Earthquake Risks and Effective of Earthquake Load and Wind Load on Behavior Of
Wind and Earthquake Load Analysis
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