Transcript Document

STRUCTURAL DYNAMICS IN
BULDING CODES
BUILDING CODES : ANALYSES
STATIC ANALYSIS
• Structures be designed to resist specified static lateral
forces related to the properties of the structure and
seismicity of the region.
• Formulas based on an estimated natural period of
vibration are specified for base shear and distribution of
lateral forces over the height of the building.
• Static analysis provides the design forces including
shears and overturning moments for various stories.
DYNAMIC ANALYSES
•
•
RESPONSE SPECTRUM ANALYSIS
RESPONSE HISTORY ANALYSIS
International Building Code - USA
Base Shear
where
Vb
=
Cs = Ce
R
&
c sw
Ce= IC
Cs corresponding to R = 1 is called the elastic seismic coefficient
W = total dead load and applicable portions of other loads
R = 1.0
I = 1.0, 1.25 or 1.5
C depends on the location of structure and the site classes defined
in the code accounting for local soil effects on ground motion. C is
also related to pseudo-acceleration design spectrum values at short
periods and and at T = 1 second.
International Building Code - USA
LATERAL FORCES
Fj
=
k
Vb wjh j
n
∑ wihik
i=1
Where K is a coefficient related to the vibration period .
International Building Code - USA
Story Forces
The design values of story shears are determined by static
analysis of the structure subjected to the lateral forces;
the effects of gravity and other loads should be included.
Similarly determined overturning moments are multiplied
by a reduction factor J defined as follows: J = 1.0 for top
10 stories; between 1.0 and 0.8 for the next 10 stories
from the top; varying linearly with height; 0.8 for
remaining stories.
National Building Code of Canada
Base Shear
Vb
=
c sw
where
Cs = Ce U
&
Ce = vSIF
R
U= 0.6 Calibration Factor
zonal velocity
v = 0 to 0.4
Seismic importance factor I = 1.5, 1.3, 1.0
Foundation factor
F = 1.0, 1.3, 1.5, or 2.0
Seismic response factor S varies with fundamental
natural vibration period of the building. Canada is divided
in 7 velocity and acceleration related seismic zones
National Building Code of Canada
LATERAL FORCE
Fj
= (Vb-Ft)
wjhj
n
∑ i=1wihi
with the exception that force at the top floor is increased
by an additional force , the top force, Ft .
National Building Code of Canada
STORY FORCES
The design value of story shears are determined by
static analysis of the structure subjected to these
lateral forces. Similarly determined overturning
moments are multiplied by reduction factors J and
Ji at the base and at the i th floor level.
EuroCode 8
Base Shear
Vb
=
c sw
Cs = Ce / q’
Ce = A/g
-1/3
= A/g {(Tb / TI) }
q’ = 1+(T1 / Tb) (q-1)
= q
Seismic behavior factor q varies between 1.5 and 8
depending on various factors including structural
materials and structural system.
where
EuroCode 8
LATERAL FORCES
Fj = Vb
wj Φj1
∑ni=1wi ΦJ1
where Φj1 is the displacement of the jth floor in the
fundamental mode of vibration. The code permits linear
approximation of the this mode which becomes:
Fj = Vb
wjhj
∑ni=1wihi
EuroCode 8
STORY FORCES
The design values of story shears, story overturning
moments, and element forces are determined by static
analysis of the building subjected to these lateral forces;
the computed moments are not multiplied by a reduction
factor.
FUNDAMENTAL VIBRATION PERIOD
Period formulae used in IBC, NBCC and others codes
are derived out of Rayleigh’s method using the shape
function given by the static deflection, Ui due to a set
of lateral forces Fi at the floor levels.
ELASTIC SEISMIC COEFFICIENT
• Elastic seismic coefficient Ce is related to the
pseudo – acceleration spectrum for linearly elastic
systems.
• The Ce and A/g as specified in codes are not
identical.
• The ratio of Cc  A/g is plotted as a function
of period and it exceeds unity for most
periods.
CONCLUSION
 There can be major design deficiencies, if the
building code is applied to structures whose
dynamic properties differ significantly from
these of ordinary buildings.
 Building codes should not be applied to special
structures, such as high-rise buildings, dams,
nuclear power plants, offshore oil- drilling
platforms, long spane bridges etc.
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REQUIREMENT OF RC DESIGN
• Sufficiently stiff against lateral displacement.
• Strength to resist inertial forces imposed by
the ground motion.
• Detailing be adequate for response in
nonlinear range under displacement reversals.
15
DESIGN PROCESS
• PRE-DIMENSIONING
• ANALYSIS.
• REVIEW.
• DETAILING.
• PRODUCTION OF STRUCTURAL
DRAWINGS.
• FINAL REVIEW.
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REQUIREMENT FOR STRUCTURAL RESPONSE
STIFFNESS
•
Stiffness defines the dynamic characteristics of the
structure as in fundamental mode and vibration
modes.
•
Global and individual members stiffness affects other
aspects of the response including non participating
structural elements behavior, nonstructural elements
damage, and global stability of the structure.
17
STRENGTH
The structure as a whole, its elements and cross
sections
within
the
elements
must
have
appropriate strength to resist the gravity effects
along with the forces associated with the
response to the inertial effects caused by the
earthquake ground motion.
18
TOUGHNESS
The term toughness describes the ability of the reinforced
concrete structure to sustain excursions in the non linear
ranges of response without critical decrease of strength.
19
SEISMIC DESIGN CATEGORIES
•
CATEGORY A: Ordinary moment resisting frames.
•
CATEGORY B.
•
Ordinary moment resisting frames.
•
Flexural
members
have
two
continuous
longitudinal bars at top & bottom
•
Columns having slenderness ratio of 5 or less
•
Shear design must be made for a factored shear
twice that obtained from analysis.
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• CATEGORY C.
• Intermediate moment frames.
• Chapter 21 of ACI 318 implemented.
• Shear walls designed like a normal wall.
• CATEGORY D, E AND F.
• Special moment frames
• Special reinforced concrete walls.
25
Earth
Earth
quake
quake
Design
Design
Ground
ground
Motion
Motion
•
Maximum Considered Earthquake and
Design Ground Motion

For most regions, the minimum considered earthquake
ground motion is defined with a uniform likelihood of
excudance of 2% in 50 years (approximate return period of
2500 years).

In regions of high seismicity, it is considered more
appropriate to determine directly maximum considered
earthquake ground motion base on the characteristic
earthquakes of these defined faults multiplied by 1.5.
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 Site Classification
 Where
Vs
= average shear wave velocity.
N
= average standard penetration resistance.
Nch
= average standard penetration -
resistance for cohesiveless
soils.
Su
= average un-drianed shear
strength in cohesive soil.
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 All ordinates of this site specific response spectrum
must be greater or aqual to 80% of the spectural
value of the response spectra obtained from the
umpped values of Ss and Si, as shown on previous
slide.
 Use Groups.
As per SEI/ASCE 7-02.
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 Required Seismic Design Category
The structure must be assigned to the most
severe seismic design category
obtained from.
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Reinforced concrete lateral Force – Resisting Structural
System

Bearing Wall.
Any concrete or masonry wall that
supports more than 200 lbs/ft of vertical loads in addition to
its own weight.

Braced Frame.
An essentially vertical bent, or its
equivalent of the concentric or eccentric type that is
provided in a bearing walls, building frame or dual system
to resist seismic forces .

Moment frame.
A frame in which members and joints
are capable of resisting forces by flexure as well as along the
axis of the members.
Contd
36
 Shear Wall.
A wall bearing or non bearing
designed to resist lateral seismic forces acting on
the face of the wall.
 Space Frame.
A structural system composed of
inter connected members. Other than bearing
walls, which are capable of supporting vertical
loads and, when designed for such an application,
are capable of providing resistance to seismic
forces.
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
The approximate fundamental building period Ta is seconds
is obtained
Ta = C1 hxn
42

The over turning moment at any storey MX is obtained from
MX = ∑n Fi (hi – hx)
i=x
43
Reinforced Brick Masonry

Allowable stress design provisions for reinforced masonry
address failure in combined flexural and axial compression
and in shear.

Stresses in masonry and reinforcement are computed using
a cracked transformed section.

Allowable tensile stresses in deformed reinforcement are
the specified field strength divided by a safety factor of 2.5.

Allowable flexural compressive stresses are one third the
specified compressive strength of masonry.
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
Shear stresses are computed elastically, assuming a
uniform distribution of shear stress.

If allowable stresses are exceeded, all shear must be
resisted by shear reinforcement and shear stresses in
masonry must not exceed a second, higher set of allowable
values.
45
Seismic Design Provisions for Masonry in IBC

General.

The three basic characteristics to determine the building’s
“Seismic design category” are

Building geographic location

Building function

Underlying soil characteristics

Categories

Determination of Seismic Design Forces.
A to F
Forces are based
on

Structure Location

Underlying soil type

Degree of structural redundancy
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Seismic related Restriction on Materials

In seismic Design categories A through C, no additional
seismic related restrictions apply beyond those related to
design in general.

In seismic design Categories D & E, type N mortar and
masonry cement are prohibited because of their relatively
low tensile bond strength.

Seismic Related Restrictions on Design Methods

Seismic Design Category A.
Strength
design,
allowable stress design or empirical design can be used.
47

Seismic Design Category B and C elements that are part of
lateral force resisting system can be designed by strength
design or allowable stress design. Non-contributing
elements may be designed by empirical design.

Seismic Design Category D, E and F.
Elements that are
part of lateral force resisting system must be designed by
either strength design or allowable stress design. No
empirical design be used.
48

Seismic Related Requirement for Connectors.

Seismic Design Category A and B.
No
mechanical
connections are required between masonry walls and
roofs or floors.

Seismic Design Category C, D E and F. Connectors are
required to accommodate story drift.

Seismic Related Requirements for Locations and Minimum
Percentage of Reinforcement

Seismic Design Categories A and B. No restriction .

Seismic Design Category C.

In Seismic Design Categories A and B. No requirement.
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
In Seismic Design category C, masonry partition walls must
have reinforcement meeting requirements for minimum
percentage and maximum spacing. Masonry walls must
have reinforcement with an area of at least 0.2 sq in at
corners.

In seismic design category D, masonry walls that are part of
lateral
force-resisting
system
must
have
uniformly
distributed reinforcement in the horizontal and vertical
directions with a minimum percentage of 0.0007 in each
direction and a minimum summation of 0.002 (both
directions). Maximum spacing in either direction is 48 in.
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
In Seismic Design
Categories E and F, stack bonded
masonry
walls
partition
have
minimum
horizontal
reinforcement requirements.

Analysis Approaches for Modern U.S. Masonry

Analysis of masonry structures for lateral loads, along or in
combination with gravity loads, must address the following
issues.

Analytical approaches

Elastic vs. inelastic behavior

Selection of earthquake input

Two dimensional vs. three dimensional behavior
Contd
51

Modeling of materials

Modeling of gravity loads

Modeling of structural elements

Flexural working

Soil foundation Flexibility

Floor diaphragm flexibility
52
Overall Analytical Approach

Hand type approaches usually emphasize
the plan
distribution of shear forces in wall elements.

Hand methods are not sufficiently accurate for computing
wall movements, critical design movements can be
overestimated by factors as high as 3.

Elastic vs Inelastic Behavior

Flexural yielding or shear degradation of significant
portions of a masonry structure in anticipated, inelastic
analysis should be considered.
53

In many cases, masonry structures can be expected to
respond in the cracked elastic regime, even under extreme
lateral loads.

Selection of Earthquake Input.
Because structural response in generally expected to be
linear elastic, linear elastic response spectra are sufficient.
54

Two Dimensional vs three Dimensional Analysis of Linear
Elastic Structures
In two dimensional analysis, a building is modified as an
assemblage of parallel plan as frames, free to displace
laterally in their own planes only subject to the
requirement
of
lateral
displacements
compatibility
between all frames at each floor level.
In the “Pseudo three dimensional” approach, a building is
modeled as an assemblage of planar framers, each of
which is free to displace parallel and perpendicular to its
own place. The frames exhibit lateral displacement
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compatibility at each floor level.

Modeling of Gravity Loads
Gravity loads should be based on self weight plus an
estimate of the probable live load.
A uniform distribution of man should be assumed over
each floor except exterior walls.

Modeling of Material Properties
Material properties should be estimated based on test
results.
A poisson's ratio of 0.35 can be used for masonry.

Modeling of Structural Elements
 Masonry wall buildings are normally modeled using
56
beams and panels with occasional columns.

Flexural Cracking of Walls
 Flexural Cracking Criterion.
The cracking movement
for a wall should be determined by multiplying the
modulus of rapture of the wall under in plane flexure, by
the section modulus of the wall.
Consequences of Flexural Cracking of walls. Flexural
cracking reduces the wall’s stiffness from that of the uncracked transformed section so that of the cracked
transformed section.
57

Soil Foundation Flexibility.
Regardless of how the building’s foundation in modeled,
the building’s periods of vibration significantly increase,
and lateral force levels can change significantly.
 If the building’s foundation is considered flexible the
resulting increase in support flexibility at the basis of wall
elements causes their base movement
to decrease
substantially.

In –Plane Floor Diaphragm Flexibility
Structures in general an often modeled using special
purpose analysis programs that assume that floor
diaphragms are rigid in their own planes.
58
Many masonry wall structures
have floor slabs with
features that could increase the affects of in-plane floor
flexibility.
Small openings in critical sections of the floor slab.
Rectangular floor plans with large aspect ratios in plan.
Variations of in-plane rigidity with in slab.

Explicit Inelastic Design and Analysis of Masonry Structures
Subjected to Extreme Lateral loads.
If in elastic response of a masonry structure is anticipated,
a general design and analysis approach involving the
following steps in proposed.
59
Select a stable collapse mechanism for the wall, with
reasonable inelastic deformation
demand in hinging
regions.
Using general plans section theory to describe the flexural
behavior
of
reinforced
masonry
elements,
provide
sufficient flexural capacity and flexural ductility in hinging
regions.
Using a capacity design philosophy, provide wall elements
with sufficient shear capacity to resist the shear consistent
with the development of intended collapse mechanism.
60
Using reinforcing details from current strength design
provisions detail the wall reinforcement to develops the
necessary strength and inelastic deformation capacity.

Inelastic Finite Element Analysis of Masonry Structure
In the absence of experimental data, finite element
analysis in the most viable method to quantify
the
ductility and post peak behavior of masonry structures
61
The load – deformation relation of a masonry components
obtained from a finite element analysis can be used to
calibrate structural component models which can in turn
be used for the push over analysis or dynamic analysis of
large structural systems.
62
Structural Dynamics in Binary Codes
Beam
Shear
CANADA
IBC
Euro Code
Vb=csw
Vb=csw
Vb=csw
Where Cs=Ce U
R
Ce = ‫ע‬SIF
Where U=0.6
‫ =ע‬0 to 0.4
i= 1.3 or 1.5
S=fundamental natural
vibration period
Lateral
Forces
Fj=(Vb-Ft) wjhj
∑Ni=1wihi
Where Cs=Ce
R
Ce= IC
W= total dead load
R=1
I = 1.0, 1.25 or 1.5
CS= seismic coefficient
Ce =
Elastic seismic coefficient
Where Cs=Ce
Fj=Vb
Fj= Vb
wjhj
∑Ni=1wihik
Where K= coefficient related to
the vibration period T1
θ’
Cc= A/g
A/g {1+0.5r[1-(Tc /TI)]}
θ’ = { θ 1+(T1/Tb)(θ -1)}
Where θ varies from 1 to 4
wj Φj1
∑Ni=1wi ΦJ1
Code Allows Linear approx.
Fj=Vb
wjhj
∑Ni=1wihi
Storey
Forces
J=Reduction Factor for over
turning moments
J=Reduction Factor for over turning
moments 1 to 0.8
Computed over tuning moments are not
reduced