dynamic analysis of four story building

1

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 in Civil Engineering in the Graduate School of Syracuse University

10th May 2010

Approved ______________________________ Professor Eric M. Lui

Grade___________________________________

2

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.

3

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

4

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 24 Model 5 Showing Rubber Isolator.



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


5

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 3

Table 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

6

1 Introduction

All real physical structures behave dynamically when subjected to loads or displacements. The additional inertia forces, from Newton’s 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 static analysis. 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 a finite number of massless members and a finite number of node (joint) displacements that will simulate the behavior of the real structure.

Therefore based on the complexity involved in the hand calculation an computer model is made using SAP 2000 based on the model, simulate the behavior of the real structure under a dynamic loading .To accomplish the good understanding of dynamic behavior I selected a four story concrete 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

7

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 live load is to be considered for roof. Hence, the effective weight at all floors, except at the roof will

be 140 0.25125 171.25 Psf, and the effective weight for roof will be 140 psf. The Plan area is 48 ft x 96ft = 4608 ft2. Hence Seismic weights of various levels are: W1 = W2 = W3 = 1 st, 2nd & 3rd Story weight,

W1 = W2 = W3 = 4608 x 0.17125 = 789.1 Kips & W4 = 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 = Ct * hn3/4

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

T = 0.030* 483/4 = 0.55 sec

Occupancy Importance Factor:

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

8

0 2 4 6 8 10 120

10

20

30

40

50

60

70

Seattle Spectra for Zip Code 94704

Seattle Spectra

Period (sec)

Spec

tral

acc

eler

ation

Sa

(inch

/sec

^2)

Figure 3 Seattle Spectra (Response Spectrum Curve)

TABLE 1: Function - Response Spectrum -IBC2006

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

9

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 rock

Damping: 0.05Zip Code: 94704

Results:

Short Period (T = 0.2 sec) Ss = 3.046673g

Long Period (T = 1 sec) S1= 1.170548 g

Site Class = B for rock

Site coefficient = Fa = 1 SDS = 2.031115

Site coefficient = Fv = 1 SD1 = 0.780365

Soil Modified Response Spectral Acceleration:

SMS = Fa Ss = 3.046673

SM1 = Fv S1 = 1.170548

Design Response Spectral Acceleration:

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

SD1 = 2* 1.170548 / 3 SD1 = 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 = SDS*IE/R = 0.253889

Check minimum value for Cs :

Cs ¿ 0.044 * SD1 * IE = 0.03433606……………… Good!

10

Cs ¿ S1*0.5*IE/R = 0.073159……………………… Good!

Then

Cs = 0.253889

Base Shear Force:

V = Cs * 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 loading in this case it also includes 25% of live load as per IBC code provision

Vertical Force Distribution:

F = V Wx h xk

∑Wi hi

For, T = 0.55 sec > 0.5 sec

K = 1.025 (by Interpolation)

Table2 : Calculation of Seismic Lateral Force

Level hx

(ft)Wx

(Kip)hx

k

(ft)Wx hx

k

(Kip-ft)Fx

(Kip)Vx

(Kip)Mx

(Kip-ft)4 48 645.1 52.88 34113 274.25 274.253 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 =ζ∗∑ Fihi−hx (as calculated above in table)

ζ = 1 (for top 10 story)

11

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 reduction factor of R = 8. That is, they are allowed to be designed for a base shear equal to one-eighth of the value obtained from an elastic response analysis. Moment frames are generally flexible lateral systems; therefore, strength requirements may be controlled by the minimum base shear equations of the code. Base shear calculations for long-period structures, has been checked and may govern the strength requirements of special moment frames.

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

Stiffness Computation:

Kcol = 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” Iextcol = 8000 in4

b) Interior Column : 12” x 24” Iintcol = 13824 in4

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

Kextcol.1= 115.47 Kip/inch Kextcol.2= 115.47 Kip/inch

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

Kintcol.1= 200 Kip/inch Kintcol.2= 200 Kip/inch

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

KTotal Col 2= 18*115.47 + 9* 200 = 3878.46 Kip/inch

3 rd Story and 4 th Story Stiffness Computation:

a) Exterior Column : 12” x 16” Iextcol = 4096 in4

b) Interior Column : 12” x 20” Iintcol = 8000 in4

12

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


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

Kintcol.3= 115.47 Kip/inch Kintcol.4= 115.47 Kip/inch

Total Stiffness: KTotal Col 3= 18*59.25 + 9* 115.47 = 2105.73 Kip/inch

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

Beams Stiffness

Kbeam= 3*E*I / L3


Lbeam = 24’-0”

1 st Story to 4 th Story Stiffness Computation:

Beam Size: 20” x 20” Ibeam = 13333.33 in4

Kbeam= 6.028 Kip/inch

Total Stiffness: KTotal Beam 1= 42*6.028 = 253.176 Kip/inch

KTotal Beam 1= KTotal Beam 2= KTotal Beam 3= KTotal Beam 4= 253.176 Kip/inch

Material Properties

Rebar: Reinforcement for Beams and Columns

Type: A615Gr60 Fy = 60 Ksi

Weight per unit volume = 0.49 Kip/ft3 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/ft3

13

***Use of light weight concete(LWC) is made for columns, beams & floors & Concrete use for the 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 region falls 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 of thickness 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-1st Floor 12’-0” 11’-0”

1st to 2nd Floor 12’-0” 11’-0”2nd to 3rd Floor 12’-0” 11’-0”3rd to 4th Floor 12’-0” 15’-0”

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

14

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:

Kcol = 12*E*I / L3


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

1 st Story and 2 nd Story Stiffness Computation:

c) Exterior Column : 12” x 20” Iextcol = 8000 in4

d) Interior Column : 12” x 24” Iintcol = 13824 in4

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


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

Kintcol.1= 259.65 Kip/inch Kintcol.2= 259.65 Kip/inch

Total Stiffness: KTotal Col 1= 18*150.26+ 9* 259.65 = 5041.53 Kip/inch


3 rd Story and 4 th Story Stiffness Computation:

c) Exterior Column : 12” x 16” Iextcol = 4096 in4

d) Interior Column : 12” x 20” Iintcol = 8000 in4

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


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

Kintcol.3= 150.26. Kip/inch Kintcol.4= 59.26 Kip/inch

15

Total Stiffness: KTotal Col 3= 18*76.93+ 9* 150.26 = 2737.08 Kip/inch


Beams Stiffness

Kbeam= 3*E*I / L3


Lbeam = 24’-0”

1 st Story to 4 th Story Stiffness Computation:

Beam Size: 20” x 20” Ibeam = 13333.33 in4

Kbeam= 6.028 Kip/inch

Total Stiffness: KTotal Beam 1= 42*6.028 = 253.176 Kip/inch

KTotal Beam 1= KTotal Beam 2= KTotal Beam 3= KTotal Beam 4= 253.176 Kip/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. KTotal Beam KTotal Col Λ KTotal Beam KTotal Col λ1 253.176 3878.46 0.0653 253.176 5041.53 0.05022 253.176 3878.46 0.0653 253.176 5041.53 0.05023 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, λ = KTotal Beam / KTotal Col

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

16

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

Floor Model 3 (Soft Story) compare with Model2No. 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

0 0.05 0.1 0.15 0.2 0.250

0.51

1.52

2.53

3.54

4.5

Comparasion of Stiffness ratio for2 Models

Uniform Ht. Story

Soft Story

Stiffness of Beam/Stiffness of Column

Floor

17

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 and components 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. of the column above and below the 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 live load (Table 4-1) and shown below)

Floors Description Uniform (psf)1st , 2nd & 3rd 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 many earthquakes. This approach allow us obtain an maximum value of Umax. For that reason to obtain conservative study about earthquake analysis I selected IBC 2006 building code for design 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 Response Spectrum 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 explained above 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 very handful for multi story building with a unsymmetrical plan. It is mainly devoted to a single

18

component of ground motion, typically one of the horizontal components. Combining the structural response determined from such independent analysis for each excitation components gives 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)

0 10 20 30 40 50 60 70

-8

-6

-4

-2

0

2

4

6

8

10

Time History Spectra- For LACCO

Time History Spectra- For LACCO

Time (s)

Psuedo acceleration

in/sec2

19

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 wall 3. Frame Properties: Beams and columns were grouped into

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

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

Figure 6 Showing Beam & Exterior Column Arrangement

20

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 always activates all 6 Degree of freedom at each connected joints. Results for internal forces and moments are good.

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

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

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 membrane deformation. Concrete floors which has very high in- plane stiffness. Hence diaphragm reduces error in plane stiffness in floor.

7. Assign joint restraints at base level Z = 0 for all model fixed support except for Model 5link/support properties Isolator are provided.

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

21

9. Define Functions: For Model 1 to 3 we analyzed using Response Spectrum IBC 2006 and for Model 4 & 5 we analyzed using Lacco Time History Function. As we have discuss how we obtain spectra using SAP 2000. These loads are used for applying ground accelerations 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 and summed over the whole structure. Acceleration load for the analysis are transformed from global co-ordinate system to local co-ordinate system.

10. Addition of Load Cases: Spectra generated from function will now be added to the load cases Model 1 to 3 - Response Spectrum IBC 2006 - Spectra generated “Seattle Spectra” Now we select CQC method of modal combination because it is the most conservative method that is used to estimate a peak value displacement or force within a structure This approach assumes that the maximum modal values for all modes occurs at the same point in time.CQC method takes into account the statistical coupling between closely 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 force or stress quantity in the structure, modal combination produces single positive results for each 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 (U1) and Y (U2) direction here lot of study has been conducted about assigning the earthquake motion from all possible direction.Orthogonal effects in spectral analysis: The member in the structure should be designed for 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 when maximum when maximum ground acceleration occurs, a principal direction exists. But exact 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 “Ѳ” and at the same point in time resist earthquake motion at

90 degree to the angle “Ѳ”.For the Model with RSA I have tested with 100% of IBC 2006 called “Seattle Spectra” in Y-(U2) direction and 30% of IBC 2006 called “Seattle Spectra” in X-(U1) 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 can multiply by the factor safety to the spectra so that it reads out analysis for higher values and give more conservative results then needed.

13. Modal Load Case Modification here we have to decide what modes we have to put for the analysis no. of modes are not arbitrary it depends on D.O.F but we for this building we have many D.O.F we don’t want to put the many no’s of D.O.F it is trail to try with 20 and 30 and see the Modal participating mass ratios if it reaches to 95% then it will be

22

reasonable analysis to accept with it. Even the importance of mentioning “Types of mode area” there are 2 modes of area. Eigenvector Analysis and Ritz vector Analysis it important to know which gives better results. Eigen vector analysis determine the undamped free vibration mode shapes and frequencies of the structure, but lot of research have been conducted the natural free vibration mode shapes are not the best basis for a mode superposition analysis of structures subjected to dynamic loads. Ritz vectors yield more accurate results than eigenvector. Because ritz vectors gives better results because taking 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 and Y-direction.

14. Model 4 &5 analysis I/p explanation the Lacco Time History data obtained from SAP 2000 file it is just a record of single earthquake the data obtained it is applied to the structure using local co-ordinate, here the orthogonality will not come in role, the importance of time history analysis which super cedes the RSA the input of Lacco Time History data assigned , for SAP 2000 it is possible to perform a large amount of dynamic analyses at various angles of input where we can check all points for critical earthquake direction. Here In Model 5 in co-operated the non linear analysis, because the advantage compare to RSA we have that we can perform non linear analysis in THA. RSA has limitation in nonlinear analysis

15. Model 5, to perform non linear analysis Here new load case is defined in the name of Grav this is restricted to the dead load only the manner in which applied was selected RAMPTH Function it is pattern of function applied to the structure. This is the initial condition use when Lacco Time History Non linear analysis is performed .Here Modal damping is modified for 1st 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

23

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)

140 psf

Roof

24

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)

50 psf

125 psf

25

5 Analysis

Response Spectrum Analysis Results: To perform analysis for Seattle Spectra generated using IBC 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 of generation of spectra, No advance damping was defined for the model.

2. Accelerations: For each mode acceleration are printed in local co-ordinate system, so when we proceed for reading results in this project it identified by the symbol U1 AccAnd U2 Acc.(this value are the acceleration for each mode are the actual values interpolated at the modal period from the spectra curve.)

3. Modal Amplitude: The response spectrum modal amplitude give the multipliers of the mode shapes that contribute to the displaced shape for the each direction of acceleration load. In the result it is identified as U1AMP & U2AMP.

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 seismic spectra. In the result it is identified as U1 & U2

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

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

Modal Analysis Results: To perform analysis for Acclerated load applied in Ux and Uy and look 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 for complete system.

2. Eigen value is obtained for each mode Identified in the results as ω2 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 and Sum of Uy.

26

Model 1 3-D Four Story building without shear wall. And performed Response Spectrum Analysis for the model.

Figure10: Showing displacement under Seattle Spectra-Model 1

Figure11: Showing shear force under Seattle Spectra- Model 1

U1 1.752”

Maximum value Shear force was noticed at base level Int Col 1&2Vu Dynamic due to Seattle SpectraShould be considered for the design

27

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

`Area of interest strong columns needed (Playing with reinforcement criterion good idea to see the change in behavior)

28

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

Figure13: Showing Displacement under Seattle Spectra-Model 2

Figure14: Showing shear force under Seattle Spectra- Model 2

U2

1.1

Maximum value Shear force was noticed at top level Int Col 3&4V Dynamic due to Seattle SpectraShould be considered for the design

29


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.


Maximum Moment in beam was noticed adjacent to the wall

U2 1.138”

30

Figure17 Showing shear force under Seattle Spectra- Model 3


MaximumShear force was noticedAt Int Col. 3

Maximum Moment in beam was noticed adjacent to the wall

31


Table 8: Comparison Tables and Result Obtained for 3 models

TABLE: Response Spectrum Modal Information 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 0.6992Floo

rJoin

t Displacment DisplacmentDisplacemen

tDisplacemen

tDisplacemen

tDisplacemen

t

MaximumMoment was Noticed in Int .Col.4

MaximumMoment was noticed in Beam at 3rd floor

32

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

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Comparision of Displacement for 3 different models seattle spectra x-dirn displacement model1seattle spectra-y dirn displacement-model 1seattle spectra x- dirn displacement model2seattle spectra y dirn displacement model2seattle spectra x-dirn displacement-soft storyseattle spectra Y-dirn displacement-soft story

Displacement in inch

Floors

Figure 20: Comparison of Displacement for 3 different models

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

33

Comparison Calculation

Floor

Comparison of U1

Model 2 &3Comparison of U2

Model 2 &3

% Displacement Reduction in U1 due

to soft story

% Displacement Reduction in U2 due

to soft 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 reactiondue to soft story

TABLE: Base Reactions Comparison table

OutputCaseGlobalF

XGlobalF

YGlobalM

XGlobalM

Y

Text Kip Kip Kip-in Kip-inSEATTLE SPECTRA

ANALYSISModel 1

1336.864

2800.527

1126741.653

561191.13

SEATTLE SPECTRA

ANALYSISModel 2

1954.772

6424.492

2865226.938

844083.04

SEATTLE SPECTRA

ANALYSISModel 3

1883.922

6250.226 2720878 794093.6

Difference (Model2 -Model

3) 70.85 174.266144348.93

849989.43

7Reduction in (%)

base shear for soft story on

comparison of model 2

3.624464

2.712526

5.037958288

5.9223364


34

Response Spectrum Analysis Model 1

Mode Period CircFreqEigenvalu

e U1Acc U2Acc U1Amp U2AmpUnitles

s Sec(ω)rad/

secrad2/sec2 in/sec2 in/sec2 in in

10.95961

7 6.5476 42.871 95.026316.75

43.19E-

1721.4468

3

20.75816

6 8.2873 68.68120.95

9403.19

62.25E-

163.97E-

14

30.57505

4 10.926 119.38160.55

6535.18

53.82213

6-7.00E-

17

4 0.33584 18.709 350.02235.44

7784.82

33.98E-

182.25085

6

50.27324

2 22.995 528.77235.44

7784.82

3-2.30E-

174.24E-

17

60.21169

1 29.681 880.95235.44

7784.82

3-

0.302966.82E-

18

70.20887

3 30.081 904.89235.44

7784.82

31.19E-

17 0.4261

80.16911

3 37.154 1380.4235.44

7784.82

35.65E-

187.87E-

17

90.16376

8 38.366 1472235.44

7784.82

3-1.00E-

170.16868

8

100.13514

6 46.492 2161.5235.44

7784.82

3-

0.051279.50E-

18


Response Spectrum Analysis Model 2StepNu

m PeriodCircFre

qEigenvalu

e U1Acc U2Acc U1Amp U2AmpUnitless Sec rad/sec rad2/sec2 in/sec2 in/sec2 in in

10.35391

2 17.754 315.19235.44

7784.82

32.10927

8-

0.09369

20.21195

1 29.645 878.8235.44

7784.82

30.01151

72.51581

6

30.15469

8 40.616 1649.6235.44

7784.82

3-1.00E-

161.50E-

15

40.08896

1 70.629 4988.4235.44

7784.82

30.06943

3-

0.00171

50.07526

4 83.482 6969.2232.54

8775.15

9 0.00206-

0.005496 0.06568 95.663 9151.4 214.92 716.43 0.00021 -

System is not Stiff

hence higher

value is noticed in

natural period

System is Stiff hence

reduction is noticed in

natural period

35

1 9 4 0.00599

70.06345

3 99.021 9805.2210.83

3702.77

7-

0.000420.01341

6

80.06226

4 100.91 10183208.64

8695.49

4-

0.00076 -0.0018

90.05762

4 109.04 11889200.11

8 667.060.00030

8-

0.01643

100.05487

4 114.5 13111195.06

2650.20

5-

0.00019-

0.07391


Response Spectrum Analysis Model 3StepNu

m PeriodCircFre

qEigenvalu

e U1Acc U2Acc U1Amp U2AmpUnitless Sec rad/sec rad2/sec2 in/sec2 in/sec2 in in

10.34610

1 18.154 329.58235.44

7784.82

3 1.96549-

0.08366

20.20513

6 30.629 938.16235.44

7784.82

30.01007

42.31322

5

30.15042

1 41.771 1744.8235.44

7784.82

39.40E-

187.71E-

15

40.09356

8 67.151 4509.3235.44

7784.82

30.08162

1-

0.00178

5 0.0735 85.486 7307.8229.30

4764.34

80.00088

6-

0.00533

60.06390

9 98.315 9665.9211.67

1705.57

1-

0.000140.00634

3

70.06256

7 100.42 10085209.20

5697.34

90.00022

8-

0.01629

80.06088

3 103.2 10651206.10

8687.02

80.00035

2 0.00447

90.05707

8 110.08 12118199.11

4663.71

30.00008

6-

0.07213

100.05620

5 111.79 12497197.50

9658.36

4-

0.00026-

0.04667

Table 14: Comparison of effect of soft story in RSA

Floor Model 3 (Soft Story)

DisplacementReduction

DisplacementReduction

Base Reactions

System is very stiff

hence reduction is noticed in

natural period

36

No. Comparison of stiffness increase in stiffness in Model 3

% Displacement Reduction in

U1 due to

soft story

% Displacement Reduction in

U2 due to

soft story

Reduction in (%) base shear for soft story on comparison 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 see clearly from the graph (fig. 20) where displacements for Model 1 is very high for U1 and U2 . 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 building with seismic resistance. So provision of shear wall is one of the seismic resistant structures.

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

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

4. When comparing the base reaction in global direction for Model 2 with 3, we can notice that reduction of base reaction in Model 3 (Table 14 shows the value). So we can say to resist 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 Mu Seattle & Vu Seattle.Based on the maximum value and use of some conservative reinforcing pattern should be adopted. For the model I have consider #9 longitudinal bars and #4 Confinement bars and confinement 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 provided

37

iv. 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 don’t need n no. of modes to evaluate results for all three model for all 3 model the result were obtain 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 and U2 .So result are complete

7. When comparing Model 1,2 and 3 result for each mode shape was check for correctness when 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 mass matrix is an identity matrix)

ii. Modal Stiffness for each mode was obtained as (natural frequency )2 equal to eigenvalue 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 to model 2 and 3. When we compare Model 1 period with theoretical period based on IBC 2006. We can say theoretical period are very approximate value design cannot be performed based on theoretical basis. Comparing Model 2 with Model 3. Reduction in period is notice for each mode by mode comparison.

9. Modal Amplitude obtain from (table 11,12 &13) identified as U1AMP & U2AMP are the multiplier of the mode shapes that has contribute to displaced shape. We can notice from the table clearly that U2 Amp contribution is very high for Model 1 because it does not have resistive wall in the model. For Comparing Model 2 with Model 3 U2 Amp contribution is high for Model 2 compare to Model 3.

10. Analysis was performed by now changing 30% of IBC 2006 in Y-direction & 100% of IBC 2006 in X-direction. The Displacement result where lower. The control direction of loading is 100% of IBC 2006 in Y-direction and 30% of IBC 2006 in X-directions

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

38

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

Maximum Joint Displacement at Joint 10 U 2 3.2059 inch

Maximum Joint Displacement at Joint 90 U 1 3.557542 inch

39

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

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

40

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

TABLE: Modal Periods And 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 9805.28 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: Base Reactions

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

LACCO SPECTRA LinModHist 1802.357 2499.414 1128363.425 798825.409

41

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.

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)

Rubber IsolatorProvided

42

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)

43

Table 17: Modal period and frequencies-Model 5

TABLE: Modal Periods And Frequencies

StepNum Period CircFreq EigenvalueUnitless Sec rad/sec rad2/sec2

1 12.20939 0.51462 0.264832 12.20847 0.51466 0.264873 11.91553 0.52731 0.278064 0.332325 18.907 357.465 0.311778 20.153 406.136 0.239744 26.208 686.857 0.168803 37.222 1385.58 0.158349 39.679 1574.49 0.135287 46.443 2157

10 0.132027 47.59 2264.811 0.125196 50.187 2518.712 0.122749 51.187 2620.113 0.121475 51.724 2675.414 0.105582 59.51 3541.515 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 Sec1 12.20939 0.353912 34.49838

2 12.20847 0.211951 57.600453 11.91553 0.154698 77.024474 0.332325 0.088961 3.7356265 0.311778 0.075264 4.1424596 0.239744 0.065681 3.6501277 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

Mode Period Period (Tb/Tf)

Natural Period is very high

44

Isolator(Tb)

Fixed(Tf)

12 0.122749 0.050546 2.42846113 0.121475 0.044782 2.71258514 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

45


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

TABLE: Base ReactionsOutputCase GlobalFX GlobalFY GlobalMX GlobalMYText Kip Kip Kip-in Kip-inLAC-Model 4 1802.357 2499.414 1128363 798825.4LAC-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 and table 18) and because of isolator provision in Model 5 reduces the pseudo acceleration for the mode.

2. In Model 5 the first vibration mode of isolated structure involves deformation in the isolator 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 (U2 & U1) 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 difference in the displacement at each level, the effect of isolator is that structure is moving as a rigid 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

46

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

47

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)

48

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”, 5th 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

Documents