Effects of Vertical Irregularity in Steel Frame with Shear Linked Steel Bracings

This paper deals with the irregular pro le of braced steel frame building along the vertical direction with shear link bracing systems. The underlying fact of the paper is the e ect of the seismic force in braced frames with di erent types of irregularities including geometric irregularity, column discontinuity, and overhanging mass. For each successive model, the position of shear link bracings has been xed to make the study e ective. This study has investigated the vulnerable e ect of irregular pro les in steel frame buildings. To attain the nonlinear property of each element of the frame, the pushover analysis method along with the equivalent static force method has been adopted for the present study. UBC97 code has been used here for linear static analysis while the parameters for nonlinear static analysis are authenticated from FEMA356. Investigations on di erent frames exhibit that regular pro le with symmetry in mass is more e cient while using overhanging mass is detrimental as the formation of nonlinear hinge occurs at minimum load in the model with overhanging mass compared to other frames.


Introduction
Steel bracings have become a common system to retrot steel framed buildings for the last few Studies with vertical shear links depict that they provide more lateral stiness to withstand the seismic force [1]. The bracings are provided not only in regular shaped framed structures but also in irregular shaped framed structures.
The studies can be carried out either experimentally or numerically. In the case of experimental studies, the shaking table test is often adopted.
Shaking Finally, a comparison has been made among the irregular frames which contain shear link bracing systems. These frames contain geometric irregularity or column discontinuity. The outcome of the study shows certain eects due to the geometric irregularity/column discontinuity or overhanging mass in a frame that is rehabilitated with shear link steel bracing or invert "Y" bracing. This is because the fact turns into a challenge for a designer to opt for the optimum system for acceptable rehabilitation.

Materials
Specications of materials for numerical analysis have been adopted from the manual of the American Institute of Steel Construction [14]. The details of the member specications are listed in    Table 1).

Pushover analysis
Pushover analysis is incorporated to assess the nonlinear behavior of the models. The pushover analysis method is mainly adopted in the case of existing structures and to nd the nonlinear properties of frames. Several properties: eective stiness, secant stiness, and ductility and target displacements along a certain direction can be determined using pushover analysis. The steel frames are assumed as ordinary momentresisting frames and ordinary braced frames.
Pushover parameters are estimated from FEMA t cases. Furthermore, the consequences of using on all types of frames have been reported. Four regular framed structures have been considered study. Two of them comprise geometric ; one is with column discontinuity in the upper the remaining frame is with an overhanging e higher story. Shear link braces have been used ual systems. The shear link includes the bracing of invert "Y". Finally, a comparison has been ng the irregular frames which contain shear link ystems. These frames contain geometric or column discontinuity. The outcome of the ws certain effects due to the geometric /column discontinuity or overhanging mass in a is rehabilitated with shear link steel bracing or bracing. This is because the fact turns into a for a designer to opt for the optimum system for rehabilitation.

rials:
cations of materials for numerical analysis have ted from the manual of the American Institute of struction [14]. The details of the member ons are listed in Table 1. The loading conditions considered following the guidelines of UBC97 mation of different parameters for pushover computed as per the guidelines of FEMA 356 e relevant properties of the frame are ted in Table 1. The cross-sectional properties of and columns of all models are the same. The and sections are kept the same for braces and ell. All types of material sections and property has been added as well to observe the behavio strength of the dissimilar steel frames with irregularities. Four irregular steel frames have considered for the study. Fig. 1 (Model-1) represe frame as vertically irregular and asymmetric as we 6-story frame having a geometric irregularity in e floors has been taken for pushover analysis. The geo area, as well as the mass of floor, decreased 25 per the 3 rd story and 50 percent in the 5 th story. Fig. 2 (M 2) constitutes a frame that has geometric irregularit the third floor but has symmetry along the vertica Geometric area and floor mass decreased on the 4 with a value of 50 percent. Fig. 3 (Model-3) de frame that has column discontinuity at the fourth sto 4 (Model-4), on the other hand, depicts an overh mass on the fourth floor. The bay width and story he each model are kept constant (refer to Table 1).

Pushover analysis:
Pushover analysis is incorporated to assess the nlinear behavior of the models. The pushover analysis thod is mainly adopted in the case of existing structures to find the nonlinear properties of frames. Several perties: effective stiffness, secant stiffness, and ctility and target displacements along a certain direction be determined using pushover analysis. The steel mes are assumed as ordinary moment-resisting frames ordinary braced frames. Pushover parameters are imated from FEMA 356 [7]. The behavior of structures be explained from the force-displacement curve which recognized as the capacity curve. From Fig. 5, the avior of the force-displacement curve can be observed. per the notations in Fig. 5, point "A" represents the gin while point "B" represents the endpoint of the ( Figure 5). After point D, the ele substantially reduced strength to poin from UBC97 [6] have been listed i pushover criteria are shown in Table 3 Fig. 5. Force vs. deformation/deforma

. Pushover analysis:
Pushover analysis is incorporated to assess the nlinear behavior of the models. The pushover analysis ethod is mainly adopted in the case of existing structures d to find the nonlinear properties of frames. Several operties: effective stiffness, secant stiffness, and ctility and target displacements along a certain direction n be determined using pushover analysis. The steel ames are assumed as ordinary moment-resisting frames d ordinary braced frames. Pushover parameters are timated from FEMA 356 [7]. The behavior of structures n be explained from the force-displacement curve which recognized as the capacity curve. From Fig. 5, the havior of the force-displacement curve can be observed. s per the notations in Fig. 5, point "A" represents the igin while point "B" represents the endpoint of the levels are computed when the forces r ( Figure 5). After point D, the elem substantially reduced strength to poin from UBC97 [6] have been listed in pushover criteria are shown in Table 3 Fig. 5. Force vs. deformation/deforma

Pushover analysis:
Pushover analysis is incorporated to assess the nonlinear behavior of the models. The pushover analysis method is mainly adopted in the case of existing structures and to find the nonlinear properties of frames. Several properties: effective stiffness, secant stiffness, and ductility and target displacements along a certain direction can be determined using pushover analysis. The steel frames are assumed as ordinary moment-resisting frames and ordinary braced frames. Pushover parameters are estimated from FEMA 356 [7]. The behavior of structures can be explained from the force-displacement curve which is recognized as the capacity curve. From Fig. 5, the behavior of the force-displacement curve can be observed. As per the notations in Fig. 5, point "A" represents the origin while point "B" represents the endpoint of the nonlinear hinges starts from point "B" as shown in Figure  5. The nonlinear hinges start from point "B". The hinge levels are computed when the forces reach IO, LS, and CP ( Figure 5). After point D, the element responds with substantially reduced strength to point E. The parameters from UBC97 [6] have been listed in Table 2 while the pushover criteria are shown in Table 3.   substantially reduced strength to point E. The parameters from UBC97 [12] have been listed in Table 2 while the pushover criteria are shown in Table 3.
The Base shears which have been applied for pushover analysis were derived from the following equations. The base shear is distributed over the height of the models and used as a load pattern for pushover analysis. The computed base shear (V) from equation (1) must be less than that calculated by equation (3) and must be greater than that calculated by equation (4). In equation (1), W indicates the self-weight of the frame.
STAAD.pro v8i has been used for pushover analysis. The assumptions through which the pushover analysis has been followed are listed below: (i) The frames are moment resisting frames.
(ii) The geometric nonlinearity has been considered.
(iii) The expected yield strength has been assumed as 250 MPa.
(iv) Total Load step is 100 and the nonlinear hinges have been presumed as per FEMA356.
(v) Deduction of the damping ratio is 5% and the site class is Sc (vi) Mapped spectral acceleration factor, Fa= 1.2 and Fv=1.7 (vii) A certain value has been entered to terminate the pushover analysis after an irrefutable limit.

Results and discussion
The analysis of the models is conducted following the provisions of UBC97 [12] and FEMA356 [13] for linear static and pushover analysis se-  Table 4 presents the lateral displacements obtained from linear static analysis while Table 5 and Table 6 dene the results of pushover analysis. Azad et al. [15]. The base shear has been nor-

V. ACKNOWLEDGEMENT
The authors would like to thank Md. Saiful Alam Lecturer, English Language and Literature, Univer Creative Technology Chittagong, for his sincere t bring grammatical accuracy in this manuscript.