1
DYNAMIC ANALYSIS OF FOUR STORY BUILDING
By
Kalpesh 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.
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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
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 14 Showing shear force under Seattle Spectra- Model 2
Figure 15 Showing bending moment (at grid line 1) under Seattle Spectra-Model2
Figure 16 Showing displacement under Seattle Spectra-Model 3
Figure 17 Showing shear force under Seattle Spectra- Model 3
Figure 18 Showing bending moment (at grid line 1) under Seattle Spectra-Model3
Figure 19 Showing bending moment (at grid line 2) under Seattle Spectra-Model3
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 5
Figure 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
Figure 30 Isolator Deformations –Model 5-Link Set 2
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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 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 12: Response Spectrum Analysis Model 2
Table 13: Response Spectrum Analysis Model 3
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. 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
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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 live
load is to be considered for roof. Hence, the effective weight at all floors, except at the roof will
be 140  0.25 125  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
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TABLE 1: Function - Response Spectrum -IBC2006
Seattle Spectra for Zip
Code 94704
70
Spectral acceleration
Sa (inch/sec^2)
60
Seattle Spectra
50
40
30
20
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
10
0
0
2
4
6
Period (sec)
8
Figure 3 Seattle Spectra (Response Spectrum Curve)
10
12
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: 0.05
Zip 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!
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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 ℎ𝑥 𝑘
∑𝑊𝑖 ℎ𝑖
For, T = 0.55 sec > 0.5 sec
K = 1.025 (by Interpolation)
Table2 : Calculation of Seismic Lateral Force
Level
4
3
2
1
hx
(ft)
48
36
24
12
Wx
(Kip)
645.1
781.1
781.1
781.1
hxk
(ft)
52.88
39.37
25.98
12.77
Wx h x k
(Kip-ft)
34113
30752
20293
9974
95132
Fx
(Kip)
274.25
247.23
163.145
80.186
Vx
(Kip)
274.25
521.48
684.625
764.811
Mx
(Kip-ft)
3291
9548.76
17764.26
30604.02
Overturning Moment:
Mx =𝜁 ∗ ∑𝐹𝑖 ℎ𝑖 − ℎ𝑥
𝜁 = 1 (for top 10 story)
(as calculated above in table)
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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 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”
1st Story and 2nd Story Stiffness Computation:
a) Exterior Column : 12” x 20”
b) Interior Column : 12” x 24”
a) Exterior Column for First Story
Kextcol.1= 115.47 Kip/inch
b) Interior Column for First Story
Kintcol.1= 200 Kip/inch
Iextcol = 8000 in4
Iintcol = 13824 in4
a) Exterior Column for Second Story
Kextcol.2= 115.47 Kip/inch
b) Interior Column for Second Story
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
3rd Story and 4th Story Stiffness Computation:
a) Exterior Column : 12” x 16”
b) Interior Column : 12” x 20”
Iextcol = 4096 in4
Iintcol = 8000 in4
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a) Exterior Column for Third Story
a) Exterior Column for Forth Story
Kextcol.3= 59.25 Kip/inch
b) Interior Column for Third Story
Kextcol.4= 59.25 Kip/inch
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
Econc = 3600 Ksi = modulus of elasticity of concrete
Lbeam = 24’-0”
1st Story to 4th 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
Weight per unit volume = 0.49 Kip/ft3
Fy = 60 Ksi
Fu = 90 Ksi
Modulus of Elasticity (E) = 29000 Ksi
Concrete: Use for Beams, Columns, Floors and Wall
Concrete compressive Strength Fc’ = 4000 Psi
LWC Shear Reduction Factor = 0.8
Modulus of Elasticity (E) = 3600 Ksi
Weight per unit volume = 0.15 Kip/ft3
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***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 coordinate 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
Ground-1st Floor
1st to 2nd Floor
2nd to 3rd Floor
3rd to 4th Floor
Model 2 (Story) ht in ft
12’-0”
12’-0”
12’-0”
12’-0”
Model 3 (Soft Story) ht in ft
11’-0”
11’-0”
11’-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.
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Table 4: Shear wall dimensioning
Name
Wall Panel A-B
Wall Panel 1-2
Wall Panel H-J
Wall Panel 2-3
Size (ft)
12’-0” x 1’-0” x 48’-0”
12’-0” x 1’-0” x 48’-0”
12’-0” x 1’-0” x 48’-0”
12’-0” x 1’-0” x 48’-0”
Start Co-ordinate(ft)
-48’-0”, 24’-0”, 48’-0”
-48’-0”, -24’-0”, 48’-0”
48’-0”, - 24’-0”, 48’-0”
48’-0”, 0’-0”, 48’-0”
End Co-ordinate(ft)
-36’-0”, 24’-0”, 48’-0”
-48’-0”, 0’-0”, 48’-0”
-36’-0”, -24’-0”, 48’-0”
48’-0”, 24’-0”, 48’-0”
Stiffness Computation For Soft Story:
Kcol = 12*E*I / L3
Econc = 3600 Ksi = modulus of elasticity of concrete
LCol = 11’-0” ( for 1 to 3rd Story)
LCol = 12’-0” ( for 4th Story)
1st Story and 2nd Story Stiffness Computation:
c) Exterior Column : 12” x 20”
d) Interior Column : 12” x 24”
c) Exterior Column for First Story
Kextcol.1= 150.26 Kip/inch
d) Interior Column for First Story
Kintcol.1= 259.65 Kip/inch
Iextcol = 8000 in4
Iintcol = 13824 in4
c) Exterior Column for Second Story
Kextcol.2= 150.26 Kip/inch
d) Interior Column for Second Story
Kintcol.2= 259.65
Kip/inch
Total Stiffness: KTotal Col 1= 18*150.26+ 9* 259.65 = 5041.53 Kip/inch
KTotal Col 2= 18*150.26 + 9* 259.65 = 5041.53 Kip/inch
3rd Story and 4th Story Stiffness Computation:
c) Exterior Column : 12” x 16”
d) Interior Column : 12” x 20”
c) Exterior Column for Third Story
Kextcol.3= 76.93 Kip/inch
d) Interior Column for Third Story
Kintcol.3= 150.26. Kip/inch
Iextcol = 4096 in4
Iintcol = 8000 in4
c) Exterior Column for Forth Story
Kextcol.4= 30.34 Kip/inch
d) Interior Column for Forth Story
Kintcol.4= 59.26 Kip/inch
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Total Stiffness: KTotal Col 3= 18*76.93+ 9* 150.26 = 2737.08 Kip/inch
KTotal Col 4= 18*30.34 + 9* 59.26 = 1079.46 Kip/inch
Beams Stiffness
Kbeam= 3*E*I / L3
Econc = 3600 Ksi = modulus of elasticity of concrete
Lbeam = 24’-0”
1st Story to 4th 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
No.
1
2
3
4
Model 2 (Uniform ht Story)
KTotal Beam
KTotal Col
Λ
253.176
3878.46
0.0653
253.176
3878.46
0.0653
253.176
2105.73
0.120
253.176
2105.73
0.120
Model 3 (Soft Story)
KTotal Beam
KTotal Col
λ
253.176
5041.53
0.0502
253.176
5041.53
0.0502
253.176
2737.08
0.0924
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
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Table 6: Effect of Stiffness due to soft story model (ht variation)
Floor
No.
Model 3 (Soft Story) compare with Model2
Comparison of stiffness (Model 3 compared to Model 2)
1
2
3
4
29.9879 % increase
29.9879 % increase
29.9879 % increase
48.73702% decrease
Figure 4: Comparison of Stiffness ratio for Model 2 and Model 3
Comparasion of Stiffness ratio for
2 Models
Uniform Ht. Story
Soft Story
Floor
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0
0.05
0.1
0.15
0.2
Stiffness of Beam/Stiffness of Column
0.25
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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 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
Total load on each floor
Description
Loads from IBC (psf)
Dead load estimated due to
140
(floor slab, beam, half wt. of
the column above and below
the floor partion wall)
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)
st
nd
rd
1 , 2 & 3 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
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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)
Time History Spectra- For LACCO
10
Time History Spectra- For
LACCO
8
6
4
Psuedo
acceleration 2
in/sec2
0
0
10
20
30
40
-2
-4
-6
-8
Time (s)
50
60
70
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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 wall
3. Frame Properties: Beams and columns were grouped into
i.
Beam
ii.
External Column 1st level & 2nd level
iii. External Column 3rd level & 4th level
iv.
Internal Column 1st level & 2nd level
v.
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 frame
5. 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 Ritzvector 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
Roof
140
psf
Figure 8: Model with dead load
(We can see on left hand side color band Load applied to the Floors 140 psf)
24
125 psf
50 psf
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)
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 Acc
And 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/sec
3. 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.
U1
1.752”
Figure10: Showing displacement under Seattle Spectra-Model 1
Maximum value Shear force was
noticed at base level Int Col 1&2
Vu Dynamic due to Seattle Spectra
Should be considered for the
design
Figure11: Showing shear force under Seattle Spectra- Model 1
27
Figure12: Showing bending moment (at grid line 2) under Seattle SpectraModel1
`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.
U2
1.19
Figure13: Showing Displacement under Seattle Spectra-Model 2
Maximum value
Shear force was
noticed at top level
Int Col 3&4
V Dynamic due to
Seattle Spectra
Should be
considered for the
design
Figure14: Showing shear force under Seattle Spectra- Model 2
29
Maximum Moment in
beam was noticed
adjacent to the wall
Figure15: Showing bending moment (at grid line 1) under Seattle
Spectra-Model2
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.
U2 1.138”
Figure 16 Showing displacement under Seattle Spectra-Model 3
30
Maximum
Shear force
was noticed
At Int Col. 3
Figure17 Showing shear force under Seattle Spectra- Model 3
Maximum
Moment in
beam was
noticed
adjacent to
the wall
Figure18: Showing bending moment (at grid line 1) under Seattle Spectra-Model3
31
Maximum
Moment was
Noticed in Int
.Col.4
Maximum
Moment was
noticed in Beam
at 3rd floor
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 Modal
Information Model 1
Displacemen
Displacemen
t
t
Floo Join
r
t
in U1
in U2
Model 2
Displacemen Displacemen
t
t
Model 3
Displacemen Displacemen
t
t
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
32
Floo
r
Join
t
Displacment
Displacment
Displacemen
t
Displacemen
t
Displacemen
t
Displacemen
t
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
Comparision of Displacement for 3 different models
seattle spectra x-dirn displacement model1
seattle spectra-y dirn displacement-model 1
seattle spectra x- dirn displacement model2
seattle spectra y dirn displacement model2
seattle spectra x-dirn displacement-soft story
seattle spectra Y-dirn displacement-soft story
4.5
4
3.5
3
2.5
Floors
2
1.5
1
0.5
0
0
1
2
3
4
5
6
Displacement in inch
7
8
Figure 20: Comparison of Displacement for 3 different models
9
10
33
Table 9: Comparison Calculation for finding % reduction of displacement
due to soft story
Comparison Calculation
Comparison of U2
Model 2 &3
% Displacement
Reduction in U1 due
to
soft story
% Displacement
Reduction in U2 due
to
soft story
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
Floor
Comparison of
U1
Model 2 &3
Nos
Table 10: Comparison of base reaction due to all 3 model & % reduction of base reaction
due to soft story
TABLE: Base
Reactions
Comparison table
OutputCase
GlobalFX
GlobalFY
GlobalMX
GlobalMY
Text
SEATTLE
SPECTRA
ANALYSIS
Model 1
SEATTLE
SPECTRA
ANALYSIS
Model 2
SEATTLE
SPECTRA
ANALYSIS
Model 3
Kip
Kip
Kip-in
Kip-in
1336.864
2800.527
1126741.653
561191.13
1954.772
6424.492
2865226.938
844083.04
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 comparison
of model 2
3.624464
2.712526
5.037958288
5.9223364
34
Table 11: Response Spectrum Analysis Model 1
Response Spectrum Analysis Model 1
Mode
Period
CircFreq
Eigenvalue
U1Acc
U2Acc
U1Amp
U2Amp
Unitless
Sec
(ω)rad/sec
rad2/sec2
in/sec2
in/sec2
in
in
1
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
0.575054
10.926
119.38
160.556
535.185
3.822136
3.97E-14
-7.00E17
4
0.33584
18.709
350.02
235.447
784.823
2.250856
5
0.273242
22.995
528.77
235.447
784.823
3.98E-18
-2.30E17
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
7.87E-17
9
0.163768
38.366
1472
235.447
784.823
5.65E-18
-1.00E17
0.168688
10
0.135146
46.492
2161.5
235.447
784.823
-0.05127
9.50E-18
System is
not Stiff
hence
higher
value is
noticed in
natural
period
4.24E-17
Table 12: Response Spectrum Analysis Model 2
Response Spectrum Analysis Model 2
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
2 0.211951
29.645
878.8
235.447
3 0.154698
40.616
1649.6
235.447
784.823 0.011517 2.515816
-1.00E784.823
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
-0.0018
9 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
-0.09369
-0.07391
System is
Stiff hence
reduction is
noticed in
natural
period
35
Table 13: Response Spectrum Analysis Model 3
Response Spectrum Analysis Model 3
StepNum
Period
CircFreq Eigenvalue
U1Acc
U2Acc
U1Amp
U2Amp
Unitless
Sec
rad/sec
rad2/sec2
in/sec2
in/sec2
in
in
1
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
System is
very stiff
hence
reduction is
noticed in
natural
period
Table 14: Comparison of effect of soft story in RSA
Floor
Model 3 (Soft
Story)
Displacement
Reduction
Displacement
Reduction
Base Reactions
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
%
1
29.9879 % increase
17.62452107
15.08982036
2
29.9879 % increase
17.36882915
15.75107296
3
29.9879 % increase
15.63169165
15.39206196
4
48.73702%decrease
2.238879574
4.50616766
(Fx) %
(Fy) %
(Mx) %
(My) %
3.62446362
2.7125258
5.0379583
5.92233641
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.
36
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 adopted
iii. Seismic Hooks, Cross tie and hoops can be provided
iv.
To design for Frame Flexural Members should be adopted
v.
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 U1 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
37
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.
Maximum Joint Displacement
at Joint 90 U 1 3.557542 inch
Maximum Joint Displacement
at Joint 10 U 2 3.2059 inch
Figure 21 Showing displacement under LACCO NOR earthquake record-Model 4
38
Figure 22 Comparison of Joint displacement under LACCO NOR earthquake record-Model 4
(U2 displacement is at 9.62 sec 0.4741 inch)
39
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 Periods
And Frequencies
StepNum
Unitless
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Period
Sec
0.353912
0.211951
0.154698
0.088961
0.075264
0.065681
0.063453
0.062264
0.057624
0.054874
0.0511
0.050546
0.044782
0.041648
0.040872
CircFreq
rad/sec
17.754
29.645
40.616
70.629
83.482
95.663
99.021
100.91
109.04
114.5
122.96
124.31
140.3
150.86
153.73
Eigenvalue
rad2/sec2
315.19
878.8
1649.6
4988.4
6969.2
9151.4
9805.2
10183
11889
13111
15119
15452
19685
22760
23633
Table 16: Base Reaction for LACCO Spectra-Model 5
TABLE: Base
Reactions
OutputCase
Text
LACCO SPECTRA
CaseType
Text
LinModHist
GlobalFX
Kip
1802.357
GlobalFY
Kip
2499.414
GlobalMX
Kip-in
1128363.425
GlobalMY
Kip-in
798825.409
40
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.
Rubber
Isolator
Provided
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)
41
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)
42
Table 17: Modal period and frequencies-Model 5
TABLE: Modal Periods
And Frequencies
StepNum
Unitless
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Natural
Period is
very high
Period
Sec
12.20939
12.20847
11.91553
0.332325
0.311778
0.239744
0.168803
0.158349
0.135287
0.132027
0.125196
0.122749
0.121475
0.105582
0.102957
CircFreq
rad/sec
0.51462
0.51466
0.52731
18.907
20.153
26.208
37.222
39.679
46.443
47.59
50.187
51.187
51.724
59.51
61.028
Eigenvalue
rad2/sec2
0.26483
0.26487
0.27806
357.46
406.13
686.85
1385.5
1574.4
2157
2264.8
2518.7
2620.1
2675.4
3541.5
3724.4
Table 18: Comparison of Period of Model 4 & Model 5
Comparison of Periods
Mode
Unitless
1
2
3
4
5
6
7
8
9
10
11
Period
Isolator
(Tb)
Sec
12.20939
12.20847
11.91553
0.332325
0.311778
0.239744
0.168803
0.158349
0.135287
0.132027
0.125196
Period
Fixed
(Tf)
Sec
0.353912
0.211951
0.154698
0.088961
0.075264
0.065681
0.063453
0.062264
0.057624
0.054874
0.0511
(Tb/Tf)
34.49838
57.60045
77.02447
3.735626
4.142459
3.650127
2.660284
2.543187
2.347754
2.406003
2.45002
43
Mode
12
13
14
15
Period
Isolator
(Tb)
0.122749
0.121475
0.105582
0.102957
Period
Fixed
(Tf)
0.050546
0.044782
0.041648
0.040872
Figure 28 Layout of Link Element
Figure 29 and Figure 30 shows the plot of Isolator deformation
Figure 29 Isolator Deformations –Model 5-Link Set 1
(Tb/Tf)
2.428461
2.712585
2.535104
2.519011
44
Figure 30 Isolator Deformations –Model 5-Link Set 2
Table 19: Comparison of Base Reaction of Model 4 & Model 5
TABLE: Base Reactions
OutputCase
Text
LAC-Model 4
LAC-Model 5
% Reduction of Base
Reaction due to isolator addition
GlobalFX
Kip
1802.357
0
GlobalFY
Kip
2499.414
106.819
GlobalMX
Kip-in
1128363
28316.15
GlobalMY
Kip-in
798825.4
1124.768
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
45
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.
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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”, 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.