dynamic-analysis-of-four-story-building.docx

8/10/2019 dynamic-analysis-of-four-story-building.docx

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DYNAMIC ANALYSIS OF FOUR STORY BUILDING

ByKalpesh Parikh

Pursuing Master of Science, Syracuse University

Term Report

Submitted in partial fulfillment of the requirements for the course requirement of Master of Science inCivil Engineering in the Graduate School of Syracuse University

10 th May 2010

Approved ______________________________Professor Eric M. Lui

Grade___________________________________


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Acknowledgment

My deepest gratitude goes to Dr. Eric M. Lui , Assistant professor, for his continuous and constructive

advice and follow-up. His successive advisories and comments were the pillars in my every step during

the analysis process of the project. I am thankful to him for the fact that he has inspired and helped me to

know about the Dynamic & Earthquake Engineering.


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Table of Content

S.No. Title Page

No

Acknowledgement

Table of contents

List of Figures

List of Tables

1 Introduction 6

2 Loads and Functions 17

3 Modeling and Analysis Description 19

4 Load Models 23

5 Analysis 25

6 Conclusions 46

7 References 47


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LIST OF FIGURES

Figure 1 Original Plan View of the Four Story Building

Figure 2 Elevation View of the Four Story Building (Y-Z axis)

Figure 3 Seattle Spectra ( Response Spectrum Curve)Figure 4 Comparison of Stiffness ratio for Model 2 and Model 3

Figure 5 Time History Spectra- LACCO NOR earthquake record (obtained using SAP 2000)

Figure 6 Showing Beam & Exterior Column Arrangement

Figure 7 Showing Beam & Interior Column Arrangement

Figure 8 Model with Dead load

Figure 9 Model with Live Load

Figure 10 Showing displacement under Seattle Spectra-Model 1

Figure 11 Showing shear force under Seattle Spectra- Model 1

Figure 12 Showing bending moment (at grid line 2) under Seattle Spectra-Model1

Figure 13 Showing Displacements under Seattle Spectra-Model 2







Figure 20 Comparison of Displacement for 3 different models

Figure 21 Showing displacement under LACCO NOR earthquake record-Model 4

Figure 22 Comparison of Joint displacement under LACCO NOR earthquake record-Model 4

Figure 23 Comparison of Joint displacement under LACCO NOR earthquake record-Model 4

Figure 24 Model 5 Showing Rubber Isolator.

Figure 25 Comparison of Joint displacement under LACCO NOR earthquake record-Model 5Figure 26 Comparison of Joint displacement under LACCO NOR earthquake record-Model 5

Figure 27 Comparison of Joint Vs Base Shear under LACCO NOR earthquake record-Model 5

Figure 28 Layout of Link Element

Figure 29 Isolator Deformations Model 5-Link Set 1



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LIST OF TABLES

Table 1 : Function of Response Spectrum Function-IBC 2006

Table 2 : Calculation of Seismic Lateral Force

Table 3 : Floor height description for model 2 and model 3Table 4 : Shear wall dimensioning

Table 5: Summary of Stiffness for Beams and Columns for Model 2 and Model 3(Soft Story):

Table 6: Effect of Stiffness due to soft story model (ht variation)

Table 6a : Summary of Dead Load (IBC, minimum design dead load (Table C3-1))

Table 7: Summary of Live Load (Obtained from the IBC minimum uniformly distributed live

load (Table 4-1) and shown below)

Table 8 : Comparison Tables and Result Obtained for 3 models

Table 9: Comparison Calculation for finding % reduction of displacement due to soft story

Table 10: Comparison of base reaction due to all 3 model & % reduction of base reaction

due to soft story

Table 11: Response Spectrum Analysis Model 1



Table 14: Comparison of effect of soft story in RSA

Table 15: Modal Periods and Frequencies for LACCO NOR earthquake-Model 4

Table 16: Base Reaction for LACCO Spectra- Model 5

Table 17: Modal period and frequencies- Model 5

Table 18: Comparison of Period of Model 4 & Model 5

Table 19: Comparison of Base Reaction of Model 4 & Model 5


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1 Introduction

All real physical structures behave dynamically when subjected to loads or displacements. Theadditional inertia forces, from Newtons second law, are equal to the mass times the acceleration.If the loads or displacements are applied very slowly, the inertia forces can be neglected and a

static load analysis can be justified. Hence, dynamic analysis is a simple extension of staticanalysis. In addition, all real structures potentially have an infinite number of displacements.Therefore, the most critical phase of a structural analysis is to create a computer model with afinite number of massless members and a finite number of node (joint) displacements that willsimulate the behavior of the real structure.

Therefore based on the complexity involved in the hand calculation an computer model is madeusing SAP 2000 based on the model, simulate the behavior of the real structure under a dynamicloading .To accomplish the good understanding of dynamic behavior I selected a four storyconcrete building, located in Seattle, Washington ( seismic zone 3 ) below are the plan showing

how the floor plan looks like for Stories 1 to 4.

Figure 1 Original Plan View of the Four Story Building


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Figure 2 Elevation View of the Four Story Building (Y-Z axis)

Seismic weight at various floors :

For a Warehouse, the design load should include a minimum of 25% of the live load. No liveload is to be considered for roof. Hence, the effective weight at all floors, except at the roof will

be Psf, and the effective weight for roof will be 140 psf. The Plan area is 48 ft x96ft = 4608 ft 2. Hence Seismic weights of various levels are: W 1 = W2 = W3 = 1 st, 2

nd & 3rd Storyweight,

W 1

= W 2

= W 3 = 4608 x 0.17125 = 789.1 Kips & W

4 = 4608 x 0.140 = 645.1 Kip

The total Seismic weight of the building is then W = 789.1 x 3 + 645.1 = 3012.4 Kip

Fundamental Period of Building:

T = C t * h n3/4

Where:C t = 0.030 (for reinforcing concrete moment-resisting frame)hn = 48 ft (total height of the building)

T = 0.030* 48 3/4 = 0.55 sec

Occupancy Importance Factor:

Warehouse (SUG) = I = 1 and Occupancy importance factor, I E = 1

140 0.25125 171.25


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Period( sec) Accel (in/sec^2)

0 26.1607612

0.076841 65.401903

0.384205 65.401903

0.6 41.8796098

0.8 31.4097154

1 25.127753

1.2 20.939821

1.4 17.9484088

1.6 15.7048416

1.8 13.9598592

2 12.5638926

2.5 10.0511012

3 8.3759284

3.5 7.1793764

4 6.2819302

4.5 5.583963

5 5.0255506

5.5 4.568697

6 4.1879642

6.5 3.8658032

7 3.5896882

7.5 3.3503778

8 3.1409812

8.5 2.7823054

0

10

20

30

40

50

60

70

0 2 4 6 8 10 12

S p e c t r a

l a c c e

l e r a t i o n

S a

( i n c

h / s e c ^ 2

)

Period (sec)

Seattle Spectra for ZipCode 94704

Seattle Spectra

Figure 3 Seattle Spectra ( Response Spectrum Curve)


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Mapped Response Spectral Acceleration: (Use of SAP 2000) as shown above spectra:

Computer I/P:

Code Selection: IBC 2006 ( IBC 2010 not available)

Soil Class: B for rockDamping: 0.05

Zip Code: 94704

Results:

Short Period (T = 0.2 sec) S s = 3.046673g

Long Period (T = 1 sec) S 1= 1.170548 g

Site Class = B for rock

Site coefficient = F a = 1 S DS = 2.031115

Site coefficient = F v = 1 S D1 = 0.780365

Soil Modified Response Spectral Acceleration:

SMS = F a Ss = 3.046673

SM1 = F v S1 = 1.170548

Design Response Spectral Acceleration:

SDS = 2* 3.046673 / 3 S DS = 2.031115 ( Same as obtain from SAP 2000)

SD1 = 2* 1.170548 / 3 S D1 = 0.780365 ( Same as obtain from SAP 2000)

Response Modification Factor:

R= 8 for Special Reinforced Concrete Moment Frame (obtained using table 12.2-1 Design coefficient and factors for seismic force resisting system ASCE 7-05)

Seismic Design Category = D

Seismic Coefficient:

Cs = S DS* IE/R = 0.253889

Check minimum value for Cs :

Cs 0.044 * S D1 * IE = 0.03433606 Good!


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Cs S1*0.5*I E/R = 0.073159 Good!

Then

Cs = 0.253889

Base Shear Force:

V = C s * W

V= 0.253889 * 3012.4

V = 764.815 Kip

Where:V = Seismic Base Shear.

Cs = Seismic Response Coefficient.

W = Seismic weight of the structure that includes the dead weight and any permanent loadingin this case it also includes 25% of live load as per IBC code provision

Vertical Force Distribution:

F =

For, T = 0.55 sec > 0.5 secK = 1.025 (by Interpolation)

Table2 : Calculation of Seismic Lateral Force

Level h x(ft)

W x(Kip)

h xk

(ft)W x h x

k

(Kip-ft)F x

(Kip)Vx

(Kip)M x

(Kip-ft)4 48 645.1 52.88 34113 274.25 274.25 3 36 781.1 39.37 30752 247.23 521.48 32912 24 781.1 25.98 20293 163.145 684.625 9548.761 12 781.1 12.77 9974 80.186 764.811 17764.26

95132 30604.02

Overturning Moment:

Mx = (as calculated above in table)

= 1 (for top 10 story)


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Story Drift and Lateral Displacement:

Both strength and stiffness need to be considered in the design of special moment frames.According to ASCE 7, special moment frames are allowed to be designed for a force reductionfactor of R = 8. That is, they are allowed to be designed for a base shear equal to one-eighth ofthe value obtained from an elastic response analysis. Moment frames are generally flexiblelateral systems; therefore, strength requirements may be controlled by the minimum base shearequations of the code. Base shear calculations for long-period structures, has been checked andmay govern the strength requirements of special moment frames.

The allowable story drift, a = 0.025 h x = 3.6 inch (where h x is the story height)

Stiffness Computation:

K col = 12*E*I / L3

Econc = 3600 Ksi = modulus of elasticity of concrete

LCol = 12 -0

1 st Story and 2 nd Story Stiffness Computation:

a) Exterior Column : 12 x 20 I extcol = 8000 in 4 b) Interior Column : 12 x 24 I intcol = 13824 in 4

a) Exterior Column for First Story a) Exterior Column for Second Story

K extcol.1 = 115.47 Kip/inch K extcol.2 = 115.47 Kip/inch

b) Interior Column for First Story b) Interior Column for Second Story

K intcol.1 = 200 Kip/inch K intcol.2 = 200 Kip/inch

Total Stiffness: K Total Col 1 = 18*115.47 + 9* 200 = 3878.46 Kip/inch

K Total Col 2 = 18*115.47 + 9* 200 = 3878.46 Ki p/inch

3rd Story and 4 th Story Stiffness Computation:

a) Exterior Column : 12 x 16 I extcol = 4096 in 4 b) Interior Column : 12 x 20 Iintcol = 8000 in 4


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a) Exterior Column for Third Story a) Exterior Column for Forth Story


b) Interior Column for Third Story b) Interior Column for Forth Story

K intcol.3 = 115.47 Kip/inch K intcol.4 = 115.47 Kip/inch

Total Stiffness: K Total Col 3 = 18*59.25 + 9* 115.47 = 2105.73 Ki p/inch

K Total Col 4 = 18*59.25 + 9* 115.47 = 2105.73 Kip/inch

Beams Stiffness

K beam = 3*E*I / L 3


L beam = 24 -0

1 st Story to 4 th Story Stiffness Computation:

Beam Size: 20 x 20 I beam = 13333.33 in 4

K beam = 6.028 Kip/inch

Total Stiffness: K Total Beam 1 = 42*6.028 = 253.176 Ki p/inch

K Total Beam 1 = K Total Beam 2 = K Total Beam 3 = K Total Beam 4 = 253.176 Ki p/inch

Material Properties

Rebar: Reinforcement for Beams and Columns

Type: A615Gr60 Fy = 60 Ksi

Weight per unit volume = 0.49 Kip/ft 3 Fu = 90 Ksi

Modulus of Elasticity (E) = 29000 Ksi

Concrete : Use for Beams, Columns, Floors and Wall

Concrete compressive Strength Fc = 4000 Psi Modulus of Elasticity (E) = 3600 Ksi

LWC Shear Reduction Factor = 0.8 Weight per unit volume = 0.15 Kip/ft 3


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***Use of light weight concete(LWC) is made for columns, beams & floors & Concrete use forthe Shear Walls use of Normal Weight concrete is made**

Rubber Isolator: Isolated Pad for Supports

Weight of each isolator pad = 32.2 lb (too small but mass of base slab is provided above it)Vertical Axial Stiffness = 10000 k/in Initial Shear Stiffness in each direction = 10 k/in

Shear Yield Force in each direction = 5 kips

Ratio of Post Yield Shear Stiffness to Initial shear stiffness =0.2

Soil Type :

Site is located in the Seattle, Washington as per IBC site class definition

Site Class : B

Soil Profile Name: Rock

Seismic Zone Factor :

The seismic zone factor z is computed by referring a Seismic zone map where seattle regionfalls under Zone 3 , Z=0.3

Description about dimensioning Floors:

Floor Dimension : Rectangular plan 48 -0 x 96 -0 (same for each story 1 to 4). Please co -ordinate with Plan Drawing. Floor slab used for the building is shell plate thin element ofthickness 10 inch both in membrane and bending.

Floor to Floor height :

Table 3 : Floor height description for model 2 and model 3

Floor Model 2 (Story) ht in ft Model 3 (Soft Story) ht in ftGround-1 st Floor 12 -0 11 -0

1s to 2 n Floor 12 -0 11 -0 2n to 3 r Floor 12 -0 11 -0 3r to 4 t Floor 12 -0 15 -0

Shear Wall: Shear wall is being considered in Model 3. For that the material properties is beingchanged from LWC to NWC . Thickness of the wall considered 12 thick. Its placement inoriented by following 3-dimensional co-ordinate .To give revelation can be co-ordinate withmodel and plan.


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Table 4 : Shear wall dimensioning

Name Size (ft) Start Co-ordinate(ft) End Co-ordinate(ft)Wall Panel A-B 12-0 x 1 -0 x 48 -0 -48 -0, 24 -0, 48 -0 -36 -0, 24 -0, 48 -0 Wall Panel 1-2 12 -0 x 1 -0 x 48 -0 -48 -0, -24 -0, 48 -0 -48 -0, 0 -0, 48 -0

Wall Panel H-J 12 -0 x 1 -0 x 48 -0 48 -0, - 24 -0, 48 -0 -36 -0, -24 -0, 48 -0 Wall Panel 2-3 12 -0 x 1 -0 x 48 -0 48 -0, 0 -0, 48 -0 48 -0, 24 -0, 48 -0

Stiffness Computation For Soft Story:

K col = 12*E*I / L 3


LCol = 11 -0 ( for 1 to 3 rd Story) L Col = 12 -0 ( for 4 th Story)

1 st Story and 2 nd Story Stiffness Computation:

c) Exterior Column : 12 x 20 I extcol = 8000 in 4 d) Interior Column : 12 x 24 I intcol = 13824 in 4

c) Exterior Column for First Story c) Exterior Column for Second Story


d) Interior Column for First Story d) Interior Column for Second Story

K intcol.1 = 259.65 Kip/inch K intcol.2 = 259.65 Kip/inch

Total Stiffness: K Total Col 1 = 18*150.26+ 9* 259.65 = 5041.53 Ki p/inch

K Total Col 2 = 18*150.26 + 9* 259.65 = 5041.53 Ki p/inch

3rd Story and 4 th Story Stiffness Computation:

c) Exterior Column : 12 x 16 I extcol = 4096 in 4 d) Interior Column : 12 x 20 I intcol = 8000 in 4

c) Exterior Column for Third Story c) Exterior Column for Forth Story


d) Interior Column for Third Story d) Interior Column for Forth Story

K intcol.3 = 150.26. Kip/inch K intcol.4 = 59.26 Kip/inch


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Total Stiffness: K Total Col 3 = 18*76.93+ 9* 150.26 = 2737.08 Ki p/inch

K Total Col 4 = 18*30.34 + 9* 59.26 = 1079.46 Ki p/in ch

Beams Stiffness

K beam = 3*E*I / L 3


L beam = 24 -0

1 st Story to 4 th Story Stiffness Computation:

Beam Size: 20 x 20 I beam = 13333.33 in 4

K beam = 6.028 Kip/inch

Total Stiffness: K Total Beam 1 = 42*6.028 = 253.176 Ki p/inch

K Total Beam 1 = K Total Beam 2 = K Total Beam 3 = K Total Beam 4 = 253.176 Ki p/inch

Table 5: Summary of Stiffness for Beams and Columns for Model 2 and Model 3(Soft Story):

Floor Model 2 (Uniform ht Story) Model 3 (Soft Story)

No. K Total Beam K Total Col K Total Beam K Total Col 1 253.176 3878.46 0.0653 253.176 5041.53 0.05022 253.176 3878.46 0.0653 253.176 5041.53 0.0502 3 253.176 2105.73 0.120 253.176 2737.08 0.09244 253.176 2105.73 0.120 253.176 1079.46 0.2345

Where , = K Total Beam / K Total Col

Remark: We can see because increase in ht at the 4 th level the columns stiffness for each Floorrearrange as shown below


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Table 6: Effect of Stiffness due to soft story model (ht variation)

Floor Model 3 (Soft Story) compare with Model2 No. Comparison of stiffness (Model 3 compared to Model 2)

1 29.9879 % increase2 29.9879 % increase3 29.9879 % increase4 48.73702% decrease

Figure 4: Comparison of Stiffness ratio for Model 2 and Model 3

00.5

11.5

22.5

33.5

44.5

0 0.05 0.1 0.15 0.2 0.25

Floor

Stiffness of Beam/Stiffness of Column

Comparasion of Stiffness ratio for2 Models Uniform Ht. Story

Soft Story


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2 Loads and Functions

This building is to be analyzed for dead, live, and earthquake functional load.

Dead load : Dead Loads are the weights of materials, equipments or components that remains

constant throughout the structure's life. In the project it includes weight of the materials andcomponents which are used for floor, ceiling, partitioning and roof..

Table 6a : Summary of Dead Load (IBC, minimum design dead load (Table C3-1))

Type Description Loads from IBC (psf) Total load on each floor Dead load estimated due to

( floor slab, beam, half wt. ofthe column above and belowthe floor partion wall)

140

Live Load : Which is weight which is superimposed on, or temporarily attached to, a structure(people, machinery and equipment, furniture, appliances, etc.).

Table 7: Summary of Live Load (Obtained from the IBC minimum uniformly distributed liveload (Table 4-1) and shown below)

Floors Description Uniform (psf)1st , 2 n & 3 r Floor Warehouse 125 psf

Roof Warehouse 50 psf

Response-Spectrum Functions:

Design Spectra are not uneven curves; the spectra are intended to be the average of manyearthquakes. This approach allow us obtain an maximum value of Umax. For that reason toobtain conservative study about earthquake analysis I selected IBC 2006 building code fordesign spectra to obtain.

Where we can define, a response spectrum function is a series of digitized pairs of structural period and corresponding pseudo-spectral acceleration values. Based on the function ResponseSpectrum Curve is generated with respect of I/P data assigned to computer and we obtain an o/p

of digitized points of pseudo-acceleration response versus period of structure. As explainedabove a I/P data was assigned to SAP 2000 software and we obtain o/p as shown in figure 3.

Time-History Functions:

The response history analysis is presented for an arbitrary structural configuration and veryhandful for multi story building with a unsymmetrical plan. It is mainly devoted to a single


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component of ground motion, typically one of the horizontal components. Combining thestructural response determined from such independent analysis for each excitation componentsgives the response of linear system to multi-component excitation.

Based on that I picked up LACCO NOR File from SAP 2000 this is what we get as an I/P.

Figure 5: Time History Spectra- LACCO NOR earthquake record (obtained using SAP 2000)

-8

-6

-4

-2

0

2

4

6

8

10

0 10 20 30 40 50 60 70

Psuedoacceleration

in/sec2

Time (s)

Time History Spectra- For LACCO

Time History Spectra- ForLACCO


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3 Modeling and Analysis Description

Preparation of 5 models is performed and they are discussed as below:1. Model 1 3-d four Story building without shear wall. And performed Response Spectrum

Analysis for the model.2. Model 2 3-d four Story building with shear wall. And performed Response Spectrum

Analysis for the model.3. Model 3 3-d four Story ( soft story, 1.e. floor ht. variation was performed ) building with

shear wall. And performed Response Spectrum Analysis for the model.4. Model 4 3-d four Story building with shear wall. And performed Time History Analysis

for the model.5. Model 5 3-d four Story building ( here rubber isolator and mass slab is provided) with

shear wall. And performed Time History Analysis for the model.

Discussion about Modeling and Analysis I/p:

1. Rectangular 3- d frame of 96 -0 x 48 -0 x 48 -0 was generated. 2. Material: Concrete was defined for the building except shear wall material of concrete

used is NWC and for shear wall3. Frame Properties: Beams and columns were grouped into

i. Beamii. External Column 1 st level & 2 nd level

iii. External Column 3 rd level & 4 th leveliv. Internal Column 1 st level & 2 nd levelv. Internal Column 3 rd level & 4 th level

Figure 6 Showing Beam & Exterior Column Arrangement


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Figure7 Showing Beam & Interior Column Arrangement

4. Frame Meshing was at joints and at intersection with frame5. Area Section was defined

Advantage: Shell element has it own local co-ordinate system. The shell element alwaysactivates all 6 Degree of freedom at each connected joints. Results for internal forcesand moments are good .

i. Floor: Plate thin shell element was defined reason the plate bending behaviorincludes two way, out-of plane. Plate rotational stiffness components and atranslation stiffness component in the direction normal to the plane of theelement. By default it neglects shearing deformation and it is recommended touse plate structure for floor slab.

ii. Shear wall: Use of Shell thin element. reason why we use this because when wecompute an analysis to RSA if we provide thin panel element then the peak valueof the shear stress will be good estimation of the damage index ( For story driftcalculation)

6. Assigned Joints Constraints: Assigning of diaphragm constraint causes all of its

constraint joint to move together as a planar diaphragm which is rigid against membranedeformation. Concrete floors which has very high in- plane stiffness. Hence diaphragmreduces error in plane stiffness in floor.

7. Assign joint restraints at base level Z = 0 for all model fixed support except for Model5link/support properties Isolator are provided.

8. Assigning area loads uniform shell, defining loads as shown in table mentioning deadload and live load.


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9. Define Functions: For Model 1 to 3 we analyzed using Response Spectrum I BC 2006and for Model 4 & 5 we analyzed using L acco Time H istory F unction. As we havediscuss how we obtain spectra using SAP 2000. These loads are used for applying groundaccelerations in response-spectrum analyses and are used as starting load vectors for Ritz-vector analysis. Here the acceleration load is computed for each joint and element andsummed over the whole structure. Acceleration load for the analysis are transformedfrom global co-ordinate system to local co-ordinate system.

10. Addition of Load Cases: Spectra generated from function will now be added to the loadcases Model 1 to 3 - Response Spectrum IBC 2006 - Spectra generated Seattle

Spectra Now we select CQC method of modal combination because it is the mostconservative method that is used to estimate a peak value displacement or force within astructure This approach assumes that the maximum modal values for all modes occurs atthe same point in time. CQC method takes into account the statistical coupling betweenclosely Space mode caused by modal damping. Key thing is if damping is zero it

degenerates to SRSS method.11. For Directional combination SRSS method is better because for each displacement forceor stress quantity in the structure, modal combination produces single positive results foreach direction of acceleration the value for a given response combine to produce single

positive results. SRSS methods combine the response for different direction of loading.12. Now assigning the Seattle spectra in X (U 1) and Y (U 2) direction here lot of study has

been conducted about assigning the earthquake motion from all possible direction.Orth ogonal eff ects in spectral analysis: The member in the structure should be designedfor 100% of prescribed seismic forces in one direction plus 30% of prescribed forces in

perpendicular direction. Here it can be reasonable to assume that motion that takes place

during an earthquake has one principal direction or during a finite period of time whenmaximum when maximum ground acceleration occurs, a principal direction exists. Butexact nature of 3dimensional wave propagation is not known. Based on the assumption,we can conclude that a structure must resist a major earthquake motion of magnitude of X for all possible angles and at the sa me point in time resist earthquake motion at90 degree to the angle .For the Model with RSA I have tested with 100% of IBC 2006 called Seattle Spectra in Y-(U 2) direction and 30% of IBC 2006 called Seattle Spectra in X-(U 1) direction.The Model is also tested vice versa and notice the difference in displacement.

For a structure of importance and estimate over conservative analysis we canmultiply by the factor safety to the spectra so that it reads out analysis for higher valuesand give more conservative results then needed.

13. Modal Load Case Modification here we have to decide what modes we have to put forthe analysis no. of modes are not arbitrary it depends on D.O.F but we for this buildingwe have many D.O.F we dont want to put the many nos of D.O.F it is trail to try with20 and 30 and see the Modal participating mass ratios if it reaches to 95% then it will be


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reasonable analysis to accept with it. Even the importance of mentioning Types of modearea there are 2 modes of area. Eigenvector Analysis and Ritz vector Analysis itimportant to know which gives better results. Eigen vector analysis determine theundamped free vibration mode shapes and frequencies of the structure, but lot of researchhave been conducted the natural free vibration mode shapes are not the best basis for amode superposition analysis of structures subjected to dynamic loads. Ritz vectors yieldmore accurate results than eigenvector. Because ritz vectors gives better results becausetaking into account the spatial distribution of dynamic loading. Knowing this we can

proceed with applying accelerated load in global co-ordinate system in X-direction andY-direction.

14. Model 4 &5 analysis I/p explanation the L acco Time H istory data obtained from SAP2000 file it is just a record of single earthquake the data obtained it is applied to thestructure using local co-ordinate, here the orthogonality will not come in role, theimportance of time history analysis which super cedes the RSA the input of L acco Ti me

H istory data assigned , for SAP 2000 it is possible to perform a large amount of dynamicanalyses at various angles of input where we can check all points for critical earthquakedirection. Here In Model 5 in co-operated the non linear analysis , because the advantagecompare to RSA we have that we can perform non linear analysis in THA. RSA haslimitation in nonlinear analysis

15. Model 5, to perform non linear analysis Here new load case is defined in the name ofGrav this is restricted to the dead load only the manner in which applied was selectedRAMPTH Fu nction it is pattern of function applied to the structure. This is the initialcondition use when Lacco Ti me Hi story Non li near analysis is performed . Here Modaldamping is modified for 1 st three modes. Only difference in Modal load case we add Link

so that it specify the results for the isolator. Isolator is an Link/Support element.16. Run Analysis is performed to interpreted the results


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4 Load Model

Figure 8: Model with dead load (We can see on left hand side color band Load applied to the Floors 140 psf)

140sf

Roof


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Figure 9: Model with Live Load(We can see on left hand side color band Load applied to the Floors 125psf

And 50 psf to the roof)

50125


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5 Analysis

Response Spectrum Analysis Results: To perform analysis for Seattle Spectra generated usingIBC 2006 by SAP. Model1 , Model2, Model3 have been tested using spectra and results are

obtained.

1. Damping: In all three model damping ratio was assigned to 0.05 during an I/P ofgeneration of spectra, No advance damping was defined for the model.

2. Accelerations: For each mode acceleration are printed in local co-ordinate system, sowhen we proceed for reading results in this project it identified by the symbol U 1 AccAnd U2 Acc. (this value are the acceleration for each mode are the actual valuesinterpolated at the modal period from the spectra curve.)

3. Modal Amplitude: The response spectrum modal amplitude give the multipliers of themode shapes that contribute to the displaced shape for the each direction of acceleration

load. In the result it is identified as U1 AMP & U2 AMP . 4. Displacement: Noted the Joint displacement at point A,B & C for each floor ( Refer the

plan drawing) for the Model1 , Model2 & Model3 under the application of seismicspectra. In the result it is identified as U1 & U 2

5. Shear Force and Bending Moment: For the Model1 , Model2 & Model3 forces andmoment were noted under a Seattle spectra

6. Base reaction: For the models base reaction are noted , which says the total forces andmoment about the global origin required of the supports (restraint and spring) to resistthe inertia forces due to response spectrum loading. In the result they are identified as asin the gloabal co-ordinate Fx, Fy, Mx & My)

Modal Analysis Results: To perform analysis for Acclerated load applied in Ux and Uy andlook for Modal participation mass ratio. The idea behind the modal analysis is to decouple vector

1. Period (T) in sec which identified in the results which represent the period of a mode forcomplete system.

2. Eigen value is obtained for each mode Identified in the results as 2 in rads/sec3. Modal Mass was seen in the result as an unity.. 4. Modal Stiffness was seen as modal eigenvalue .

5. Modal Load applied in Ux and Uy there dynamic participation was checked.6. Modal Participating Mass ratios were checked that it reaches to 99% of Cumulative sums

of participating mass ratio for all modes) . In the result it is identified Sum of Ux andSum of Uy.


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M odel 1 3-D Four Story building without shear wall. And performed Response SpectrumAnalysis for the model.

Figure10 : Showing displacement under Seattle Spectra-Model 1

Figure11 : Showing shear force under Seattle Spectra- Model 1

U11.752

Maximum value Shear force wasnoticed at base level Int Col 1&2Vu Dynamic due to Seattle SpectraShould be considered for thedesign


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Figure12: Showing bending moment (at grid line 2) under Seattle Spectra-Model1

`Area of intereststrong columnsneeded ( Playing withreinforcementcriterion good ideato see the change in

behavior)


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M odel 2 3-d four Story building with shear wall. And performed Response SpectrumAnalysis for the model.

Figure13 : Showing Displacement under Seattle Spectra-Model 2

Figure14: Showing shear force under Seattle Spectra- Model 2

U2

Maximum valueShear force wasnoticed at top levelInt Col 3&4V Dynamic due to

Seattle SpectraShould beconsidered for thedesign


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Figure15: Showing bending moment (at grid line 1) under SeattleSpectra-Model2

M odel 3 3-d four Story ( soft story, 1.e. f loor ht. vari ation was perfor med ) building with shearwall. And performed Response Spectrum Analysis for the model.


Maximum Moment inbeam was noticedadjacent to the wall

U2


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Figure17 Showing shear force under Seattle Spectra- Model 3

Figure18 : Showing bending moment (at grid line 1) under Seattle Spectra-Model3

MaximumShear forcewas noticedAt Int Col. 3

MaximumMoment inbeam wasnoticedadjacent tothe wall


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Figure19: Showing bending moment (at grid line 2) under Seattle Spectra-Model3

Table 8: Comparison Tables and Result Obtained for 3 models

TABLE: Response Spectrum ModalInformation Model 1 Model 2 Model 3

Floor

Joint

Displacement

Displacement

Displacement

Displacement

Displacement

Displacement

in U1 in U2 in U1 in U2 in U1 in U2

Nos Nos inch inch Inch inch inch inch

1 122 0.435 2.8177 0.1305 0.167 0.1075 0.1418

1 127 0.435 2.8177 0.1305 0.167 0.1075 0.1418

1 132 0.435 2.8177 0.1305 0.167 0.1075 0.1418

2 123 0.8847 5.6134 0.3869 0.466 0.3197 0.3926

2 128 0.8847 5.6134 0.3869 0.466 0.3197 0.3926

2 133 0.8847 5.6134 0.3869 0.466 0.3197 0.3926

3 124 1.4362 8.0379 0.7005 0.8264 0.591 0.6992

MaximumMoment wasNoticed in Int.Col.4

MaximumMoment wasnoticed in Beamat 3 rd floor


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Floor

Joint Displacment Displacment

Displacement

Displacement

Displacement

Displacement

in U1 in U2 in U1 in U2 in U1 in U2

Nos Nos inch inch Inch inch inch inch

4 125 1.7516 9.4159 1.0139 1.1917 0.9912 1.138

4 130 1.7516 9.4159 1.0139 1.1917 0.9912 1.138

4 135 1.7516 9.4159 1.0139 1.1917 0.9912 1.138

Figure 20: Comparison of Displacement for 3 different models

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 1 2 3 4 5 6 7 8 9 10

Floors

Displacement in inch

Comparision of Displacement for 3 different modelsseattle spectra x-dirn displacement model1seattle spectra-y dirn displacement-model 1seattle spectra x- dirn displacement model2seattle spectra y dirn displacement model2

seattle spectra x-dirn displacement-soft storyseattle spectra Y-dirn displacement-soft story


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Table 9: Comparison Calculation for finding % reduction of displacementdue to soft story

Comparison Calculation

Floor

Comparison ofU1

Model 2 &3Comparison of U2

Model 2 &3

% DisplacementReduction in U1 due

tosoft story

% DisplacementReduction in U2 due

tosoft story

Nos inch inch % %

1 0.023 0.0252 17.62452107 15.08982036

2 0.0672 0.0734 17.36882915 15.75107296

3 0.1095 0.1272 15.63169165 15.39206196

4 0.0227 0.0537 2.238879574 4.50616766

Table 10: Comparison of base reaction due to all 3 model & % reduction of base reaction

due to soft story

TABLE: BaseReactions Comparison table

OutputCase GlobalFX GlobalFY GlobalMX GlobalMY

Text Kip Kip Kip-in Kip-inSEATTLESPECTRA

ANALYSISModel 1 1336.864 2800.527 1126741.653 561191.13

SEATTLESPECTRA

ANALYSISModel 2 1954.772 6424.492 2865226.938 844083.04

SEATTLESPECTRA

ANALYSISModel 3 1883.922 6250.226 2720878 794093.6

Difference (Model2 -Model 3) 70.85 174.266 144348.938 49989.437

Reduction in (%)base shear for soft

story on comparisonof model 2 3.624464 2.712526 5.037958288 5.9223364


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Response Spectrum Analysis Model 1

Mode Period CircFreq Eigenvalue U1Acc U2Acc U1Amp U2Amp

Unitless Sec ()rad/sec rad2/sec2 in/sec2 in/sec2 in in1 0.959617 6.5476 42.871 95.026 316.754 3.19E-17 21.44683

2 0.758166 8.2873 68.68 120.959 403.196 2.25E-16 3.97E-14

3 0.575054 10.926 119.38 160.556 535.185 3.822136-7.00E-

17

4 0.33584 18.709 350.02 235.447 784.823 3.98E-18 2.250856

5 0.273242 22.995 528.77 235.447 784.823-2.30E-

17 4.24E-17

6 0.211691 29.681 880.95 235.447 784.823 -0.30296 6.82E-18

7 0.208873 30.081 904.89 235.447 784.823 1.19E-17 0.4261

8 0.169113 37.154 1380.4 235.447 784.823 5.65E-18 7.87E-17

9 0.163768 38.366 1472 235.447 784.823-1.00E-

17 0.168688

10 0.135146 46.492 2161.5 235.447 784.823 -0.05127 9.50E-18



StepNum Period CircFreq Eigenvalue U1Acc U2Acc U1Amp U2Amp

Unitless Sec rad/sec rad2/sec2 in/sec2 in/sec2 in in

1 0.353912 17.754 315.19 235.447 784.823 2.109278 -0.09369

2 0.211951 29.645 878.8 235.447 784.823 0.011517 2.515816

3 0.154698 40.616 1649.6 235.447 784.823-1.00E-

16 1.50E-15

4 0.088961 70.629 4988.4 235.447 784.823 0.069433 -0.00171

5 0.075264 83.482 6969.2 232.548 775.159 0.00206 -0.00549

6 0.065681 95.663 9151.4 214.929 716.43 0.000214 -0.00599

7 0.063453 99.021 9805.2 210.833 702.777 -0.00042 0.013416

8 0.062264 100.91 10183 208.648 695.494 -0.00076 -0.00189 0.057624 109.04 11889 200.118 667.06 0.000308 -0.01643

10 0.054874 114.5 13111 195.062 650.205 -0.00019 -0.07391

System isnot Stiff

hence

highervalue is

noticed innaturalperiod

System isStiff hence

reduction isnoticed in

naturalperiod


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StepNum Period CircFreq Eigenvalue U1Acc U2Acc U1Amp U2Amp

Unitless Sec rad/sec rad2/sec2 in/sec2 in/sec2 in in1 0.346101 18.154 329.58 235.447 784.823 1.96549 -0.08366

2 0.205136 30.629 938.16 235.447 784.823 0.010074 2.313225

3 0.150421 41.771 1744.8 235.447 784.823 9.40E-18 7.71E-15

4 0.093568 67.151 4509.3 235.447 784.823 0.081621 -0.00178

5 0.0735 85.486 7307.8 229.304 764.348 0.000886 -0.00533

6 0.063909 98.315 9665.9 211.671 705.571 -0.00014 0.006343

7 0.062567 100.42 10085 209.205 697.349 0.000228 -0.01629

8 0.060883 103.2 10651 206.108 687.028 0.000352 0.00447

9 0.057078 110.08 12118 199.114 663.713 0.000086 -0.07213

10 0.056205 111.79 12497 197.509 658.364 -0.00026 -0.04667

Table 14: Comparison of effect of soft story in RSA

Floor Model 3 (SoftStory)

DisplacementReduction

DisplacementReduction

Base Reactions

No. Comparison ofstiffness increase instiffness in Model 3

%DisplacementReduction in

U1due to

soft story

%DisplacementReduction in

U2due to

soft story

Reduction in (%) base shear for soft story oncomparison of model 2

% % % (Fx) % (Fy) % (Mx) % (My) %

1 29.9879 % increase 17.62452107 15.08982036

3.62446362 2.7125258 5.0379583 5.922336412 29.9879 % increase 17.36882915 15.75107296

3 29.9879 % increase 15.63169165 15.39206196

4 48.73702%decrease 2.238879574 4.50616766

Interpretation:

1. Discussion about displacement comparison Model 1 with Model 2 and 3 we can seeclearly from the graph ( fig. 20) where displacements for Model 1 is very high for U 1 andU2 . The reason is very simple that the provision of shear wall was made in Model 2 and 3 which was oriented in all direction as can be seen from the model. It provides buildingwith seismic resistance. So provision of shear wall is one of the seismic resistantstructures.

System isvery stiff

hence

reduction isnoticed in

naturalperiod


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2. For member force for Model 1 we can see from ( fig. 11 & 12) when analyzing forcomplete building the maximum Shear force and Bending Moment was noticed in thegrid line 2 of plan (the strong columns and resistant to seismic is needed at the interiorcolumn at first floor.)

3. When comparing the displacement Model 2 with 3 from ( fig. 20 and Table 14) we cannotice that due to increase of stiffness in floor 1, 2 & 3 there is a reduction indisplacement in the floors. But when there is a decrease of stiffness in floor 4 there is areduction in displacement in the 4 th floors but now the reduction of displacement is lesscompare to the floor 1, 2 & 3.Overall soft story can achieve reduction in displacement ifstiffness is rearrange in the building.

4. When comparing the base reaction in global direction for Model 2 with 3, we can noticethat reduction of base reaction in Model 3 (Table 14 shows the value). So we can say toresist the inertia forces due to Response spectrum is less for the soft story.

5. Warily studies was performed for the member forces for Model 2 with 3(refer fig. 14, fig

15, fig 17, fig 18 & fig 19) where comment are listed by noticing the M u Seattle & V u Seattle .Based on the maximum value and use of some conservative reinforcing pattern should beadopted. For the model I have consider #9 longitudinal bars and #4 Confinement bars andconfinement ties ( for Beams and Columns)

i. The ductile frame joint based on the high seismic study ( there are standard guidelines available to adopt in high seismic region)

ii. Requirement of the boundary members should be adoptediii. Seismic Hooks, Cross tie and hoops can be providediv. To design for Frame Flexural Members should be adoptedv. Transverse Confinement in the Flexural member should be adopted.

vi. Providing a Bond Beam.( Information obtain from Michael R Lindeburg, Seismic Design of Building Structure )

6. Study of Modal Analysis for an ndof we have n no. of mode for the project we dontneed n no. of modes to evaluate results for all three model for all 3 model the result wereobtain for 10 modes modal participating mass ratios reaches to 98% and modal load

participation factor reaches 100% of what we applied (i.e. Seattle Spectra) in both U 1 andU2 .So result are complete

7. When comparing Model 1,2 and 3 result for each mode shape was check for correctnesswhen we look to structural o/p of the SAP 2000, looking for Modal Participation factor in which I obtained for each mode .

i. Modal Mass is an Unity ( speaking in terms of theoretical terms Modal massmatrix is an identity matrix)

ii. Modal Stiffness for each mode was obtained as (natural frequency ) 2 equal toeigenvalue which is tabulated in (eigenvalue- table 11,12 &13)

8. Comparing period for all 3 model we can see model 1 has very high period compare tomodel 2 and 3. When we compare Model 1 period with theoretical period based on IBC


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Figure 22 Comparison of Joint displacement under LACCO NOR earthquake record-Model 4(U2 displacement is at 9.62 sec 0.4741 inch)


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Figure 23 Comparison of Joint displacement under LACCO NOR earthquake record-Model 4(U1 displacement is at 7.31 sec 0.9826 inch)

Table 15: Modal Periods and Frequencies for LACCO NOR earthquake-Model 4

TABLE: Modal PeriodsAnd Frequencies

StepNum Period CircFreq EigenvalueUnitless Sec rad/sec rad2/sec2

1 0.353912 17.754 315.192 0.211951 29.645 878.83 0.154698 40.616 1649.64 0.088961 70.629 4988.45 0.075264 83.482 6969.26 0.065681 95.663 9151.47 0.063453 99.021 9805.2

8 0.062264 100.91 101839 0.057624 109.04 11889

10 0.054874 114.5 1311111 0.0511 122.96 1511912 0.050546 124.31 1545213 0.044782 140.3 1968514 0.041648 150.86 2276015 0.040872 153.73 23633

Table 16: Base Reaction for LACCO Spectra- Model 5

TABLE: BaseReactions

OutputCase CaseType GlobalFX GlobalFY GlobalMX GlobalMYText Text Kip Kip Kip-in Kip-in

LACCO SPECTRA LinModHist 1802.357 2499.414 1128363.425 798825.409


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M odel 5 3-d four Story building ( here ru bber i solator and mass slab is provided) with shearwall. And performed Time History Analysis for the model.

Figure 24 Model 5 Showing Rubber Isolator.

Figure 25 Comparison of Joint displacement under LACCO NOR earthquake record-Model 5(U2 displacement very little difference between each floor displacement)

RubberIsolatorProvided


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Figure 26 Comparison of Joint displacement under LACCO NOR earthquake record-Model 5(U1 displacement is very high)

Figure 27 Comparison of Joint Vs Base Shear under LACCO NOR earthquake record-Model 5(U1 displacement is very high)


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Table 17: Modal period and frequencies- Model 5

TABLE: Modal PeriodsAnd Frequencies

StepNum Period CircFreq Eigenvalue

Unitless Sec rad/sec rad2/sec21 12.20939 0.51462 0.26483

2 12.20847 0.51466 0.26487

3 11.91553 0.52731 0.27806

4 0.332325 18.907 357.46

5 0.311778 20.153 406.13

6 0.239744 26.208 686.85

7 0.168803 37.222 1385.5

8 0.158349 39.679 1574.4

9 0.135287 46.443 215710 0.132027 47.59 2264.8

11 0.125196 50.187 2518.7

12 0.122749 51.187 2620.1

13 0.121475 51.724 2675.4

14 0.105582 59.51 3541.5

15 0.102957 61.028 3724.4

Table 18: Comparison of Period of Model 4 & Model 5

Comparison of Periods

Mode

PeriodIsolator

(Tb)

PeriodFixed(Tf) (Tb/Tf)

Unitless Sec Sec

1 12.20939 0.353912 34.49838

2 12.20847 0.211951 57.600453 11.91553 0.154698 77.02447

4 0.332325 0.088961 3.735626

5 0.311778 0.075264 4.1424596 0.239744 0.065681 3.650127

7 0.168803 0.063453 2.6602848 0.158349 0.062264 2.5431879 0.135287 0.057624 2.347754

10 0.132027 0.054874 2.40600311 0.125196 0.0511 2.45002

NaturalPeriod isvery high


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Mode

PeriodIsolator

(Tb)

PeriodFixed(Tf) (Tb/Tf)

12 0.122749 0.050546 2.428461

13 0.121475 0.044782 2.712585

14 0.105582 0.041648 2.53510415 0.102957 0.040872 2.519011

Figure 28 Layout of Link Element


Figure 29 and Figure 30 shows the plot of Isolator deformation


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Table 19: Comparison of Base Reaction of Model 4 & Model 5

TABLE: Base Reactions

OutputCase GlobalFX GlobalFY GlobalMX GlobalMY

Text Kip Kip Kip-in Kip-in

LAC-Model 4 1802.357 2499.414 1128363 798825.4

LAC-Model 5 0 106.819 28316.15 1124.768

% Reduction of BaseReaction due to isolator addition 100 95.72624 97.49051 99.8592

Interpretation:

1. When comparative study done between Model 4 & Model 5 , Base Isolation lengthen the period the fundamental vibration of the structure which can be seen from ( table 17 andtable 18) and because of isolator provision in Model 5 reduces the pseudo accelerationfor the mode.

2. In Model 5 the first vibration mode of isolated structure involves deformation in theisolator link element. The structure is moving as a rigid body on the top of the isolator.

3. From fig. 21 we can see that maximum displacement (U 2 & U 1) in the structure occurs at

different time. From fig. 22 & 23 we can see the difference of displacement in each story. Now at same point we study for model 5 (fig. 25 & 26) we can see there is no differencein the displacement at each level, the effect of isolator is that structure is moving as arigid body on the top of the isolator.

4. From fig 29 & 30 we can see clearly deformation in the isolator is very high.5. When comparing the Model 4 & Model 5 for base reaction we can see the inertia force

required to resist the structure from LACCO Nor earthquake record is less for Model 5


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as we can make out from comparison table 19 were we can see that due to provision isolator tothe building the reduction of the earthquake forces imparted to the structure. It is no surprise thatreduction in base shear is a pink in health for Structure.


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6 Conclusions

1. After vigilant assessment we can distinguish that for concrete structures, additional

development work is required to develop a completely rational method. As we can see

that RSA assessment is restricted to linear analysis as RSA analysis have one of the

limitation it does not perform nonlinear analysis. When looking to the Model 1, 2 & 3

Model 3 is preferable compare to other 1 & 2, reason is because if we know were to put

what size of columns and beams. ( if we work out with right Math work for assembling

stiffness & rearrangement we can achieve reduction in the displacement due to pseudo

ground acceleration)

2. To obtain rational design forces for the concrete member it will be good idea to analyze

the structure 3 or 4 earthquake record using time history analysis as they can furnish the

design forces required for the critical area. The forces obtain in Model 1, 2,& 3 would be

an good approximation for V dynamic & M dynamic but it will be always be good idea to scale

out higher value then what we obtain.

3. Time history analysis performed for Model 4 & 5 reduction in base shear was achieved

significantly, due to addition of isolator. Hence effectiveness of reduction of earthquake

induced forces in a model 5 was achieved by provision of isolator.

4. If System is very stiff there will be reduction in the natural period, which can be noticed a

in the Period comparison for Model 1, 2& 3. For a Model3 it is very stiff system so we

can say it is mass sensitive so if we want change in behavior of the system we have to

look at the mass and based on that we can achieve the changes in the system (Tuned mass

system would be an good recommendation)


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References

1. Anil K. Chopra, Dynamics of Structures - Theory and Applications to Earthquake

engineering, Pearson Prentice Hall, NJ, ISBN 0-13-156174 (Obtained from The TISCH

Library at Tufts University).

2. Mario Paz, Structural Dynamics - Theory and Computation, 5 th edition, Kluwer

Academic Publisher, Boston, ISBN 1-4020-7667-3 ( Obtained from Lehigh University)

3. Ajaya Kumar Gupta, Response Spectrum Method In Seismic Analysis and Design of

Structures CRC Press, Boca Raton, ISBN 0-8493-8628-4 ( Obtained from Union College)

4. W.F.Chen & E.M. Lui, Earthquake Engineering for Structural Design, CRC Press, Boca

Raton, ISBN 0-8493-7234-8 ( Obtained from New York State Library)

5. CSI - Introductory Tutorial & Reference Manual for SAP 2000-Linear and Nonlinear

Static and Dynamic Analysis and Design of Three- Dimensional Structures, Berkeley CA

6. Michael R. Lindeburg & Majid Baradar, Seismic Design of Building Structures,

Professional Publications Inc, Belmont, CA, ISBN 1-888577-52-5 ( Obtained from

Library CECIL C TYRRELL)

7. International building Code 2006- ISBN 1-58001-251-5 ( Obtained from Syracuse

University-Civil & Environmental Department)

8. Edward L. Wilson, Three Dimensional Static and Dynamic Analysis of Structures- A

physical approach with Earthquake Engineering (Obtained from Website) 9. SAP 2000 Software- Syracuse University Civil Engineering Computer Lab.

dynamic-analysis-of-four-story-building.docx

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