dynamic analysis

INTRODUCTION

Slab thickness = mm

Beam size = 600 x 350 mm

Column size ( first 6 story ) = 750 x 750 mm

Column size ( rest ) = 600 x 600 mm

A fifteen story building with a story height of 3.5m (total height of 52.5m) will be located close to

the proposed Kottawa new town the building consist of ordinary moment resisting frame of

reinforce concrete .The building has a rectangular plan with dimensions of 30m x49m .The main

structural element are as follows

175

Due to recent past earthquake activities in the Southern region in Sri Lanka ,the consultant of the

project has been requested to design this building for earthquake. This building may also be used

for post earthquake recovery.

Since Sri Lanka has no specific earthquake design standards, it has been decided to use Australian

Standard AS 1170.4

7 x

7 m

= 4

9 m

7 x 7 m = 49 m

7 x

7 m

= 4

9 m

Building location is similar with condition in Townsville, Australia with 30m deep medium hard clay

soil (Assume earth quake acts in the Y direction only)

1. Classify the structure and determine the type of earthquake analysis required

acceleration coefficient (a) = [table 2.3]

site factor (S) = [table 2.4a]

a x S = 0.07 x 1.25

= < 0.1

Structure classification = General structures [Cl 2.2]

Structure type = Type III (Post earth quake recovery)

Design category = [table 2.6]

For general structures of earthquake category C

Regular and irregular structures of earthquake design category C shall be analyzed by

Static analysis ( in accordance with Section 6 ) or

Dynamic analysis ( in accordance with Section 7 )

2. Conduct the static earthquake analysis and determined the following

2.a The earthquake base shear for the Y direction

0.07

1.25

0.09

C

Importance factor (I) = [table 2.5]

Acceleration coefficient (a) = [table 2.3]

Site factor (S) = [table 2.4a]

Structural response factor (Rf) = [table 6.2.6a]

(with special moment resisting frame ,RF concrete shear walls)

Fundamental period(T) = [Eq 6.2.4(1)]

= s

Earthquake design coefficient(C) = [Eq 6.2.3]

=

0.07

1.25

8.00

=52.5

46

1.14

0.08

1.25

Dead load (G)

Dead load on slab

Slab = 0.175 x 24

= kN/m2

Finishes = kN/m2

Partitions = kN/m2

Total dead = 4.20 + 0.75 + 1.50

= kN/m2

total on slabs = 30 x 49 x 15 x 6.45

= kN

due to beams = ( 30 x 8 +49 x 6 ) x 15 x 0.425 x 0.350 x 24

= kN

due to column(first six story) = 48 x 3.5 x 6 x 0.750 x 0.750 x 24

= kN

due to column(rest) = 48 x 3.5 x 9 x 0.600 x 0.600 x 24

= kN

due to shear wall = ( 7 x 2 + 6 x 2 ) x 0.15 x 3.5 x 15 x 24

= kN

Total dead load = 142223 + 28596 + 13608 + 13064 +4914

= kN

Live load (Q)

142223

28596

13608

13064

4914

202404

4.20

0.75

1.50

6.45

Live load (Q)

Live load on slab = kN/m2 ψc = 0.4

Total live load on all slabs = 30 x 49 x 15 x 3.00

= kN

Gravity load (Gg) =

= 202404 + 0.4 x 66150

= kN

Earthquake base shear (V) =

= 1.25 x 0.08 x 1.25 x 228864

= kN

V max =

= 1.25 x 2.5 x 0.07 x 228864

= kN

66150

3.00

228864

8

3576

8

6258

V min =

= 0.01 x 228864

= kN

therefore ,

Earthquake base shear (V) = kN

2.b Vertical distribution of horizontal earthquake forces

Gravity load per floor

Horizontal force at each floor level

[Eq 6.3(1)]

[Eq 6.3(2)]

1764

Total 15747 14931

1906

2268 1452

328 328

Beams

Columns

Shear walls

Live load x ψc

1906

1764

9482 9482

Up to 6th floor Above 6th floor

Slab

3576

2289

T = s

k = by interpolating

0.004 15

1.00 3576

7.0 15747

3

2

1

0.026 95

0.018 65

0.011 38

0.053 188

0.044 158

0.036 127

0.084 301

0.073 262

0.063 224

0.119 426

0.107 383

0.095 341

0.135 484

0.131 470

513848

351426

205721

82361

19407553

3.5 15747

∑

2625005

2548297

2310709

2078914

1853237

1634051

1421792

1216974

1020221

855045

689952

14.0 15747

10.5 15747

24.5 14931

21.0 15339

17.5 15747

35.0 14931

31.5 14931

28.0 14931

45.5 14931

42.0 14931

38.5 14931

52.5 14041

49.0 14931

8

7

6

5

4

13

12

11

10

9

1.32

15

14

1.14

Floor level(x)

3D Model of the building

Earthquake load assigned (assigned to 8 nodes per each floor)

50.0

0.0

10.0

20.0

30.0

40.0

50.0

0 200 400 600

2.c Deflected shepe,maximum deflection at top and drift index

The deflection,

deflection amplification factor Kd = 6.5 [Table 6.2.6(a)]

deflection determined by elastic analysis =

load combination considered,

5

4

3

2

10

9

8

7

6

15

14

13

12

11

Storey (mm) (mm)

131.1

124.8

116.9

12.1

10.5

8.8

7.1

5.7

4.2

2.9

1.8

78.8

68.1

57.3

46.4

36.8

27.4

18.8

0.0030

0.0031

0.0031

0.0027

0.0027

0.0025

0.0021

11.0

9.6

9.3

8.6

7.4

108.3

99.0

89.1

20.2

19.2

18.0

16.7

15.2

13.7

5.9

0.0018

0.0023

0.0025

0.0027

0.0028

0.0030

Storey drift index

6.2

7.9

8.7

9.3

9.9

10.3

10.6

10.8

Storey drift

(mm)

0.001711.5

Maximum top deflection is 131.1 mm

2

1

1.8

0.9

5.9

5.6

-

0.0017

0.0016

-0.0

11.5

5.6

0.00

3. Carryout the response spectrum dynamic earthquake analysis for this building

Importance factor (I) = [table 2.5]

Acceleration coefficient (a) = [table 2.3]

Site factor (S) = [table 2.4a]

Structural response factor (Rf) = [table 6.2.6a]

(with special moment resisting frame ,RF concrete shear walls)

Response spectra for S=1.25 from figure 7.2

1.60

1.80

2.00

2.20

2.40

0.00

0.20

0.40

0.49

0.60

0.80

1.508

1.245

0.725

0.676

Period

Spectral

acceleration

2.50

2.50

2.50

2.50

2.20

1.81

1.56

1.38

1.25

1.14

1.06

0.98

0.92

0.87

1.00

1.20

1.40

0.634

0.599

1.25

0.07

1.25

8.00

acceleration

1.717

1.717

1.717

1.717

accel: x ( I / Rf)

0.268

0.268

0.268

0.268

0.236

0.195

0.168

0.148

0.134

0.123

0.113

0.106

0.099

0.094

1.073

0.950

0.857

0.784

2.40

2.60

2.80

3.00

0.87

0.83

0.79

0.75

0.599

0.567

0.540

0.516

0.094

0.089

0.084

0.081

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50time(s)

acceleration (ms-2)

Acceleration response spectrum

Response spectrum function

Mass source

Load case data

3.a Base shear for Y direction3.a Base shear for Y direction

Joint reaction table for response spectrum load case

TABLE: Joint Reactions

29 Response Spectrum 0 5 34














3 160


F2

KN

F3

KN

1

Output Case

Text

Response Spectrum 1

Joint

Text

F1

KN


























Base shear force kN









2372

3.b Deflected shepe,maximum deflection at top and drift index

The deflection,

deflection amplification factor Kd = 6.5 [Table 6.2.6(a)]

deflection determined by elastic analysis =

load combination considered,

Storey (mm) (mm)

Storey drift

(mm) Storey drift index

15 11.4 74.2 3.5 0.0010

14 10.9 70.7 4.5 0.0013

13 10.2 66.2 4.8 0.0014

12 9.5 61.4 5.2 0.0015

11 8.7 56.2 5.5 0.0016

10 7.8 50.8 5.7 0.0016

9 6.9 45.1 5.9 0.0017

8 6.0 39.3 5.9 0.0017

7 5.1 33.3 6.1 0.0017

6 4.2 27.2 5.4 0.0015

5 3.4 21.8 5.3 0.0015

4 2.5 16.5 4.9 0.0014

3 1.8 11.6 4.4 0.0013

2 1.1 7.2 3.6 0.0010

1 0.6 3.6 3.6 0.0010

Maximum top deflection is 74.2 mm

1 0.6 3.6 3.6 0.0010

0 0.0 0.0 - -

4. Comparison of analysis results obtained by static and dynamic techniques

4.a Base shear

Base shear for static analysis = kN

Base shear for dynamic analysis = kN

Static to dynamic ratio =

Dynamic Analysis

where , is component of uniform ground acceleration.

Static Analysis

3576

2372

1.51

Dynamic analysis was performed with the Response Spectrum Analysis. Response spectrum

function is a series of digitized pairs of structural period and corresponding pseudo- spectral

acceleration values .The ground motion of the response spectrum correspond to building is given

by ,

Response Spectrum Analysis seeks the likely maximum response to above equation. Response

Spectrum was performed using mode supervision. Modes have been computed using Ritz vector

analysis as they give more reliable results. The base reaction is the total force about the global

origin required of supports to resist the inertia force due to response spectrum loading. For the

ground motion in Y- direction the maximum base shear was computed throughout the structure

for each of the vibration modes. Dynamic analysis results are non conservative approximations.

(t)umkuucum gyy

(t)u gy

The base shear calculated in static analysis is considerably higher than the base shear calculated in

dynamic analysis. In static analysis ground motion is replaced by an effective earthquake force at

each floor level and considered fixed at base. The base shear is equal to all effective earthquake

forces at each level. Here average value of dynamic force is used and convert it to get maximum

effect to be accounted by a large factor. This factor accounts for unforeseen effects of dynamic

analysis. Hence results of the static analysis are conservative.

(t)umkuucum gyy

(t)u gy

4.b Maximum deflection at top and drift index

Maximum deflection at top for static analysis = mm

Maximum deflection at top for dynamic analysis = mm

Static to dynamic ratio =

15

14

13

Dynamic

0.0010

0.0013

0.0014

1

0

Static

0.0018

0.0023

0.0025

0.0027

0.0028

0.0030

0.0030

0.0031

0.0031

0.0027

0.0027

0.0025

0.0021

0.0017

0.0016

-

12

11

10

9

8

0.0017

0.0017

0.0017

0.0015

0.0015

0.0014

3

2

7

6

5

4

0.0013

0.0010

0.0010

-

Storey drift index

Storey

Static to

dynamic

ratio

1.78

1.76

1.80

1.79

1.81

1.83

1.82

1.82

1.79

1.78

1.75

1.74

1.66

1.65

1.57

0.0015

0.0016

-

0.0016

131.1

74.2

1.77

0 - - -

The deflections calculated in static analysis are considerably higher than deflections calculated in

dynamic analysis. Because, the lateral force acts in the building frame is high in static analysis as

described in base shear above

5. Shifting of the Lift core from A to B

The Procedure to account for the Torsion Effects

Calculation of the Static Eccentricity (es) [Cl 6.5.2]

es = m

Calculation of the Design Eccentricities (ed1 & ed2) [Cl 6.5.3]

es/b = 10.5/49

=

A1 = [ 2.6 - 3.6 (es/b)] or 1.4 whichever is grater

= [ 2.6 - 3.6 (0.214)] or 1.4 whichever is grater

An earthquake induces horizontal inertia forces associated with the mass distribution in a

structure. At any particular level, the resultant may be considered to act through the centre of

mass at that floor level. These inertia forces are resisted by the vertical components of the

earthquake resisting system and the resultant acts through the shear centre of the storey under

consideration.

Shear centre and centre of the mass of the building coincide when the lift core is at Location A.

But, Shear centre and centre of mass of the building move apart when the lift core is shifted to the

location B. As a result of the movement, torsion moments will be induced

The line of action of the horizontal earthquake force acts through the centre of mass of the

building and shear centre is located 8 m from the centre of mass.

10.5

0.214

= [ 2.6 - 3.6 (0.214)] or 1.4 whichever is grater

=

A2 =

ed1 = A1es + 0.05b

= 1.83 x 10.5 + 0.05 x 49

=

ed2 = A2es - 0.05b

= 0.5 x 10.5 - 0.05 x 49

=

Calculation of the Horizontal Torsion Moment

ed1 or ed2

1.83

0.5

21.665

2.8

Horizontal torsion moment at any storey x can be calculated by multiplying the horizontal

earthquake force at that level by

Addition of the design action effects resulting from torsion moments to the design

actions. (Clause 6.5.5). In this case shear walls have to bear much higher lateral forces due to eccentricity for both ed1 and ed2 cases. Therefore reinforcements and wall

thickness have to be enhanced to account for those forces.

6.a Performance criteria

Earthquake performance level required for this building is immediate occupancy

therefore we have to limit the storey drift to 1% for each floors

6.b Check the building for selected performance criteria

Maximum storey drift in this building according to dynamic analysis result is 0.17%

There for building is satisfactory

6.c Vibration control technique

Viscous damper defined as follows

6.Define your own performance criteria for building under earthquake loads .If the building is

unsatisfactory with required performance ,propose suitable vibration control technique to control the

vibration of the building to achieve required performance level .Analyze the building with the propose

technique and compare the results

But to control storey drift it is proposed to use fluid viscous dampers at mid bay of building in Y

direction to absorbed earthquake energy

Viscous dampers applied to building as follows

Storey (mm) (mm)

Storey drift

(mm) Storey drift index

15 35.2 1.4 0.0004

14 33.8 1.7 0.0005

5.4

5.2

13 32.1 1.9 0.0005

12 30.2 2.0 0.0006

4.9

4.7

11 28.2 2.2 0.0006

10 26.0 2.4 0.0007

4.3

4.0

9 23.6 2.6 0.0007

8 21.0 2.7 0.0008

3.6

3.2

7 18.3 2.9 0.0008

6 15.3 2.7 0.0008

2.8

2.4

5 12.6 2.8 0.0008

4 9.7 2.8 0.0008

1.9

1.5

3 7.0 2.5 0.0007

2 4.4 2.2 0.0006

1.1

0.7

1 2.2 2.2 0.0006

0 0.0 - -

0.3

0.0

Comparison of storey drift before and after application of fluid viscous dampers

Storey

Storey drift index

Before After

13 0.0014 0.0005

12 0.0015 0.0006

15 0.0010 0.0004

14 0.0013 0.0005

9 0.0017 0.0007

8 0.0017 0.0008

11 0.0016 0.0006

10 0.0016 0.0007

5 0.0015 0.0008

4 0.0014 0.0008

7 0.0017 0.0008

6 0.0015 0.0008

1 0.0010 0.0006

0 - -

3 0.0013 0.0007

2 0.0010 0.0006

dynamic analysis

Documents

aa x s

dead load gdead load

live load qlive load

static earthquake analysis

total live load

post earthquake recovery

kntotal dead load

story building