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STRUCTURAL DYNAMICS IN BULDING CODES

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Title: STRUCTURAL DYNAMICS IN BULDING CODES


1
STRUCTURAL DYNAMICS IN BULDING CODES
2
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
  • .

3
International Building Code - USABase Shear
Vb csw where
Cs Ce Ce IC
R 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.

4
International Building Code - USALATERAL FORCES
Fj Vb
wjhkj
?ni1wihik Where K is a
coefficient related to the vibration period .

5
International Building Code - USAStory 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.
6
National Building Code of CanadaBase Shear
Vb csw
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

7
National Building Code of CanadaLATERAL FORCE
Fj
(Vb-Ft) wjhj

?ni1wihi with the exception that force at the
top floor is increased by an additional force ,
the top force, Ft .
8
National Building Code of CanadaSTORY 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.
9
EuroCode 8Base Shear
Vb csw
where Cs Ce / q

Ce
A/g
A/g (Tb / TI)-1/3
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.
10
EuroCode 8LATERAL FORCES

Fj Vb wj Fj1

?ni1wi FJ1 where Fj1 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

?ni1wihi
11
EuroCode 8STORY 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.
12
Fundamental Vibration Period Period formulae
used in IBC, NBCC and others codes are derived
out of Rayleighs method using the shape function
given by the static deflection, Ui due to a set
of lateral forces Fi at the floor levels.
13
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.

14
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.

15
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.

16
Design Process
  • Pre-dimensioning
  • Analysis.
  • Review.
  • Detailing.
  • Production of structural drawings.
  • Final Review.

17
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.
  • Contd

18
  • 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.

19
  • 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.

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24
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.

25
  • 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.

26
Earth quake Design Ground Motion
Earth quake Design ground 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.

27
  • 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
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  • 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

37
  • 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

43
  • The over turning moment at any storey MX is
    obtained from
  • MX ?n Fi (hi hx)
  • ix

44
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.

45
  • 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.

46
Seismic Design Provisions for Masonry in IBC
  • General.
  • The three basic characteristics to determine the
    buildings Seismic design category are
  • Building geographic location
  • Building function
  • Underlying soil characteristics
  • Categories A to F
  • Determination of Seismic Design Forces. Forces
    are based on
  • Structure Location
  • Underlying soil type
  • Degree of structural redundancy
  • System expected in elastic deformation capacity

47
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.

48
  • 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.

49
  • 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.

50
  • 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.

51
  • In Seismic Design Categories E and F, stack
    bonded masonry partition walls 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

52
  • Modeling of materials
  • Modeling of gravity loads
  • Modeling of structural elements
  • Flexural working
  • Soil foundation Flexibility
  • Floor diaphragm flexibility

53
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.

54
  • 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.

55
  • 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 compatibility
    at each floor level.

56
  • 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 beams and panels with occasional columns.

57
  • 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 walls stiffness
    from that of the un-cracked transformed section
    so that of the cracked transformed section.

58
  • Soil Foundation Flexibility.
  • Regardless of how the buildings foundation in
    modeled, the buildings periods of vibration
    significantly increase, and lateral force levels
    can change significantly.
  • If the buildings 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.

59
  • 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.

60
  • 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.

61
  • 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

62
  • 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.

63
Structural Dynamics in Binary Codes
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