Wind and Earthquake Load Analysis

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Wind Load Calculation Wind load was analyzed using the procedure of BS6399 Part 2 while assuming basic site wind speed of 28.0m/s. Wind load Analysis Bs 6399:2 Cl. 2.2.2.1 Cl. 2.2.2.2 Cl.2.2.2.3 Cl. 2.2.2.4 Cl. 2.2.2.5 Cl. 2.2.3 Cl.1.7.3.3 Table 4 Basic wind speed= Vb Site wind speed Vs= Vb × Sa × Sd × Ss × Sp Altitude factor Sa= 1+0.001s (assume topography not significant) s=1795m Sa=1+0.0001×1795 =2.795 Direction factor :Sd=1.0 (assume orientation is unknown) Seasonal factor :Sd =1.0 (permanent building) Probability factor :Sp =1.0 (for design application) Since the basic wind speed for Nairobi = 28m/s (site altitude incorporated) Site Wind Speed = 28×1.0×1.0×1.0 =28.0 m/s Effective Wind Speed Ve= Vs × Sb Terrain and building factor Sb Overall Building height above Foundation; H=48m Obstructer height :Ho = unknown Reference height Hr=42m Cross wind breath =50.25m Inwind depth =24.25m Displacement height=0.8Ho Effective height He =Hr = 42m Sb= = 1.91 Ve =1.91×28 = 53.48m/s

Transcript of Wind and Earthquake Load Analysis

  • Wind Load Calculation

    Wind load was analyzed using the procedure of BS6399 Part 2 while assuming basic site wind

    speed of 28.0m/s.

    Wind load Analysis

    Bs 6399:2

    Cl. 2.2.2.1

    Cl. 2.2.2.2

    Cl.2.2.2.3

    Cl. 2.2.2.4

    Cl. 2.2.2.5

    Cl. 2.2.3

    Cl.1.7.3.3

    Table 4

    Basic wind speed= Vb

    Site wind speed Vs= Vb Sa Sd Ss Sp

    Altitude factor Sa= 1+0.001s (assume topography not significant)

    s=1795m Sa=1+0.00011795

    =2.795

    Direction factor :Sd=1.0 (assume orientation is unknown)

    Seasonal factor :Sd =1.0 (permanent building)

    Probability factor :Sp =1.0 (for design application)

    Since the basic wind speed for Nairobi = 28m/s (site

    altitude incorporated)

    Site Wind Speed = 281.01.01.0

    =28.0 m/s

    Effective Wind Speed

    Ve= Vs Sb

    Terrain and building factor Sb

    Overall Building height above Foundation; H=48m

    Obstructer height :Ho = unknown

    Reference height Hr=42m

    Cross wind breath =50.25m

    Inwind depth =24.25m

    Displacement height=0.8Ho

    Effective height He =Hr = 42m

    Sb= = 1.91

    Ve =1.9128 = 53.48m/s

  • Cl. 2.1.2

    Cl.2.1.3.1

    Figure 4

    Table 5

    Table 5a

    Cl.2.1.3.2

    Dynamic pressure = qs

    qs=0.613Ve2

    =0.613 x 53.482

    =1753.3N/m2

    =1.753kN/m2

    Wind pressure

    a) Pressure on external surface

    Pe= qs Cpe Ca

    Size effect factor Ca

    Horizontal distance from grid 4 to 11 = 35m

    Diagonal dimension a 42 35 54.67m

    He= 42m

    Using curve B: Ca=0.82

    External measure coefficient Cpe

    D/H= 24.25/42 0.577 1.0

    D=24.25m

    +0.85 -0.5

    B=50.25m

    Plan

    (Net overall pressure coefficient for

    .

    . 2.07/ 1.0) optional

    Cpe= 1.2

    Pe (front) = 1.7530.850.82= +1.222kN/m2

    Pe(rear) = 1.7530.82-0.5 = -0.72kN/m2

    b) Internal surface pressure, Pi = qs CpiCa

    a= 10volume' 103 ( 24.25 ( 50.25' 154

  • Table 6

    Pp= 0.85 (1.652- -1.007) (1+0.04)A

    =2.35kN/m2 A

    =2.35A kN

    Friction Component, PF= qs Cf As Ca

    Friction drag coefficient, Cf = 0.02

    PF = 1.7530.020.82As = 0.029 As kN

    About the Weaker Axis of the Building;

    A= (1550.25)+(640.25) +(930.25) +(1220.25) = 1510.5m2

    and

    As= (1524.25)+(2718.25) = 856.5m2

    Table 16

    Figure 4

    Cl.2.1.3.6

    Table 1

    Figure 3

    Ca= 0.72

    Cpi = +0.2 or -0.2

    Pi1= 1.753(-0.3)0.82= -0.43kN/m2

    Pi2=1.753 (+0.2)0.82= +0.287kN/m2

    Net surface pressure P=Pe-Pi

    = 1.222- -0.43

    Pform(max) =1.652kN/m2 max

    Prear(max)

    = -0.72-0.287

    = -1.007km/m2

    Overall load

    Pp=0.85( Pform-Prear)1+Cr

    Where Cr = dynamic augmentation factor

    Building type factor Kb = 1.0 (assuming open plan office)

    Building height H=42m

    Cr=0.04

  • Pp= 2.351510.5 =3550 kN

    Pf= 0.029856.5=24.8 kN

    Total lateral load due to wind

    P=Pp+Pf

    = 3550+24.8

    = 3574.8 kN

    About the Stronger Axis of the Building;

    A = (1524.25)+(2718.25) = 856.5m2

    and

    As = (1550.25)+(640.25) +(930.25) +(1220.25) = 1510.5m2

    Pp= 2.35856.5 = 2012.8 kN

    Pf= 0.0291510.5 =43.8 kN

    Total lateral load due to wind

    P=Pp+Pf

    =2012.8+43.8

    =2056.6 kN

  • Earthquake Analysis

    (a) Storey Load Calculation (1.0 Gk+ 0.25 Qk)

    (Un-factored Dead Load plus Permanent Live Load taken as 25% of Live Load)

    i. Upper Basement Level

    Slab

    Area = 1181.563 m2

    Voids: Lifts cores = 35.175=15.525 m2

    Service Ducts 1.5813 m2

    Total Area of Voids 17.1 m2

    Total Area of Slab (Less Voids) = 1164.46 m2

    Total net dead weight = 1164.465.9 = 6870.3 kN

    Beams

    600200 Beams = 0.2 0.45 24 (4.72538) = 387.8 kN

    600300 Beams = 0.3 0.45 24 (23.759+49.453) = 1173.2 kN

    Total dead weight of Beams = 1561 kN

    External Walling (Basement wall)

    Total dead weight of walling= 0.25324148 =2664 kN

    Lift core walls

    Total dead weight of walling= 0.252.42421.25 =306 kN

    Columns

    Weight of Column C1 = )( 0.75 ( 2.4 ( 24 ( 3 73.35*+

    Weight of Column C2/C2a = )( 0.6 ( 2.4 ( 24 ( 4 65.15*+

    Weight of Column C3/C3a = )( 0.6 ( 2.4 ( 24 ( 6 97.73*+

    Weight of Column C4/C4a = )( 0.6 ( 2.4 ( 24 ( 6 97.73*+

    Weight of Column C5/C5a = )( 0.5 ( 2.4 ( 24 ( 6 67.86*+

    Weight of Column C6 = 0.5 ( 0.5 ( 2.4 ( 24 ( 4 57.6*+

    Weight of Column C9 = 0.3 ( 0.3 ( 2.4 ( 24 ( 1 5.2*+

    Weight of Column C10/C10a = 0.4 ( 0.4 ( 2.4 ( 24 ( 3 27.65*+

  • Total dead weight of Columns = 492.27 kN

    1.0 Gk = 6870.3+1561+2664+306+492.27 = 11893.6kN

    Add 25% Live Load = 0.252.51164.46 = 727.8 kN

    Total Storey Load, w = 12621.4 kN

    ii. Ground Floor Level

    Slab

    Area = 1181.563 m2

    Voids: Lifts cores = 35.175=15.525 m2

    Service Ducts 1.5813 m2

    Total Area of Voids 17.1 m2

    Total Area of Slab (Less Voids) = 1164.46 m2

    Total net dead weight = 1164.465.9 = 6870.3 kN

    Beams

    600200 Beams = 0.2 0.45 24 (4.72538) = 387.8 kN

    600300 Beams = 0.3 0.45 24 (23.759+49.453) = 1173.2 kN

    Total dead weight of Beams = 1561 kN

    External Walling

    Total dead weight of walling= 0.22.422122.5 =1293.6 kN

    Glazing

    Total dead weight of glazing= 1.02.448.5 =116.4 kN

    Lift core walls

    Total dead weight of walling= 0.252.42421.25 =306 kN

    Columns

    Weight of Column C1 = )( 0.75 ( 2.4 ( 24 ( 3 73.35*+

    Weight of Column C2/C2a = 0.5 ( 0.5 ( 2.4 ( 24 ( 4 57.6*+

    Weight of Column C3/C3a = )( 0.6 ( 2.4 ( 24 ( 6 97.73*+

  • Weight of Column C4/C4a = )( 0.6 ( 2.4 ( 24 ( 6 97.73*+

    Weight of Column C5/C5a = )( 0.5 ( 2.4 ( 24 ( 6 67.86*+

    Weight of Column C6 = )( 0.45 ( 2.4 ( 24 ( 4 36.64*+

    Weight of Column C7/C7a = 0.3 ( 0.25 ( 2.4 ( 24 ( 30 129.6*+

    Weight of Column C8/C7a = 0.3 ( 0.2 ( 2.4 ( 24 ( 3 10.37*+

    Weight of Column C9 = 0.3 ( 0.3 ( 2.4 ( 24 ( 1 5.2*+

    Weight of Column C10/C10a = 0.4 ( 0.4 ( 2.4 ( 24 ( 3 27.65*+

    Total dead weight of Columns = 603.73 kN

    1.0 Gk = 6870.3+1561+1293.6+116.4+306+603.73 = 10751.03kN

    Add 25% Live Load = 0.2541164.46 = 1164.46 kN

    Total Storey Load, w = 11915.5 kN

    iii. Mezzanine Floor Level

    Slab

    Area = 1010 m2

    Voids: Lifts cores = 35.175=15.525 m2

    Service Ducts 1.5813 m2

    Total Area of Voids 17.1 m2

    Total Area of Slab (Less Voids) = 1010-17.1 = 992.9 m2

    Total net dead weight = 992.96.86 = 6811.3 kN

    Beams

    600200 Beams = 0.2 0.53 24 (211) = 536.84 kN

    Total dead weight of Beams = 536.84 kN

    External Walling

    Total dead weight of walling= 0.22.422131.5 =1388.64 kN

    Glazing

    Total dead weight of glazing= 1.02.458.8 =141.12 kN

  • Lift core walls

    Total dead weight of walling= 0.252.42421.25 =306 kN

    Columns

    Weight of Column C1 = )( 0.75 ( 2.4 ( 24 ( 3 73.35*+

    Weight of Column C2/C2a = 0.5 ( 0.5 ( 2.4 ( 24 ( 4 57.6*+

    Weight of Column C3/C3a = )( 0.6 ( 2.4 ( 24 ( 6 97.73*+

    Weight of Column C4/C4a = )( 0.6 ( 2.4 ( 24 ( 6 97.73*+

    Weight of Column C5/C5a = )( 0.5 ( 2.4 ( 24 ( 6 67.86*+

    Weight of Column C6 = )( 0.45 ( 2.4 ( 24 ( 4 36.64*+

    Weight of Column C7/C7a = 0.3 ( 0.25 ( 2.4 ( 24 ( 30 129.6*+

    Weight of Column C8/C8a = 0.3 ( 0.2 ( 2.4 ( 24 ( 3 10.37*+

    Weight of Column C9 = 0.3 ( 0.3 ( 2.4 ( 24 ( 1 5.2*+

    Weight of Column C10/C10a = 0.4 ( 0.4 ( 2.4 ( 24 ( 3 27.65*+

    Weight of Column C11 = 0.3 ( 0.2 ( 2.4 ( 24 ( 4 13.82*+

    Total dead weight of Columns = 617.55 kN

    1.0 Gk = 6811.3+536.84+1388.64+141.12+306+617.55 = 9801.45kN

    Add 25% Live Load = 0.253.5992.9 = 868.8 kN

    Total Storey Load, w = 10670.25 kN

    iv. Typical 1st- 4th Floor Level

    Slab

    Area = 1060 m2

    Voids: Lifts cores = 35.175=15.525 m2

    Service Ducts 1.5813 m2

    Total Area of Voids 17.1 m2

    Total Area of Slab (Less Voids) = 1060-17.1 =1042.9 m2

    Total net dead weight = 1042.96.86 = 7154.3 kN

    Beams

  • 600200 Beams = 0.2 0.53 24 (197.6) = 502.7 kN

    Total dead weight of Beams = 502.7 kN

    External Walling

    Total dead weight of walling= 0.22.422131.5 =1388.64 kN

    Glazing

    Total dead weight of glazing= 1.02.448.5 =116.4 kN

    Lift core walls

    Total dead weight of walling= 0.252.42421.25 =306 kN

    Columns

    Weight of Column C1 = )( 0.6 ( 2.4 ( 24 ( 3 48.86*+

    Weight of Column C2/C2a = 0.5 ( 0.5 ( 2.4 ( 24 ( 4 57.6*+

    Weight of Column C3/C3a = )( 0.6 ( 2.4 ( 24 ( 6 97.73*+

    Weight of Column C4/C4a = )( 0.6 ( 2.4 ( 24 ( 6 97.73*+

    Weight of Column C5/C5a = )( 0.45 ( 2.4 ( 24 ( 6 54.97*+

    Weight of Column C6 =0.3 ( 0.3 ( 2.4 ( 24 ( 4 20.74*+

    Weight of Column C7/C7a = 0.3 ( 0.25 ( 2.4 ( 24 ( 30 129.6*+

    Weight of Column C8/C8a = 0.3 ( 0.2 ( 2.4 ( 24 ( 3 10.37*+

    Weight of Column C9 = 0.3 ( 0.3 ( 2.4 ( 24 ( 1 5.2*+

    Weight of Column C10/C10a = 0.4 ( 0.4 ( 2.4 ( 24 ( 3 27.65*+

    Total dead weight of Columns = 550.45 kN

    1.0 Gk = 7154.3+502.7+1388.64+116.4+306+550.45 = 10018.5kN

    Add 25% Live Load = 0.253.51042.9 = 912.5 kN

    Total Storey Load, w = 10931 kN

    v. 5th and 6th Floor Levels

    Slab

    Area = 688.5 m2

    Voids: Lifts cores = 35.175=15.525 m2

  • Service Ducts 1.5813 m2

    Total Area of Voids 17.1 m2

    Total Area of Slab (Less Voids) = 688.5-17.1 =671.4 m2

    Total net dead weight = 671.46.86 = 4605.8 kN

    Beams

    600200 Beams = 0.2 0.53 24 (157) = 399.4 kN

    Total dead weight of Beams = 399.4 kN

    External Walling

    Total dead weight of walling= 0.22.42299.6 =1051.8 kN

    Glazing

    Total dead weight of glazing= 1.02.436 =86.4 kN

    Lift core walls

    Total dead weight of walling= 0.252.42421.25 =306 kN

    Columns

    Weight of Column C1 = )( 0.6 ( 2.4 ( 24 ( 3 48.86*+

    Weight of Column C2/C2a = 0.4 ( 0.4 ( 2.4 ( 24 ( 4 36.86*+

    Weight of Column C3/C3a = )( 0.6 ( 2.4 ( 24 ( 6 97.73*+

    Weight of Column C4/C4a = )( 0.45 ( 2.4 ( 24 ( 6 54.97*+

    Weight of Column C5/C5a =0.4 ( 0.4 ( 2.4 ( 24 ( 6 55.3*+

    Weight of Column C8/C8a = 0.3 ( 0.2 ( 2.4 ( 24 ( 15 51.85*+

    Weight of Column C9 = 0.3 ( 0.3 ( 2.4 ( 24 ( 1 5.2*+

    Total dead weight of Columns = 350.78 kN

    1.0 Gk = 4605.8+399.4+1051.8+86.4+306+350.78 = 6800.2kN

    Add 25% Live Load = 0.253.5671.4 = 587.5kN

    Total Storey Load, w= 7387.68 kN

  • vi. 7th ,8th and 9th Floor Levels

    Slab

    Area = 455.3 m2

    Voids: Lifts cores = 35.175=15.525 m2

    Service Ducts 1.5813 m2

    Total Area of Voids 17.1 m2

    Total Area of Slab (Less Voids) = 455.3-17.1 =438.2 m2

    Total net dead weight = 438.26.86 = 3006.1 kN

    Beams

    600200 Beams = 0.2 0.53 24 (120.5) = 306.55 kN

    Total dead weight of Beams = 306.55 kN

    External Walling

    Total dead weight of walling= 0.22.42271 =749.76 kN

    Glazing

    Total dead weight of glazing= 1.02.426 =62.4 kN

    Lift core walls

    Total dead weight of walling= 0.252.42421.25 =306 kN

    Columns

    Weight of Column C1 = )( 0.45 ( 2.4 ( 24 ( 3 27.48*+

    Weight of Column C2/C2a = 0.4 ( 0.4 ( 2.4 ( 24 ( 4 36.86*+

    Weight of Column C3/C3a = )( 0.45 ( 2.4 ( 24 ( 6 54.97*+

    Weight of Column C4/C4a =0.4 ( 0.4 ( 2.4 ( 24 ( 6 55.3*+

    Weight of Column C8/C8a = 0.3 ( 0.2 ( 2.4 ( 24 ( 3 10.37*+

    Weight of Column C9 = 0.3 ( 0.3 ( 2.4 ( 24 ( 1 5.2*+

    Total dead weight of Columns = 190.2 kN

    1.0 Gk = 3006.1+306.55+749.76+62.4+306+190.2 = 4621kN

    Add 25% Live Load = 0.253.5438.2 = 383.43kN

    Total Storey Load, w = 5004.43 kN

  • vii. Typical 10th ,11th and 12th Floor Levels

    Slab

    Area = 322.8 m2

    Voids: Lifts cores = 35.175=15.525 m2

    Service Ducts 1.5813 m2

    Total Area of Voids 17.1 m2

    Total Area of Slab (Less Voids) = 322.8-17.1 =305.7 m2

    Total net dead weight = 305.76.86 = 2097.1 kN

    Beams

    600200 Beams = 0.2 0.53 24 (85.5) =217.5 kN

    Total dead weight of Beams = 217.5 kN

    External Walling

    Total dead weight of walling= 0.22.42241.5 =438.24 kN

    Glazing

    Total dead weight of glazing= 1.02.426 =62.4 kN

    Lift core walls

    Total dead weight of walling= 0.252.42421.25 =306 kN

    Columns

    Weight of Column C1 = )( 0.45 ( 2.4 ( 24 ( 3 27.48*+

    Weight of Column C2/C2a = 0.4 ( 0.4 ( 2.4 ( 24 ( 4 36.86*+

    Weight of Column C3/C3a = )( 0.45 ( 2.4 ( 24 ( 6 54.97*+

    Weight of Column C8/C8a = 0.3 ( 0.2 ( 2.4 ( 24 ( 3 10.37*+

    Weight of Column C9 = 0.3 ( 0.3 ( 2.4 ( 24 ( 1 5.2*+

    Total dead weight of Columns = 134.9 kN

    1.0 Gk = 2097.1+217.5+438.24+62.4+306+134.9 = 3256.1kN

    Add 25% Live Load = 0.253.5305.7 = 267.5kN

    Total Storey Load, w = 3523.6 kN

  • viii. Roof slab Level

    Slab

    Area = 322.8 m2

    Voids: skylight = 7.87.8=60.84 m2

    Total Area of Slab (Less Voids) = 322.8-60.841 =261 m2

    Dead weight slab = 2615.8 = 1513.8 kN

    Dead weight pressed steel tanks = 6515 = 975 kN

    Dead weight skylight roof =60.840.45 = 27.38 kN

    Total Dead weight =2516.2 kN

    Beams

    600200 Beams = 0.2 0.45 24 (12.5) =27 kN

    600300 Beams = 0.3 0.45 24 (26) =84.24 kN

    450200 Beams = 0.2 0.3 24 (78) =112.32 kN

    450300 Beams = 0.3 0.3 24 (28) =60.48 kN

    300200 gutter = 0.2 0.3 24 (67.6) =97.35 kN

    Total dead weight of Beams = 381.4 kN

    External Walling (parapet)

    Total dead weight of walling= 0.21.22277.25 =407.9 kN

    1.0 Gk = 2516.2+381.4+407.9 = 3305.5kN

    Add 25% Live Load = 0.250.25 261 = 16.3kN

    Total Storey Load, w = 3321.8 kN

    Total weight W

    =3321.8+ (3*3523.6) + (3*5004.43) + (2*7387.68) + (4*10931) +10670.25+11915.5+12621.4

    = 122612.4 kN

  • (b) Earthquake load calculation

    The procedure for calculation of the total base shear due to earthquakes and its distribution to

    each floor is given herein below:

    Total lateral force due to Earthquake, . /01

    Where, C= Earthquake coefficient

    W = Total weight of Building used to calculate Earthquake

    Earthquake Zone (Nairobi) = VII

    Soil type = Soft ground

    Building type = flexible

    Number of storey, N =16

    Using Table 2

    From table 2 of the Kenyan code, C = 0.03

    From above total weight W = 122612.4 kN

    F = 0.03122612.4 = 3678.4 kN

    Using Period of vibration of building

    Height of building above base, H = 316 = 48m

    Width of building in the x direction, D = 24.25m

    Period of vibration, 2 .345

    0.09 ( 6.

    0.877

    0.1N = 0.1 16 =1.6

    take T = 1.6

    C basic .8

    .9.:'

    0.04275

    Table 3: coefficient of modification = 0.65

    C value = 0.65 0.04275 = 0.0278 < 0.03

    adopt C = 0.03 and F = 3678.4kN

    NB: Maximum Base shear due to Wind = 3574.8 kN

    Maximum Base shear due to Earthquake = 3678.4kN

    Design for Earthquake

  • (c) Earthquake Load Distribution Per Storey

    The total lateral force (Base shear) due to Earthquake, F has been distributed as follows:

    To the roof or top level: ;< 0.004.=>[email protected]

    Where hn = height of uppermost storey above base

    = 48m

    Ds = plan dimension of lateral system resisting the Earthquake forces at ground floor level

    = 24.25m

    F = Maximum Base shear due to Earthquake = 3678.4kN

    ;< 0.004 ( 3678.4= 6.

    A 57.65*+

    Balance = 3678.4-57.65 = 3620.75 kN

    The Balance is distributed between storeys including the roof as follows:

    ;0 =. L ;

  • Lateral Earthquake Force Distribution per Storey

    wi hi wi*hi Earthquake Force

    storey kN m kNm Per storey, Fx (kN)

    ROOF 3321.8 48 159446.4 298

    12TH 3523.6 45 158562 239

    11TH 3523.6 42 147991.2 223

    10H 3523.6 39 137420.4 207

    9TH 5004.43 36 180159.48 272

    8TH 5004.43 33 165146.19 249

    7TH 5004.43 30 150132.9 226

    6TH 7387.68 27 199467.36 301

    5TH 7387.68 24 177304.32 267

    4TH 10931 21 229551 346

    3RD 10931 18 196758 297

    2ND 10931 15 163965 247

    1ST 10931 12 131172 198

    M 10670.25 9 96032.25 145

    G 11915.5 6 71493 108

    UB 12621.4 3 37864.2 57

    LB

    122612.4 2402465.7 3678

    (d) Earthquake Load Distribution Per Frame

    The distribution of

    Stiffness calculations

    In order to distribute the earthquake loading per floor to various frames based on their

    respective stiffness, stiffness calculations of beams, columns and frames had to be done.

    The building plan is symmetric, that is to say that the lateral loading on the structure is not

    expected to cause major horizontal plane torque in addition to the transverse shear.

  • The total external lateral load per floor due to direct earthquake load was distributed to each

    frame and shear walls in proportion of their shear rigidities (storey stiffness) at that floor level.

    To establish the storey stiffness of columns, the following formula was used

    Storey stiffness of frame, PN J

  • Stiffness of Beams along Z-Axis

    Level

    Beam

    Type Beam Dimension Ixx Iyy Stiffness(KB)

    Length

    (m) Depth(m) Width(m) (m) (m) KBxx KByy

    U.B-Ground 600300 5 0.6 0.3 0.0054 0.00135 0.00108 0.00027

    Mezz-12th

    Fl 600200 5 0.6 0.2 0.0036 0.0004 0.00072 0.00008

    2.5 0.6 0.2 0.0036 0.0004 0.00144 0.00016

    300650 5 0.3 0.65 0.001463 0.006866 0.000293 0.001373

    300870 5 0.3 0.87 0.001958 0.016463 0.000392 0.003293

    Roof Slab 600200 5 0.6 0.2 0.0036 0.0004 0.00072 0.00008

    450300 5 0.45 0.3 0.002278 0.001013 0.000456 0.000203

    450200 5 0.45 0.2 0.001519 0.0003 0.000304 0.00006

    Step 2: Stiffness of Columns

    Level

    Column

    Type

    Column Dimensions

    Ixx Iyy Stiffness,KC(m)

    Height

    (m)

    Depth

    diamete

    r

    (m)

    Widt

    h

    (m) (m) (m) KCxx KCzz

    Lower Basement

    to

    Ground

    C1 3 0.75 0.01553 0.01553 0.00518 0.00518

    C2/C2a 3 0.6 0.00636 0.00636 0.00212 0.00212

    C3 3 0.75 0.01553 0.01553 0.00518 0.00518

    C3a 3 0.6 0.00636 0.00636 0.00212 0.00212

    C4/C4a 3 0.6 0.00636 0.00636 0.00212 0.00212

    C5/C5a 3 0.5 0.00307 0.00307 0.00102 0.00102

    C6 3 0.5 0.5 0.00521 0.00521 0.00174 0.00174

    C9 3 0.3 0.3 0.00068 0.00068 0.00023 0.00023

    C10/C10a 3 0.4 0.4 0.00213 0.00213 0.00071 0.00071

    Ground-1st Floor

    C1 3 0.75 0.01553 0.01553 0.00518 0.00518

    C2/C2a 3 0.5 0.5 0.00521 0.00521 0.00174 0.00174

    C3 3 0.75 0.01553 0.01553 0.00518 0.00518

  • C3a 3 0.5 0.5 0.00521 0.00521 0.00174 0.00174

    C4/C4a 3 0.6 0.00636 0.00636 0.00212 0.00212

    C5/C5a 3 0.5 0.00307 0.00307 0.00102 0.00102

    C6 3 0.45 0.00201 0.00201 0.00067 0.00067

    C7/C7a 3 0.3 0.25 0.00056 0.00039 0.00019 0.00013

    C8/C8a 3 0.3 0.2 0.00045 0.00020 0.00015 0.00007

    C9 3 0.3 0.3 0.00068 0.00068 0.00023 0.00023

    C10/C10a 3 0.4 0.4 0.00213 0.00213 0.00071 0.00071

    C11 3 0.3 0.2 0.00045 0.00020 0.00015 0.00007

    1st Floor

    To

    4th Floor

    C1 3 0.6 0.00636 0.00636 0.00212 0.00212

    C2/C2a 3 0.5 0.5 0.00521 0.00521 0.00174 0.00174

    C3 3 0.6 0.00636 0.00636 0.00212 0.00212

    C3a 3 0.5 0.5 0.00521 0.00521 0.00174 0.00174

    C4/C4a 3 0.6 0.00636 0.00636 0.00212 0.00212

    C5/C5a 3 0.45 0.00201 0.00201 0.00067 0.00067

    C6 3 0.3 0.3 0.00068 0.00068 0.00023 0.00023

    C7/C7a 3 0.3 0.25 0.00056 0.00039 0.00019 0.00013

    C8/C8a 3 0.3 0.2 0.00045 0.00020 0.00015 0.00007

    C9 3 0.3 0.3 0.00068 0.00068 0.00023 0.00023

    C10/C10a 3 0.4 0.4 0.00213 0.00213 0.00071 0.00071

    4th Floor

    To

    6th Floor

    C1 3 0.6 0.00636 0.00636 0.00212 0.00212

    C2/C2a 3 0.4 0.4 0.00213 0.00213 0.00071 0.00071

    C3 3 0.6 0.00636 0.00636 0.00212 0.00212

    C3a 3 0.4 0.4 0.00213 0.00213 0.00071 0.00071

    C4/C4a 3 0.45 0.00201 0.00201 0.00067 0.00067

    C5/C5a 3 0.4 0.4 0.00213 0.00213 0.00071 0.00071

    C8/C8a 3 0.3 0.2 0.00045 0.00020 0.00015 0.00007

    C9 3 0.3 0.3 0.00068 0.00068 0.00023 0.00023

    6th Floor- 9th

    Floor

    C1 3 0.45 0.00201 0.00201 0.00067 0.00067

    C2/C2a 3 0.4 0.4 0.00213 0.00213 0.00071 0.00071

  • C3 3 0.45

    0.00201 0.00201 0.00067 0.00067

    C3a 3 0.4 0.4 0.00213 0.00213 0.00071 0.00071

    C4/C4a 3 0.4 0.4 0.00213 0.00213 0.00071 0.00071

    C8/C8a 3 0.3 0.2 0.00045 0.00020 0.00015 0.00007

    C9 3 0.3 0.3 0.00068 0.00068 0.00023 0.00023

    9th Floor- Roof

    C1 3 0.45 0.00201 0.00201 0.00067 0.00067

    C2/C2a 3 0.4 0.4 0.00213 0.00213 0.00071 0.00071

    C3 3 0.45 0.00201 0.00201 0.00067 0.00067

    C3a 3 0.4 0.4 0.00213 0.00213 0.00071 0.00071

    C8/C8a 3 0.3 0.2 0.00045 0.00020 0.00015 0.00007

    C9 3 0.3 0.3 0.00068 0.00068 0.00023 0.00023

    Steps 3: Storey Stiffness of Frames

    These were calculated using the following formula

    i) Ground floor

    a) outer column

    KBI

    K=Z[9Z\

    a =.]Z]Z

    b) inner column

    KB1 KB2 K= Z[9]Z[

    Z\

    a =.]Z]Z

    KC

  • ii) upper floor

    a) outer columns

    KB1 K = Z[9Z\

    a = Z]Z

    KC

    KB1

    b) inner column

    KB1 KB2 K= Z[9]Z[

    Z\

    a = Z]Z

    KC

    KB1 KB2

    iii) Storey stiffness of column

    = 9^_ZS

    >

    where

    E = Modulus of elastically

    h = storey height

    Kc = stiffness of columns

    KB = stiffness of beams

  • STEP 3: STOREY STIFFNESS OF FRAMES

    STOREY Frame storey

    height

    h (m)

    column

    Type

    column

    stiffness

    Kcx m)

    Beam stiffness a storey stiffnes of

    columns K1 in

    muliples of E

    storey stiffnes of

    Frame Kf in

    muliples of E

    Fraction of

    lateral load

    Taken by frame LEVEL gridline KB (m) KB (m)

    Upper

    Basement

    Floor

    4

    3 C7 0.00019 0.00000 0.01278 68.18133 0.97863 0.00024

    0.00691

    0.1308

    3 C6 0.00174 0.01758 0.01405 18.22061 0.92582 0.00214

    3 C6 0.00174 0.01405 0.01758 18.21888 0.92581 0.00214

    3 C6 0.00174 0.01758 0.01278 17.48736 0.92303 0.00214

    3 C7 0.00019 0.01278 0.00000 68.18133 0.97863 0.00024

    5

    3 C7 0.00019 0.00000 0.00098 5.23636 0.79271 0.00020

    0.00284

    0.0537

    3 C5a 0.00102 0.00098 0.00083 1.77221 0.60235 0.00082

    3 C5 0.00102 0.00083 0.00083 1.62302 0.58598 0.00080

    3 C5a 0.00102 0.00083 0.00098 1.76968 0.60209 0.00082

    3 C7 0.00019 0.00098 0.00000 5.22667 0.79244 0.00020

    6

    3 C7 0.00019 0.00000 0.00098 5.23636 0.79271 0.00020

    0.00438

    0.0829

    3 C4a 0.00212 0.00098 0.00083 0.85465 0.47454 0.00134

    3 C4 0.00212 0.00083 0.00083 0.78271 0.46096 0.00130

    3 C4a 0.00212 0.00083 0.00098 0.85343 0.47432 0.00134

    3 C7 0.00019 0.00098 0.00000 5.22667 0.79244 0.00020

    7

    3 C7 0.00019 0.00000 0.00098 5.23636 0.79271 0.00020

    0.00552

    0.1044

    3 C3a 0.00212 0.00098 0.00083 0.85465 0.47454 0.00134

    3 C3 0.00518 0.00083 0.00083 0.32060 0.35361 0.00244

    3 C3a 0.00212 0.00083 0.00098 0.85343 0.47432 0.00134

    3 C7 0.00019 0.00098 0.00000 5.22667 0.79244 0.00020

    8

    3 C7 0.00019 0.00000 0.00180 9.60000 0.87069 0.00022

    0.00606

    0.1146

    3 C9 0.00023 0.00180 0.00216 17.60000 0.92347 0.00028

    3 C2a 0.00212 0.00216 0.00083 1.41017 0.56014 0.00158

    3 C1 0.00518 0.00083 0.00083 0.32060 0.35361 0.00244

    3 C2a 0.00212 0.00083 0.00098 0.85343 0.47432 0.00134

    3 C7 0.00019 0.00098 0.00000 5.22667 0.79244 0.00020

  • 9

    3 C7 0.00019 0.00000 0.00180 9.60000 0.87069 0.00022

    0.00606

    0.1146

    3 C9 0.00023 0.00180 0.00216 17.60000 0.92347 0.00028

    3 C2 0.00212 0.00216 0.00083 1.41017 0.56014 0.00158

    3 C1 0.00518 0.00083 0.00083 0.32060 0.35361 0.00244

    3 C2 0.00212 0.00083 0.00098 0.85343 0.47432 0.00134

    3 C7 0.00019 0.00098 0.00000 5.22667 0.79244 0.00020

    10

    3 C7 0.00019 0.00000 0.00180 9.60000 0.87069 0.00022

    0.00606

    0.1146

    3 C9 0.00023 0.00180 0.00216 17.60000 0.92347 0.00028

    3 C2a 0.00212 0.00216 0.00083 1.41017 0.56014 0.00158

    3 C1 0.00518 0.00083 0.00083 0.32060 0.35361 0.00244

    3 C2a 0.00212 0.00083 0.00098 0.85343 0.47432 0.00134

    3 C7 0.00019 0.00098 0.00000 5.22667 0.79244 0.00020

    11

    3 C7 0.00019 0.00000 0.00098 5.23636 0.79271 0.00020

    0.00552

    0.1044

    3 C3a 0.00212 0.00098 0.00083 0.85465 0.47454 0.00134

    3 C3 0.00518 0.00083 0.00083 0.32060 0.35361 0.00244

    3 C3a 0.00212 0.00083 0.00098 0.85343 0.47432 0.00134

    3 C7 0.00019 0.00098 0.00000 5.22667 0.79244 0.00020

    12

    3 C7 0.00019 0.00000 0.00098 5.23636 0.79271 0.00020

    0.00438

    0.0829

    3 C4a 0.00212 0.00098 0.00083 0.85465 0.47454 0.00134

    3 C4 0.00212 0.00083 0.00083 0.78271 0.46096 0.00130

    3 C4a 0.00212 0.00083 0.00098 0.85343 0.47432 0.00134

    3 C7 0.00019 0.00098 0.00000 5.22667 0.79244 0.00020

    13

    3 C7 0.00019 0.00000 0.00098 5.23636 0.79271 0.00020

    0.00284

    0.0537

    3 C5a 0.00102 0.00098 0.00083 1.77221 0.60235 0.00082

    3 C5 0.00102 0.00083 0.00083 1.62302 0.58598 0.00080

    3 C5a 0.00102 0.00083 0.00098 1.76968 0.60209 0.00082

    3 C7 0.00019 0.00098 0.00000 5.22667 0.79244 0.00020

    14

    3 C7 0.00019 0.00000 0.00098 5.23636 0.79271 0.00020

    3 C10a 0.00071 0.00098 0.00083 2.54895 0.67025 0.00064

    3 C10 0.00071 0.00083 0.00083 2.33438 0.65393 0.00062

  • 3 C10a 0.00071 0.00083 0.00098 2.54531 0.66999 0.00064

    0.00229

    0.0433 3 C7 0.00019 0.00098 0.00000 5.22667 0.79244 0.00020

    Total storey

    stiffness 0.05286

    GROUND

    Floor

    4

    3 C7 0.00019 0.00000 0.01278 68.18133 0.97150 0.00024

    0.00881

    0.2328

    3 C6 0.00174 0.01278 0.01758 17.48851 0.89738 0.00208

    3 C6 0.00174 0.01758 0.01405 18.22061 0.90109 0.00209

    3 C6 0.00174 0.01405 0.01758 18.21888 0.90108 0.00209

    3 C6 0.00174 0.01758 0.01278 17.48736 0.89737 0.00208

    3 C7 0.00019 0.01278 0.00000 68.18133 0.97150 0.00024

    5

    3 C7 0.00019 0.00000 0.00098 5.23636 0.72362 0.00018

    0.00225

    0.0595

    3 C5a 0.00102 0.00098 0.00083 1.77221 0.46981 0.00064

    3 C5 0.00102 0.00083 0.00083 1.62302 0.44797 0.00061

    3 C5a 0.00102 0.00083 0.00098 1.76968 0.46945 0.00064

    3 C7 0.00019 0.00098 0.00000 5.22667 0.72325 0.00018

    6

    3 C7 0.00019 0.00000 0.00098 5.23636 0.72362 0.00018

    0.00285

    0.0753

    3 C4a 0.00212 0.00098 0.00083 0.85465 0.29939 0.00085

    3 C4 0.00212 0.00083 0.00083 0.78271 0.28127 0.00080

    3 C4a 0.00212 0.00083 0.00098 0.85343 0.29909 0.00085

    3 C7 0.00019 0.00098 0.00000 5.22667 0.72325 0.00018

    7

    3 C7 0.00019 0.00000 0.00098 5.23636 0.72362 0.00018

    0.00301

    0.0795

    3 C3a 0.00212 0.00098 0.00083 0.85465 0.29939 0.00085

    3 C3 0.00518 0.00083 0.00083 0.32060 0.13815 0.00095

    3 C3a 0.00212 0.00083 0.00098 0.85343 0.29909 0.00085

    3 C7 0.00019 0.00098 0.00000 5.22667 0.72325 0.00018

    8

    3 C7 0.00019 0.00000 0.00180 9.60000 0.82759 0.00021

    3 C9 0.00023 0.00180 0.00216 17.60000 0.89796 0.00027

    3 C2a 0.00212 0.00216 0.00083 1.41017 0.41352 0.00117

    3 C1 0.00518 0.00083 0.00083 0.32060 0.13815 0.00095

    3 C2a 0.00212 0.00083 0.00098 0.85343 0.29909 0.00085

  • 3 C7 0.00019 0.00098 0.00000 5.22667 0.72325 0.00018 0.00363 0.0958

    9

    3 C7 0.00019 0.00000 0.00180 9.60000 0.82759 0.00021

    0.00363

    0.0958

    3 C9 0.00023 0.00180 0.00216 17.60000 0.89796 0.00027

    3 C2 0.00212 0.00216 0.00083 1.41017 0.41352 0.00117

    3 C1 0.00518 0.00083 0.00083 0.32060 0.13815 0.00095

    3 C2 0.00212 0.00083 0.00098 0.85343 0.29909 0.00085

    3 C7 0.00019 0.00098 0.00000 5.22667 0.72325 0.00018

    10

    3 C7 0.00019 0.00000 0.00180 9.60000 0.82759 0.00021

    0.00363

    0.0958

    3 C9 0.00023 0.00180 0.00216 17.60000 0.89796 0.00027

    3 C2a 0.00212 0.00216 0.00083 1.41017 0.41352 0.00117

    3 C1 0.00518 0.00083 0.00083 0.32060 0.13815 0.00095

    3 C2a 0.00212 0.00083 0.00098 0.85343 0.29909 0.00085

    3 C7 0.00019 0.00098 0.00000 5.22667 0.72325 0.00018

    11

    3 C7 0.00019 0.00000 0.00098 5.23636 0.72362 0.00018

    0.00301

    0.0795

    3 C3a 0.00212 0.00098 0.00083 0.85465 0.29939 0.00085

    3 C3 0.00518 0.00083 0.00083 0.32060 0.13815 0.00095

    3 C3a 0.00212 0.00083 0.00098 0.85343 0.29909 0.00085

    3 C7 0.00019 0.00098 0.00000 5.22667 0.72325 0.00018

    12

    3 C7 0.00019 0.00000 0.00098 5.23636 0.72362 0.00018

    0.00285

    0.0753

    3 C4a 0.00212 0.00098 0.00083 0.85465 0.29939 0.00085

    3 C4 0.00212 0.00083 0.00083 0.78271 0.28127 0.00080

    3 C4a 0.00212 0.00083 0.00098 0.85343 0.29909 0.00085

    3 C7 0.00019 0.00098 0.00000 5.22667 0.72325 0.00018

    13

    3 C7 0.00019 0.00000 0.00098 5.23636 0.72362 0.00018

    0.00225

    0.0595

    3 C5a 0.00102 0.00098 0.00083 1.77221 0.46981 0.00064

    3 C5 0.00102 0.00083 0.00083 1.62302 0.44797 0.00061

    3 C5a 0.00102 0.00083 0.00098 1.76968 0.46945 0.00064

    3 C7 0.00019 0.00098 0.00000 5.22667 0.72325 0.00018

    14

    3 C7 0.00019 0.00000 0.00098 5.23636 0.72362 0.00018

    3 C10a 0.00071 0.00098 0.00083 2.54895 0.56034 0.00053

  • 3 C10 0.00071 0.00083 0.00083 2.33438 0.53857 0.00051

    0.00193

    0.0511 3 C10a 0.00071 0.00083 0.00098 2.54531 0.55999 0.00053

    3 C7 0.00019 0.00098 0.00000 5.22667 0.72325 0.00018