Dynamic Loads.pdf

7/27/2019 Dynamic Loads.pdf

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Prof. Dr. Zahid A. Siddiqi, UET, Lahore.

DYNAMIC LOADSThere are two types of forces/loads that may act

on structures, namely static and dynamic forces.

Static forces are those that are gradually applied

and remain in place for longer duration of time.

These forces are either not dependent on time or

have less dependence on time.

Live load acting on a structure is considered as a

static load because it usually varies gradually in

magnitude and position.


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Similarly moving loads may also be considered

as statically applied forces.

Dynamic forces are those that are very much

time dependent and these either act for smallinterval of time or quickly change in magnitude or

direction.

Earthquake forces, machinery vibrations and blast

loadings are examples of dynamic forces.

Structural response is the deformation behavior

of a structure associated with a particular loading.


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Similarly, dynamic response is the deformationpattern related with the application of dynamic

forces.

In case of dynamic load, response of the

structure is also time-dependent and hence

varies with time.

Dynamic response is usually measured in terms

of deformations (displacements or rotations),velocity and acceleration.


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Dynamic force, F(t), is defined as a force that

changes in magnitude, direction or sense in muchlesser time interval or it has continuous variation

with time.

Impact loadis the other extreme where the load isapplied only for an infinitesimal interval of time with

some momentum and is considered separate from

the dynamic loads.

The variation of a dynamic force with time is called

history of loading.

Prescribed dynamic loadingis regularly varying

loading in which well-defined cycles of loading arerepeated after equal intervals of time.


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F(t)

t

Fig. A Typical Dynamic Force.

Example of prescribed loading is a regularvibration of machinery with a certain amplitude

and frequency.


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Amplitude of vibration is the maximum

structural displacement during one completecycle of load.

Frequencyis the number of loading cycles in aunit time (usually one second).

Types Of Prescribed Loading

a) Periodic loading

i) Sinusoidal Loading:ii) Stepped Loading:

iii) Complex Variation Loading:


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F(t)

t

F(t)

t

F(t)

t

Typical Sinusoidal Loading.

Typical Stepped Loading.

Typical Complex

Variation Loading.


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b) Non-periodic loading

F(t)

t

Typical Impulsive Loading.

F(t)

t

Typical Earthquake Loading.


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EARTHQUAKES

An earthquake is the vibration of earth produced

by rapid release of energy from within itself.

This extra energy may be stored in earth and

released at intervals due to many different

phenomena, some of which are as under:1. Plate tectonics.

2. Volcanic eruptions.3. Atomic explosions.

4. Collision of massive meteorites with thesurface of earth.


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Plate Tectonics

Crust: Crust is the outermost layer of earth

consisting of solid material varying in temperature

from surface temperature to a maximumtemperature of 1000 C. Its thickness under deepoceans is between 4 to 6 km and the thickness

under continents is approximately 30 to 40 km.

Mantle: This layer has an approximate thickness

of 3000 km and consists of semi-solid to plasticmaterial. The temperature ranges from 1000 to

3500 C.


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Outer Core: Outer core is a thickness of

approximately 2250 km and consists of liquid at atemperature of 3500 to 4000 C.

Inner Core: The inner core has a radius of

approximately 1200 km and is a layer of solid

material at temperature higher than 4000 C.

The outer layer of earth having a thickness of 100

km is relatively rigid and is called lithosphere.

The layer of earth below lithosphere having a

thickness of 400 km is softer and is called

asthenosphere.


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The lithosphere acts as rigid plate that moves over

partly molten asthenosphere.

According to this theory, lithosphere is cracked in

places or broken in to smaller pieces or plates.

This may have happened during initial drying of

the earth from a molten state.

There are seven large and several small plates.

The largest plates are the Pacific plate, the NorthAmerican plate, the Eurasian plate, the Antarctic

plate, the Indo-Australian plate and the African

plate.


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Plate boundaries

a) Mid-Oceanic Ridge:

b) Subduction Zone:

Further, there are three types of plate boundaries

depending on the relative movement between thetwo adjoining plates.

i) Convergent Plate Boundary:ii) Divergent Plate Boundary:

iii) Transform Plate Boundary:


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According to continental drift theory, all thecontinents were once part of a huge landmass,

which have slowly moved apart.

The Indian sub-continent was not a part of Asia.It drifted over millions of years from Australia to

Asia and the collision produced Himalayas.

Modern techniques such as GIS and GPS prove

such movements of continents.

Faults are cracks which are developed within the

main plates.


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Focus And Epicenter

The point within the earth along the rupturing

geological faults where an earthquake originates

is called the focus orhypocenter.

The point on the earths surface directly above

the focus is called the epicenter. Earthquakewaves radiate out from the focus.

The focal depth is the depth of the hypocenter

below the epicenter.

Focal distance is the distance from the

hypocenter to a given reference point.


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Earthquake / Seismic Waves

The waves originated at the rupture zone are

called body waves and are of the following two

types:

(1) P-Waves or Primary Waves or Dilation

Waves:

These waves involve particle movement parallel to

the direction of propagation of the wave, as shownin Fig.

The speed of travel of these waves is appr. 1.73

times greater than the other waves.


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These waves are felt earlier in an earthquake

and cause relatively less damage.

There is usually an after-shockat an interval

during which the other more damaging wavesapproach the area.

Wave Direction Wave Direction

Particle Movement

Particle Movement

(a) P-Waves (b) S-Waves


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(2) S-Waves or Secondary Waves or Shear

Waves:

These waves involve particle movement

perpendicular to the direction of propagation of thewave (refer the Fig.).

When body waves reach the ground surface, part

of these is reflected back while other part

produces surface waves.

Surface waves are the waves produced on theearths surface due to an earthquake and are of

following two types:

P f D Z hid A Siddi i UET L h


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(1) R-Waves or Rayleigh Waves:These waves produce a circular motion

analogous to the motion of ocean waves.

Hence, rotation along with vertical movements

takes place in case of Rayleigh waves (Fig.).

Movement of Particles in Rayleigh Waves.



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(2) L-Waves or Love Waves:

These waves produce horizontal motion along theground surface transverse to the direction of

propagation.

Earthquake magnitude and Richter scale

Earthquake magnitude is a measure of the energy

released during an earthquake.

It defines the size of the seismic event but is not

related with damage or effect of earthquake at agiven location.

The magnitude of earthquake is usually measuredon Richter scale, which is a log scale.



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A magnitude of M5 Richter scale is ten-times

greater than a magnitude of M4 and isassociated with an increase in energy release of

31.6 times.

A magnitude of M5 is 100 times greater than a

magnitude of M3 scale.

Earthquake intensity and Mercalli scale

Intensity is an assessment of the effect of the

earthquake at a given location and is not directlyrelated to the earthquake magnitude.



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This is determined not by reading instruments butby observing the effects on structures, human life

and disturbance to the ground surface.

Modified Mercalli index is based on the observed

effects of an earthquake at a specific site.



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Total destruction. Waves seen on ground.XII.

Almost all structures fall. Bridges wrecked. Very wide cracks in ground.XI.

Many structures damaged. Ground is badly cracked.X.

All buildings considerably damaged, many shift off at foundations.Noticeable cracks in ground.

IX.

Specially designed structures damaged slightly, others collapse.VIII.

Everyone runs outdoors. Poorly built structures considerably damaged; slight

damage elsewhere.

VII.

Felt by all; many people run outdoors. Furniture moved, slight damage

occurs.

VI.

Felt by nearly everyone; many people awakened. Swaying trees and poles

may be observed.

V.

Felt indoor by many. Feels like a truck has struck the building.IV.

Tremor noticed by many, but they often do not realize it as an earthquake.III.

Felt by very few people.II.

Felt by almost no one.I.

EffectMercalli

Scale

Prof Dr Zahid A Siddiqi UET Lahore


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Main Considerations For Seismic Design

Design of structures to withstand the maximum

intensity earthquake is highly expensive and may

not even be possible due to the following factors:

1. The magnitude, intensity and other

characteristics of future earthquakes are notprecisely known.

2. Stiffer structures attract more earthquakeloads. These structures cannot dissipate

energy and all the energy is stored in them

making them unstable.



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3. Heavier design means more mass of the

structure. Due to larger mass, moreinertial forces are produced during the

ground excitation.

The most common method to design

earthquake resistant structures is to design for

mild earthquakes of expected commonoccurrence in the elastic range or in the

inelastic range with less or no permanent

deformations.

Ductility is then provided for maximum expected

intensity of earthquakes.



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Ductilityis a measure of inelastic deformationsthat may be produced in a structure before its

collapse.

Inelastic deformations release energy in the form

of heat and make the structure stable.

Permanent deformations may be produced in thestructure with considerable cracking and structure

may not be useable after a severe earthquake.

However, the life is saved as the people may

escape out of the building.



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In essence the main aim of earthquake resistant

design is to avoid loss of life and then less loss toproperty is the second criterion.

It may be tried that the damage is repairable formoderate earthquakes.

Methods Of Analysis For Earthquake Loading

1 Free Vibration Analysis

2 Response History Analysis (RHA)3 Response Spectrum Analysis (RSA)

4 Equivalent Static orPseudo-Static Load Method



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Related Methods Of Dealing With Earthquakes

1 Base Isolation Method

2 Use Of Special Energy Dissipating Devices

DAMPING

Damping means the presence of frictional forces

in the structure, which transforms the mechanicalenergy of system in to other forms of energy,

such as, heat.

If damping is completely absent in an ideal

system, a structure once excited will oscillate

indefinitely with constant amplitude at its naturalfrequency.



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The viscous damping forces produced areproportional to the velocity of the piston.

However, the actual damping in a structure may

result from looseness of joints, dry friction between

components (called Coulomb damping), material

damping (or internal damping found by examining

the area within the hysteresis loop between

stresses and acceleration), structural damping

(general term for all types of damping in astructure) and many other complex causes that

would lead to nonlinear behavior of the structure.



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Critical Damping (ccr): It is defined as that

amount of damping due to which a freely excitedsystem does not oscillate but returns to its

original position in the shortest possible time.

Damping Ratio Of System ():

Damping ratio of a system is defined as the ratioof damping present in a system to its critical

damping. = c / ccr.

Citical damping coefficient usually ranges

between 2 to 10% of ccr( = 0.02 to 0.10) for

actual structures.



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= 1 critically damped response

> 1 over-damped response < 1 under- damped response

EQUIVALENT STATIC LOAD METHOD

The parameters discussed in the following

sub-sections are required to be evaluated toget the values of equivalent static loads

according to UBC-97.



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Seismic Zone Factor (Z)

The zone factor (Z) is given as a factor of peak

acceleration with respect to acceleration due to

gravity (g) and it varies from 0.075 to 0.40.

The suggested values correspond to recurrence

interval of 475 years giving a 10 percentprobability of being exceeded in a 50 years

period.

0.0750.150.200.300.40Effective Peak Ground

Acceleration (EPA)

12A2B34Zone

Table. Seismic Zones and Effective Peak Ground Accelerations.



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q , ,

Soil Profile Types

The ground vibrations traveling through the soil

may be amplified or reduced depending upon the

fundamental period and type of strata.

UBC classifies soils into six profile types, as

given in Table.

This classification depends on the average shear

wave velocity in the top 30m of material.



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q , ,

Detailed investigations requiredVery soft clayey soilSF

< 180Soft soilSE

180 to 360Stiff soilSD

360 to 760Soft rockSC

760 to 1500RockSB

> 1500Hard rockSA

Shear Wave Velocity

(m/s)

Description of SoilSoil Profile Type

Table. Soil Profile Types.



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q , ,

Seismic Source Types

The seismic source types are decided based on

the maximum moment magnitude potential of a

fault and its slip rate per year.Type C represents almost an inactive fault in

Table.

2.0 6.5C

The fault which is not A or CB

5.0 7.0A

Slip Rate (mm/year)Maximum Moment Potential

Source CharacteristicsSeismic Source

Type

Table. Seismic Source Characteristics.



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q

Near-Source Factors

Two factors, Na and Nv, are used to considerincreased ground motions near a fault.

The factorNa is the acceleration-based factorthat is important for short-period structures and

velocity-based factorNv that is important for

periods exceeding one second.

1.01.01.01.01.21.01.61.3B1.01.01.21.01.61.22.01.5A

Nv

Na

Nv

Na

Nv

Na

Nv

Na

15 km10 km5 km 2 kmDistance From FaultSeismic

Source

Type

Table. Near Source Factors (Na

and Nv) for Various Seismic Source Types.



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Ground Response Coefficients

The two ground response coefficients, Ca and Cv,

give indication of the vibration amplification

capacity of a soil depending on zone factor (Z), soilprofile factor (S) and the near-source factors (Naand Nv).

The fundamental period of a structure determines

whetherCa orCv is more important for design of a

structure.



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0.96 Nv

0.36 Na

0.840.360.640.340.500.300.260.19SE

0.64 Nv

0.44 Na

0.540.360.400.280.320.220.180.12SD

0.56 Nv

0.40 Na

0.450.330.320.240.250.180.130.09SC

0.40 Nv

0.40 Na

0.300.300.200.200.150.150.080.08SB

0.32 Nv0.32 Na0.240.240.160.160.120.120.060.06SA

Cv

Ca

Cv

Ca

Cv

Ca

Cv

Ca

Cv

Ca

Zone 4Zone 3Zone 2BZone 2AZone 1Soil

Profile

Table. Ground Response Coefficients, Ca

and Cv

.



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When soil parameters are unknown, soil profile

type SD may be assumed in seismic zones 3 and 4and profile SEmay be assumed in other zones.

For a regular structure, the near source factor

needs not exceed 1.3.

Fundamental Time Period Of A Structure

The time period of a structure may exactly be

calculated by performing free vibration analysis of

the structure, which involves lengthy calculations.

Following empirical methods are also available to

reasonably guess the fundamental time period ofa structure:



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Approximate method

Fundamental time period, T = sec10

storiesofnumber

Method A of UBC

TA =4

3

)( nt hC

wherehn = height of the roof above the base in

meters, not including the height of parapets.



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Ct = 0.085 for steel moment resisting frames

= 0.073 for reinforced concrete moment

resisting frames and eccentric braced steel

frames

= 0.050 for all other buildings

Method B of UBC

TB =

ii

ii

fg

W

2

2

1.4TA for Zones 1,2 and 3

1.3 TA for Zones 4



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where

i = static elastic deflection at level i dueto the forces applied at all levels,

increasing in a linear way with height.

The value of deflection must be withrespect to the base in mm.

= 1floorth-atforcelateraltotal

+ iiki

ki = shear stiffness of columns under floor i

fi = lateral force at level i, N

wi = dead load located at level i, Nand

g = acceleration due to gravity

= 9810 mm/sec



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Ductility

Ductility of an element shows its capacity todeform in the inelastic range without collapse.

Due to these inelastic deformations, the energyis dissipated making the structure relatively

stable against earthquake forces.

If these deformations successfully occur in the

two opposite directions causing reversal of

stresses in the members, hysteresis loops areproduced dissipating energy in each cycle of

loading, unloading and loading in the opposite

direction.



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Response Modification Factor (R)

The response modification factor of a structure (R)

is ratio of the seismic base shear of an elastic

system to a reduced design base shear dependingupon ductility, energy absorbing capacity, increase

in natural period due to yielding and increase in

damping ratio of the structure.

If shear walls or braced frames provide support to

gravity loads and all the lateral loads, the structuralsystem is a Bearing Wall System (BWS). In other

words, the gravity loads are resting on walls.



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If separate systems are provided to resist lateral and

gravity loads, the structural system is called BuildingFrame System (BFS).

No special detailing is required for gravity load

supporting frames.

Special Moment Resisting Frames (SMRF) are

frames specially detailed to provide high ductility andsupport for lateral and gravity loads by flexural action.

Moment Resisting Frames With Masonry ShearWalls are called MRWFsystems.

Dual Systems are those in which more than one

systems are used together.



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Many other types given in UBC

None8.59. Concrete shear walls with SMRF

496.58. Masonry MRWF

None8.57. Steel or concrete SMRF

736.46. BFS with steel ordinary braced frames

495.55. BFS with masonry shear walls

735.54. BFS with concrete shear walls

737.03. BFS with steel eccentrically braced frames

494.42. BWS with steel braced frames

494.51. BWS with concrete or masonry shear walls

Height Limit(m)

RStructural System

Table. Response Modification Factor, R.



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The value of the response modification factor (R) isdetermined from consideration of a structures

over-strength capacity beyond the point at which

the elastic response of the structure is exceeded.

The value ofRalways exceeds unity, which

indicates that all structures are designed for forcesless than would be produced in a completely

elastic structure.

This reduced force level is made possible by the

energy absorption and dissipation capacity of the

structure at displacements in excess of initial yield.



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Seismic Importance Factor (I)

The factor is equal to 1.25 for essential and

hazardous facilities and 1.00 for special

occupancy, standard occupancy andmiscellaneous structures.

Seismic Response Coefficient (Cs

)

The seismic response coefficient (Cs) is the

fraction of total dead load of the structure that is

acting as base shear on the structure.

This means that the base shear (V) is: V= Cs W.



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This factor depends upon velocity of acceleration

based ground response coefficient (CvorCa),importance factor (I), response modification factor

(R) and time period (T).

Response time Ts =a

v

C

C

5.2and Ta = 0.2Ts

Cs =RTICv (ifT> Ts) subjected to maximum

and minimum values

Max. value = 2.5 Ca I / R(Controls when T= Ta to Ts)

Min. value = 0.11 Ca I(OR) 0.8ZNvI / Rfor zone-4



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Seismic Dead Load (W)

The seismic dead load (W) consists of the

following:

i)Dead load of the structure.

ii)25 percent of the floor live load for storage and

warehouses.

iii)A minimum allowance of 50 kg/m2 for movable

partitions.

iv)The total weight of permanent equipment and

fittings.



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Magnitude Of Base Shear (V)

1 UBC refined formula

Base shearV = Cs WMaximum inelastic displacement m = 0.7 RsWhere s = the displacement corresponding tothe shear V, given above.

2 UBC simplified formula

Base shearV = (3.0 Ca / R)W



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This is a conservative formula having the

following restrictions:

i)Ordinary occupancy type.

ii)Light-frame construction not exceeding 3stories.

iii)Any construction, except bearing wallsystems, but not exceeding two stories.

Distribution Of Base Shear

At Various Story Levels

Shear at a particular story, FX

=

ii

xx

aW

aWV



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Where

V = modal base shearWi= seismic dead load at level-i

ai= mode shape component at

level-i for the given modewx= seismic dead load located at

level-x

and ax= mode shape component atlevel-x for the given mode

For uniform distribution of mass over height and

for first linear mode, the distribution of base

shear may be simplified as follows:



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FX

=

iixx

hW

hWV

1

Where V1 = base shear corresponding to first

mode

hi = height above the base to level-i

and hx

= height above the base to level-x

In order to account for higher mode effects in the

above expression for long period buildings, anadditional force Ft is added at the top of the

structure.



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Ft

= 0.07 T V when T> 0.7 sec

Where V= total base shear

= Ft+ Fx

In such cases: FX =

ii

xxt

hW

hWFV )(

RESPONSE SPECTRUM ANALYSIS (RSA)

Spectral response means the maximumdisplacement, velocity or acceleration response.



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Pseudo-Acceleration is the maximum

displacement of the structure multiplied withsquare of natural circular frequency.

Pseudo-Velocityis the maximum displacementof the structure during an earthquake multiplied

with the natural circular frequency.

Sd = spectral displacement

Sv = spectral velocity

= Sd

Sa = spectral acceleration

= Sv = 2 Sd



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Because of this inter-relationship, all three spectra

may be plotted on the same graph using tripartiteaxes and logarithmic scales.

A response curve orresponse spectrum is agraph of the spectral (or maximum) response of a

range of single-degree-of-freedom oscillators to a

specified ground motion, plotted against thefrequency or period of the oscillators.



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1,000

500

200

100

50

20

10

0.0550

0.10 0.20 0.50 1 52 10Time Period, sec (on log scale)

Spectral Velocity

(Sv), mm/sec (on

log scale)

= 0 % = 2 % = 5 %

= 10 %

A Typical Out-of-Scale Response Spectrum.


Procedure To Use Response


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Spectra For SDOF Systems

The procedure to use response spectrum to calculate

the earthquake lateral forces for single degree of

freedom systems is summarized as under:

i) Calculate angular speed and time period T

for the structure.

ii) Estimate the damping ratio, .

iii) Use applicable response spectrum for aparticular area and find SdorSvorSa (the

values are inter-convertible) against the time

period.



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iv) Find shear force in each column as:

S.F = Sd k

v) Find the total lateral force by adding shear

forces in all the columns.


Spectra For MDOF Systems

The procedure to use response spectrum for the

calculation of the earthquake lateral forces incase of multiple degrees of freedom systems is

summarized as under:



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1. Calculate angular speed and time period T

for the desired mode of vibration of the structure.

2. Find the mode shape ai.

3. Estimate the damping ratio .

4. Find Sd, Sv and Sa from the response

spectrum or calculate others after knowing oneout of these.

5. Calculate the effective weight as follows:

WE =( )( )

2

2

ii

ii

aW

aW



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iiii

aW

aWV

6. Calculate the base shear as follows:

V = WESa / g

7. Find the lateral force at each level as follows:

Fi =

Example : Determine the base shear for the

fundamental mode with = 0.05. Also determine

the lateral load at each level for the fundamentalmode.

= 15.1 rad/sec

=86.295.1

00.1

ia



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Frame For Example.

880 kg/m2

880 kg/m2

590 kg/m2

30m 30m

1

3

2



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Solution:Dead Loads:

Level 1 & 3 = (880)(30)(30) = 7770 kN

Level 2 = (590)(30)(30) = 5209 kN

= 15.1 rad/sec

T = 2 / = 0.416 sec

From the response spectrum, Sv = 350 mm/sec

Sa = Sv = 5285 mm/sec2 = 5.285 m/sec2



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The calculations are made in Table using the

following expressions:

( )

( )

2

2

ii

ii

aW

aW

ii

ii

aW

aWV

WE =

V = WESa / g and Fi =

9530911324015020749Total527563555222222.8677703

241119807101581.9552092

1844777077701.0077701kNkN-mm

2

kN-mmmmkN

Fi

Wiai

2Wiai

ai

Wi

Level

Table. Calculation Sheet For Example.


( )2


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( )

( )91132

401502

81.9

285.517689

WE =

= 17689 kN

= 9530 kNV =



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UBC RESPONSE

SPECTRUM METHOD

UBC Design Response Spectrum is an elasticresponse spectrum for 5 percent equivalent

viscous damping used to represent the dynamic

effects of the Design Basis Ground Motion forthe design of structures.

This response spectrum may be developed for a

site-specific spectrum based on geologic,

tectonic, seismological and soil characteristics

associated with a specific site.



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Alternatively, the spectrum constructed inaccordance with the spectral shape given in UBC

using the site-specific values ofCa and Cvand

multiplied by the acceleration of gravity, 9.815m/sec.2.



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According to UBC 1633 the following


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According to UBC 1633, the following

requirements must be satisfied:

1. Only the elements of the designated

seismic-force-resisting system need to be

used to resist design forces.

2. The individual components should be

designed to resist the prescribed designseismic forces acting on them.

3. All building components in Seismic Zones

2, 3 and 4 shall be designed to resist the

effects of the calculated seismic forces and

the effects of gravity loadings from dead,floor live and snow loads.



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4. Consideration shall be given to design for

uplift effects caused by seismic loads.

5. In Seismic Zones 2, 3 and 4, provision should

be made for the effects of earthquake forcesacting in a direction other than principal axes.

6. If the axial load in the column due to seismic

forces acting in either direction is less than 20 %

of the column capacity, the orthogonal effects

may simply be considered by designing for 100% of the design seismic forces in one direction

plus 30 % of the design seismic forces in the

perpendicular direction.



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7. The combination requiring the greater

component strength should be used for design.

8. Alternatively, the effects of the two orthogonal

directions may be combined on a square root ofthe sum of the squares (SRSS) basis.

9. When the SRSS method of combining

directional effects is used, each term computed

shall be assigned the sign that will result in the

most conservative result.10. The strength and stiffness of the framing

between the base and the foundation shall not

be less than that of the superstructure.



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According to UBC 1633.2.7, concrete frames

that are part of the lateral-force-resisting

system should conform to the following:1. Should be special moment-resisting

frames in Seismic Zones 3 and 4.

2. Should be a minimum of intermediate

moment-resisting frames in Seismic

Zone 2.



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According to UBC 1631.4.1, response spectrumanalysis is defined as an elastic dynamic analysis

of a structure utilizing the peak dynamic response

of all modes having a significant contribution tototal structural response.

Peak modal responses are calculated using theordinates of the appropriate response spectrum

curve which correspond to the modal periods.

Maximum modal contributions are combined in astatistical manner to obtain an approximate total

structural response.



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This condition is considered satisfied by

demonstrating that for the modes considered, at

least 90 percent of the participating mass of the

structure is included in the calculation of responsefor each principal horizontal direction.

The peak member forces, displacements, story

forces, story shears and base reactions for eachmode should be combined by recognized methods.

When three-dimensional models are used foranalysis, modal interaction effects shall be

considered when combining modal maxima.


Reduction of Loads Based On Ductility


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According to UBC 1631.5.4, the Elastic

Response Parameters may be reduced for

purposes of design in accordance with thefollowing items, with the limitation that that the

corresponding design base-shear should not be

less than the Elastic Response Base Sheardivided by the value ofR.

The corresponding reduced design seismicforces shall be used for design.

Reduction of Loads Based On Ductility



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1. For all regular structures where the ground

motion representation complies with Ground

Motion definition of UBC using designspectrum, Elastic Response Parameters

may be reduced such that the corresponding

design base shear is not less than 90percent of the base shear determined in

accordance with Static Force Procedure.



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2. For all regular structures where the ground

motion representation complies with Ground

Motion definition of UBC using site-specific designspectrum, Elastic Response Parameters may be

reduced such that the corresponding design base

shear is not less than 80 percent of the base

shear determined in accordance with Static Force

Procedure.



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3. For all irregular structures, regardless of the

ground motion representation, ElasticResponse Parameters may be reduced such

that the corresponding design base shear is

not less than 100 percent of the base sheardetermined in accordance with Static Force

Procedure.



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4. The vertical component of ground motion may

be defined by scaling corresponding horizontal

accelerations by a factor of two-thirds.Alternative factors may be used when

substantiated by site specific data. Where the

Near Source Factor, Na, is greater than 1.0,

site-specific vertical response spectra should be

used in place of the factor of two-thirds.

Dynamic Loads.pdf

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