PSG-Civil 22.03.2014 01

Indian Institute of Technology Delhi (IIT)
New Delhi, INDIA
Prof. T. K. Datta
Department of Civil Engineering,
Indian Institute of Technology Delhi
Saturday, 22nd, March 2014
IIT Delhi
1

IIT Delhi Structural Dynamics for Practicing Civil Engineers
2
Understanding
Dynamics and
SDOF

The excitation is a time-varying
force usually expressed as
Acceleration time history
Pressure time history
Force time history
Distinction between Static and
Dynamic Motions
Force is a
constant
Structure would respond to any “external
disturbance”
Forc
e
Buildi
ng
Respon
se
Displacement
Acceleration
Base Shear
Inter-storey drift
Stresses
In static
problems…
In Dynamic
problems…
Response is a
constant
Response is time-
varying
Response is
dependent only on
the static load
Response is dependent
on excitation force,
inertial force and
dissipative forces
2

4
In static problems…
Elastic properties, K
Inertial Properties, M
Dissipative Properties, C
Elastic Properties, K
ExcitationForce
Time
Time
Response
In Dynamic
problems…
Buildi
ng
Buildi
ng

5
How do we define the dynamic motion
of a building?

)(tPKxxCxM t
 
It all starts with this…
Or sometimes with this…
)(),( tPxxFxCxM t
 
6

Dynamic Force
Equilibrium
Equation
Let us consider a simple
case…
)(tPKxxCxM t
 
gXMtPKxxCxM   )(
7
Let us consider a simple
case…
Dynamic Force
Equilibrium
Equation
Let us try to understand its
each force components…

t
xMInertial Force
8
Inertial Force
Understanding Mass in a better
light…
Newton’s First Law of
Motion
All objects have the tendency to resist changes in their state of motion
This tendencyis called Inertia
maFI 
 JTI
What is
inertia?It is the resistance of an
object to change its state
of motion (magnitude and
direction)
An object at rest stays at rest and an object in
motion stays in motion with the same speed and in
the same direction unless acted upon by an
unbalanced force.
REST IS A STATE OF MOTION WITH
ZERO VELOCITY
D’Alembert's
Principle
Mass as a measureof
amountof inertia
Direction is
opposite to
that of
motion
On Dynamic
equilibrium
Mass moment
of Inertia
Inertial Force

Idealizatio
ns
9
Point of application of Inertial
force: At center of mass
If there was no concept
of inertia force then…
Ball would have
stopped here!
Galileo's
EXPERIMENTS
No loss of
energy due to
friction or other
means
Point
Particl
e
Rigid
Body
Deformable
Idealizatio
ns
Let’s see
Is this sufficient to define the dynamic
problem?
NOT
E

Dissipative
Force
10
xC Dissipative
Force
DissipativeForce
Velocity
n
D xF 
xcFD

For practical purposes, in the
analysis of buildings, a linear
relationship maybe assumed,
thus
This constant of proportionality, is
called the damping constant.
c
Viscous
Damping
In reality, the dissipative force
is a frequency-dependent
quantity.
It is hard to quantify
explicitly different
factors for energy loss.
Thus an approximate
model maybe chosen…
Exponentially
decaying (for
viscous damping)
Displacemen
t
Tim
e
NOT
E

11
Elastic
Force
Kx Elastic
Force
This maybe familiar to you
from the static analysis…
Nevertheless, this is also an
integral part of the dynamic
force equilibrium
Elastic
Force
Displace
ment
For a conventional building
we will assume it to have a
linear relationship.
NOT
E

12
It is now clear as to why M, C and K are
included in the part of your dynamic analysis of
a structure
Time-varying External
force or pressure
Time-varying
boundary/support condition
Recall
)( g
t
XxMxM  
Inertial force is the
product of inertial mass
and “absolute”
acceleration
Support
acceleration
How are dynamic forces induced in
the structure?
A
B

13
Earthquake Force
Wind Force
Blast Force
Force induced due
to time-varying
pressure on building
surface.
Force induced due
to time-varying
boundary condition.
Force induced due
to time-varying
blast wave pressure
on building surface
as well as ground
vibration.
Earthquake Force
Wind Force
Blast Force

14
A Schematic diagram for the
dynamic force equilibrium
equation
k1
c1
m1
X
Tim
e
Time
period, T
Amplitude
, A
Harmonic
Motion
t
T


2
tAx  sin
xAtA
dt
dx
x  cos
xAtA
dt
xd
x 22
2
2
sin 
NOT
E
Displacem
ent
Velocity
Accelerati
on
x
A
SDOF Spring-Mass-dashpot
system
SDOF Spring-Mass-dashpot
system
x

15
tAx  sin tAx  cos tAx  sin2
Earlier we noted
that…
xMFI
xCFD
KxFk 
We note that, if excitation frequency is increased
inertial and dissipative forces increase
 DF IF
The increase in inertial and dissipative forces due to
increase in excitation frequency do not necessarily mean that
responses of the building increases.
Increase in frequency do signify that inertial forces and
dissipative forces can no longer be ignored in the analysis of
a building  Problem can no longer be treated as static.
Earlier we noted
that…
Inertial
Force
Dissipative
Force
Elastic
Force

16
“Engineering judgment is key to
structural modelling”
We shall now see how the responses of a SDOF
system gets affected due to the dynamic
characteristics of a building

17
k
c
m
tp sin0
k
c
m 0p

n
D

Equation of motion for a viscous damped SDOF
system subjected to harmonic excitation
Equation of motion for a viscous damped SDOF
system subjected to harmonic excitation
Tim
e
Time
period,
Amplitude
, p0



2
T
For
ce
Harmonic
excitation
Mass of SDOF
system
Coefficient of
Stiffness
Coefficient of Damping
Amplitude of excitation
force
Angular frequency of excitation
Natural frequency of SDOF
system
Damped natural frequency of
SDOF system
Damping ratio
m
k
n  2
1  nD
 nmc 2
tpkuucum  sin0
0gu

18
Damped structure
Undamped structure
)0(u
t
e 

nT
dT
Displacem
ent
Time
Effect of damping
on free Vibration
 tBtAetu DD
tn
 
sincos)( )0(uA 
D
nuv
B



)0()0(
where,

19
Amplitu
de
 2TPeriod,
0)(
)(
stu
tu
Total
response
Steady-state
response
P
(a) Harmonic force;
(b) Response of
undamped system
subjected to
harmonic force; ω/ωn
= 0.2; u(0)=0; and
v(0) = (ωnp0)/k
tu
v
tutu nst
n
n 









 sin
1
)0(
cos)0()( 2
wt
ust
sin
1 2


Transi
ent
Steady-
state
k
p
ust
0

n


where,

2
0
DeformationResponse
Factor,Rd
1.0
0
180
Phase
Angle
Frequency
Ratio,
n
1.0
0
0
 0
0
st
d
u
u
R 
Deformation
response factor and
phase angle for an
undamped system
)sin(sin
1
)( 2
twt
u
tu n
st



0)0()0(  vuFor,
)sin()(  wtRutu dst
n for0
n for180

21
0)(
)(
stu
tu
Envelope
curve

nT
t
Response of
undamped system to
sinusoidal force of
frequency ω=ωn;
u(0)= v(0)=0

2
2
Transient Steady-State
0)(
)(
stu
tu
nT
t
Total
response
Steady-state
response
Response of damped
system to harmonic
force ω/ωn=0.2, ζ =
0.05 u(0)=0; and v(0)
=ωn p0/k
tu
v
tutu nst
n
n 









 sin
1
)0(
cos)0()( 2
)sin(
4)1( 2222


 wt
ust
Transi
ent
Steady-
state
k
p
ust
0

n


where,








 
2
1
1
2
tan
dampingofbecause)(,0when  tuc
nDnntw
st
t
e
u
tu n


 
andfor,cos
)1(2
)(At
resonance

2
3
2
1
2
1
0)(
)(
stu
tu
nT
t
Envelope
curve
Steady-state
amplitudes
Response of undamped
system with ζ = 0.05 to
sinusoidal force of
frequency ω=ωn; u(0)=
v(0)=0

2
4
Steady state
response of damped
system (ζ = 0.2 to
sinusoidal force for
three value of the
frequency ratio; (a)
= ω/ωn=0.5, (b)
ω/ωn=1, (c) ω/ωn=2
0)(
)(
stu
tu
0)(
)(
stu
tu
0)(
)(
stu
tu
nT
t
nT
t
nT
t
29.1dR
5.2dR
32.0dR
5.0 n
0.1 n
2 n

2
5
DeformationResponse
Factor,Rd
1.0
0
180Phase
Angle
Frequency
Ratio,
n
1.0
0
0
 0
0
st
d
u
u
R 
%01.0
10.0
20.0
70.0
00.1
Deformation response
factor and phase angle
for a damped system
excited by harmonic
force

2
6
Solution of SDOF system for sinusoidal excitation
consists of two parts: transient and steady state.
Transient response depends upon initial conditions u(0)
and v(0) and dies down with time for c ≠ 0 ; when c =0,
transient response continues forever.
If there were no inherent damping in the structure, all
structures would have failed due to continuous
oscillation (fortunately, this is not so!)
Steady state response is of interest for c≠0
Some important Observation from SDOF
subjected to Harmonic excitation…
1/
8

Steady state response is sinusoidal like excitation but
with a phase lag ϕ.
Amplitude of response = static response × DAF; ϕ
depends upon ω/ωn and damping.
DAF Vs ω/ωn for displacement, velocity and
acceleration (Rd, Rv and Ra) reveal many interesting
dynamic behaviour of structures.
The relation between Ra, Rd, Rv i.e. Rv = (ω/ωn) Rd and Ra
= (ω/ωn)2Rd makes it possible to plot them in a single
graph in four way logarithmic plot.
2
6
2/
8

2
8
Characteristics of Rd Vs ω/ωn
() plotMaximum value of Rd takes
place not at ω=ωn but at
2
21 n
2.0
DAF 
> 1 0.5 to 1.35
≈ 1 0.5
< 1 1.35
< 0.25 >>2


2
1
dR
For rational
damping ratio,
3/
8

2
9
At resonance ф = 900 ;  >2, ф 1800 and  <0.5, ϕ  0.
At resonance, damping force predominates and equilibrates the
external force.
As a thumb rule, frequency of SDOF should be designed such
that  should not lie within the bound given by 0.75 ≤  ≤ 1.25;
effect of damping is very significant within this range.
Effect of damping becomes insignificant for  >1.5
4/
8

3
0
Characteristics of Rv
Vs Maximum value of Rv takes place at ω=ωn
and
0.2 
• As a thumb rule, for
tow DAF  should not
fall within
0.75<<1.25 ; effect
of damping is very
significant within this
range.
• Effect of damping
becomes insignificant
for >1.6.


2
1
maxvR
For rational damping ratio,
DAF 
> 1 0.75 to 1.6
<1 < 0.75
< 1 > 1.6
< 0.35 > 2.5
2.0
5/
8

31
Characteristics of
Ra Vs 
Maximum value of Ra takes place not at ω=ωn,
but at
• As a thumb rule,
for low DAF  should
not fall within 0.8< 
<1.5 ; effect of
damping is very
significant within
this range.
• Effect of
damping becomes
insignificant for  >
2
For rational value of
DAF 
> 1 0.75
1 >3
< 1 > 0.75
2.0
2
21 

 n


2
1
maxaR
6/
8

3
2
Characteristics of TR Vs 
TR denotes the fraction of the vibratory force
transmitted to the foundation when an isolator is in
between the force and the foundation.
For rational damping, 2.0 DAF 
> 1 0.5 to 1.4
<1 >2
<< 1 > 3
7/
8

3
3
For practical design, it is better to avoid the range of 
as 0.75<  <1.3
(TR)max is at  =1.
TR also denotes the transmission of ground acceleration
to the rigid mass attached to a spring dash pot system
(idealization of isolator).
The same characteristics hold good.
8/
8

3
4
Modelling of
Buildings

BED ROCK
Primary members resisting seismic forces-
Columns (Imposed design consideration)
Understanding the deformation profile
Assessing the independent dynamics degrees of
freedom
35
Modelling of BuildingModelling of Building

BED ROCK
Primary members resisting seismic forces-
Columns (Imposed design consideration)
Understanding the deformation profile
Assessing the independent dynamics degrees of
freedom
36

BED ROCK
Primary members resisting seismic
forces- Columns (Imposed design
consideration)
Understanding the deformation
profile
Assessing the independent dynamics
degrees of freedom
3
7
Modelling of
Building
Modelling of Building

Primary members resisting seismic
forces- Columns (Imposed design
consideration)
Understanding the deformation
profile
Assessing the independent
dynamics degrees of freedom
3
8
Modelling of
Building

3
9
In reality a structure will
have infinite degrees of
freedom.
NOT
E
Modelling of
Building

For practical purposes, one degree
of freedom is needed to be
considered at each floor level.Mass should be attached to
dynamic D.O.F.
D.O.F. other than dynamic D.O.F.
are condensed out.
Point mass lumping does
not have MI.
Floor is assumed to be rigid in its own
plane
4
0
Modelling of
Building

3
12
L
EI
F


3
12
L
EI
F


2
6
L
EI
M


2
6
L
EI
M


For unit lateral
displacement, 1
In one single column…
41

k1 k2
m1 m2
1k
2k
1m
2m









211
11
kkk
kk
K






2
1
0
0
m
m
M
31
12
L
EI
k 
4
2
Modelling of
Building

1k
2k
1m
2m
k1
c1
k2
c2
m1 m2
1c
2c
31
12
L
EI
k 









211
11
kkk
kk
K






2
1
0
0
m
m
M
1 2
1
Rayleigh’s
Damping
KMC 
4
3







2
1
x
x
X
Modelling of
Building

Understanding the degrees
of freedom in a 3-
Dimensional model
4
4
Modelling of
Building

Understanding the degrees
of freedom in a 3-
Dimensional model
Center of
mass
4
5
Modelling of
Building

CM
The floor slab is assumed to be rigid
and the total mass of the floor is
lumped at its center of mass.
Dynamic D.O.F. are considered at
center of mass.
The stiffness matrix written in terms
of nodal D.O.F. is condensed to the
stiffness matrix corresponding to the
D.O.F. at center of mass using
transfer matrix.
Modeling in STAAD.Pro is different.
Dynamic D.O.F = 3N (N = No. of Storey)
D.O.F at each node
CM
CM
x
yθz
4
6
Modelling of
Building

When to go for 3D analysis?
2D
47Asymmetri
c
Symmetric
3D 3D

Center of
mass
Center of
rigidity
Inertial forces acts at the center of
mass.
Center of rigidity is the point through
which a force, if applied, will produce only
a translation motion in that direction.
4
8
Asymmetric
Building

Coupling between D. O. F at
center of mass.
3D analysis is done unless it is
torsionally very stiff.
For translational component of
ground motion, there is
torsion.ith floor
Shear
wall
Core wall
Center of
mass
Center of
rigidity
xe
ye
4
9
Asymmetric
Building

CG of CM lines vertically
eccentricity
Translation mass and mass moment
of inertia are lumped at floor
levels on CG of CM lines
Asymmetric
Building
CG of CM
lines
CMCR
CM CR
5
0

Center of
mass
No coupling between D.O.F. at
center of mass.
Can be easily analyzed with 2D
approximation.
For translational component of
ground motion, no torsion.
51
Symmetric Building

Asymmetric Buildings undergo
torsion.
Symmetric Buildings also undergo
torsion because of:
• Lack of correlation of wind
forces on the face of the wall
(Time lag Effect)
• Torsional component of
ground motion.
• Accidental eccentricity
Center of
mass
Symmetric Building
Not
e
5
2

Observations on Asymmetric Building
Stiffer sections will
carry more load
Loads are shared according to the stiffness of elements.
Extent of torsion decides the distress of corner columns and edge
columns. Corner column is subjected more stresses.
1
2
C1
C2
21
Center of mass
Center of rigidity
C1 and C2 are columns of same stiffness.
 12
C2 is stressed more than C1
53

Positioning of the core and shear walls in the building decides the
asymmetry and torsional stiffness of the building.
 Torsionally
stiff but
symmetric
 Torsionally
stiff but
Asymmetric
3
5
4
Observations on Asymmetric Building

Assumptions
The springs are linear.
Both yawning and lateral deformation of foundation on the soil is considered.
Soil is homogeneous.
BED ROCK BED ROCK
In soft soil
Radiation important
Full analysis
Substructure analysis
with iteration
5
5
Soil-Structure
Interaction

5
6
BED ROCK
Understanding the motion
kh
ch
kv cv
kθ
cθ
Spring-dashpot model
for foundation
Soil-Structure
Interaction

BED ROCK
Free-field
ground motion
Kinematic
InteractionInertial
Interaction
Ground motions maybe
amplified at surface
with respect to the bed
rock.
Radiation
Soil-Structure
Interaction

5
8
Response
Analysis

5
9
)(tPKxxCxM t
 
Coming back to the governing
differential equation of motion…







2
1
x
x
X
Coming back to the governing
differential equation of motion…
How do we now solve
this?
t
X
x
X
“Absolute”
acceleration
“Relative” velocity w.r.t.
support/ground
“Relative” displacement w.r.t.
support/ground

6
0
How do we now solve
this?
How do we now solve
this?
Solving the equation yields us the required response
quantity of interest: acceleration, velocity and
displacement in the building
Basically, we are just solving
a differential equation
NOT
E
Modal Analysis
(Based on Normal Mode
Theory)
Numerical Integration Methods
METHODS

61
Physical Model Modal Model
Physical
Space
Modal Space
k1
c1
k2
c2
m1 m2
1,, 11 
222 ,, 
Coupled in physical
space
Decoupled in modal
space
Equations will need to be
solved simultaneously in
physical space
Equations can be solved individually
in modal space and later on be
transformed back into physical space
in a “simple manner”
Modal Analysis
Theory)
Modal Analysis
Theory) 


M
C
K

6
2
BED ROCK
Physical World
Assumptions
Building remains elastic during the excitation.
One lateral degree-of-freedom at each floor level is
considered.
Columns are inextensible and weightless.
Building is classically damped.
1,, 11  222 ,, 
Modal World
)(and 2121 
For 2 D.O.F. there
will be two natural
frequencies
NOT
E
Buildi
ng
Buildi
ng

6
3
More on mode
shapes…
Each natural frequency has an associated mode shape.
Free vibration shape of the structure in a natural
frequency is called mode shape of the structure.
When pulled laterally and allowed to go it vibrates in
frequency 1 called fundamental frequency of vibration.
In order to make it vibrate in frequency 2, more
energy is required. So when allowed to vibrate freely it
vibrates in 1It is difficult to make the structure vibrate only in
second mode/nth mode.
However by resonance test, it is possible to make the
structure vibrate almost (nearly) in the nth mode for
many structures.
For N D.O.F. there will be N natural frequencies
and mode shapes
More on mode
shapes…

6
4
3rd Mode1st Mode
1
2nd Mode
2
3
1st Mode
2nd Mode
3rd Mode
Tall chimneys/Frames may have
widely Spaced frequencies
Suspension bridge may have
closely spaced frequencies
Mode Shapes-
Chimney/Frame/Suspension Bridge
Mode Shapes-
Chimney/Frame/Suspension Bridge

6
5
1 3 42
Symmetric
Symmetric
1st Mode-
X dir
3rd Mode-
X dir
2nd Mode-
Y dir
4th Mode-
Y dir
X
Y
Mode Shapes-
Asymmetric Building
Mode Shapes- Symmetric
Building

6
6
X Y θ
1st mode (ω1)
Coupled mode
Closely spaced frequencies
X Y θ
2nd Mode (ω2)
X
Y
Center of
mass
Center of
rigidity
Mode Shapes-
Asymmetric Building
Mode Shapes-
Asymmetric Building

6
7
)(tPKxxCxM t
  








211
11
kkk
kk
K






2
1
0
0
m
m
M







2221
1211
cc
cc
KMC
Coupling terms
By using Eigen
value analysis
Eigen vectors (mode
shapes),
Eigen values (Natural
frequencies),
These Eigen vectors are then used to transform the
physical model to modal model by pre- and post-multiply
the equations of motions to yield decoupled equations of
motion
Let’s find out how to calculate the
mode shapes and natural
frequencies first…
How do we decouple the coupled
equations of motion ?
How do we decouple the coupled
equations of motion ?

2


6
8
0 KxxMThus,
When a structure vibrates freely in any of its modes of vibration,
every point of the structure undergoes a SHM with a frequency
equal to the natural frequency of that mode. So, it is possible to
write
tXX  sin0







2
1
x
x
X







20
10
0
x
x
X
Thus the equation of motion
becomes 000
2
 KxXM
oMXKx 0
oIXKxM 
0
1
)( 1
IMM 

Pre-multiplying with M-1 we get
wher
e
oXAx 0
2

Classical Eigen
Value Problem
NOT
E
Eigen values and Eigen
vectors of matrix A give
the natural frequencies
and mode shapes of the
structure.
Number (n) of natural
frequencies and mode
shapes is equal to the
size of matrix A.
As we stated earlier, free vibration of a
structure gives the mode shapes…
As we stated earlier, free vibration of a
structure gives the mode shapes…

6
9
Mode shapes and natural frequencies are the two key
dynamic characteristics of structures. They are used to
study and analyse the response of structures to dynamic
loads.
Mode shapes of structure may be compared with human
moods which display intrinsic human characteristics
DancingSingin
g
Compromisi
ng
Talkativ
e
Dynami
c
Aggressive
Response
to
Disturba
nce
More…More…

7
0
In other words, response of a structure to dynamic force
is a weighted summation of its mode shapes.
In a similar way, a structure responds to any dynamic
disturbance by combining its natural modes of vibration in
different proportion.
Responds to disturbance by combining different
characteristics (moods) in different proportion, say,
aggression is having maximum weightage.
1 2
)(1 tq )(2 tq)(tx
Weighing
functions
)()()( 2211 tqtqtx 
This theory is called
Normal mode theory
of dynamics
More…More…

71
This theory is called Normal mode theory of
Dynamic analysis.
Most popular but valid for linear classically damped
system.
Most attractive feature of the normal mode theory is that
is converts the solution of a MDOF system to the
summation of the solutions of a number of SDOF systems.
This is possible because of the orthogonal property of
mode shapes.
More…More…







2
1
0
0
m
m
MT








 2
2
2
1
0
0
KT Mode shape, is mass-
normalized
if
NOT
E
: There are no more coupling
terms

7
2
 q
x
x
tx })(
2
1








                 )(tPqKqCqM TTTT
 
iiii pqkqcqm  
iiii pqkqcqm  
     Cc T
i
     Mm T
i
     Kk T
i
whe
re
Each equation represents a
SDOF
Solution of SDOF to dynamic excitation is
straight forward.
More…More…
    )()({)( 2211 tqtqqtx 
      21 
Back to
physical space
with…

7
3
For earthquake excitation each SDOF (modal
equation)
For earthquake excitation each SDOF (modal
equation)
g
T
iiii xMIqkqcqm  
giiii xqqq   2
2
2
i
i
i
m
k
  iii mc 2
rir
rir
i
m
m
2
factorionparticipatMode



ωi determines dynamic magnification for
the mode
NOTE
Normal mode theory reduces
the size of the problem.
Normal mode theory gives
better insight into the
response of the structure
through the modal behavior
and its contributions.
Mode shapes and
frequencies are also used
for damage detection.
Modal
Participation for
first mode = ~90%
(for stiff buildings)
NOT
E

7
4
Tips for
Designers

7
5
Symmetric buildings may under go torsion under
earthquake and wind excitation because of
• Accidental (uncertain) eccentricity.
• Torsional component of ground motion.
• Kinematic interaction of foundations with
soil.
• Lack of Spatial Correlation
Salient
Points
Salient
Points

7
6
Asymmetric buildings have generally closely
spaced frequencies and coupled modes; pure
torsional / pure translational modes are hardly
present; more number of modes are required to
get good response.
For asymmetric buildings, corner and edge
colums are stressed more; the degree depends
upon the torsional response.
Salient
Points
Salient
Points

7
7
Shear walls / core walls relieve column stresses
and are beneficial for reducing torsional
response.
Core walls may undergo significant warping
stresses.
Drifts are more towards the bottom storey.
Higher modes contribute significantly to the
bending stress.
Salient
Points
Salient
Points

7
8
More number of modes are excited in hard soil
as compared to soft soil.
Mat foundation tends to alter the free field
ground motion leading to somewhat different
dynamic behaviour than anticipated.
Buildings may undergo considerable rocking
motion (in relatively soft soil) and hence,
deflection and stresses in members may be more
than anticipated.
Salient
Points
Salient
Points

7
9
For tall buildings wind induced acceleration at
the top storey levels is of great concern.
Ductility demand is high near the bottom storey
of the buildings.
For taller buildings the ductility demand is
generally less in the middle storeys compared to
the upper and lower storeys.
Salient
Points
Salient
Points

8
0
Deviation of storey ductility from the assumed
ones increases for taller buildings.
Rotation at the joints are actually limited by
infill panels, therefore, full ductility may
______________________?
Bidirectional interaction effect alters the
yielding and ductility of column elements that
are generally envisaged; floor acceleration could
also be of concern in certain cases.
Salient
Points
Salient
Points

8181
Effect of blast is more at lower levels; taller
structures have less effects.
Behaviour of buildings could be different in soft
soil; relatively tall buildings may be more
effected in soft soil.
Buildings which are irregular in plan have
complex dynamic behaviour both due to wind and
earthquake.
Out of plane failure of brick walls is of more
concern in masonry constructions / for infill
panels.
Salient
Points
Salient
Points

8
2
Thank You

PSG-Civil 22.03.2014 01

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