry = Sry.py 50.13 x 275 12.57 kN.m (Mx/Mrx)Z1+(My/Mry)Z2 (1.726/61.471)²+(0.001/12.57)1= 0.65 OK

Equivalent Uniform Moment Factors mLT, mx, my and myx mLT=0.2+(.15M2+.5M3+.15M4)/Mmax 0.2+(.15x3+.5x13+.15x11)/13 0.44 0.85 Table 18

my=0.2+(.1M2+.6M3+.1M4)/Mmax 0.2+(.1x0+.6x0+.1x0)/0 .8x0/0 0.9 Table 26 mx=0.2+(.1M2+.6M3+.1M4)/Mmax 0.2+(.1x10+.6x6+.1x7)/13 .8x11/13 0.679 Table 26

myx=0.2+(.1M2+.6M3+.1M4)/Mmax 0.2+(.1x0+.6x0+.1x0)/0 .8x0/0 0.8 Table 26

Lateral Buckling Check Mb Le = 1.00 L 1 x 3.8 = 3.8 m λ = Le/ryy 3.8 / 2.16 175.93 OK v = Fn (x,Le,ryy,λ) 31.63, 3.8, 2.16, 175.93 0.792 Table 19 λLT= u.v.λ.βW 0.868 x 0.792 x 175.93 1 120.88

pb = Fn (py,λLT) 275, 120.88 94.52 N/mm² Table 16 Mb = Sxx.pb Mc 480.8 x 94.52 132.22 = 45.446 kN.m

Simplified Approach py.Zx 275x415.87 114.364 kN.m F/Pc+mx.Mx/py.Zx 0+0.679x12.7/114.4 0.075 OK F/Pcy+mLT.MLT/Mb 0+0.85x12.7/45.4 0.237 OK

More Exact Approach Max=Mcx/(1+.5F/Pcx) 132.2/(1+.5x0/320.4) 132.22 kN.m F/Pcx+mx.Mx/Max 0/320.4+0.679x12.7/132.2 0.065 OK

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F/Pcy+mLT.MLT/Mb 0/234.5+0.85x12.7/45.4 0.237 OK

Deflection Check - Load Case 12 δ Span/360 23.48 19166 / 360 23.48 mm OK

14.7. - DESIGN OF DIAGONAL MEMBERS AT AXE B.

STRUT AND TIE (MEMBER)

Member 992 (N.46-N.47) @ Level 3 : Diagonal Classification and Properties (BS 5950: 2000) Section (24.4 kg/m) 2No 100x100x8 ANG 24.4 (0mm) [Grade 43] Class = Fn(b,d,t,py) 100, 100, 8, 275 (Axial: Non-Slender) SemiComp Auto Design Load Cases 1-2, 6 and 8-10

Double Angles Tie Connected Through One Leg Only : 4.6.3.1 (Case 1) Ae = Fn(Ag - 0.3 a2) 31.2 - 0.3 x 15.2 26.64 cm² Tc = Ae.py 26.64x275/10 = 732.6 kN F (Tie)/Tc 436.343 / 732.6 0.596 OK

14.8. - DESIGN OF DIAGONAL MEMBERS AT AXE F.

STRUT AND TIE (MEMBER)

Member 1049 (N.184-N.193) @ Level 3 : Diagonal Classification and Properties (BS 5950: 2000) Section (17.98 kg/m) 2No 75x75x8 ANG 17.98 (0mm) [Grade 43] Class = Fn(b,d,t,py) 75, 75, 8, 275 (Axial: Non-Slender) Compact Auto Design Load Cases 1-2, 6 and 8-10

Double Angles Tie Connected Through One Leg Only : 4.6.3.1 (Case 1) Ae = Fn(Ag - 0.3 a2) 22.8 - 0.3 x 10.8 19.56 cm² Tc = Ae.py 19.56x275/10 = 537.9 kN F (Tie)/Tc 246.584 / 537.9 0.458 OK

14.9. - DESIGN OF DIAGONAL MEMBERS AT AXE W.

STRUT AND TIE (MEMBER)

Member 1212 (N.561-N.562) @ Level 3 : Diagonal Classification and Properties (BS 5950: 2000) Section (23.8 kg/m) 2No 80x80x10 ANG 23.8 (0mm) [Grade 43] Class = Fn(b,d,t,py) 80, 80, 10, 275 (Axial: Non-Slender) Plastic Auto Design Load Cases 1-2, 6 and 8-10

Strut Connected to One Side by One Row of Bolts or Equivalent Weld : 4.7.10.3(b) (Case 9) λ = Fn(Lx,Ly,Lv,rx,ry,rv) 2.77,2.77,0.693,2.41,3.36,1.55 114.95 OK Pc = Area.pc 30.2x103.45/10 = 312.418 kN Table 24 c F (Strut)/Pc 11.771 / 312.418 0.038 OK

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Double Angles Tie Connected Through One Leg Only : 4.6.3.1 (Case 2) Ae = Fn(Ag - 0.3 a2) 30.2 - 0.3 x 14.2 25.94 cm² Tc = Ae.py 25.94x275/10 = 713.35 kN F (Tie)/Tc 10.696 / 713.35 0.015 OK

14.10. - DESIGN OF VERTICAL MEMBERS AT AXE B.

STRUT AND TIE (MEMBER)

Member 1259 (N.45-N.46) @ Level 3 : Diagonal Classification and Properties (BS 5950: 2000) Section (29.6 kg/m) 2No 120x120x8 ANG 29.6 (0mm) [Grade 43] Class = Fn(b,d,t,py) 120, 120, 8, 275 (Axial: Non-Slender) SemiComp Auto Design Load Cases 1-2, 6 and 8-10

Strut Connected to One Side by One Row of Bolts or Equivalent Weld : 4.7.10.3(b) (Case 1) λ = Fn(Lx,Ly,Lv,rx,ry,rv) 2,2,0.667,3.71,4.93,2.39 67.74 OK Pc = Area.pc 37.6x185.73/10 = 698.353 kN Table 24 c F (Strut)/Pc 501.244 / 698.353 0.718 OK

14.11. - DESIGN OF VERTICAL MEMBERS AT AXE F.

STRUT AND TIE (MEMBER)

Member 1313 (N.186-N.193) @ Level 3 : Diagonal Classification and Properties (BS 5950: 2000) Section (21.8 kg/m) 2No 90x90x8 ANG 21.8 (0mm) [Grade 43] Class = Fn(b,d,t,py) 90, 90, 8, 275 (Axial: Non-Slender) SemiComp Auto Design Load Cases 1-2, 6 and 8-10

Strut Connected to One Side by One Row of Bolts or Equivalent Weld : 4.7.10.3(b) (Case 1) λ = Fn(Lx,Ly,Lv,rx,ry,rv) 2,2,0.667,2.75,3.72,1.77 80.91 OK Pc = Area.pc 27.8x159.47/10 = 443.333 kN Table 24 c F (Strut)/Pc 266.948 / 443.333 0.602 OK

14.12. - DESIGN OF VERTICAL MEMBERS AT AXE W.

STRUT AND TIE (MEMBER)

Member 1457 (N.546-N.550) @ Level 3 : Diagonal Classification and Properties (BS 5950: 2000) Section (24.4 kg/m) 2No 100x100x8 ANG 24.4 (0mm) [Grade 43] Class = Fn(b,d,t,py) 100, 100, 8, 275 (Axial: Non-Slender) SemiComp Auto Design Load Cases 1-2, 6 and 8-10

Strut Connected to One Side by One Row of Bolts or Equivalent Weld : 4.7.10.3(b) (Case 1) λ = Fn(Lx,Ly,Lv,rx,ry,rv) 2,2,0.667,3.06,4.11,1.97 75.75 OK Pc = Area.pc 31.2x169.64/10 = 529.268 kN Table 24 c F (Strut)/Pc 415.033 / 529.268 0.784 OK

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14.13. - DESIGN OF LATERAL SUPPORT FOR BOTTOM CHORD . Spacing 4.00 m Design Force 0.02*FMax FMax for bottom chord = 900 KN Design force for support = 0.02*900 = 18 Kn.

COMPRESSION RESISTANCE PC Classification and Properties (BS 5950: 2000) Section (3.08 kg/m) 50x50x4 ANG 3.08 [Grade 43] Class = Fn(b,d,t,py) 50, 50, 4, 275 Slender Effective Area Area = 3.76 (3.92) cm²

Compression Resistance Pc λx = Lex/rvv 100x1x1.75/0.99 = 177.5 OK Pcx = Area.pcx 3.76x53.09/10 = 19.979 kN Table 24 c λy = Ley/rvv 100x1x1.75/0.99 = 177.5 OK Pcy = Area.pcy 3.76x53.09/10 = 19.979 kN Table 24 c F/Pc 18/19.979 = 0.901 OK

14.14. - DESIGN OF WALL BEAM.

AXIAL WITH MOMENTS (MEMBER)

Members 49 and 51 (N.80-N.83) @ Level 3 in Load Case 1 : Secondary Beam

Member Loading and Member Forces Loading Combination : 1 UT + 1.4 D0 + 1.4 D1 + 1.6 L1 + 1.4 A1

D1 UDLY -003.500 ( kN/m )

L1 UDLY -001.313 ( kN/m )

A1 UDLY -002.100 ( kN/m )

D1 D 078.500 ( kN/m³)

Member Forces in Load Case 1 and Maximum Deflection from Load Case 12

Mem

ber

No.

Node

End1

End2

Axial

Force

(kN)

Torque

Moment

(kN.m)

Shear Force

(kN)

Bending Moment

(kN.m)

Maximum Moment

(kN.m @ m)

Maximum

Deflection

(mm @ m) x-x y-y x-x y-y x-x y-y

80 76.36C 0.00 9.36 0.00 0.00 0.01 4.33 0.96

83 76.36C 0.00 -9.36 0.00 0.00 0.00 @ 0.918 @ 0.918

Classification and Properties (BS 5950: 2000) Section (12.96 kg/m) 127x76 UB 13 [Grade 43] Class = Fn(b/T,d/t,py,F,Mx,My) 5, 24.15, 275, 76.36, 4.33, 0.01 (Axial: Non-Slender) Plastic Auto Design Load Cases 1-2, 6 and 8-10

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Local Capacity Check Fvx/Pvx 0.001 / 83.82 = 0 Low Shear Mcx = py.Sxx1.2 py.Zxx 275 x 84.21.2 x 275 x 74.69 = 23.155 kN.m

Fvy/Pvy 0.001 / 171.547 = 0 Low Shear Mcy = py.Syy1.2 py.Zyy 275 x 22.61.2 x 275 x 14.89 = 4.914 kN.m Pz = Ag.py 16.51 x 275 = 454.025 kN n = F/Pz 76.356 / 454.025 = 0.168 OK Srx = Fn(Sxx, n) 84.2, 0.168 79.38 cm³ Mrx = Srx.py 79.38 x 275 21.83 kN.m Sry = Fn(Syy, n) 22.6, 0.168 22.45 cm³ Mry = Sry.py 22.45 x 275 4.914 kN.m (Mx/Mrx)Z1+(My/Mry)Z2 (4.329/21.83)²+(0.006/4.914)1= 0.041 OK

Compression Resistance Pc λx = Lex/rxx 100x1x1/5.36 = 18.7 OK Pcx = Area.pcx 16.51x274.136/10 = 452.598 kN Table 24 a λy = Ley/ryy 100x1x1/1.85 = 54.1 OK Pcy = Area.pcy 16.51x230.41/10 = 380.400 kN Table 24 b

Equivalent Uniform Moment Factors mLT, mx, my and myx mLT=0.2+(.15M2+.5M3+.15M4)/Mmax 0.2+(.15x3+.5x4+.15x3)/4 0.44 0.925 Table 18

my=0.2+(.1M2+.6M3+.1M4)/Mmax 0.2+(.1x0+.6x0+.1x0)/0 .8x0/0 0.983 Table 26

mx=0.2+(.1M2+.6M3+.1M4)/Mmax 0.2+(.1x3+.6x4+.1x3)/4 .8x4/4 0.95 Table 26 myx=0.2+(.1M2+.6M3+.1M4)/Mmax 0.2+(.1x0+.6x0+.1x0)/0 .8x0/0 0.871 Table 26

Lateral Buckling Check Mb Le = 1.00 L 1 x 1.85 = 1.85 m λ = Le/ryy 1.85 / 1.85 100 OK v = Fn (x,Le,ryy,λ) 16.356, 1.85, 1.85, 100 0.768 Table 19 λLT= u.v.λ.βW 0.899 x 0.768 x 100 1 69.1 pb = Fn (py,λLT) 275, 69.1 190.61 N/mm² Table 16 Mb = Sxx.pb Mc 84.2 x 190.61 23.155 = 16.050 kN.m

Combined Axial Compression and Bending to Annex I rb=mLT.MLT/Mb 0.925x4.3/16 0.249 rc=Fc/Pcy 76.4/380.4 0.201 λr=(rbλLT+rcλy)/(rb+rc) (0.249•69.1+0.201•54.1)/(0.249+0.201) 62.393 λro=17.15 ε (2rb+rc)/(rb+rc) 17.15•1(2•0.249+0.201)/(0.249+0.201) 26.654 Mob= Mb(1-Fc/Pcy) 16.050(1-76.4/380.4) 12.828 Mxy= Mcx(1-Fc/ Pcy)

½ 23.155(1-76.4/380.4)½ 20.701 Mox= Mcx(1-Fc/Pcx)/(1+0.5Fc/Pcx) 23.155(1-76.4/452.6)/(1+0.5•76.4/452.6) 17.751 Moy= Mcy(1-Fc/Pcy)/(1+ky(Fc/Pcy)) 4.914(1-76.4/380.4)/(1+1.0(76.4/380.4)) 3.271 Mab=fn( λr, λro, ε, Mxy, Mob) 62.393, 26.654, 1.000, 20.701, 12.828 16.390 Max=fn( λx, ε, Mrx, Mox) 18.657, 1.000, 21.830, 17.751 21.740 May=fn( λy, ε, Mry, Moy) 54.054, 1.000, 4.914, 3.271 4.031 mx.Mx/Max+.5myx.My/Mcy(1-Fc/Pcx) 0.95x4.3/21.7+.5x0.871x0/(4.9(1-76.4/452.6)) 0.190 OK mLT.MLT/Mab+my.My/May 0.925x4.3/16.4+0.983x0/4 0.246 OK mx.Mx/Max+my.My/May 0.95x4.3/21.7+0.983x0/4 0.191 OK Compare with Simplied to 4.8.3.3 0.402, 0.452, 0.452 0.452 Compare with MoreExact to 4.8.3.3 0.362, 0.452, 0.227 0.452

Deflection Check - Load Case 12 δ Span/360 0.96 1850 / 360 0.96 mm OK

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14.15. - DESIGN OF BASE CONNECTION.

BASE PLATE AT : N.41 - LEVEL 3

Base-Plate Connection to BS 5950

LOADING CASE 001 : ULTIMATE LIMIT STATE (FINAL STAGE)

Basic Data Applied Forces at Interface Resultant Forces M, Fv, F Moment +0.0 kNm, Shear +473.7 kN, Axial +500.0 kN (Axial Compression)

Basic Dimensions Column: 406x178UB54 [43] D=402.6, B=177.7, T=10.9, t=7.7, r=10.2, py=275 Data grout, Fcu, Fcv, py, slope 25 N/mm², 40 N/mm², 0.35 N/mm², 275 N/mm², 30 deg to vertical Design to BS 5950-1: 2000 and the SCI Green Book: Joints in Steel Construction : Moment Connections: SCI-P-207/95 Column Capacities Mc, Fvc, Fc 290.0 kN.m, 511.5 kN, 1896.1 kN Fvc = 511.5 kN OK

Summary of Results (Unity Ratios) Concrete Pressure 1.00 OK Base-Plate thickness in Compression 0.43 OK Horizontal Shear 0.87 OK Flange & Web Welds 0.46 0.46 OK

Step 1: Base-Plate Pressure Allowable Pressure=0.60•Fcu 0.60•25 15.0 N/mm² Pressure Configuration Compression Only with Optimised Compression Area Ac=x2•wf+x3•ww+x4•wf 44.74•211.54 + 346.96•41.54 + 44.74•211.54 333.4 cm² Conc Cap C=0.60•Fcu•Ac 0.60•25•33339.6 500.1 kN OK Pressure=P•1000/Ac 500.0•1000/33340 15.00 N/mm² OK

Step 2a: Plate Compression Bending e=L1 16.9 16.9 mm Mapp=p•e²/2 15.0•16.9²/2 2146 Nmm/mm tp=(6•Mapp/py) (6•2146/275) 6.8 mm OK

Note: Axial Load Axial Using Elastic Modulus Zp (4.13.2.2)

Step 4: Shear Base Friction Friction Fr=0.40•Fc 0.40•+500.0 kN 200.0 kN

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Bolt Bearing Pss=Min(Bs, Cb, Pb, Bb)•nbs Min(132.4, 86.4, 123.6, 384.0) = 86.4•2 172.8 kN Pts=Min(Bsten, Cb, Pb, Bb)•nbt Min(132.4, 86.4, 123.6, 384.0) = 86.4•2, (no tension) 172.8 kN

Total Shear Capacity Total Cap=Fr+Pss+Pts 200.0 + 172.8 + 172.8 545.6 kN OK

Step 5: Flange & Web Welds Load dispersal Flanges resist Moment and Axial, Web resists Axial and Shear. Direct Bearing therefore design for tensile forces only. Areas A, Af, Aw 69.0, 19.4, 29.3 cm²

Flange Welds Fapp=F•Af/A 500.0•19.4/69.0 0.0 kN No Resultant Tensile Force

Web Welds Web weld load=Fv/(D-2(fw+T)) 473.7/(402.6 - 2(6 +10.9)) 1.28 kN/mm Fcap w=2•0.7•leg•Py 2•0.7•9•220 2.77 kN/mm OK

14.16. - DESIGN OF SPLICE CONNECTION-BOTTOM CHORD AT AXE B.

APEX JOINT AT : N.58 - LEVEL 2 : MEMBERS 18, 20, 24, 27, 29, 31-32, 34, 36

AND 38 (N.45-N.68)

Beam to Beam End-Plated Connection to BS 5950

LOADING CASE 001 : ULTIMATE LIMIT STATE (FINAL STAGE)

Basic Data Applied Forces at End-plate Interface Resultant Forces M, Fv, F 25.9 kNm, 14.4 kN, -510.4 kN Load directions Top of Joint in Tension, Rafter moving Down and in Tension.

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Design to BS 5950-1: 2000 and the SCI Green Book: Joints in Steel Construction : Moment Connections: SCI-P-207/95 Rafter Capacities Mc, Fvc, Fc 181.1 kN.m, 384.9 kN, 1368.4 kN Fc = 1368.4 kN OK

Summary of Results (Unity Ratios) Tensile Capacity 0.76 OK Moment Capacity 219.7 kNm (for 5 rows of bolts) (Modified Applied Moment Mm=145.3 kNm) 0.66 OK Moment Capacity 162.2 kNm (for the 2 rows of bolts required in the tension zone) 0.90 OK Shear Capacity 0.02 OK Shear Capacity (Fv & T) 0.01 OK Beam Tension Stiffener at row 2 0.00, 0.35, 0.84, 0.84 0.84 OK Extended End-plate Stiffener 0.49, 0.25, 0.51, 0.70, 0.34, 0.54 0.70 OK Flange Welds 0.81, 0.36 0.81 OK Web Welds 0.27, 0.02 0.27 OK Beam compression stiffener 0.76 OK

Step 1: Tension Zone BOLT ROW 1 End Plate row 1 only Mp=Leff•tk•tk •py/6 129.1•24.0•24.0•265.0/6 3283.1 kN.mm T2.5: 7 Prmode1=4•Mp/m 4•3283.1/26.90 488.2 kN Eq 2.1 Pr=min(Prmode1,3) min(488.2, 219.5) 219.5 kN

BOLT ROW 2 End Plate row 2 only Mp=Leff•tk•tk •py/6 169.0•24.0•24.0•265.0/6 4299.8 kN.mm T2.5: 5 Prmode1=4•Mp/m 4•4299.8/26.90 639.4 kN Eq 2.1 Pr=min(Prmode1,3) min(639.4, 219.5) 219.5 kN Triangular limit Ptri= Pr1•La/lamax 219.5•360.6/450.6 175.7 Pr 2=Min(Pr 2+PrResid, Ptri) Min(219.5 & 0.0, 175.7) 175.7 kN modified New Residual PrResid=Pr 2-Ptri 219.5 - 175.7 43.9 kN

BOLT ROW 3 End Plate row 3 only Mp=Leff•tk•tk •py/6 169.0•24.0•24.0•265.0/6 4299.8 kN.mm T2.5: 2 Prmode1=4•Mp/m 4•4299.8/26.90 639.4 kN Eq 2.1 Pr=min(Prmode1,3) min(639.4, 219.5) 219.5 kN Triangular limit Ptri= Pr1•La/lamax 219.5•270.6/450.6 131.8 Pr 3=Min(Pr 3+PrResid, Ptri) Min(219.5 & 43.9, 131.8) 131.8 kN modified New Residual PrResid=Pr 3-Ptri 219.5 - 131.8 87.7 kN

BOLT ROW 4 End Plate row 4 only Mp=Leff•tk•tk •py/6 157.6•24.0•24.0•265.0/6 4009.3 kN.mm T2.5: 1 Prmode1=4•Mp/m 4•4009.3/26.90 596.2 kN Eq 2.1 Pr=min(Prmode1,3) min(596.2, 219.5) 219.5 kN Triangular limit Ptri= Pr1•La/lamax 219.5•180.6/450.6 88.0 Pr 4=Min(Pr 4+PrResid, Ptri) Min(219.5 & 87.7, 88.0) 88.0 kN modified New Residual PrResid=Pr 4-Ptri 219.5 - 88.0 131.6 kN

BOLT ROW 5 End Plate row 5 only Mp=Leff•tk•tk •py/6 157.6•24.0•24.0•265.0/6 4009.3 kN.mm T2.5: 1 Prmode1=4•Mp/m 4•4009.3/26.90 596.2 kN Eq 2.1 Pr=min(Prmode1,3) min(596.2, 219.5) 219.5 kN Triangular limit Ptri= Pr1•La/lamax 219.5•110.6/450.6 53.9 Pr 5=Min(Pr 5+PrResid, Ptri) Min(219.5 & 131.6, 53.9) 53.9 kN modified New Residual PrResid=Pr 5-Ptri 219.5 - 53.9 165.7 kN

Potential Tension Capacity Sigma Pri 219.5 + 175.7 + 131.8 + 88.0 + 53.9 kN 668.8 kN OK

Step 2: Compression Zone Beam Compression

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Beam Compression Zone Stiffener in Compression Utilising 20% OverStressing Total Area Stiffener 12.0 x45.7 5.5 cm² Pcbeam 5.5•275•1.20 181.0 kN Eq 2.9

Potential Compression Capacity Pcmin 181.0 181.0 kN OK

Step 4: Moment Capacity Fc=Min(Pri+N, Pc) min(668.8 + -510.4,181.0) 158.4 kN Fri=Fc-Axial 158.4 - -510.4 668.8 kN Pδ=Pri -Fri 668.8 - 668.8 0.0 kN

Final Bolt Forces and Moment Capacities Bolt row 5 Mc5=Pr5•h5 53.9•110.6 6.0 kN.m Bolt row 4 Mc4=Pr4•h4 88.0•180.6 15.9 kN.m Bolt row 3 Mc3=Pr3•h3 131.8•270.6 35.7 kN.m Bolt row 2 Mc2=Pr2•h2 175.7•360.6 63.3 kN.m Bolt row 1 Mc1=Pr1•h1 219.5•450.6 98.9 kN.m Mc 219.7 kN.m Mm=M-N•Hn 25.9 - -510.4•233.9 145.3 kN.m OK Tension Bolts Only the first 2 rows are required to resist the applied moment The remaining rows shall be considered to be part of the shear zone. Mc' for 2 rows 98.9, 63.3 162.2 kN.m Ft for 2 rows 219.5, 175.7 395.2 kN Ftdesign=Ft •Mapp/Mc' 395.2•145.3/162.2 353.8 kN

Step 5: Shear Bolts Bolt Shear Capacity BSC=91.875, tg=48 91.9 kN Bearing Capacity-End Plate pb=460, edge=40.0, ?=20, tk=24, kbs=1.00 220.8 kN Bearing Capacity-Bolts pb=1000, ?=20, tk=24 480.0 kN Pss=Min(bearing...,shear) Min(220.8, 480.0, 91.9) 91.9 kN Pts Min(bearing...,0.4•shear) Min(220.8, 480.0, 36.8) 36.8 kN V=Ns•Pss+Nt•Pts 8•91.9 + 4•36.8 882 kN OK

Combined Tension & Shear Ftave=F/n 510/10 51.0 kN Fs=Ps•(1.4-Ft/Pt) 91.9 • ( 1.4 - 51.0 / 109.8) 85.9 kN V=Ns•Pss+Nt•Pts 2•91.9 + 10•85.9 1043 kN OK

Step 6C: Beam Tension Stiffeners Stiffener at Bolt Row 2 Asn=2•Bsn•ts 2(72 - 10)•12 1488 mm² Lt=Lu+P+Ll 45.0 + 90 + 45.0 180.0 mm Tension Asnreq =(Fu+Fl)/pyt-Lt•t (175.7 + 131.8)/275 - 180.0•7 0.0 mm² OK F1=Fu•m1/(m1+m2u) 175.7•26.9/(26.9 + 31.0) 81.6 kN F2=Fl•m1/(m1+m2l) 131.8•26.9/(26.9 + 31.0) 61.2 kN Bending Asnreq =(F1+F2)/py (81.6 + 61.2)/275 519.5 mm² OK Stiff Len > 1.8•bsg 140.0 >= 1.8•72.0 129.6 mm OK Ten weld leg >= Stk•0.7 10 >= 12•0.7 10 >= 8.4 OK

Extended End-plate Stiffener Asn=Bsn•ts 80•12 960 mm² Fapp=Fu•m1/(m1+m2) 219.5•35.2/(35.2 + 24.2) 130.1 kN Tension Asnreq=Fapp/pyt 130.1/275 473.0 mm² OK Bending fs=3•F•la/(Ls•Ls•ts) 3•130.1•40.0/(140•140•12) 66.4 N/mm² OK Shear fv=F/(Ls-snipe)/ts 130.1/(140 - 10)/12 83.4 N/mm² pv=0.6•py 0.6•275.0 165.0 N/mm² OK Weld Tension fs=F/lt/(2•0.7•leg) 130.1/80/(2•0.7•6) <= 275 193.6 N/mm² OK Weld Bending fmw=fm•ts/(2•0.7•leg) 66.4•12/(2•0.7• 6) <= 275 94.8 N/mm² OK Weld Shear fvw=fv•ts/(2•0.7•leg) 83.4•12/(2•0.7•6) 119.1 N/mm² OK

Step 7: Welds Flange Tension Weld Fapp=min(B•T•Py, Ftdesign) Min(126.0•10.7•275, 353.8) 353.8 kN FwCap=2•0.7•ts•L•Pyw 2•0.7•10•(126.0 - 2•6)•275 438.9 kN OK

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Flange Compression Weld Fapp=Ft+N 353.8 + -510.4 -156.6 kN FwCap=2•0.7•ts•B•Pyw 2•0.7•10•(126.0 - 2•6)•275 438.9 kN OK

Web Welds in Tension Zone Lwt=L-proj-T-root+1.73•g/2 130 - 80 - 10.7 - 10.2 + 1.73 70/2 89.7 mm Load per row Row1=K1•Fr1 0•220 0.0 kN Row2=K2•Fr2 (31/(27 + 31))•176 94.1 kN Total Load Ft 0.0, 94.1 94.1 kN FwCap=2•0.7•ts•Lwt•Pyw 2•0.7•10•89.7•275 345.2 kN OK

Web Welds in Shear Zone Lws=D-(Tt+Tb )-rt-rb-Lwt 353.4 - 21.4 - 10.2 - 10.2 - 90 222.0 mm FwCap=2•0.7•ts•Lws•Pyw 2•0.7•10•222.0•220 683.6 kN OK

Beam Compression Stiffener Stiffener Compression load Fc 45.7•12•275 150.8 kN Fcmod= (Fc-Faxial)•Mapp/Mcap+Faxial (81.6--510.4)•145.3/162.2+-510.4 81.6 kN Weld Axial Cap=hc•weld•py 45.7•(0.7•6•2)•275 107.7 kN OK Weld Shear Cap=L•weld•py 140•(0.7•6•2)•220 264.0 kN OK Stiff Shear Cap=L•ts•0.6•py 140•12•0.6•275 277.2 kN OK

14.17. - DESIGN OF SPLICE CONNECTION-BOTTOM CHORD AT AXE

F&W.

APEX JOINT AT : N.176 - LEVEL 2 : MEMBERS 111, 114, 119, 123, 128, 135-136, 139, 141 AND 143 (N.150-N.186)

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Beam to Beam End-Plated Connection to BS 5950

LOADING CASE 001 : ULTIMATE LIMIT STATE (FINAL STAGE)

Basic Data Applied Forces at End-plate Interface Resultant Forces M, Fv, F 8.9 kNm, 10.8 kN, -480.1 kN Load directions Top of Joint in Tension, Rafter moving Down and in Tension. Design to BS 5950-1: 2000 and the SCI Green Book: Joints in Steel Construction : Moment Connections: SCI-P-207/95 Rafter Capacities Mc, Fvc, Fc 132.2 kN.m, 340.5 kN, 1150.1 kN Fc = 1150.1 kN OK

Summary of Results (Unity Ratios) Tensile Capacity 0.59 OK Moment Capacity 177.4 kNm (for 4 rows of bolts) (Modified Applied Moment Mm=82.8 kNm) 0.47 OK Moment Capacity 125.7 kNm (for the 2 rows of bolts required in the tension zone) 0.66 OK Shear Capacity 0.02 OK Shear Capacity (Fv & T) 0.01 OK Beam Tension Stiffener at row 2 0.42, 0.87, 0.98, 0.98 0.98 OK Extended End-plate Stiffener 0.41, 0.18, 0.39, 0.59, 0.25, 0.42 0.59 OK Flange Welds 0.79, 0.59 0.79 OK Web Welds 0.25, 0.02 0.25 OK Beam compression stiffener 0.15 OK

Step 1: Tension Zone BOLT ROW 1 End Plate row 1 only Mp=Leff•tk•tk •py/6 145.4•16.0•16.0•275.0/6 1705.8 kN.mm T2.5: 7 Prmode1=4•Mp/m 4•1705.8/31.90 213.9 kN Eq 2.1 Prmode2=(2•Mp+n•Nb•Pt')/(m+n) (2•1705.8 + 39.88•2•137.2)/(31.90 + 39.88) 200.0 kN Eq 2.2 Pr=min(Prmode1,2,3) min(213.9, 200.0, 219.5) 200.0 kN

BOLT ROW 2 End Plate row 2 only Mp=Leff•tk•tk •py/6 200.4•16.0•16.0•275.0/6 2351.8 kN.mm T2.5: 5 Prmode1=4•Mp/m 4•2351.8/31.90 294.9 kN Eq 2.1 Prmode2=(2•Mp+n•Nb•Pt')/(m+n) (2•2351.8 + 39.88•2•137.2)/(31.90 + 39.88) 218.0 kN Eq 2.2 Pr=min(Prmode1,2,3) min(294.9, 218.0, 219.5) 218.0 kN

BOLT ROW 3 End Plate row 3 only Mp=Leff•tk•tk •py/6 200.4•16.0•16.0•275.0/6 2351.8 kN.mm T2.5: 2 Prmode1=4•Mp/m 4•2351.8/31.90 294.9 kN Eq 2.1 Prmode2=(2•Mp+n•Nb•Pt')/(m+n) (2•2351.8 + 39.88•2•137.2)/(31.90 + 39.88) 218.0 kN Eq 2.2 Pr=min(Prmode1,2,3) min(294.9, 218.0, 219.5) 218.0 kN

BOLT ROW 4 End-Plate rows 3 to 4 combined Leff(Row 3)=Max(ii/2, iii-ii/2) Max(190.1/2, 200.4-190.1/2) 105.4 mm Leff(Row 4)=(ii / 2) 190.1/2 95.1 mm Leff=Leff(Row 3)+P+Leff(Row 4) 105.4 + 90.0 + 95.1 290.4 mm Mp=Leff•tk•tk •py/6 290.4•16.0•16.0•275.0/6 3407.8 kN.mm T2.6: 4 & 1 Prmode1=4•Mp/m 4•3407.8/31.90 427.3 kN Eq 2.1 Prmode2=(2•Mp+n•Nb•Pt')/(m+n) (2•3407.8 + 39.88•4•137.2)/(31.90 + 39.88) 399.8 kN Eq 2.2 Pr=min(Prmode1,2,3) min(427.3, 399.8, 439.0) 399.8 kN Pr net=Pr-Pr3,3 399.8 - 218.0 181.9 kN

Potential Tension Capacity Sigma Pri 200.0 + 218.0 + 218.0 + 181.9 kN 817.8 kN OK

Step 2: Compression Zone Beam Compression Beam Compression Zone Stiffener, Flange and Web in Compression Utilising 20% OverStressing

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Total Area Stiffener, Flange and Web 12.0 x90.0 + 102.4•10.8 + 6.6•72.0 26.6 cm² Pcbeam 26.6•275•1.20 878.2 kN Eq 2.9

Potential Compression Capacity Pcmin 878.2 878.2 kN OK

Step 4: Moment Capacity Fc=Min(Pri+N, Pc) min(817.8 + -480.1,878.2) 337.7 kN Fri=Fc-Axial 337.7 - -480.1 817.8 kN Pδ=Pri -Fri 817.8 - 817.8 0.0 kN

Final Bolt Forces and Moment Capacities Bolt row 4 Mc4=Pr4•h4 181.9•80.3 14.6 kN.m Bolt row 3 Mc3=Pr3•h3 218.0•170.3 37.1 kN.m Bolt row 2 Mc2=Pr2•h2 218.0•255.3 55.6 kN.m Bolt row 1 Mc1=Pr1•h1 200.0•350.3 70.0 kN.m Mc 177.4 kN.m Mm=M-N•Hn 8.9 - -480.1•153.9 82.8 kN.m OK Tension Bolts Only the first 2 rows are required to resist the applied moment The remaining rows shall be considered to be part of the shear zone. Mc' for 2 rows 70.0, 55.6 125.7 kN.m Ft for 2 rows 200.0, 218.0 418.0 kN Ftdesign=Ft •Mapp/Mc' 418.0•82.8/125.7 275.3 kN

Final Web Compression Zone Height Reducing Compression zone for applied moments. F red=PCbeam-Ft design 878.2 - 275.3 602.9 kN h red=F red/t/py/1.2 602.9/6.6/275/1.2 276.8 mm h=max(0, h old-h red) max(0,72.0 - 276.8) 0.0 mm OK

Step 5: Shear Bolts Bolt Shear Capacity BSC=91.875, tg=32 91.9 kN Bearing Capacity-End Plate pb=460, edge=40.0, ?=20, tk=16, kbs=1.00 147.2 kN Bearing Capacity-Bolts pb=1000, ?=20, tk=16 320.0 kN Pss=Min(bearing...,shear) Min(147.2, 320.0, 91.9) 91.9 kN Pts Min(bearing...,0.4•shear) Min(147.2, 320.0, 36.8) 36.8 kN V=Ns•Pss+Nt•Pts 6•91.9 + 4•36.8 698 kN OK

Combined Tension & Shear Ftave=F/n 480/8 60.0 kN Fs=Ps•(1.4-Ft/Pt) 91.9 • ( 1.4 - 60.0 / 109.8) 78.4 kN V=Ns•Pss+Nt•Pts 2•91.9 + 8•78.4 811 kN OK

Step 6C: Beam Tension Stiffeners Stiffener at Bolt Row 2 Asn=2•Bsn•ts 2(45 - 10)•14 980 mm² Lt=Lu+P+Ll 47.5 + 85 + 45.0 177.5 mm Tension Asnreq =(Fu+Fl)/pyt-Lt•t (218.0 + 218.0)/275 - 177.5•7 413.8 mm² OK F1=Fu•m1/(m1+m2u) 218.0•31.9/(31.9 + 27.5) 117.1 kN F2=Fl•m1/(m1+m2l) 218.0•31.9/(31.9 + 27.5) 117.1 kN Bending Asnreq =(F1+F2)/py (117.1 + 117.1)/275 851.4 mm² OK Stiff Len > 1.8•bsg 150.0 >= 1.8•45.0 81.0 mm OK Ten weld leg >= Stk•0.7 10 >= 14•0.7 10 >= 9.8 OK

Extended End-plate Stiffener Asn=Bsn•ts 80•12 960 mm² Fapp=Fu•m1/(m1+m2) 200.0•35.2/(35.2 + 29.2) 109.3 kN Tension Asnreq=Fapp/pyt 109.3/275 397.5 mm² OK Bending fs=3•F•la/(Ls•Ls•ts) 3•109.3•40.0/(150•150•12) 48.6 N/mm² OK Shear fv=F/(Ls-snipe)/ts 109.3/(150 - 10)/12 65.1 N/mm² pv=0.6•py 0.6•275.0 165.0 N/mm² OK Weld Tension fs=F/lt/(2•0.7•leg) 109.3/80/(2•0.7•6) <= 275 162.7 N/mm² OK Weld Bending fmw=fm•ts/(2•0.7•leg) 48.6•12/(2•0.7• 6) <= 275 69.4 N/mm² OK Weld Shear fvw=fv•ts/(2•0.7•leg) 65.1•12/(2•0.7•6) 92.9 N/mm² OK

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36

Step 7: Welds Flange Tension Weld Fapp=min(B•T•Py, Ftdesign) Min(102.4•10.8•275, 275.3) 275.3 kN FwCap=2•0.7•ts•L•Pyw 2•0.7•10•(102.4 - 2•6)•275 348.0 kN OK

Flange Compression Weld Fapp=Ft+N 275.3 + -480.1 -204.8 kN FwCap=2•0.7•ts•B•Pyw 2•0.7•10•(102.4 - 2•6)•275 348.0 kN OK

Web Welds in Tension Zone Lwt=L-proj-T-root+1.73•g/2 135 - 80 - 10.8 - 7.6 + 1.73 80/2 105.8 mm Load per row Row1=K1•Fr1 0•200 0.0 kN Row2=K2•Fr2 (28/(32 + 28))•218 100.9 kN Total Load Ft 0.0, 100.9 100.9 kN FwCap=2•0.7•ts•Lwt•Pyw 2•0.7•10•105.8•275 407.3 kN OK

Web Welds in Shear Zone Lws=D-(Tt+Tb )-rt-rb-Lwt 312.7 - 21.6 - 7.6 - 7.6 - 106 170.1 mm FwCap=2•0.7•ts•Lws•Pyw 2•0.7•10•170.1•220 523.9 kN OK

Beam Compression Stiffener Stiffener Compression load Fc 90•12•275 297 kN Fcmod= (Fc-Faxial)•Mapp/Mcap+Faxial (31.8--480.1)•82.8/125.7+-480.1 31.8 kN Weld Axial Cap=hc•weld•py 90.0•(0.7•6•2)•275 212.1 kN OK Weld Shear Cap=L•weld•py 150•(0.7•6•2)•220 282.9 kN OK Stiff Shear Cap=L•ts•0.6•py 150•12•0.6•275 297.0 kN OK

14.18. - DESIGN OF SPLICE CONNECTION-TOP CHORD AT AXE B&F&W.

APEX JOINT AT : N.60 - LEVEL 3 : MEMBERS 16-17, 19, 21-23, 25-26, 28, 30, 33, 35, 37, 39-40, 42 AND 44 (N.41-N.74)

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Beam to Beam End-Plated Connection to BS 5950

LOADING CASE 001 : ULTIMATE LIMIT STATE (FINAL STAGE)

Basic Data Applied Forces at End-plate Interface Resultant Forces M, Fv, F 0.0 kNm, 312.0 kN, 667.5 kN Load directions Rafter moving Down and in Compression. Design to BS 5950-1: 2000 and the SCI Green Book: Joints in Steel Construction : Moment Connections: SCI-P-207/95 Rafter Capacities Mc, Fvc, Fc 290.0 kN.m, 511.5 kN, 1896.1 kN Fvc = 511.5 kN OK

Summary of Results (Unity Ratios) Moment Capacity (for 3 rows of bolts) 0.00 OK Moment Capacity 26.6 kNm (for the 1 rows of bolts required in the tension zone) 0.00 OK Shear Capacity 0.50 OK Flange Welds 0.00, 0.95 0.95 OK Web Welds 0.14, 0.65 0.65 OK

Step 1: Tension Zone BOLT ROW 1 End Plate row 1 only Mp=Leff•tk•tk •py/6 219.7•16.0•16.0•275.0/6 2577.9 kN.mm T2.5: 3 Prmode1=4•Mp/m 4•2577.9/36.35 283.7 kN Eq 2.1 Pr=min(Prmode1,3) min(283.7, 219.5) 219.5 kN

BOLT ROW 2 End-Plate rows 1 to 2 combined Leff(Row 1)=Max(ii/2, iii/2) Max(211/2, 228.4/2) 114.2 mm Leff(Row 2)=(ii / 2) 211/2 105.5 mm Leff=Leff(Row 1)+P+Leff(Row 2) 114.2 + 100.0 + 105.5 319.7 mm Mp=Leff•tk•tk •py/6 319.7•16.0•16.0•275.0/6 3751.3 kN.mm T2.6: 3 & 1 Prmode1=4•Mp/m 4•3751.3/36.35 412.8 kN Eq 2.1 Pr=min(Prmode1,3) min(412.8, 439.0) 412.8 kN Pr net=Pr-Pr1,1 412.8 - 219.5 193.3 kN

BOLT ROW 3 End-Plate rows 1 to 3 combined Leff(Row 1)=Max(ii/2, iii/2) Max(211/2, 228.4/2) 114.2 mm Leff(Row 3)=(ii / 2) 211/2 105.5 mm Leff=Leff(Row 1)+P+Leff(Row 3) 114.2 + 213.0 + 105.5 432.7 mm Mp=Leff•tk•tk •py/6 432.7•16.0•16.0•275.0/6 5077.1 kN.mm T2.6: 3 & 1 Prmode1=4•Mp/m 4•5077.1/36.35 558.7 kN Eq 2.1 Pr=min(Prmode1,3) min(558.7, 658.6) 558.7 kN Pr net=Pr-Pr2,1 558.7 - 412.8 145.9 kN

Potential Tension Capacity Sigma Pri 219.5 + 193.3 + 145.9 kN 558.7 kN

Step 2: Compression Zone Beam Compression Beam Compression Zone Flange and Web in Compression Utilising 20% OverStressing Total Area Flange and Web 177.7•10.9 + 7.7•41.0 22.5 cm² Pcbeam 22.5•275•1.20 743.4 kN Eq 2.9

Potential Compression Capacity Pcmin 743.4 743.4 kN OK

Step 4: Moment Capacity Fc=Min(Pri+N, Pc) min(558.7 + 667.5,743.4) 743.4 kN Fri=Fc-Axial 743.4 - 667.5 75.9 kN Pδ=Pri -Fri 558.7 - 75.9 482.8 kN

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38

Final Bolt Forces and Moment Capacities Bolt row 3: Mc3 =(Pr3-Pδ )• h3 145.9 - 482.8 = 0.0•138.3 0.0 kN.m Bolt row 2: Mc2 =(Pr2-Pδ )• h2 193.3 - 336.9 = 0.0•251.3 0.0 kN.m Bolt row 1: Mc1 =(Pr1-Pδ )• h1 219.5 - 143.7 = 75.9•351.3 26.6 kN.m Mc 26.6 kN.m Mm=M-N•Hn 0.0 - 667.5•195.0 -130.1 kN.m OK Mm is -ve. Joint in full compression. No tension zone generated OK Tension Bolts Only the first 1 rows are required to resist the applied moment The remaining rows shall be considered to be part of the shear zone. Mc' for 1 rows 26.6 26.6 kN.m Ft for 1 rows 75.9 75.9 kN Ftdesign=Ft •Mapp/Mc' 75.9•0.0/26.6 0.0 kN

Final Web Compression Zone Height Reducing Compression zone for applied moments. F red=PCbeam-Ft design 743.4 - 0.0 743.4 kN h red=F red/t/py/1.2 743.4/7.7/275/1.2 292.5 mm h=max(0, h old-h red) max(0,41.0 - 292.5) 0.0 mm OK

Step 5: Shear Bolts Bolt Shear Capacity BSC=91.875, tg=32 91.9 kN Bearing Capacity-End Plate pb=460, edge=65.0, ?=20, tk=16, kbs=1.00 147.2 kN Bearing Capacity-Bolts pb=1000, ?=20, tk=16 320.0 kN Pss=Min(bearing...,shear) Min(147.2, 320.0, 91.9) 91.9 kN Pts Min(bearing...,0.4•shear) Min(147.2, 320.0, 36.8) 36.8 kN V=Ns•Pss+Nt•Pts 6•91.9 + 2•36.8 625 kN OK

Step 7: Welds Flange Tension Weld Fapp=min(B•T•Py, Ftdesign) Min(177.7•10.9•275, 0.0) 0.0 kN FwCap=2•0.7•ts•L•Pyw 2•0.7•8•(177.7 - 2•8)•275 498.0 kN OK

Flange Compression Weld Flange Weld OK if >= 0.7•T 8 >= 0.7•10.9 >= 7.6 mm OK

Web Welds in Tension Zone Lwt=L-proj-T-root+1.73•g/2 65 - 20 - 10.9 - 10.2 + 1.73 90/2 101.8 mm Load per row Row1=K1•Fr1 (28/(36 + 28))•76 32.8 kN Total Load Ft 32.8 32.8 kN FwCap=2•0.7•ts•Lwt•Pyw 2•0.7•6•101.8•275 235.0 kN OK

Web Welds in Shear Zone Lws=D-(Tt+Tb )-rt-rb-Lwt 402.6 - 21.8 - 10.2 - 10.2 - 102 258.7 mm FwCap=2•0.7•ts•Lws•Pyw 2•0.7•6•258.7•220 478.0 kN OK

14.19. - DESIGN OF CONNECTION BETWEEN WALL BEAM AND TOP

CHORD.

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BEAM TO BEAM: FLEXIBLE END-PLATE CONNECTION AT N.149 - LEVEL 3

Beam to Beam Flexible End-plate Connection to BS 5950

Basic Data Applied Forces at Interface Shear Forces Left = 31.0 kN, Right = 0.0 kN Design to BS 5950: Pt 1: 2000 and the SCI Green Book: Joints in Steel Construction: Simple Connections: SCI-P212: 2002

Basic Dimensions Left-127x76 UB 13 [43] D=127.0, B=76.0, T=7.6, t=4.0, r=7.6, py=275 Supporting-406x140 UB 46 [43] D=403.2, B=142.2, T=11.2, t=6.8, r=10.2, py=275

Summary of Results (Unity Ratios) Left Hand Beam Bolt Shear & Bearing 0.13, 0.05 0.13 OK Plate Bearing 0.11 OK Plate Shear 0.09, 0.09, 0.08 0.09 OK Web Shear & Weld 0.49, 0.18 0.49 OK Web Bending 0.73 OK

Supporting Beam Bolt Bearing 0.07 OK Plate Bearing 0.15 OK Web Bearing & Shear 0.15, 0.11, 0.10 0.15 OK

Left Hand Beam Applied Shear Loads Q = 31.0 kN, fv = 31.0 / 4 = 7.8 kN

Bolt Shear & Bearing Ps= 16 mm ? Grade 8.8 Bolts 58.9 kN > fv OK Pbb=pb•t•? 1000 x 10 x 16 160.0 kN > fv OK

Plate Bearing PbsEnd=Fn(pb,t,?,edge,kbs) 460, 10, 16, 30, 1.00 69.0 kN PbsInt=Fn(pb,t,?,edge,kbs) 460, 10, 16, 41, 1.00 73.6 kN BearCap=(PbsEnd+N•PbsInt)•2 (69.0 + 73.6•1 ) • 2 285.2 kN > Q OK

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Plate Shear: Check 9 Plane Shear Av=0.9•D•tk 0.9 x 120 x 10.0 1080 mm² Avnet=Av-n•?•tk 1080 - 2 x 18.0 x 10.0 720 mm² Pv=0.6•py•Av 0.6 x 275 x 1080 178.2 kN > Q/2 OK Pvnet=0.7•py•Ke•Avnet 0.7 x 275 x 1.2 x 720 166.3 kN > Q/2 OK

Block Shear Lv=(n-1)•vcc+edge (2 - 1) x50 + 30 80 mm Pr=0.6•py•t•(Lv+Ke(Lt-k•D')) 0.6 x275 x10 x (80 + 1.2 x (35 - 0.5 x 18.0 ) 183.5 kN > Q/2 OK

Web Weld & Local Shear: Checks 2 & 4 Pweld=Pyw•2•(d-2•tw)•0.7•tw 220 x 2 x (107 - 2 x 6) x 0.7 x 6 175.6 kN > Q OK Pv=0.6•Py•(0.9•d•t) 0.6 x 275 x (0.9 x 107 x 4.0) 63.6 kN > Q OK

Web Bending: Check 5 Mapp=Q•la 31.0 x 80 2.5 kN.m Znet Fn(Section, Tnotch, Bnotch) 127x76 UB 13, 20, 0 12.4 cm³ Shear Capacity Pv=0.6•1•py•t•L 0.6 x 1 x 275.0 x 4.0 x 107 70.6 kN Shear Classification Fv/Pv 31.0 / 70.6 0.439 <= 0.75 Low Shear Mcap=py•Znet 275 x 12.4 3.4 kN.m OK

Single Notched Web Stability (restrained): Check 6 Data D/tw =31.8, Dc max =64 mm, C max = 127 mm Notch Length C = 80 - 10 70 mm OK Notch Depth Dc=Max(Dc1, Dc2) Max (20, 0) 20 mm OK

Supporting Beam Q=Max(Q1,Q2,Q1+Q2) Max(31.0, 0.0, 31.0 + 0.0) 31.0 kN fv =Q1/nb1+Q2/nb2 31.0/4 + 0.0/0 7.8 kN Qc =Fn(Q1, Q2, nb1, nb2) 31.0, 0.0, 4, 0 31.0 kN

Bolt Bearing Pbb=pb•t•? 1000 x 6.8 x 16 108.8 kN > fv OK

Web Bearing & Shear: Check 10 Pbs=Fn(pb,t,?,edge,kbs) 460, 7, 16, 41, 1.00 50.0 kN > fv OK Av=(et+(n-1)p+eb)•tw (50 + (2 -1) x 50 + 30) x 6.8 884 mm² Pv=0.6•Py•Av 0.6 x 275 x 884 145.9 kN > Qc/2 OK Pv=0.7•py•Ke•Av.net 0.7 x 275 x 1.2 x 639 147.7 kN > Qc/2 OK

14.20. - DESIGN OF DIAGONAL CONNECTION-120X120X8 mm. LIMCON V3.5

15-DEC-10

12:26:42

Connection: 120X120X8

Type: Bracing Cleat Connection

3: Double angles - connected on long legs

Country: UK

Units: Metric

Design code: BS 5950

Brace: Mark=BR Section=EA120X120X8 Grade=S275

D = 120 mm Root rad. = 13.0 mm fyf = 275 N/mm2

B = 120 mm Area = 1.8800E+03 fyw = 275 N/mm2

Tf = 8.0 mm Sx = 5.3888E+04 fu = 410 N/mm2

Tw = 8.0 mm

Angle between brace and normal to support = 45.00 deg.

Support: Section=UC152X152X30 Grade=S275

D = 158 mm Root rad. = 7.6 mm fyf = 275 N/mm2

B = 153 mm Area = 3.8300E+03 fyw = 275 N/mm2

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Tf = 9.4 mm Sx = 2.4800E+05 fu = 410 N/mm2

Tw = 6.5 mm

Brace connected to column flange.

Cleat (gusset):

300x200x12 Gr./fy/fu=S275/275/410 N/mm2

Whitmore section . . . . . . . . . . . . . 189 mm

Bolts 6-M20 8.8/N in 2 col(s). at 60 pitch and 50 gauge.

Weld 6 FW fu=440 N/mm2 to support.

Clearances:

Clearance between brace/cleat and column . 35.4 mm

MINIMUM ACTION CHECK

Specified minimum design actions:

Tension 0% of JNs ( 465.3) = 0.0 kN

Compression 0% of JNs ( 465.3) = 0.0 kN

NOTE: Input design actions are not automatically increased if they are less than

the specified minimum actions. Minimum actions may be set in any load case.

This check warns if any design action is less than the specified minimum

for all load cases.

INPUT DESIGN ACTIONS

Axial, N* . . . . . . . . . . . . . . . . . 501.0 kN (tens.)

Using ASI 1994/1996 model...

DESIGN CAPACITY CHECKS - Tension

Capacity ratio --------+

Design action --+ |

+-- Design capacity | |

| | |

Bracing member:

Brace section tension capacity . . . . . . 930.6 > N* = 501.0 1.86 Pass

Brace bearing capacity . . . . . . . . . . 883.2 > N* = 501.0 1.76 Pass

Brace internal tearing capacity . . . . . . 1081.9 > N* = 501.0 2.16 Pass

Brace end tearing capacity . . . . . . . . 772.8 > N* = 501.0 1.54 Pass

Brace block shear capacity (mode I) . . . . 751.6 > N* = 501.0 1.50 Pass

Brace block shear capacity (mode II) . . . 523.4 > N* = 501.0 1.04 Pass

Bolts:

Bolt group shear capacity . . . . . . . . . 1102.5 > N* = 501.0 2.20 Pass

Bracing cleat (gusset):

Cleat bearing capacity . . . . . . . . . . 662.4 > N* = 501.0 1.32 Pass

Cleat internal tearing capacity . . . . . . 811.4 > N* = 501.0 1.62 Pass

Cleat end tearing capacity . . . . . . . . 579.6 > N* = 501.0 1.16 Pass

Cleat weld capacity . . . . . . . . . . . . 528.0 > N* = 501.0 1.05 Pass

Cleat tension capacity . . . . . . . . . . 587.2 > N* = 501.0 1.17 Pass

Cleat block shear capacity . . . . . . . . 563.7 > N* = 501.0 1.13 Pass

CRITICAL LIMIT STATE . . . Brace block shear capacity (mode II)

UTILIZATION RATIO . . . . 96%

CAPACITY RATIO, J.Ru/S* . 1.045 Pass

14.21. - DESIGN OF DIAGONAL CONNECTION-100X100X8 mm.

LIMCON V3.5

15-DEC-10

12:40:56

Connection: 100X100X8

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42

Type: Bracing Cleat Connection

3: Double angles - connected on long legs

Country: UK

Units: Metric

Design code: BS 5950

Brace: Mark=BR Section=EA100X100X8 Grade=S275

D = 100 mm Root rad. = 12.0 mm fyf = 275 N/mm2

B = 100 mm Area = 1.5600E+03 fyw = 275 N/mm2

Tf = 8.0 mm Sx = 3.6928E+04 fu = 410 N/mm2

Tw = 8.0 mm

Angle between brace and normal to support = 30.00 deg.

Support: Section=UC152X152X30 Grade=S275

D = 158 mm Root rad. = 7.6 mm fyf = 275 N/mm2

B = 153 mm Area = 3.8300E+03 fyw = 275 N/mm2

Tf = 9.4 mm Sx = 2.4800E+05 fu = 410 N/mm2

Tw = 6.5 mm

Brace connected to column flange.

Cleat (gusset):

260x200x10 Gr./fy/fu=S275/275/410 N/mm2

Whitmore section . . . . . . . . . . . . . 217 mm

Bolts 6-M20 8.8/N in 2 col(s). at 70 pitch and 55 gauge.

Weld 6 FW fu=440 N/mm2 to support.

Clearances:

Clearance between brace/cleat and column . 18.3 mm

MINIMUM ACTION CHECK

Specified minimum design actions:

Tension 0% of JNs ( 386.1) = 0.0 kN

Compression 0% of JNs ( 386.1) = 0.0 kN

NOTE: Input design actions are not automatically increased if they are less than

the specified minimum actions. Minimum actions may be set in any load case.

This check warns if any design action is less than the specified minimum

for all load cases.

INPUT DESIGN ACTIONS

Axial, N* . . . . . . . . . . . . . . . . . 350.0 kN (tens.)

Using ASI 1994/1996 model...

DESIGN CAPACITY CHECKS - Tension

Capacity ratio --------+

Design action --+ |

+-- Design capacity | |

| | |

Bracing member:

Brace section tension capacity . . . . . . 757.8 > N* = 350.0 2.17 Pass

Brace bearing capacity . . . . . . . . . . 883.2 > N* = 350.0 2.52 Pass

Brace internal tearing capacity . . . . . . 1302.7 > N* = 350.0 3.72 Pass

Brace end tearing capacity . . . . . . . . 772.8 > N* = 350.0 2.21 Pass

Brace block shear capacity (mode I) . . . . 855.4 > N* = 350.0 2.44 Pass

Brace block shear capacity (mode II) . . . 526.1 > N* = 350.0 1.50 Pass

Bolts:

Bolt group shear capacity . . . . . . . . . 1102.5 > N* = 350.0 3.15 Pass

Bracing cleat (gusset):

Cleat bearing capacity . . . . . . . . . . 552.0 > N* = 350.0 1.58 Pass

Cleat internal tearing capacity . . . . . . 814.2 > N* = 350.0 2.33 Pass

Cleat end tearing capacity . . . . . . . . 483.0 > N* = 350.0 1.38 Pass

Cleat weld capacity . . . . . . . . . . . . 431.1 > N* = 350.0 1.23 Pass

Cleat tension capacity . . . . . . . . . . 489.3 > N* = 350.0 1.40 Pass

Cleat block shear capacity . . . . . . . . 534.6 > N* = 350.0 1.53 Pass

CRITICAL LIMIT STATE . . . Cleat weld capacity

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Made By : TAMER MOHAMMED

Date : 06/04/2010

Checked : HANY AHMED HASSAN

Approved : HANY AHMED HASSAN

43

UTILIZATION RATIO . . . . 81%

CAPACITY RATIO, J.Ru/S* . 1.232 Pass

1.1. - DESIGN OF DIAGONAL CONNECTION-80X80X8 mm. LIMCON V3.5

15-DEC-10

12:43:56

Connection: 80X80X8

Type: Bracing Cleat Connection

3: Double angles - connected on long legs

Country: UK

Units: Metric

Design code: BS 5950

Brace: Mark=BR Section=EA80X80X8 Grade=S275

D = 80.0 mm Root rad. = 11.0 mm fyf = 275 N/mm2

B = 80.0 mm Area = 1.2300E+03 fyw = 275 N/mm2

Tf = 8.0 mm Sx = 2.3168E+04 fu = 410 N/mm2

Tw = 8.0 mm

Angle between brace and normal to support = 30.00 deg.

Support: Section=UC152X152X30 Grade=S275

D = 158 mm Root rad. = 7.6 mm fyf = 275 N/mm2

B = 153 mm Area = 3.8300E+03 fyw = 275 N/mm2

Tf = 9.4 mm Sx = 2.4800E+05 fu = 410 N/mm2

Tw = 6.5 mm

Brace connected to column flange.

Cleat (gusset):

200x100x10 Gr./fy/fu=S275/275/410 N/mm2

Whitmore section . . . . . . . . . . . . . 80.8 mm

Bolts 2-M20 8.8/N at 70 pitch.

Weld 6 FW fu=440 N/mm2 to support.

Clearances:

Clearance between brace/cleat and column . 32.0 mm

MINIMUM ACTION CHECK

Specified minimum design actions:

Tension 0% of JNs ( 304.4) = 0.0 kN

Compression 0% of JNs ( 304.4) = 0.0 kN

NOTE: Input design actions are not automatically increased if they are less than

the specified minimum actions. Minimum actions may be set in any load case.

This check warns if any design action is less than the specified minimum

for all load cases.

INPUT DESIGN ACTIONS

Axial, N* . . . . . . . . . . . . . . . . . 150.0 kN (tens.)

Using ASI 1994/1996 model...

DESIGN CAPACITY CHECKS - Tension

Capacity ratio --------+

Design action --+ |

+-- Design capacity | |

| | |

Bracing member:

Brace section tension capacity . . . . . . 608.9 > N* = 150.0 4.06 Pass

Brace bearing capacity . . . . . . . . . . 294.4 > N* = 150.0 1.96 Pass

Brace internal tearing capacity . . . . . . 434.2 > N* = 150.0 2.89 Pass

Brace end tearing capacity . . . . . . . . 257.6 > N* = 150.0 1.72 Pass

Brace block shear capacity (mode I) . . . . 415.8 > N* = 150.0 2.77 Pass

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Job ref : Job Ref

Sheet : 44

Made By : TAMER MOHAMMED

Date : 06/04/2010

Checked : HANY AHMED HASSAN

Approved : HANY AHMED HASSAN

44

Brace block shear capacity (mode II) . . . 311.2 > N* = 150.0 2.07 Pass

Bolts:

Bolt group shear capacity . . . . . . . . . 367.5 > N* = 150.0 2.45 Pass

Bracing cleat (gusset):

Cleat bearing capacity . . . . . . . . . . 184.0 > N* = 150.0 1.23 Pass

Cleat internal tearing capacity . . . . . . 271.4 > N* = 150.0 1.81 Pass

Cleat end tearing capacity . . . . . . . . 161.0 > N* = 150.0 1.07 Pass

Cleat weld capacity . . . . . . . . . . . . 215.6 > N* = 150.0 1.44 Pass

Cleat tension capacity . . . . . . . . . . 244.6 > N* = 150.0 1.63 Pass

Cleat block shear capacity . . . . . . . . 249.9 > N* = 150.0 1.67 Pass

CRITICAL LIMIT STATE . . . Cleat end tearing capacity

UTILIZATION RATIO . . . . 93%

CAPACITY RATIO, J.Ru/S* . 1.073 Pass

1.2. - DESIGN OF WELDING LENGTH FOR DIAGONAL MEMBER. LIMCON V3.5

15-DEC-10

12:49:33

Connection: Welding

Type: Weld Group

Country: UK

Units: Metric

Design code: BS 5950

Weld

6 FW fu=440 N/mm2

Design actions:

Force, F*x . . . . . . . . . . . . . . . . 0.0 kN

Force, F*y . . . . . . . . . . . . . . . . 250.0 kN

Moment, M*z . . . . . . . . . . . . . . . . 0.00 kN.m

Angle of applied load from vertical (deg.) -180.0

Eccentricity . . . . . . . . . . . . . . . 0.0 mm

Using ASI 2006 model...

Type 2: Double vertical welds

|| D: 200 mm

||

D ||

||

||

Weld group properties:

Lwx . . . . . . . . . . . . . . . . . . . . 400 mm

Lwy . . . . . . . . . . . . . . . . . . . . 400 mm

Lwz . . . . . . . . . . . . . . . . . . . . 400 mm

Iwx . . . . . . . . . . . . . . . . . . . . 1.3333E+06 mm3

Iwy . . . . . . . . . . . . . . . . . . . . 0.0000E+00 mm3

Iwz . . . . . . . . . . . . . . . . . . . . 1.3333E+06 mm3

ANALYSIS RESULT

Forces on weld elements, kN/mm:

Point X Y vx vy vz vres

3 0.0 100.0 0.000 0.625 0.000 0.625

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Job ref : Job Ref

Sheet : 45

Made By : TAMER MOHAMMED

Date : 06/04/2010

Checked : HANY AHMED HASSAN

Approved : HANY AHMED HASSAN

45

4 0.0 -100.0 0.000 0.625 0.000 0.625

For 6 FW fu=440 N/mm2

Weld capacity . . . . . . . . . . . . . . . 0.933 kN/mm

CRITICAL LIMIT STATE . . . Weld capacity

UTILIZATION RATIO . . . . 67%

CAPACITY RATIO, J.Ru/S* . 1.493 Pass