LINEAR TIME HISTORY ANALYSIS: AN ADVANCE ANALYSIS

LINEAR TIME HISTORY ANALYSIS : AN ADVANCE ANALYSIS

Bangladesh is one of the most densely populated country of the world.Due to large population and small per capita area,the construction of mid to high rise buildings is becoming quite familiar in the country.As,Bangladesh is located in one of the most active seismic region of the world,consideration of earthquake loads in structural design has become a significant issue.The behavior of a building during an earthquake depends on several factors,stiffness,adequate lateral strength and ductility,simple and regular configurations.

At the time of any disaster like earthquake,cyclone or tornado,failure of structures starts at points of weakness.This weakness arises due to discontinuity in  mass,stiffness and geometry of structure.The structures having this discontinuity are termed as irregular structure.Irregularities are one of the major reasons of failures of structures during earthquake.

Increased availability of strong motions,improved computational capabilities and availability ofopen-source software make Linear Time History Analysis(LTHA),a potential more rigorous analysis approach for the design of structures.This methodology is not explicitly codified in the EUROCODE(Volume.8) & it requires some "Code-friendly" for its implementation in practice.A new optimized design method for braces is presented for the smooth implementation of both Response Spectrum Analysis(RSA) and LTHA. In  fact,the tension only design approach for CBF in EUROCODE(Volume.8) has some criticalities arising even when a routine RSA  is employed.The design process is rather smooth only in the case of linear Static approach Classically implemented for regular,mid-rise structures.

---Information on Time-wise fluctuations of structural parameters.(forces,deflections)

--- Can indicate peak demands are only very frequent,short duration spikes for which structure or soil can not respond to.

The design of CBFS(-Concentrically Braced Frame Structure) is dealt in two different ways (tension-only and Compression only ).To reduce analysis Complexity,a tension only philosophy is adopted in accordance with EUROCODE (Volume.8) design prescription.In the tension only design,the storey shear is entirely resisted by the tension braces.

Conversely,the United States  Code(US Code) is based on the compression.The design of CBFS is typically carried out through Equivalent Static Frame Method and then varified through non-linear analysis approaches on the other hand in general,the routine design approach for EC8 confirming structures would be linear dynamic analysis,the effect of the earthquake on the building is represented by a system of horizontal forces,applied statically to the structure and distributed at the various floors with an inverted triangular shape( First Mode).This schematisation can be adopted if the construction is regular in height and the period of the main vibration mode (T1),in the direction in examination,does not exceed 2.5 Tc OR, Td ( Where ,Tc and Td are the boundary of the constant velocity branch of the elastic spectral shape according to EC8. This method is not suitable for TALL buildings,where second and higher modes can be important,or for Structures with any irregularity in plan or elevation when the conditions on the period and regularity are not met the Response Spectrum Analysis( RSA ),is the reference method as described in EC8.

Building Frequency Calculated from Building drift and Pushover Analysis:

The inter-storey drift can also be estimated from recorded building response,but to account for the soi-interaction(i.e- separate the foundation rocking from the relative building response) more detailed instrumentation is required than one available for this and for most buildings.In such situations,often the soil structure interaction is ignored,and the computed drift(due to deformation of the structure) plus the horizontal displacement of a floor relative to the base due to rigid body rocking of the base.

Special Consideration: Special design consideration is required for Base isolated Buildings.Base isolation has become a practical control system for protecting structures against seismic hazards.It is necessary to optimize simultaneously both the base isolation and the superstructure and as a whole in order to seek the most cost-efficient design for structures.However,the base isolation is assumed to behave non-linearity and its cost can be related to the effective horizontal stiffness of each isolator.To reduce computational effort,only critical peak drift responses over the entire time history are first identified and then included in the optimization process as design constraints.Using the principle of virtual work,the peak drift responses can be explicitly formulated and the integrated optimization problem can be solved by the optimality criteria method.

The technique is capable of achieving the optimal balance between the cost of the superstructure and isolation systems whilst the seismic drift performance of the building under multiple levels of earthquake motions can be simultaneously considered.

What is Irregular Structure: Following Three Slide will describe Irregularity for a 5 storey RCC building--

KOREAN BUILDING CODE (KBC-1988) :

Most of semi-empirical building codes like Korean Building Code (KBC) use the building period to directly proportion the magnitude of force which should be sustained by buildings at specific stress level and provide the empirical formulas to determine the lower bound fundamental period in order to establish the minimun lateral load requirements.However,such codes have not settled on a uniform method to determine the periods because the required design force level and characteristics of buildings constructed in each regions are different.To determine the design base shear for seismic design ,the formulas of the period specified in the current KBC are derived from those of the 1988 Uniform Building Code,which were based on the measured period of buildings from strong motion records during 1971 San Fernando earthquake.

Earthquake Damage Mechanism: Earthquake can damage structure in various ways--

A)  By inertial forces generated by severe ground shaking.

B) By direct fault displacement at the site.

C) By foundation failure due to consolidation settlement andliquifaction of the support soil.

D) By landslides, or other surficial movements.

E)  By water waves generated by seismic motions( tsunamis & seismic )

F)  By fires resulting from earthquake shaking.

G)  By large scale tectonic changes in ground elevation.

Characteristics of Earthquake Ground Motion: The characteristics of earthquake ground motion which are of most interest in earthquake engineering applications are--

1) Peak ground motions (acceleration,velocity and displacement) primarily influence the vibration amplitudes.

2) Duration of strong motion has a pronounced effect on the severity of the shaking.

3) Frequency constant spectral shapes relate to frequency or periods of vibration of structures(resonance condition).

Dynamic Analysis Procedure:

*** Linear Analysis may be Response Spectrum / Time history

*** Non-linear is Dynamic Time History

*** Linear results Ve must be scaled by Ie/(Rd*Ra) to get Vd .Then scaled up at least  A) 0.8*V for regular structure & B) 1V for Irregular structures  Or, Vd must be used if >V.

*** Non-Linear results do not need to be scaled,but must be peer reviewed to be rational.

Modeling Consideration: 

***Cracked sections concrete and masonry(.....0.35Ig)

***Size of members and joints(offsets)

***P-delta.

***Other effects that influence lateral stiffness and period.

Building Period (T): Importance of T Calculation --

--1.5 factor for moment resisting frame

-- 2.0 factor for braced frames and walls.

If not doing so,prepare realistic model to obtain T, which will potentially reduce V.

Direction of Loading(when dynamic required) :

*** Independent analysis if SFRS is orthogonal.

*** Non-Orthogonal: 100%,30%,30% include for vertical.

Hazards :

***  Probabilistic Approach

*** 2% in 50 years.

*** 1/2500  annual probability of exceedance

*** Median confidance level 1.5-3 times higher .

*** 84th percentile confidence level 1.5-3 times higher.

*** Designers should not place the same level of reliance on frames and deformations determined from a seismic analysis as they would for dead load and live load analysis.

Fast Non-linear  Analysis ( FNA ) : Fast Non-linear analysis is a model analysis method useful for static and dynamic evaluation of linear and non-linear structural systems.Well suited for time history over direct integration.Its efficiency is due to the separation of non-linear object force vector-while using this method.It should be insure that--

A) Analytical model should be primarily linear elastic.

B) Have limited number of predefined non-linear members.

C) Non-linear behavior with link object.

Conclusion: In conclusion .the following points should be noted regarding linear/Non-linear case data

*** We can define only single load case for both the direction to perform time history.This can be    done by adding the acceleration load in U1 and U2 direction with same scale factor.This is like applying acceleration load simultaneously in both the principle direction.However,the time history can also be applied one at a time in both direction.This can be done by creating another non-linear/linear modal history case.This is not much differences in results was observed in above two directions.

*** The starting load vector can be initial unstressed condition or,a specified load of a gravity time history.If the initial load vector is considered as unstressed condition ,no additional case needs to be defined.If the time history lateral case is suppose to start from some defined gravity case a gravity linear/non-linear time history case must be defined with dead load and scale factor as 1.The number of time steps may be less than lateral time history case for example it may be 100 steps of 0.01 time interval.The starting vector is recommended as dead load since this load will initially there on structure before earthquake event occur and hence assigning the starting load vector will give more realistic results.

*** Define mass source--

Define mass source to calculate the seismic weight of building.Mass source is used in modal analysis and time history uses modal analysis results.Hence,the mass source needs to be defined.

***Output Time History-- The time history output can be acceleration, frequency,velocity, displacement of a specific node along specific direction for all specified time steps.

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