11.203 Calculations

Project Title: Addis Hotel Job No: 11.203

Part of Structure: Roof slab – Preliminary design

Originator: EH Checker: Date: 12/04/11 Sheet No: RS-01

Calculations Status: Preliminary x Planning Tender Construction

Calculations Output

Roof SlabOne Way Spanning – Continuous Slab

LoadingGk = 0.22 x 24 + 0.5 + 0.5 = 6.28kN/m2

Qk = 5.0kN/m2

Bending Moment CheckFrom Analysis Msag = 55.8kN/m2

Mhog = 66.2kN/m2

End Span V = 61kN

Saggingb = 1000mmfcu = 30N/mm2 d = 220-20-6 = 194mmk = 55.8x106/30x1000x1942 = 0.049z = 0.942d = 182.7mm

As,req = 55.8x106/182.7x360/1.15 = 976mm2/mAs, prov → 12ø @150 c/c → 754mm2/m

Reduce Live Load Qk = 3.0kN/m2

Msag = 44.1kN/m2

Mhog = 52.8kN/m2

V = 49.1kN

As, req, sag = 771mm2/m → OK

Hoggingd = 220-20-14/2 = 193mmk = 52.8x106/30x1000x1932 = 0.047z = 0.944d = 182.2mm

As, req = 52.8x106/182.2x0.87x360/1.15 = 925.2mm2/mAs, prov 14ø @ 150c/c → 1026mm2/m → OK

Shear Check vc = 0.79 x 5311/3 x 30/251/3/1.25 = 0.54N/mm2 v = 49.1x103/193x1000 = 0.25N/mm2 → OK in Shear

Qk = 5.0kN/m2

Qk = 5.0kN/m2

Class C4 & C5Dance Hall, Concert,Pub Usage

Class C of BS63992.0 + 1.0 = 3.0kN/m2

Lower Qk 3.0kN/m2

capacity


Part of Structure: Concrete cover to EBCS-02

Originator: EH Checker: Date: 13/06/11 Sheet No: C.C-01


Calculations Output

Concrete Cover to EBCS - 02Concrete CoverTable 7.2

Minimum Cover - Internal environment = 15mm (never less than bar ø) CL 7.1.3 (7) Slab min cover = 20mm

(8) 5mm < Δh < 10mm – Instiu Concrete(9) Cast against blinding, Cover > 40mm

∴ Slabs – 20mm Beams – 25mmColumns – 30mm

(15mm + 5mm)(20ø bar + Δh (5mm)(24ø bar + Δh (5mm)

6 5 4 3 2 1 1’

36.7 Roof

7th

6th

5th

4th

3rd

2nd

1st

Service Floor

Mezzanine

Ground

Basement

3.9

3.0

3.0

3.3

3.45

3.45

3.45

3.45

3.45

4.0

Height

32.7

29.25

25.8

22.35

18.9

15.45

12.15

9.15

6.15

2.25

-2.1

-4.2

33.6

30.3

27.0

23.7

20.4

17.1

13.5

10.5

7.8

4.5

0.00

-6.2


Part of Structure: Full height section

Originator: Checker: Date: Sheet No: SK-01


Calculations

Section at G.L G


Part of Structure: Global loads

Originator: EH Checker: Date: 12/04/11 Sheet No: C-03


Calculations Output

Notional Horizontal Loads

1.5% Dead Load of Storey

Upper Floors → Gk = 354 kN per 48m2

L = 68.3m2 Floor Area = 1229.4m2

B = 18.0m2

Gk, floor = 354 x 1229.4/48 = 9066.8kN → 1.5% = 136.0kN

Say WL = 1.5kN/m218x4x1.5 = 108kN


Part of Structure: Loading

Originator: EH Checker: Date: 12/04/11 Sheet No: L-02


Calculations Output

Mezz FloorGk kN/m2

0.25 x 24 = 6.0Ceiling & Services = 0.5Finished = 0.5

7Beam, 0.3 x (0.65 -0.25) x 24 = 2.88kN/m

Qk = 5.0Partitions = 1.0

6.0

Ground FloorGk

0.2 x 24 = 4.8Ceiling & Services = 0.5Finishes = 0.5

5.8


6.0

110

379

240

100

1463

750

150

200


Part of Structure: Loading – Independent Check

Originator: EH Checker: Date: 12/04/11 Sheet No: L-01


Calculations Output

Loading to BS 6399 pt. 1

BedroomsGk kN/m2

0.22 x 24 = 5.28Ceiling & Services = 0.5Finishes = 0.5

6.28


3.0

Terrace (Assumed) Terrace (Actual) Gk kN/m2 Gk

kN/m2

0.22 x 24 = 5.28 20mm terrazzo 0.02 x 20.80.42

Ceiling & Services = 0.5 Screed 80mm ave1.84

Paviours 0.05 x 23 = 1.158.04

Screed to Falls = 2.3Asphalt = 0.2Insulation = 0.07

9.5

Qk (and plant) = 5.0

Ribbed Floors (8x8 panels)Gk

[0.24 x 0.11 x 24 x (8 - 0.3)] + [0.1 x 24 x 8 x 8] +[0.15 x 0.24 x 24 x (8 - 19 x 0.11 - 0.4)] + [0.24 x 0.4 x (8 - 0.7) x 24] + [0.24 x 0.3 x (8 - 0.3) x 24]

= 194.34kN → 194.34/8x8 = 3.04kN/m2

Qk = 7.5kN/m2

Waffle FloorGk

[0.75 x 0.2 x 24 x 2 x 8] + [0.15 x 1.863 x 8 x 24] +[0.2 x 0.45 x 24 x 1.863]

= 115.3kN → 115.3/8x1.863 = 7.74kN/m2

1460

500

600012501000


Part of Structure: Roof beams

Originator: EH Checker: Date: 12/04/11 Sheet No: RB-01


Calculations Output

Summary of ReinforcementProvided mm2/m Required mm2/mSagging 12ø @ 130 → 869 835Hogging 14ø @ 150 → 1026 1019Transverse 10ø @ 170→ 461 286

Assess effect of opes in the roof slabOpe size on Drg ST – 51Span = 6000 - 300 + 194 = 5.894mm1250 x 500 @ 1460 from G.L

Bending Moment CheckMax sagging moment= 26.1 x (1+ 1.25/2) = 42.41 kNm/mb = 1000mmd = 194mmk =42.41x106/30 x 1000 x 1942 = 0.037z = 0.95d = 184.3mmAs, req = 42.41x106/313 x 184.3 = 735.2mm2/mAs, prov to centre span 12ø @ 150c/c → 754mm2/m





Calculations Output

Gk = 6.28 kN/m2 ULS = 13.59kN/m2

Qk = 3.0 kN/m2 Use 13.59 x 6 = 81.55kN/m

Bending Moment CheckMsag = wl2/14 = 372.8kNmMhog = wl2/12.5 = 417.5kNmV = 0.6F = 391.44kN

Sagging b = 300mmd = 650 - 8 - 25 - 10 = 607mmfcu = 30N/mm2k = 372.8x106/30x300x6072 = 0.112z = 0.854d = 518.4mmAs, req = 372.8x106/518.4 x 0.87 x 360 = 2296mm2

As, prov = 5 x 20ø = 1570mm2 - not adequate

As a T-BeamMR = 0.45fcubhf(d-hf/2)b = 0.7x 8000/10 + 300 = 860mmhf = 220mmMR = 1269.4kNm → NA in flange k = 372.8x106/30x560x6072 = 0.039z = 0.95d = 576.65mmAs,req = 372.8x106/576.65x.087x360 = 2064.2mm2

Internal span as end span shorter

Further Detailed Analysis Required

Consider as 2-Way SpanningSlab Supported by beams





Calculations Output

Hogging d = 650 - 25 - 10 -24/2 = 603mmb = 300mmk = 417.5x106/30x300x6032 = 0.128z = 0.828d = 499.28mm As, req = 417.5x106/499.28x0.87x360 = 2670mm2

As,prov = 7 x 24ø → 3166mm2

As Total Beam,Provided Required1570 + 3166 = 4736mm2 4966mm2

Shear Check100As/bd = 100x3166/300x603 = 1.75 → vc = 0.76N/mm2

10ø Shear Links, Asv = 157mm2

Sv = 157x0.87x360/300x(2.16-0.76) = 116.9mm

10ø @ 70 c/c provided OK

Use more detailed analysis on RAM


Part of Structure: Roof beams – loaded by 2-way slab



Calculations Output

Gk = 7.12kN/m2 n = 14.768kN/m2

Qk = 3.0kN/m2

Self Weight = 0.3x0.65x24 = 468kN/m UDL→ Gk = 7.12 x (6-0.3) + 4.68 = 45.26kN/m

Qk = 3x6 = 18.0kN/m n = 1.4 x 17.12 + 1.6 x 3 = 14.77kN/m2

Consider Slab Loads on Beam as 2-Way Spanning BS 8110 – Table 3.15

Consider Beam GL 3Load from Slab 4B – D3 → Lx = 6m Ly/Lx = 3.33

Ly = 20m

3 Edges Discontinuous – One Long edge → βsx = 0.63 – Continuous Edge

Vsx = 0.63x14.77x6 = 55.83kN/m over 0.75 span

Slab Panel B3 to I2→ Lx = 6m Ly/Lx = 10

Ly = 60m

2 Short Edges Discontinuous → βsx = 0.54

Vsx = 0.54x14.77x6 = 47.85kN/m

∴ Total UDL on Beam = 55.83 + 47.85 = 103.68kN/m

See Attached SpreadsheetLocation As, req As, prov

MomentGrid C 3558mm2 3166mm2

542kNmB to C 3704mm2 1570mm2

829kNm


Part of Structure: Roof beams – Grid 3 – RAM Analysis



Calculations Output

AnalysisSee following RAM output for analysis results (vertical loads)

ResultsBeam GL 3Msag = 177kNmMhog = 119kNmV = 153kN

Bending Moment Checkb = 300mmd = 650-25-10-24/2 = 603mmfcu = 30N/mm2

k = 177x106/30x300x6032 = 0.054z = 0.936d = 564.41mmAs, req = 177x106/0.87x360x564.41 = 1001.92mm2 As, prov 5 x 20ø → 1571mm2

Mhog = 119kNmAs, prov 7 x 24ø → 3166mm2 > 1001mm2 (M = 177kNm) → Hogging Reinforcement

Adequate

Shear CheckV = 153kN v = 153x103/300x603 = 0.847N/mm2 < 0.8√fcu = 4.38N/mm2

100As/bd = 100x628/300x603 = 0.347 vc = 0.79x0.3471/3x(30/25)1/3/1.25 = 0.472N/mm2

v < vc + 0.4 → Provide min links Asv = 100.5mm – 2 legs of 8ø

Sv = 100.5x(300/1.15)/300x0.4 = 218.6mmSv, max = 0.75x603 = 452mm

Shear Links Provided 8ø @ 150c/c → Adequate

Deflectionl/d = 800/603 = 13.26 < 26 → OK


Part of Structure: 220 dp typical floor slab

Originator: EH Checker: Date: 08/06/11 Sheet No: SB-10


Calculations Output

Reinforcement Areas Provided RequiredSagging Steel = 12ø @ 130c/c

= 869mm2/m 773mm2/mHogging Steel = 14ø @ 150c/c

=1026mm2/m 935mm2/mTransverse Steel = 10ø @170c/c

= 461.7mm2/m 286mm2/m

Asses Effect of Centre Span Opes - 1250mm wide

Bending Moment CheckMsag = 25.4kN/mb = 1000-1250/2 = 375mmk = 25.4x106/30x375x1942 = 0.060z = 0.928d = 180.0mm

As, req = 25.4x106/180x0.87x360 = 450.5mm2

As, prov 12ø @ 150c/c → 754mm2/m

∴ Opes Adequately Provided for by adjacent strips in terms of strength

Full slab 1000 wide width resisting shear

∴ Shear ok, see previous TEDDS sheets


Part of Structure: Mezzanine slab

Originator: EH Checker: Date: 12/04/11 Sheet No: MS-01


Calculations Output

Waffle → Rib Slabs In Effect

Gk = 7.74 + 1.0 = 8.74kN/m2 x 1.4 => UDL = 21.84kN/m2

Qk = 5.0 + 1.0 = 6.0kN/m2 x 1.6

Ribs @ 1.7m c/c

Moment = wl2/8 = 21.84x1.7x122/8 = 668.3kNmShear = 21.84x1.7x0.5x8 = 148.5kN

Bending Moment Checkb = 200+1500 = 1700mmd= 900-25-8-24-12 = 831mmk = 668.3x106/30x1700x8312 = 0.019z = 0.95d = 789.45mm

As,req = 668.3x106/789.45x0.87x360 = 2703mm2

As, prov 6 x 24ø → 2714mm2

Shear CheckV = 148.5x103/200x831 = 0.894N/mm2

100As/bd = 100x2714/200x831 = 1.63vc = 0.74N/mm2

→ Min Links

Asv = 0.4x200x110/0.87x360 = 28.01mm2

→ Links OK


Part of Structure: Load Take Down

Originator: EH Checker: Date: 12/04/11 Sheet No: LTD-01


Calculations Output

Column 2/G

Roof Gk Qk

6.28x8x6 + 3.1x8 + 3.3x0.62x24 354Terrace (48-1.75x8) x (9.5-6.28) 110Imposed 5 x 48 2407 th Floor

6.28x8x6 + 3.1x8 + 3.3x0.62x24 3543x48 144

6 th Floor As Above 354As Above 144



3 rd Floor As Above 354As Above 144

2 nd Floor As Above 354As Above 144

1 st Floor As Above 354As Above 144

Service(3.02+1)x48 + 2.7x0.852x(π/4)x24 23030x48 144

Mezz7x48 + 8x2x2.88

+3.3x0.852x(π/4)x24 4276x48 288

Ground 5.3x48 + 16x2.88

+4.5x0.852x(π/4)x24 3866x48 288

BasementCol. 0.85x0.85x4.2x24 73Beams 2x0.5x16x24 384? 1.1x48x19 1003100 dp. Slab 0.1x48x24 115 1575 Qk 48 x 5 240

500 dp. Slab 0.5x(48-16x0.5)x24 480

Cumulative Gk Qk

3985 1680

6040 2208


Part of Structure: Column design

Originator: EH Checker: Date: 12/04/11 Sheet No: CD-01


Calculations Output

Column – BasementSymmetrical Loads, Short & Braced → N = 0.35fcuAc + 0.7Ascfy

10,576x103 = 0.35x35x8502 + 0.7xAscx360Asc = 7874mm2

Asc, prov = 16 x 24ø → 7238mm2

However rebar drgs say 800x800 Col.Asc, req = 12,486mm2

Links24/4 = 6 Links Provided = 8ø @ 200c/c12ø = 288 → Adequate

Fy = 360/1.15 =313.04N/mm2

Accepted as our loads higher than those used in MGM design


Part of Structure: Foundation design

Originator: EH Checker: Date: 12/04/11 Sheet No: FD-01


Calculations Output

Gk = 6040kN ULS =1.4x6040 + 1.6x2208 = 10,576kNQk = 2208kN

Punching at Column→ Disperse Load @ 2 on 1 Down Beams

Perimeter = 0.85x4 + 4x(1+1+0.5) = 13.4m

d = 500-50-16-10 = 424mmvcol = 10576x103/850x4x424 = 7.33N/mm2

→ Not permitted→ Col + Dispersal through Beams

v = 10576x103/13400x424 = 1.86N/mm2

→ OK

At top of 500 dp. Slab

Perimeter = 0.85x4 +4x(0.75x2+0.5) = 11.4m

v = 10576x103/11400x424 = 2.19N/mm2

→ OK


Part of Structure: Foundation design

Originator: EH Checker: Date: 12/04/11 Sheet No: FD-02


Calculations Output

Shade off pressure

Effective Pad Under Column(6040+2208/400)1/2 = 4.54m2

Say 4.5x4.5x0.5 dp. ‘Pad’ → Ap = 20.25m2

Area Panel = AB = 48m2

Total Load = 10,576kN ULS

p/2 = 10576/20.45+48 = 154.9kN/m2

∴ Moment on Beam B1 = wL2/24 +WL/16

154.9x4.5x1.52/24 + 154.9x1.5x0.5x1.5/16 = 76.24kNm

→ acceptable on 2000 dp. Beam

AB

p/2

p/2

Ap

B


Part of Structure: Horizontal loads perpendicular to J

Originator: EH Checker: Date: 14/04/11 Sheet No: HR-01


Calculations Output

Wall 1 L = 2.7m ; b = 0.2m ; I = 0.328m4

Wall 2, 3, 4, 5 & 6 L = 2.7m ; b=0.2m ; I = 0.328m4

Columns Grids 1 & 4Assume equal storey heights & 550x550 average dimensions

I = 0.55x0.553/12 x 9 = 0.0686m4

Grids 2 & 3 Say 600x600 average column size

I = 0.6x0.63/12 x 9 = 0.097m4

Find Centre of Twist x

REF I x Ix y Iy Iy2

W1 0.328 1.05 0.344 -2.61 -0.856 2.234W2 0.328 1.05 0.344 -0.01 -0.003 0.00W3 0.328 1.05 0.344 2.59 0.850 2.20W4 0.328 33.25 10.91 -5.36 -1.758 9.42W5 0.328 33.25 10.91 -2.76 -0.905 2.50W6 0.328 34.75 11.40 3.24 1.060 3.44W7 0.328 34.75 11.40 5.84 1.920 11.19C1 0.274 0 0 15.09 4.130 62.39C2 0.274 0 0 9.09 2.490 22.64C3 0.274 0 0 3.09 0.847 2.616C4 0.274 0 0 -2.91 -0.80 2.32

Total 2.57 45.65 120.95

x = Iy Total / I Total = 45.65/2.57 = 17.76m


Part of Structure: Horizontal loads perpendicular to J



Calculations Output


Part of Structure: Sketches of walls / columns



Calculations Output

Lift E’/3

Lift J/4

Lift 3/J’Assumed Dimensions

Shear Wall GL A Shear Wall GL J’’





Calculations Output

W8L = 6.350m ; b = 0.25m ; I = 5.33m4

W9L = 5.8m ; b = 0.2m : I = 3.25m4

W10L = 5.8m less doors, 1.1m W x 2.3m H I = 3.25 – 2(0.2x1.13/12 + 0.2x1.1x1.42) = 2.34m4

W11I = 0.2x32/12 – 0.2x1.13/12 = 0.43m4

W12I = 0.45m4

W13L = 4.35m ; b = 0.250m ; I = 1.71m4

W14 I = 0.43m4

W14I = 0.45m4

REF I y Iy y Iy Iy2

W8 5.33 9.175 48.9 -0.085 -0.45 0.04W9 3.25 8.9 28.93 0.19 0.62 0.12

W10 2.34 8.9 20.83 0.19 0.44 0.08W11 0.43 13.5 5.81 -4.41 -1.90 8.36W12 0.45 13.5 6.08 -4.41 -1.98 8.75W13 1.71 9.5 16.25 -0.41 -7.54 0.29W14 0.43 4.5 1.94 4.59 1.97 9.06W15 0.45 4.5 2.03 4.59 2.07 9.48

Total 14.39 130.77 36.18

y= Iy Total / I Total = 130.77/14.39 = 9.09m

Parallel to Walls

Perpendicular to WallsParallel to Walls

Perpendicular to Walls





Calculations Output

Eccentricity

Width = 18my = 9.09m North of Grid Line 2Eccentricity = (9.09+6) – 18/2 = 6.09m

Consider effect of perpendicular walls to horizontal loads

Shear on a wall = FH x {EIwall/∑EIwall + MeccxEIwall/∑EIy2+∑EIy2}

y = distance from centre line wall to centre of twist along y axisx = distance from centre line wall to centre of twist along x axis

Moment on wallsMwall = Mexternal x {EIwall/∑EIwall + MeccxEIwall/∑EIy2+∑EIy2}

∴ Horizontal Load Distribution

W1 = 0.328/2.57 – 6.09x0.856/120.95+36.18 = 0.094

W2 = 0.328/2.57 – 6.09x0.003/157.13 = 0.128

W3 = 0.328/2.57 + 6.09x0.85/157.13 = 0.161

W4 = 0.328/2.57 – 6.09x1.758/157.13 = 0.059

W5 = 0.328/2.57 – 6.09x0.905/157.13 = 0.093

W6 = 0.328/2.57 + 6.09x1.06/157.13 = 0.169

W7 = 0.328/2.57 + 6.09x1.92/157.13 = 0.202

C1 = 0.274/2.57 + 6.09x4.13/157.13 = 0.267

C2 = 0.274/2.57 + 6.09x2.49/157.13 = 0.203

C3 = 0.274/2.57 + 6.09x0.847/157.13 = 0.033

C4 = 0.274/2.57 – 6.09x0.80/157.13 = 0.076


Part of Structure: Shear wall – wall W7

Originator: EH Checker: Date: 14/04/11 Sheet No: SW-01


Calculations Output

Check Wall W7

FH = 20.2%

Moment at Ground Level

M = 68x40.9 + 136x(39.6+33.45+30+26.55+23.1+19.65+16.2) + 136x(12.9+8.7+4.2)

M = 31565.6kNm

Moment in Wall at Ground= 31565.6 x 0.202 = 6376.25kNm

Axial LoadSelf Weight = 0.75 + 2.7/2 x 0.2 x 24 x 36.7 = 370kN

In Basement? 0.25x24x2.7x3 = 48.6kNSlab 0.5x3.6x1.8x24 = 77.76kNBeams 1.5x3.6x2x0.5x24 = 129.6kN? 3.6x1.8x19x1.1 = 135.43kNHardcore 3.6x1.8x0.3x20 = 38.8kNScreed 0.1x24x3.6x1.8 = 15.5kNReturn Wall 3.6x2.3x0.25x24 = 49.68kNGround Slab N/A

495.4kN

Total 865.25kN

* Indicates larger floors Gk

But more resisting elements


Part of Structure: Shear wall and column check



Calculations Output

Rebar in Wall d = 2700-20-10-20/2 = 2660mmb = 200+0.7x3450/10 = 441.5mmfcu = 35N/mm2

k = 63576.25x106/441.5x35x26602 = 0.0583z = 0.93d = 2473.8mm

As, req = 6376.25x106/0.87x360x2473.8 = 8229.6mm2 Legs 370x103/0.87x360 = 1181mm2

As, net = 8229.6 – 1181 = 7048.2 mm2

As, prov = 16 x 20ø = 5026.5mm2

Column MomentsSay equal storey heights & stiffness on cross section

C1 grid takes 26.7%

Total load 136x10 + 68 = 1428kN

Load on grid C1 = 0.267x1428 = 381.3kNForce per column = 381.3x8/8x8 = 47.66kNMoment Edge Col = 47.66/2 x 4.2/2 = 50.04kNmMoment Int Col = 47.66x2/2 x 4.2/2 = 100.08kNm

Conservative hand calculation, computer model would yield more accurate results


Part of Structure: Column design



Calculations Output

Axial Load on ColumnMasonry Panel 3.45x8x0.215x21x0.85 = 105.92kN

Floor Reduction 354/2 = 177kN% Reduction 354-(177+105.92)/354 = 20%

Say 80% of Col G2 Loads→ Gk = 3985x0.8 = 3188kN

Qk = 1680x0.8 = 1344kNN ULS = 1.2x3188 + 1.2x1344x0.6 = 4793kN

600x600 Col at Gndd = 600-30-8-24/2 = 550 d/h = 0.92N/bhfcu = 4793x103/6002x35 = 0.38 ; M/bh2fcu = 1.2x100x106/600x6002x35 = 0.0159

From Design ChartsP = 0%→ Use axial load formulaN = 0.4fcuAc + 0.8Ascfy

4793x103 = 0.4x35x6002 + 0.8x360xAsc

Asc = 807mm2 => min steel Asc, prov =16 x 24ø → 7238mm2 → Column Rebar OK

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11.203 Calculations