- The document discusses the response of linear elastic single-degree-of-freedom (SDOF) systems to earthquake loading.
- It describes how the peak displacement, velocity and acceleration responses of SDOF systems depend on factors like the system's natural period and damping ratio.
- Response spectra are introduced as plots that show the peak response of SDOF systems as a function of their natural period. Different types of response spectra like deformation, pseudo-velocity and pseudo-acceleration spectra are discussed.
This document presents an example of analysis design of slab using ETABS. This example examines a simple single story building, which is regular in plan and elevation. It is examining and compares the calculated ultimate moment from CSI ETABS & SAFE with hand calculation. Moment coefficients were used to calculate the ultimate moment. However it is good practice that such hand analysis methods are used to verify the output of more sophisticated methods.
Also, this document contains simple procedure (step-by-step) of how to design solid slab according to Eurocode 2.The process of designing elements will not be revolutionised as a result of using Eurocode 2. Due to time constraints and knowledge, I may not be able to address the whole issues.
The Pushover Analysis from basics - Rahul LeslieRahul Leslie
Pushover analysis has been in the academic-research arena for quite long. The papers published in this field usually deals mostly with proposed improvements to the approach, expecting the reader to know the basics of the topic... while the common structural design practitioner, not knowing the basics, is left out from participating in those discussions. Here I’m making an effort to bridge that gap by explaining the Pushover analysis, from basics, in its simplicity.
A write up on this topic can be found at http://rahulleslie.blogspot.in/p/blog-page.html, though does not cover the full spectrum presented in this slide show.
This document presents an example of analysis design of slab using ETABS. This example examines a simple single story building, which is regular in plan and elevation. It is examining and compares the calculated ultimate moment from CSI ETABS & SAFE with hand calculation. Moment coefficients were used to calculate the ultimate moment. However it is good practice that such hand analysis methods are used to verify the output of more sophisticated methods.
Also, this document contains simple procedure (step-by-step) of how to design solid slab according to Eurocode 2.The process of designing elements will not be revolutionised as a result of using Eurocode 2. Due to time constraints and knowledge, I may not be able to address the whole issues.
The Pushover Analysis from basics - Rahul LeslieRahul Leslie
Pushover analysis has been in the academic-research arena for quite long. The papers published in this field usually deals mostly with proposed improvements to the approach, expecting the reader to know the basics of the topic... while the common structural design practitioner, not knowing the basics, is left out from participating in those discussions. Here I’m making an effort to bridge that gap by explaining the Pushover analysis, from basics, in its simplicity.
A write up on this topic can be found at http://rahulleslie.blogspot.in/p/blog-page.html, though does not cover the full spectrum presented in this slide show.
In this study the kinematic wave equation has been solved numerically using the modified Lax
explicit finite difference scheme (MLEFDS) and used for flood routing in a wide prismatic channel and a nonprismatic
channel. Two flood waves, one sinusoidal wave and one exponential wave, have been imposed at the
upstream boundary of the channel in which the flow is initially uniform. Six different schemes have been
introduced and used to compute the routing parameter, the wave celerity c. Two of these schemes are based on
constant depth and use constant celerity throughout the computation process. The rest of the schemes are based
on local depths and give celerity dependent on time and space. The effects of the routing parameter c on the
travel time of flood wave, the subsidence of the flood peak and the conservation flood flow volume have been
studied. The results seem to indicate that there is a minimal loss/gain of flow volume whatever the scheme is.
While it is confirmed that neither of the schemes is 100% volume conservative, it is found that the scheme
Kinematic Wave Model-2 (KWM-II) gives the most accurate result giving only 0.1% error in perspective of
volume conservation. The results obtained in this study are in good qualitative agreement with those obtained in
other similar studies.
We present a class of continuous, bounded, finite-time stabilizing controllers for the tranlational and double integrator based on Bhat and Bernstein's work of IEEE Transactions on Automatic Control, Vol. 43, No. 5, May 1998
Apart from TDMA, there are other iterative methods for solving the
system of equations which are faster. Unlike TDMA, which solves
the problem line by line, these iterative methods solves all
equations simultaneously. As a result these methods are faster than
TDMA. Some of the fast iterative methods are
1) SIP (strongly implicit procedure)
2) MSIP (modified SIP)
3) CG (Conjugate gradient method)
4) BiCGSTAB (bi-conjugate gradient stabilized method)
CG method is used for solving linear systems of equations which
have a symmetric coefficient matrix. All other methods mentioned
above are used for systems of equations involving non-symmetric
coefficient matrices.
ACEP Magazine edition 4th launched on 05.06.2024Rahul
This document provides information about the third edition of the magazine "Sthapatya" published by the Association of Civil Engineers (Practicing) Aurangabad. It includes messages from current and past presidents of ACEP, memories and photos from past ACEP events, information on life time achievement awards given by ACEP, and a technical article on concrete maintenance, repairs and strengthening. The document highlights activities of ACEP and provides a technical educational article for members.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
Contact with Dawood Bhai Just call on +92322-6382012 and we'll help you. We'll solve all your problems within 12 to 24 hours and with 101% guarantee and with astrology systematic. If you want to take any personal or professional advice then also you can call us on +92322-6382012 , ONLINE LOVE PROBLEM & Other all types of Daily Life Problem's.Then CALL or WHATSAPP us on +92322-6382012 and Get all these problems solutions here by Amil Baba DAWOOD BANGALI
#vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore#blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #blackmagicforlove #blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #Amilbabainuk #amilbabainspain #amilbabaindubai #Amilbabainnorway #amilbabainkrachi #amilbabainlahore #amilbabaingujranwalan #amilbabainislamabad
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
A review on techniques and modelling methodologies used for checking electrom...nooriasukmaningtyas
The proper function of the integrated circuit (IC) in an inhibiting electromagnetic environment has always been a serious concern throughout the decades of revolution in the world of electronics, from disjunct devices to today’s integrated circuit technology, where billions of transistors are combined on a single chip. The automotive industry and smart vehicles in particular, are confronting design issues such as being prone to electromagnetic interference (EMI). Electronic control devices calculate incorrect outputs because of EMI and sensors give misleading values which can prove fatal in case of automotives. In this paper, the authors have non exhaustively tried to review research work concerned with the investigation of EMI in ICs and prediction of this EMI using various modelling methodologies and measurement setups.
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
Online aptitude test management system project report.pdfKamal Acharya
The purpose of on-line aptitude test system is to take online test in an efficient manner and no time wasting for checking the paper. The main objective of on-line aptitude test system is to efficiently evaluate the candidate thoroughly through a fully automated system that not only saves lot of time but also gives fast results. For students they give papers according to their convenience and time and there is no need of using extra thing like paper, pen etc. This can be used in educational institutions as well as in corporate world. Can be used anywhere any time as it is a web based application (user Location doesn’t matter). No restriction that examiner has to be present when the candidate takes the test.
Every time when lecturers/professors need to conduct examinations they have to sit down think about the questions and then create a whole new set of questions for each and every exam. In some cases the professor may want to give an open book online exam that is the student can take the exam any time anywhere, but the student might have to answer the questions in a limited time period. The professor may want to change the sequence of questions for every student. The problem that a student has is whenever a date for the exam is declared the student has to take it and there is no way he can take it at some other time. This project will create an interface for the examiner to create and store questions in a repository. It will also create an interface for the student to take examinations at his convenience and the questions and/or exams may be timed. Thereby creating an application which can be used by examiners and examinee’s simultaneously.
Examination System is very useful for Teachers/Professors. As in the teaching profession, you are responsible for writing question papers. In the conventional method, you write the question paper on paper, keep question papers separate from answers and all this information you have to keep in a locker to avoid unauthorized access. Using the Examination System you can create a question paper and everything will be written to a single exam file in encrypted format. You can set the General and Administrator password to avoid unauthorized access to your question paper. Every time you start the examination, the program shuffles all the questions and selects them randomly from the database, which reduces the chances of memorizing the questions.
Online aptitude test management system project report.pdf
Module 6, Spring 2020.pdf
1. CE-412: Introduction to Structural Dynamics and Earthquake
Engineering
MODULE 6
1
University of Engineering & Technology,
Peshawar, Pakistan
RESPONSE OF LINEAR ELASTIC S.D.O.F SYSTEMS TO
EARTHQUAKE LOADING
2. 2
“If a civil engineer is to acquire fruitful experience in a brief span of time, expose him to
the concepts of earthquake engineering, no matter if he is later not to work in
earthquake country.”
Nathan M. Newmark and Emilo Rosenbleuth
3. 3
Earthquake Response of Linear System
In this lecture, we will study the earthquake response of linear
SDOF systems subjected to earthquake excitations.
By definition, linear systems are elastic systems.
They are also referred to as linearly elastic systems in these
lectures to emphasize both properties.
fs
fs
u
Linear elastic system
Non-linear elastic system
No energy is dissipated
by system
u
Elastic-perfectly plastic
system (Elasto plastic system)
Non-linear inelastic system
Area enclosed by the
curve = Energy
dissipated by system
4. 4
As studied in module 5, acceleration at the base of a systems can be
replaced by the effective force, which in case of earthquake can be
written as effective earthquake force (indicated by the subscript “eff”.
Since this force is proportional to the mass, thus, by increasing the
mass the structural designer increases the effective earthquake force
Effective Earthquake Force
Effective earthquake force: horizontal ground motion
Base moving with
(t)
u
m
)
t
(
p g
eff
(t)
ug
6. 6
Strong ground motions recorded in various earthquakes
t
g
u
Figure : Ground motions recorded
during several earthquakes.
7. 7
7
N-S component of horizontal ground acceleration recoded at El Centro, California
during the Imperial Valley earthquake of 1940
Ground acceleration,
Ground velocity,
Ground displacement,
g
u
g
u
g
u
Accelerogram used in these lectures
8. Equation of motion for SDOF system subjected
to EQ excitations
(t)
u
u
m
k
u
m
c
u
(t)
u
m
ku
u
c
u
m g
g
n
n
cr
ω
m
k
and
2mω
c
c
Since
(t)
u
u
ω
u
2ζ
u g
2
n
n
9. 9 9
9
(t)
u
u
ω
u
2 ζ
u g
2
n
n
The time variation of ground displacement, from the given time
variation of ground acceleration, can be determined by using any
appropriate time stepping numerical method.
Closer the time interval, more accurate will be solution. Typically, the
time interval is chosen to be 1/100 to 1/50 of a second, requiring 1500 to
3000 ordinates to describe the round motion of above given El- Centro
,1940, ground acceleration record having a duration of 30 sec.
Solution to equation of motion for SDOF
system subjected to EQ excitation
10. 10
The Holiday Inn, a 7-story, reinforced concrete frame building, was
approximately 5 miles from the closest portion of the causative fault during
1971 San Fernando Earthquake.
The recorded building motions enabled an analysis to be made of the
stresses and strains in the structure during the earthquake.
Dynamic amplification (Transmissibility effect ?)
TR ≈ 350/225=1.56
12. 12
Response quantities
Response is the structural system
reaction to a demand coming from
ground acceleration record
Thus a response quantity may be structural displacement,
velocity, acceleration, internal shear, bending moment, axial force
etc.
Sometime, the total acceleration, , of the mass would be
needed if the structure is supporting sensitive equipment and
the motion imparted to the equipment is to be determined.
t
o
u
13. 13
Response quantities
Pounding damage, Hotel de carlo, Mexico city, 1985 earthquake
One of the important response quantity is total lateral displacement
at the top end of structural system, , required to provide enough
separation between adjacent buildings to prevent their pounding
against each other during an earthquake
t
o
u
14. 14
Structural disp., , due to ground acceleration,
0.319g
ugo
g
,
ug
in
u,
g
u
2%
ζ
0.5sec,
Tn
u
El Centro,1940, ground acceleration
Corresponding relative displacement
at the top end of the SDOF frame
15. 15
(t)
u
u
ω
u
2 ζ
u g
2
n
n
The above given equation indicates that
Thus any two systems having the same values of Tn and ζ will have
the same deformation response u(t) even though one system may
be more massive than the other or one may be stiffer than the other
)
,
f(
u n
T
Influence of Tn and ζ on Peak displacement, uo ,
in a liner elastic SDOF system
16. 16 16
Effect of Tn on Deformation
response history
0.319g
go
u
g
,
ug
El Centro ground acceleration
Response of SDOF systems with different values of Tn to
El Centro ground acceleration
In general, peak value of
displacement at the top end of a
SDOF increases with the increase
in the time period of the system.
18. 18 18
18
Effect of ζ on Deformation
response history
In general, peak value of
displacement at the top end of a
SDOF increases with the decrease
in the damping ratio of the system
0.319g
ugo
g
,
ug
El Centro ground acceleration
Response of SDOF systems with different values of ζ to
El Centro ground acceleration
20. 20
Thus, structural systems with Tn=0.5sec, 1 and 2 sec may be considered
as 5, 10 and 20 story height buildings, respectively.
A building with 3 story height can be considered as Multi DOF system
with at least 3 DOFs.
To keep the discussion simple at this stage, it will be a reasonable
assumption to state that (out of 3 natural time periods of the 3 story
building) we consider only fundamental natural time period (Tn=0.3 sec)
to determine the response quantities for the building.
Later on we will discuss how all 3 vibration modes (and the
corresponding natural time periods) are calculated and are taken into
account to find the total response of a building with DOF =3
Because the empirical period formula is based on measured response of
buildings, it should not be used to estimate the period for other types of
structure (bridges, dams, towers).
Approximate Periods of Vibration
21. 21
Response spectrum concept
A plot of the peak value of a response quantity as a function of the
natural vibration period Tn of the system, or a related parameter such
as circular frequency ωn or cyclic frequency fn, is called the response
spectrum for that quantity.
Response is the structural system reaction to a demand coming
from ground acceleration record (i.e. Accelerogram) and when the
peak response commodities such as structural system displacement
, velocity and acceleration are plotted against the
structural system natural time period (or frequencies) will be called
spectrum
o
u
o
u
o
t
u
22. 22
Response spectrum concept
Peak values of response quantities and shape of response
spectrum depends on the accelerogram
Each such plot is for SDOF system having a fixed damping ratio
ζ, and several such plots for different values of ζ are included to
cover the range of damping values encountered in actual structures.
The deformation response spectrum is a plot of uo against Tn for
fixed ζ. A similar plot for is the relative velocity response
spectrum, and for is the total acceleration response spectrum.
o
u
t
o
u
23. 23
Deformation response spectrum
Figure on next slide shows the procedure to determine the
deformation response spectrum. The spectrum is developed for
El Centro ground motions, as shown in part (a) of the figure.
The time variation of deformation induced by this ground motion
in three SDF systems is presented in part (b) of the figure
The peak value of deformation D ≡ uo, determined for SDF
system with different Tn is determined and shown in part (c) of the
Figure
24. 24 24
24
(a) El-centro ground acceleration; (b) Deformation response of three SDF systems
with ζ=2% and Tn=0.5,1, and 2 sec; (c) Deformation response spectrum for ζ=2%
Construction of deformation
response spectrum
25. 25
Pseudo-velocity response spectrum
Consider a quantity V for an SDF system with natural frequency ωn
related to its peak deformation D ≡ uo due to earthquake ground
motion:
D
T
2π
V
D
ω
n
n
The quantity V has the unit of velocity and is called relative pseudo-
velocity or simply pseudo-velocity. The prefix pseudo is used
because V is not equal to the peak velocity , although it has the
correct units.
o
u
28. 28
Please note the following comments regarding pseudo commodities:
1. uo is same as D by definition.
2. Whereas is not taken as V, which by definition = ωnD
3. Similarly, is not taken as A which by definition= ωn
2D
o
u
o
t
u
A caution about Pseudo responses
29. 29
Displacement Response Spectra for Different Damping values
Higher the damping, the lower the relative displacement.
At a period of 2 sec, for example, going from zero to 5%
damping reduces the displacement amplitude by a factor of two.
While higher damping produces further decreases in displacement,
there is a diminishing return.
The % reduction in
displacement by going
from 5 to 20% damping is
much less that that for 0 to
5% damping.
Deformation response spectra for 1940 El-centro earthquake for different values of ζ
30. 30
Damping has a similar effect on pseudo acceleration. Note, however,
that the pseudo acceleration at a (near) zero period is the same for all
damping values.
Pseudo Acceleration Response Spectra for Different Damping
Values
This value is always
equal to the peak ground
acceleration, 0.319g, for
the ground motion in
question. i.e. El-centro
1940 earthquake
Pseudo Acceleration response spectra for 1940 El-centro earthquake for
different values of ζ
31. 31
Pseudo acceleration (A) Vs peak acceleration at top
The term Pseudo shall not be conceived by its meaning (i.e. false as
defined in English dictionaries). In fact it shall be taken as “an essence
similar effect to their relevant commodities ”
It can be observed from below graph that pseudo acceleration , A , and
peak value of true acceleration, have almost same values for systems
with Tn≤ 10 sec and .
It is worth mentioning that for elastic system the ζ seldomly exceed 5%
as such taking A same as negligible effect
t
o
u
0.1
ζ
t
o
u
Tn- sec
t
o
u
32. 32
Pseudo velocity (V) Vs peak system’s velocity
o
u
As shown in below graph that for medium rise buildings
(0.2≤ Tn ≤ 1 sec) as long as . Similarly
(0.2≤ Tn ≤ 3 sec) for
o
u
V
0.1
o
u
V
o
u
V
o
u
85
.
0
V
o
u
85
.
0
V
0.1
33. 33
Combined D-V-A spectrum
The deformation, pseudo-velocity and pseduo-acceleration
spectra are plotted for a wide and practical range of Tn and for a
particular value of ζ .
The above mentioned procedure is repeated for different values
of ζ.
The results for different values of ζ over a wide range of Tn are
combined in a single diagram, called combined D-V-A diagram, as
shown on next slide
34. 34 34
34
Use of D-V-A spectrum
Figure: Combined D-V-A response spectrum for El Centro ground motion; ζ = 2%.
Note the values of D,V and A determined for a SDOF system with Tn=2 sec
Refer to slides 29, 31 and 32 for D,V and A, respectively
35. 35 35
35
Combined D-V-A spectrum
Combined D-V-A response spectrum for El Centro ground motion; ζ = 0,5,10 and 20%
For a given earthquake, small variations in structural frequency
(period) can produce significantly different results (See V value
for Tn = 0.5 to3 sec for El-centro earthquake)
36. 36
Relation between peak Equivalent static force, fso , and
Pseudo acceleration, A
o
so
k.u
f
.m
ω
k
since 2
n
)
.u
m.(ω
.m).u
ω
(
k.u
f
o
2
n
o
2
n
o
so
m.A
fso
37. 37
Peak Structural Response from the response spectrum
As already discussed on previous slide, peak value of the equivalent
static force fso can be determined as:
mA
kD
f so
The peak value of base shear, Vbo, from equilibrium of above given
diagram can be written as:
m.A
f
V so
bo
38. 38
.w
g
A
.A
g
w
V
or bo
Where w is the weight of the structure and g is the gravitational
acceleration. When written in this form, A/g may be interpreted as
the base shear coefficient or lateral force coefficient . It is used in
building codes to represent the coefficient by which the structural
weight is multiplied to obtain the base shear
Peak Structural Response from the response spectrum
39. 39
The frame for use in a building is to be located on sloping ground as
shown in figure. The cross sections of the two columns are 10 in. square.
Determine the base shears in the two columns at the instant of peak
response due to the El Centro ground motion. Assume the damping ratio
to be 5%. The beam is too stiffer than the columns and can be assumed
to be rigid. Total weight at floor level = 10k
E = 3*103 k/in2
Problem M6.1
Solution
40. 40
5% Damped Elastic Displacement Response
Spectrum for El Centro Ground Motion
uo is decreasing with increase in Tn
0.67″
Solution (contd….)
Computing the shear force at the
base of the short and long columns.
g
76
.
0
ft/sec
51
.
24
)
12
/
67
.
0
(
/0.3
2
A
D
/T
2
A
7
6
.
0
D
u
2
2
2
n
o
Comments:
Although both columns go through equal deformation, however, the stiffer column
carries a greater force than the flexible column. The lateral force is distributed to the
elements in proportion to their relative stiffnesses. Sometimes this basic principle , if
not recognized in building design, lead to unanticipated damage of the stiffer elements.
41. 41
Response Spectrum normalized with peak ground parameters
thereby giving the amplification magnitudes for D,V and A e.g., for a
system with Tn = 0.5 sec and ζ =0.05. The amplification factors for
D,V and A are αD ≈ 0.2 , αV ≈ 1.9and αA≈2.3, respectively
Velocity amplification
factor
Acceleration amplification
factor
Displacement
amplification factor
D= ugo for
Tn>15 sec
go
u
A
u= -ug
u= 0
Very rigid systems
Very flexible systems
42. 42
Spectral regions in Response Spectrum
c
n
go
T
T
for
const.
u
A
Therefore region from Tn = 0
to Tc is defined Acceleration
sensitive region.
Same logic apply in
defining velocity sensitive and
displacement sensitive regions
43. 43
Design Spectrum
Response spectrum cannot be used for the design of new
structures, or the seismic safety evaluation of existing structures due
to the following reasons:
Response spectrum for a ground motion recorded during the past
is inappropriate for future design or evaluation.
The response spectrum is not smooth and jagged, specially for
lightly damped structures.
The response spectrum for different ground motions recorded in
the past at the same site are not only jagged but the peaks and valley
are not necessarily at the same periods. This can be seen from the
figure given on next slide where the response spectra for ground
motions recorded at the same site during past three earthquakes are
plotted
44. 44 44
44
Figure: Response spectra for the N-S component of ground motions recorded at the
imperial valley Irrigation district substation, El Centro, California, during earthquakes
of May 18,1949;Feb 9,1956;and April 8,1968; ζ = 2%.
Tn = 0.4 sec
1.75
3.0
4.8
45. 45
Design Spectrum
Due to the inappropriateness of response spectrum as stated on
previous slide, the majority of earthquake design spectra are
obtained by averaging a set of response spectra for ground motion
recorded at the site the past earthquakes.
If nothing have been recoded at the site, the design spectrum
should be based on ground motions recorded at other sites under
similar conditions such as magnitude of the earthquake, the
distance of the site from causative fault, the fault mechanism, the
geology of the travel path of seismic waves from the source to the
site, and the local soil conditions at the site.
46. 46
Design Spectrum
For practical applications, design spectra are presented as
smooth curves or straight lines.
Smoothing is carried , using statistical analysis, out to eliminate
the peaks and valleys in the response spectra that are not desirable
for design. For this purpose statistical analysis of response spectra is
carried out for the ensemble of ground motions.
Each ground motion, for statistical analysis is normalized (scaled
up or down) so that all ground motions have the same peak ground
acceleration, say ;other basis for normalization can be chosen.
go
u
47. 47
Construction of Design Spectrum
Researchers have developed
procedures to construct such design
spectra from ground motion
parameters. One such procedure is
illustrated in given figure.
The recommended period values
Ta = 1/33 sec, Tb = 1/8 sec, Te = 10
sec, and Tf = 33 sec, and the
amplification factors αA, αV , and αD
for the three spectral regions (given
table on next slide), were developed
by the statistical analysis of a larger
ensemble of ground motions
recorded on firm ground (rock, soft
rock, and competent sediments).
48. 48
Construction of Design Spectrum (Newmark-Hall method)
Newmark and Hall have developed procedures to construct
such design spectra from ground motion parameters. One such
procedure is illustrated in given figure.
50. 50
Construction of Design Spectrum (firm soil)
We will now develop the 84.1 percentile design spectrum
for ζ=5%
For convenience, a peak ground acceleration is
selected; the resulting spectrum can be scaled by η to obtain the
design spectrum corresponding to
The typical values of
, recommended for firm ground, are used. For , these
ratios give
g
1
ugo
ηg
ugo
6
u
u
*
u
and
in./sec/g
48
u
u
go
2
go
go
go
go
g
1
ugo
in
36
ugo
and
in/sec
48
ugo
51. 51
Using the values on
previous slide and values
given in table 6.9.2 (slide
53) for 84.1 percentile
and ζ =5%, the Pseudo-
velocity design spectrum
can be dawn as shown in
F i g u r e 6 . 9 . 4
3
.
2
v
71
.
2
A
01
.
2
D
Construction of Design Spectrum (firm soil)
52. 52
Displacement and Pseudo-acceleration design spectra can be drawn
from pseudo-velocity design spectrum using the relations being
already discussed and reproduced here for the convenience:
The Pseudo-acceleration and displacement design spectra drawn by
using above given equation are drawn in Figures 6.9.5 and 6.9.6 on
next two slides
n
n
n
n
T
2 π
V.
V ω
A
V
2 π
T
ω
V
D
Construction of Design Spectrum (firm soil)
53. 53
Construction of Design Spectrum (firm soil)
Acceleration sensitive region
Velocity sensitive region
Displacement
sensitive region
55. 55
Design Spectrum for various values of ζ
Pseudo- velocity design spectrum for ground motions with
; ζ = 1,2,5,10 and 20 %.
in.
36
u
and
in/sec,
48
u
,
1
u go
go
go
g
56. 56 56
56
Pseudo- acceleration design spectrum (84.1 th percentile) drawn on log scale for ground
motions with ; ζ = 1,2,5,10 and 20 %.
in.
36
u
and
in/sec,
48
u
,
1
u go
go
go
g
Design Spectrum for
various values of ζ
57. 57 57
57
57
57
Figure: Pseudo- acceleration design spectrum (84.1 th percentile) drawn on linear
scale for ground motions with ;
ζ = 1,2,5,10 and 20 %.
in.
36
u
and
in/sec,
48
u
,
1
u go
go
go
g
Design Spectrum for various values of ζ
58. 58
Envelope Design spectrum
For some sites a design spectrum is the envelope of two different
elastic design spectra as shown below
Site
Nearby fault producing
moderate EQ
Far away fault
producing large EQ
Site
Nearby fault producing
moderate EQ
Far away fault
producing large EQ
59. 59
(a) A full water tank is supported on an 80-ft-high cantilever tower. It is
idealized as an SDF system with weight w = 100 kips, lateral stiffness k =
4 kips/in., and damping ratio ζ = 5%. The tower supporting the tank is to
be designed for ground motion characterized by the design spectrum of
Fig. 6.9.5 scaled to 0.5g peak ground acceleration. Determine the design
values of lateral deformation and base shear.
(b) The deformation computed for the system in part (a) seemed excessive
to the structural designer, who decided to stiffen the tower by increasing
its size. Determine the design values of deformation and base shear for the
modified system if its lateral stiffness is 8 kips/in.; assume that the
damping ratio is still 5%. Comment on how stiffening the system has
affected the design requirements. What is the disadvantage of stiffening
the system?
Problem M6.2
60. 60
Design Spectra (Building code of Pakistan 2007)
T= natural time period, Ca and Cv= seismic zoning coefficients that depends on
soil type and Zoning factor, Z
65. 65
Base shear determination by static force method
(Building code of Pakistan 2007)
The total design base shear in a given direction shall be
determined from the following formula:
The total design base shear need not exceed the following:
The total design base shear shall not be less than the following:
In addition, for Seismic Zone 4, the total base shear shall also
not be less than the following:
Where V is Base shear, T= Fundamental natural time period, of structure
I= occupancy factor R= response modification factor (a measure of
ductility of structure) and W= Total weight of structure
66. 66
Determine the design values of lateral deformation and base shear for the
data mentioned in problem M 6.2. The tank is required to be constructed in
Zone 2B (as per BCP 07) on soil type SE. Consider elastic design and take
Importance factor, I= 1.0
Problem M6.3
67. 67
Solve following exercise problems (Chopra’s book, above
editions)
1. Problem 6.10
2. Problem 6.15
Further problem for practice:
6.12 to 6.14, 6.16 and 6.17
Problems for practice