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In the probabilistic seismic demand model, the peak inter-story drift along with residual inter-story drift was basically evaluated for evaluating the damage for the overall system of the buildings whether it was the structural or non-structural type of damage. This overall section was developed with respect to the numerical analysis data of peak and residual inter-story drift of the CBF and SC-CBF systems. The seismic demand model was basically evaluated on the basis of the linear regression along with some pre-selected data of IMs which were used as predictors. The main purpose of using these models was deterministic in nature and was to make ease in the evaluation of the practical application of the probabilistic model while using the terms for correcting the bias used and also helps to improve the accuracy of the predictive deterministic demand model. The formula was written as :

where, DK(x,k) = measurement of the demand

DK (x) = transformation of the suitable model predicted by a deterministic model of demand, YK(x,k) = correction of the terms by correcting the errors regarding bias and random in DK (x), k= vector of the unknown parameter of the model

Figure (a) represents peak roof drift, (b) represents peak inter-story drift (c) represents the residual inter-story drift of the CBF system & SC-CBF system of 3 cities.

CCDF (complementary cumulative distribution functions )

From the probabilistic model of demand, the fragility of seismic of CBF and the dual system was evaluated. The curves obtained from the fragility assessment gives a wider and richer view of the comprehensive perspective to the reliability of the system with respect to the failure that occurred in the normal probability regarding traditional reliable indices because they provide more information related to the system reliability. The fragility of the seismic waves was mainly defined as the probability of the conditions which attained or exceeded the quantity of the demand in a particular level of capacities for evaluating the IMs of earthquakes.

F(s) = P[ gk (x, ) <= 0 | s] = P[ Ck – Dk ] (x, ) <= 0 | s ]

where, gk (x, ) = failure mode functions of limit state,

s = vector function of normal IMs.

Ck is the capacity of kth failure mode.

In this report, the capacity of the inter-story was taken into account based on the recommendation level of performance for IO, LS, CP. However, the dual system is considered as the novel structure system, so till now, no evaluating criteria were proposed yet. The dual system has the capacity to tolerate large drift without causing any damage to the structure because it contains the properties of ductility. They also serve criteria for more structure having ductility properties which were used in dual systems of the inter-story capacity of drift. For quantifying the different kinds of fragility at different levels of performance for inter-story drift the moment-resisting frame (MRF) were highly considered. Although the residual drift was not affected by the rocking behaviour and can be quantified after the overall structure motion was completed, this kind of residual drift was used for CBF as well as dual systems also. Generally, the estimation of uncertainty of the fragility basically came from several variables such as the properties of the structure, parameters of the model, errors that occurred in the model. In the previous research articles, several model errors were shown in the demand model of probabilities which dominates the limit state of variabilities. In this report, some studies of the properties related to the structures such as the geometry of the frame, yield stress members along the section properties are defined as predetermined and were set equally according to their mean. Therefore several uncertainties were neglected in the structure and properties of the geometry along with the parameters of the models. By replacing the parameter of the models with the estimates point, one can calculate the point estimates of fragility by using these formulas:

where = cumulative function of distribution for a standard normal random variable.

D = estimate point of the demand model by using the value of mean x and ΘD, xˆ and Θ = (θk, σk) respectively.

From this above table, the curves of the fragility for IO, LS, CP level of performance were evaluated by using the above formula and as the curves were shown in the figure. `

The above value in the table indicates that the dual system shows less amount of failure for all the levels of performance. The table also shows some value of the dual system frames as compared to the braced steel frames. For dual systems the IO of inter-story drift recorded the percentage of 0.7 and residual drift with negligible rate due to the absence of the appropriate models of demand so the residual drift was not evaluated so, the curve of fragility was not developed at this stage. The LS value of the inter-story drift was recorded as 2.5 percent and the residual drift with 0.5 percent. While on the other hand the value of CP was recorded as 5.0 percent and the residual drift was estimated as 2.0 percent.

For the braced steel frames, the IO of the inter-story drift was recorded as 0.5 percent and residual drift will be recorded as negligible. Whereas the value of the LS of inter-story drift is shown as 1.5 percent and the residual drift serves with 0.5 percent. The value of the CP in inter-story drift and residual drift was recorded as 2.0 percent respectively.

According to the capacity of the residual drift from the above-mentioned table, the percentage of the residual drift can be evaluated for CBF and dual system which exceeds the maximum recommended values. From the above-mentioned table, the CBF recorded the value of IO, LS, CP as 59.56 %, 12.5%, 6.62 5 respectively. While on the other hand, the dual system recorded the value of IO, LS, CP as 5.0 %, 0.78%, 0.78 % respectively. As per the data, the self-centring in the structure of the dual system notably reduces the permanent deformation rate of the structure.

It also shows that the dual system receives smaller values of the residual drift across all the levels of performance. While comparing both the structural systems from the above figures and the mentioned table revealed that the system of CBF was more likely to attain and exceed the rate of performance for each level as per the given IMs motion of ground showed that the proposed model of dual system working mechanism as planned

The numerical analysis results showed that the SC-CBF building attained a higher value on roof drifts with respect to the CBF, because of the presence of soft characteristics behaviour in SC-CBF. Although the rocking behaviour may cause the high drift on roof values which didn’t tend to structural damage.

In this report, the self-centring of the ability to evaluate (residual inter-story drift considered as 0) after the ground motion case study was completed.

The rate of accuracy and the validation of the probabilistic peak drift model of interstory was compared with the formulated demand model in the literature, whletheproppsed model was helped in providing the unbiased predicting data and better accuracy with respect to the conventional ones.

The comparing curve of the fragility for all the levels of performance showed that the sc-CBF system of the building was less recommended as compared to the CBF building in attaining and exceeding the capacity level on the intensity measure of the seismic waves. For the peak drift the performance rate of the sc-CBF was better than the CBF ones as per the evaluated level of the performance.

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