STRUCTURAL DYNAMICS IN BULDING CODES. BUILDING CODES : ANALYSES STATIC ANALYSIS Structures be designed to resist specified static lateral forces related.

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 ShearVb = 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.

International Building Code - USA

LATERAL FORCES

Fj

= Vb wjh

kj

∑

n

i=1wihi

k

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 ShearVb = 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

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 8Base Shear

Vb = csw

where Cs = Ce / q’ Ce = A/g = A/g {(Tb / TI)

-1/3}

q’ = 1+(T

1 / T

b) (q-1)

= qSeismic behavior factor q varies between 1.5 and 8 depending on various factors including structural materials and structural system.

EuroCode 8LATERAL FORCES

Fj = Vb wj Φj1

∑n

i=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

∑n

i=1wihi

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.

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 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.

ELASTIC SEISMIC COEFFICIENT

14

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.

CONCLUSION

15

• 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.

REQUIREMENT OF RC DESIGN

16

• PRE-DIMENSIONING

• ANALYSIS.

• REVIEW.

• DETAILING.

• PRODUCTION OF

STRUCTURAL DRAWINGS.

• FINAL REVIEW.

DESIGN PROCESS

17

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

REQUIREMENT FOR STRUCTURAL RESPONSE

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.

24

• 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.

SEISMIC DESIGN CATEGORIES

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

• 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.

Earth quake Design Ground MotionEarth quake Design ground Motion

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.

30

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.

32

Required Seismic Design Category

The structure must be assigned to

the most severe seismic design

category obtained from.

Reinforced concrete lateral Force – Resisting Structural System

36

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.

42

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)

i=x

44

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.

Reinforced Brick 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

General. The three basic characteristics to determine the

building’s “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

Seismic Design Provisions for Masonry in IBC

47

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.

Seismic related Restriction on Materials

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

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.

Overall Analytical Approach

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 wall’s

stiffness from that of the un-cracked

transformed section so that of the cracked

transformed section.

58

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.

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.

Structural Dynamics in Binary Codes CANADA IBC Euro Code

Beam Shear

Vb=cswWhere Cs=Ce U

R Ce = עSIF

Where U=0.60= ע to 0.4

i= 1.3 or 1.5

S=fundamental natural vibration

period

Vb=cswWhere Cs=Ce

RCe= IC

W= total dead loadR = 1I = 1.0, 1.25 or 1.5CS= seismic coefficient Ce= Elastic seismic coefficient

Vb=cswWhere Cs=Ce

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

LateralForces

Fj=(Vb-Ft) wjhj

∑Ni=1wihi

Fj=Vb wjhj

∑Ni=1wihi

k

Where K= coefficient related to the vibration period T1

Fj= Vb 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