Seismic Vulnerability Assessment of Reinforced Concrete Haunch Beam By Nonlinear Static and Incremental Dynamic Analyses

Seismic Vulnerability Assessment of Reinforced Concrete Haunch Beam By Nonlinear Static and Incremental Dynamic Analyses | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Seismic Vulnerability Assessment of Reinforced Concrete Haunch Beam By Nonlinear Static and Incremental Dynamic Analyses Md. Foisal Haque, Md. Mozammel Hoque This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4497972/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract This research presents a novel technique of the seismic vulnerability assessment of the reinforced concrete haunch beams in terms of the probability of exceedance of the plastic hinge rotations. For this reason, the nonlinear static and incremental dynamic analyses of various structures with bays have been conducted by the ETABS. The plastic hinge rotation is controlled by the collapse prevention and life safety performance levels of beams and joints, respectively. The roof displacement controls the probability of exceedance of the plastic hinge rotations of beams and joints based on the nonlinear static analysis, which is a new insight of this research. The numerical analysis of ETABS is validated with the previously published work to obtain a good agreement of validation results. The 15-storied structure with 3 bays shows a higher vulnerability and the 4-storied structure shows a lower vulnerability according to the numerical analysis. The ranges of the normalized roof displacement and the peak ground acceleration for higher vulnerability are found to be (0.38 ~ 0.56) and (0.05 ~ 0.09) g, respectively, based on the nonlinear static and incremental dynamic analyses. Incremental Dynamic Analysis Nonlinear Static Analysis Reinforced Concrete Haunch Beam Seismic Vulnerability Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction Seismic vulnerability analysis of reinforced concrete haunch beam in terms of the plastic hinge rotation is scarce in the literature. Many studies were completed to evaluate the vulnerability of the reinforced concrete structure using nonlinear static (Kalantari et al. , 2018) and incremental dynamic (Elsanadedy et al. , 2022; Fakharifar et al. , 2015; Xu and Yan, 2023; Moniri, 2017; Kalantari et al. , 2018; Mosleh et al. , 2016) analyses. Rectangular beams may behave as more vulnerable than haunch beams because of inadequate depth at support. The haunch mechanism gives extra shear resistance capacity to the beam because of the additional depth at support. The additional depth can be capable of keeping the incremental length of stirrups. This incremental length increases the additional shear capacity. In some of the cases (Zabihi et al. , 2016; Ahmed et al. , 2019), a steel haunch mechanism was used to retrofit the rectangular reinforced concrete (RC) beam of the existing RC structure. So, the RC haunch mechanism is a novel technique to evaluate the performance and vulnerability of new and retrofitted RC structures under seismic loadings. The seismic performance of the RC structure can be evaluated by the nonlinear static analysis (NSA). The largest brick dome of Soltaniyeh in the world according to UNESCO’s world heritage site in Iran was studied by using the finite element method (FEM) considering nonlinear static analysis (NSA) and nonlinear dynamic analysis (NDA) methods (Kalantari et al. , 2018). All elements of that dome were modeled to consider 10-nodded tetrahedron. The maximum dimension of the mesh element was considered to be 300 mm. The natural frequencies of X-directional, Y-directional, and torsional modes in the Soltaniyeh dome were found to be 3.341 Hz, 3.57 Hz, and 4.93 Hz, respectively. The maximum base shear in the X-direction of the Soltaniyeh dome was obtained to be 29892 kN with a dome tip displacement of 200 mm from the NSA. Similarly, it was found to be 31885 kN with a dome tip displacement of 155 mm in the Y-direction. The dome, second, and third stories failed when the dome tip displacement/pushover stage exceeded 400 mm. The seven-time history records including three components were chosen for the NDA. Three assumptions were considered for the NDA: a) the duration of excitation must be exceeded 3 times of structure’s period or 10 seconds, b) the magnitude of the earthquake must be greater than 6.5, and c) the original record peak acceleration must be greater than 0.2g. The damping ratio of that structure was considered to be 5%. It seemed that the crack was propagated to the dome and first story. Another study (Elsanadedy et al. , 2022) was performed to evaluate the progressive collapse risk of a five-storied steel moment-resistant framed building in Ohio Union considering column buckling to use NDA. They studied the nine numbers of columns and beams. The NDA was performed by using the LS-DYNA package. Beams and columns were assumed to be 2-nodded Hughes-Liu beam elements. All connections were considered to be fully rigid. All slabs were modeled to be 4-nodded quadrilateral shell elements. The maximum rotation in the beam-column connection from NDA was found to be 0.018 rad at the location of the missing column from the exterior on the short side. So, the dynamic increase factor was recommended to be 1.5 and 1.8 for the force and deformation-controlled action of the NSA. The vulnerability study was performed for the two-span highway Reinforced Concrete (RC) Bridge due to the main and aftershocks (Fakharifar et al. , 2015). The circular column was used with a height of 6.7 m. The 25 mm diameter longitudinal bar was used as reinforcement. The diameter of the transverse reinforcement was used to be 12 mm with a spacing of 102 mm. The design yield strength of steel and compressive strength of concrete used to be 300 MPa and 28 MPa, respectively. The RC bridge pier was subjected to six incremental ground motions. The damage was observed in terms of concrete spalling, concrete cracking, longitudinal bar buckling, and longitudinal bar fracture in the plastic hinge region. The incremental dynamic analysis (IDA) was used to overcome the limitations of the NSA. The IDA was first proposed by Vamvatsikos and Cornell (2002). The progressive collapse mechanism of a suspended dome structure subjected to cable rupture was studied experimentally and numerically (Xu and Yan, 2023). The dome structure was solved by the explicit dynamic finite element program ABAQUS. The span and rise were considered 4.2 m and 0.6 m, respectively. The roof dead and live loads were considered to be 0.8 kPa and 0.5 kPa, respectively. Analytically, the Clough-Penzien spectrum excitation was used to evaluate the seismic responses of an asymmetrical suspension structure (Chen et al. , 2023). The largest suspended span was capable of consuming more seismic energy based on the previous study. So, the smaller horizontal displacements and accelerations were obtained from the test results. The seismic performance of the reinforced concrete (RC) building was evaluated to consider the near-field earthquakes by using incremental dynamic analysis (IDA) (Moniri, 2017). Three categories of models were studied such as 6, 10, and 15-storied. The compressive strength of concrete and the yield strength of steel were used to be 30 MPa and 400 MPa, respectively. For performing IDA, 14 numbers of earthquake records of near-field ground motions were considered for the analysis. Based on the numerical analysis result, it is seen that overall and relative displacements increased along with the building height. The non-linear dynamic time history analysis was performed to predict the seismic vulnerability of typical pre-1990 bridges (Mosleh et al. , 2016). The elastic behaviors were considered for the superstructure. Also, the non-linear behavior in piers was modeled by assigning plastic hinges in columns. The bridges were modeled and analyzed with the SAP2000. The fragility curve was drawn based on the damage states of slight, moderate, extensive, and complete damage. The fragility curves were generated by the lognormal distribution function considering median and dispersion. The 70 number of earthquake records were considered for the non-linear dynamic analysis. In the previous study (Luca and Verderame, 2021), a framework was proposed to assess the seismic vulnerability of reinforced concrete structures. All typical modes of failure of reinforced concrete elements were considered in the vulnerability analysis (Luca and Verderame, 2021). The seismic vulnerability of reinforced concrete buildings was studied to consider a group of 91 buildings affected by the macro seismic excitations (Ferreira et al. , 2020). Four positions of the building were considered to assess various vulnerability classes. Also, four confidence factors were selected for the assessment of vulnerability such as elevated, medium, low, and absent. A higher vulnerability index was observed for getting higher levels of damage. A shake table test was performed for the two-storied structure to predict the deficiency of the reinforced concrete structure for proposing the hunch mechanism in the beam to overcome the deficiency by using the hunch retrofitting technique (Ahmad et al. , 2019). They conducted four haunch retrofitted models. Also, special moment resisting frame (SMRF) was considered for the analysis using UBC (Uniform Building Code) 1997. The partition wall load was considered to be 1.915 kPa. Similarly, the live loads for the floor and roof were considered to be 2.873 kPa and 1.915 kPa, respectively. The compressive strength of concrete and the tensile strength of steel were considered to be 24 MPa and 414 MPa, respectively. The beam and column sizes were taken to be 300 mm x 450 mm and 300 mm x 300 mm, respectively. The retrofit technique of the haunch mechanism increased the strength and stiffness of the structure based on the previous study (Ahmad et al. , 2019). However, the vulnerability study of reinforced concrete haunch beams is limited based on the previous literature. Although, the vulnerability study of the reinforced concrete structure is available in the literature. The main goal of this research is the assessment of the vulnerability of reinforced concrete haunch beams to consider the probability of exceedance of the plastic hinge rotations of the collapse prevention performance level of beams and the life safety performance level of joints due to the seismic excitations by the non-linear static and incremental dynamic analyses. For this reason, seven numbers of earthquake records are selected to perform the vulnerability analysis. This is an innovative technique to predict the vulnerability of the reinforced concrete haunch beam. The several categorized reinforced concrete structures are considered in this research. The previous literature on the haunch beam is addressed in Table 1 to understand the general information, which helps to consider the geometry of the haunch and other properties. The vulnerability of reinforced concrete haunch beams is evaluated by satisfying the acceptance criteria of collapse prevention (CP) for beam and life safety (LS) for the beam-column joint. Table 1 Experimental test records of haunch beam from previous literature. SL References Test ID / Remarks Loadings Haunch Length (m) Haunch Thickness (m) Mid-span Depth (m) Mid-span Displacement (mm) Shear Reinforcement (%) at support 1 Albegmprli et al. , 2019 C2-2 Static (Two Points) 0.625 0.100 0.250 5.4 0.67 2 Dang and Dinh, 2017 Steel Haunch Cyclic 0.424 0.440 0.300 / / 3 Aziz et al. , 2016 TB-1S-WC Static 0.750 0.150 0.300 8.0 / 4 Colunga et al. , 2007 TASCα1-R1-c Cyclic 0.933 0.050 0.400 / / 5 Colunga et al. , 2017 TASCV3α1-R1c Cyclic 0.125 0.007 0.038 25.23 0.37 6 Suparp and Joyklad, 2021 HB-01 Static 1.200 0.120 0.460 62.49 0.24 7 Naser et al. , 2021 HB-900 Static 0.300 0.064 0.204 16 / 2. Numerical Study The numerical study is conducted by ETABS (Version 18.1.1) (ETABS, 2020). ETABS is finite element-based software. The numerical study is performed for the nonlinear static and incremental dynamic analyses. 70 numbers of seismic excitations are applied in the numerical model. Each excitation carries various PGA (Peak Ground Acceleration). The PGA is started from 0.05g ("g" is the gravitation acceleration) to 0.5g with an incremental interval of 0.05. The finite element-based numerical code of ETABS is validated with the previous experimental works before the start of this study. In the previous study (Elsanadedy et al., 2022) was used ETABS to predict progressive collapse of the frame structure. 2.1 Validation of Numerical Analysis The validation of the numerical analysis of ETABS 18.1.1 is performed for the previous (Elsanadedy et al., 2022) numerical analysis of the five-story moment resisting framed Ohio Union building. The previous nonlinear dynamic analysis was conducted by the LS-DYNA package (Elsanadedy et al., 2022). All columns and beams were modeled as 2-nodded Hughes-Liu beam elements. In ETABS, all beams and columns are modeled as 2-nodded line elements. The slab was modeled as a 4-nodded quadrilateral element. The same element of the slab is considered during modeling in ETABS 18.1.1. The total number of elements of beams and columns is the same as the present and previous studies. The masonry walls are applied as loads on the structure to avoid the complexity of numerical analysis. The building longitudinal section and plan are presented in Figs. 1 (a), and (b), respectively. The beam-column joint was used as the moment connection. The bottom of the column was used to be the pin support. The gravity load was considered a ramp function, and it was taken at a constant value at the period of 2 seconds. The displacement of the top node of the column was maintained to be 10 mm for the time history of 10 seconds. The material properties were considered from the concrete Eurocode EC2 (type 172). The column and beam sections of the Ohio Union building are shown in Table 2 . The same material properties and sections are considered for the analysis in ETABS. The ramp function is input as a time-history function in the ETABS. The basement column axial load-carrying capacity is shown in Table 3 for the previous (Elsanadedy et al., 2022) and present studies. The difference in results between the two studies is varied within 5%, which may inform a good agreement of validation. Table 2 Beams and Columns geometry of the Ohio Union building (Elsanadedy et al., 2022). Column ID Column Size Beam ID Beam Size C1 WF10 x 72 B1 B24 x 74 C2 WF12 x 133 B2 B20 x 68 C3 WF12 x 120 B3 B16 x 58 C4 WF10 x 100 B4 WF21 x 62 C5 WF10 x 89 B5 WF18 x 50 C6 WF10 x 54 B6 B14 x 17.2 C7 WF10 x 112 B7 B14 x 22 C8 WF10 x 60 B8 WF24 x 76 C9 WF10 x 33 B9 WF10 x 21 Table 3 Validation results of the axial load of the basement columns. Column ID Ultimate Axial Loads (kN) Difference in Results (%) P LS−DYNA (Elsanadedy et al., 2022) P ETABS (Present Research) C1 4162 4143 0.5 C2 7962 7890 0.9 C3 7236 7115 1.7 C4 5690 5482 3.7 C5 5056 4887 3.3 2.2 Numerical Models The numerical models are performed for the 4, 6, 9, 12, and 15-storied buildings considering the number of bays of 3, 4, and 5 for each category of structure. The widths of each bay are used to be 5, 6, and 8 m. All beams are considered to be the reinforced concrete haunch. Details of geometric and material considerations are shown in Table 4 with valid reasons. The plans of the various storied structures are presented in Fig. 2 . Also, the sectional elevations of all storied structures are shown in Fig. 3 . In this research, the finite element-based software ETABS 18.1.1 (ETABS 2020) is used for the nonlinear static and nonlinear dynamic analyses. The ETABS was used for the linear static analysis of the Ohio Union building (Elsanadedy et al., 2022). Also, the ETABS was used for the haunch retrofitting technique of the reinforced concrete frame (Ahmad et al., 2019). The beams and columns are considered to be 2-nodded line elements as previously (Elsanadedy et al., 2022; Ahmad et al., 2019) published works. The slab is assumed to be a 4-nodded quadrilateral element the same as the previous (Elsanadedy et al., 2022) study. The floor finish and roof live load are considered to be 1.2 kN/m 2 and 1.5 kN/m 2 , respectively, according to the BNBC (2020). The partition and live loads of all floors are taken to be 2.873 kN/m 2 based on the previous (Ahmad et al., 2019) study. The 5% viscous damping is considered for the analysis according to the previous (Moniri 2017; Aljawhari et al., 2020) similar types of study. The P-Δ effect is included in the geometric nonlinear analysis. Recently (Fakharifar et al., 2015; Akbar et al., 2020), the P-Δ effect was considered for the vulnerability and fragility analysis to include the geometric nonlinearity impact on the structures. The seven numbers of selected seismic excitations are applied at the base of each structure during the nonlinear dynamic analysis. These excitations are listed in Table 5 . The incremental dynamic analysis was first proposed by Vamvatsikos and Cornell (2002). Several (Fakharifar et al., 2015; Mosleh et al., 2016; Moniri 2017; Ahmad et al., 2019; Akbar et al., 2020) vulnerability and fragility studies were performed to consider the incremental dynamic analysis. The vulnerability was assessed by the fragility curve to consider the probability of damage (Fakharifar et al., 2015) and exceedance (Mosleh et al., 2016) with the PGA range of (0 ~ 1) g and (0 ~ 2) g. In this research, the vulnerability is assessed by the fragility function to consider the probability of exceedance of CP and LS levels of haunch beams and joints under various seismic excitations with PGAs (peak ground accelerations) of 0.05g, 0.10g, 0.15g, 0.20g, 0.25g, 0.30g, 0.35g, 0.40g, 0.45g, and 0.50g. The CP and LS levels are ensured by the plastic hinge rotation. This rotation is evaluated from the analysis of several numerical models. Table 4 Geometric and material properties for the numerical analysis. SL No. Items Values with Units Specific Information, if any (References) 1 Number of Stories 4, 6, 9, 12, and 15 6, 15 (Moniri, 2017); 4 (Fotopoulou et al., 2012; Aljawhari et al., 2020); 12 (Tena-Colunga, 1994) 2 Number of Bays 3, 4, and 5 3 (Moniri, 2017; Fotopoulou et al., 2012; Shafaei et al., 2016); 4 (Aljawhari et al., 2020) 3 Bays Width 5 m, 6 m, and 8 m 5 m (Fotopoulou et al., 2012; Shafaei et al., 2016); 6 m (Moniri, 2017); 4 Inter-Storey Height 3 m Moniri, 2017; Fotopoulou et al., 2012; Zabihi et al., 2016; Aljawhari et al., 2020 5 Support Conditions at Base Fixed Moniri, 2017; Shafaei et al., 2016; Aljawhari et al., 2020 6 Size of Column 300 mm x 300 mm Ahmed et al., 2019; Akbar et al., 2020; Aljawhari et al., 2020 7 Width of Beam 300 mm Fotopoulou et al., 2012; Ahmed et al., 2019; Akbar et al., 2020; Zabihi et al., 2016; Shafaei et al., 2016; Aljawhari et al., 2020 8 Depth of Beam 400 mm (Support) Zabihi et al., 2016; Shafaei et al., 2016 9 Haunch Depth 100 mm Akbar et al., 2020 10 Haunch Length 0.933L 1 Colunga et al., 2007 11 Slab Thickness 150 mm BNBC 2020; ACI 318-05 12 Cylindrical Compressive Strength of Concrete 21 MPa Ahmed et al., 2019 13 Yield Strength of Steel 414 MPa Ahmed et al., 2019 Note: L 1 is the beam length. Table 5 Various earthquake records for the nonlinear time history analysis. SL No. Year Earthquake Name Moment Magnitude, Mw PGA (g) Reference 1 1971 San Fernando 6.6 0.699 Mosleh et al., 2016 2 1987 Superstition Hills 6.5 0.793 3 1989 Loma Prieta 6.9 0.644 4 1994 Northridge 6.7 0.871 Moniri 2017 5 1999 Chi-Chi 7.6 0.568 6 1999 Kocaeli 7.4 0.415 7 1998 Umbria 4.8 0.240 Fotopoulou et al., 2012 2.3 Nonlinear Static Analysis Procedure The displacement control nonlinear static analysis is performed in ETABS considering the P-Δ effect. The displacement is monitored on the roof. The target displacement and approximate fundamental time of all structures are calculated based on the given formulae in the BNBC (2020). The normalized acceleration response spectrum is calculated according to the BNBC (2020) for the definition of earthquake force in ETABS for linear static analysis. The importance factor and zone coefficient of all structures are considered to be 1 and 0.20g, respectively, based on the BNBC (2020). It is assumed that all structures stand on the loose to medium cohesionless soil. The response reduction factor is considered for the special moment resisting frame according to the BNBC (2020). These above-describing factors are taken for the seismic force consideration of the linear static analysis, which is defined as the load during the nonlinear static analysis. The nonlinear static analysis is continued until the control point (roof) displacement is reached at least 1.5 times the target displacement. The plastic hinges are provided in the beams and beam-column joints before starting the analysis. In the beam, the plastic hinge is provided at the both supports and the middle. In the case of the support, it is placed at a relative length factor of 0.05. The iterative analysis procedure is followed to consider the Newton-Raphson method. The implicit analysis is continued until convergence is achieved. 2.3.1 Details of Plastic Hinge for Beam The shear and flexural hinges are used in the reinforced concrete haunch beam at the support and middle, respectively. The relative length is maintained to be 19.4% of the total center-to-center length in the case of the support hinge. This relative length is the average value of the shear hinge location based on the experimental (Godínez-Domínguez et al., 2015) study. The plastic hinge rotation represents the performance of beams as well as overall structures. The shear plastic hinge rotation in the case of the collapse prevention (CP) level is considered to be 0.01 radians according to the standard (FEMA 273) to assume the stirrup spacing is greater than half of the effective depth. The flexural hinge of the beam is provided in the middle. Some assumptions are assumed for the flexural hinge consideration such as (a) balance reinforcement ratio, (b) transverse reinforcement, and (c) shear demand and capacity ratio of 3 (three). The plastic hinge rotation is considered to be 0.05 radians in the case of the CP level of acceptance criteria for the secondary component. Details mechanism to define the shear and flexural plastic hinge of the beam in ETABS are shown in Table 6 . 2.3.2 Details of Plastic Hinge for Joint The joint performance is considered to be the life safety (LS) level in the case of the exterior and interior. For this reason, some assumptions are considered to evaluate the performance of joints such as (a) axial load capacity of 1% of the gross area of the concrete, (b) confirmation of the transverse reinforcement, and (c) demanding shear of 1.2 times of shear capacity. The plastic hinge rotations at the LS level of the interior and exterior joints in the case of the secondary component are found to be 0.02 and 0.015 radians according to FEMA (273). The joint plastic hinge is provided at the beam-column joint of each structure. The definition information of the joint plastic hinge in ETABS is presented in Table 6 . Table 6 Details information of various plastic hinges for defining in ETABS. Items Shear Plastic Hinge of Beam at Support Flexural Plastic Hinge of Beam at Middle Plastic Hinge at the Beam-Column Joint Hinge Type Shear Interacting M2-M3 Interacting P-M2-M3 Hinge Specification Type / Moment-Curvature Moment-Curvature Hinge Rotation Representation Type Force-Displacement / / Backbone Curve Type Symmetric Double Symmetry Double Symmetry Load Carrying Capacity Drops to Zero Drops to Zero Drops to Zero Immediate Occupancy (IO) 0.0 0.005 I O 0.0 0.0 Life Safety (LS) 0.005 0.02 0.02 0.015 Collapse Prevention (CP) 0.01 0.05 0.03 0.02 Hysteresis Type Isotropic / / Interaction Surface / Default from Material Property of Associated Frame Object Default from Material Property of Associated Frame Object Axial Load – Displacement Relationship / / Elastic-Perfectly Plastic Axial Force Associated with M2-M3 Curve / Select it after the end of the Linear Static Analysis / Note: (i) “/” means that not necessary; (ii) O = Other; (iii) I = Interior. 2.4 Incremental Dynamic Analysis Procedure In this research, the incremental dynamic analysis is related to the nonlinear dynamic as well as time history analysis. The reinforced concrete haunch and structural responses are recorded for variable PGA with a specific earthquake record. This seismic excitation is input in ETABS as a time history function. For the nonlinear time history analysis, the response reduction and structural importance factors are considered to be the unit (BNBC 2020) value according to the BNBC (2020). The nonlinear direct time integration considering the Hilber-Hughes-Taylor method (Elsanadedy et al., 2022) is followed to predict the performance of the structure. The seismic excitation is applied from the two orthogonal directions of each structure. 3. Vulnerability Analysis Each structure is divided into four categories based on the arrangement of plastic hinges such as normal beam at support (NBS), haunch beam at support (HBS), haunch beam at support and middle (HBSM), and haunch beam at support-middle-joint (HBS-M-J). Figure 4 depicts the various plastic hinge arrangements at the beams and joints of structures. The probability of exceedance of the plastic hinge rotation with the help of the fragility function assesses the vulnerability. Collapse prevention (CP) and life safety (LS) performance levels are controlled by beams and joints, respectively. The mean ( \(\theta\) ) of the exceedance of CP or LS levels depends on the total ( \({n}_{i}\) ) and failure ( \({r}_{i}\) ) beams and joints. Failure means the exceedance of CP and LS levels of plastic hinge rotation. The mean, standard deviation ( \(\beta\) ), and probability of exceedance ( \({p}_{i}\) ) are expressed in Eqs. (1), (2), and ( 3 ), respectively, according to the FEMA (273). $$\theta =\frac{1}{{n}_{i}}\sum _{i=1}^{{n}_{i}}ln\left({r}_{i}\right) \left(1\right)$$ $$\beta =\sqrt{\frac{1}{\left({n}_{i}-1\right)}\sum _{i=1}^{{n}_{i}}{\left\{ln\left(\raisebox{1ex}{${r}_{i}$}\!\left/ \!\raisebox{-1ex}{$\theta $}\right.\right)\right\}}^{2}} \left(2\right)$$ $${p}_{i}=\varphi \left(\frac{ln\left(\raisebox{1ex}{${r}_{i}$}\!\left/ \!\raisebox{-1ex}{$\theta $}\right.\right)}{\beta }\right) \left(3\right)$$ 3.1 Assessment of Vulnerability by Nonlinear Static Analysis The roof displacement is monitored in the nonlinear static analysis. It depends on the plastic hinge rotations of beams and joints. The roof displacement is normalized by dividing the target displacement. The probability of exceedance in terms of plastic hinge rotations of beams and joints is a new insight. Another novelty is the representation of the probability of exceedance in terms of the normalized roof displacement. These variations for all structures including bays and plastic hinge placement conditions are presented in Fig. 5 . The plastic hinges of both opposite supports of the beam exceed the CP level, then the middle hinge exceeds the CP level. Finally, the beam-column joint exceeds the LS level. The vulnerability rate increment means the exceedance of the CP and LS levels within the shorter range of the normalized roof displacement. The vulnerability increases with the increment of the number of stories due to the decrement of the overall structural stiffness to hamper the individual beam stiffness to cause an exceedance of CP level within the shorter normalized roof displacement. The normal or rectangular beam is more vulnerable than the haunch beam because of the lower stiffness. The HBS-M-J shows less vulnerability because of controlling the joint performance level. In addition, the HBS-M-J is the critical condition for all structures due to the plastic hinge formation of beams and adjacent joints under successive seismic excitation. The normalized roof displacement range for the probability of exceedance of the HBS-M-J condition is (0.4 ~ 0.8) considering all structures with 3 bays. The probability of exceedance considering all structures and bays is performed for the bay width of 5 m because the higher width shows more vulnerability than the lower. The vulnerability reduces gradually with the increment of the number of bays due to the increment of the structural stiffness reducing the achievement of plastic hinge rotation of CP and LS levels. The higher vulnerability shows the 15-storied structure of 3 bays for the placement condition of the plastic hinge of NBS. The lower vulnerability shows the 4-storied structure of 5 bays for the placement condition of the plastic hinge of HBS-M-J. The ranges of the normalized roof displacements in the case of the higher and lower vulnerabilities are (0.38 ~ 0.56) and (0.87 ~ 1.0), respectively. 3.2 Assessment of Vulnerability by Incremental Dynamic Analysis The incremental dynamic analysis is performed based on the probability of exceedance of the plastic hinge rotation. This is a new insight into the vulnerability evaluation considering successive variations of the PGA. The incremental dynamic analysis was performed to consider the probability of exceedance of various types of damage such as slight, moderate, extensive, and complete damage states (Mosleh et al., 2016). Also, it was conducted to predict the probability of exceedance of several parameters such as idealized yield, code drift limit, and incipient collapse (Ahmad et al., 2019). In this research, the plastic hinge rotation is controlled by the exceedance of the CP and LS performance levels of beams and joints. For the incremental dynamic analysis, the HBS-M-J is the critical condition because of the exceedance of the CP level of the beam at the support and middle and LS levels of the joint. So, the higher value of the PGA is required to satisfy the condition of HBS-M-J. The lower value of the PGA is required to satisfy the condition of NBS. The incremental vulnerability rate is NBS > HBS > HBSM > HBS-M-J according to the probability of exceedance as shown in Fig. 6 . The incremental dynamic analysis results are listed in Fig. 6 to consider the maximum value of PGA among the seven earthquake records. Structures are shown to be more vulnerable to the maximum intense earthquake. The vulnerability rate increases gradually with the increment of the number of stories due to the reduced stiffness increasing plastic hinge rotation under seismic excitations. The vulnerability rate gradually decreased with the increment of the number of bays because of the increment of overall structural stiffness. The lower and higher vulnerabilities show the 4-storied structure with 5 bays and the 15-storied structure with 3 bays as shown in Fig. 6 (a) and (m). The incremental dynamic analysis is performed for the bay width of 5 m because the lower width shows less vulnerability than the higher one. The PGA ranges of lower and higher vulnerabilities are found to be (0.45 ~ 0.5) g and (0.05 ~ 0.09) g, respectively. The NBS condition shows a higher vulnerability, and the HBS-M-J represents a lower vulnerability. 4. Conclusion This research evaluates the seismic vulnerability of the reinforced concrete haunch beam by the nonlinear static analysis considering roof displacement and incremental dynamic analysis considering various peak ground accelerations. For this reason, several numerical analyses have been performed by ETABS considering various structures with variable bays. The seven numbers of seismic excitations are chosen for the nonlinear time history analysis. Each structure is classified into four categories based on the plastic hinge location and beam types. The probability of exceedance of the plastic hinge rotation of the collapse prevention performance level of beams and the life safety performance level of joints assesses the vulnerability. The roof displacement controls the vulnerability of reinforced concrete rectangular and haunch beams based on the nonlinear static analysis. The new insight in this research is the assessment of the seismic vulnerability in terms of the plastic hinge rotations of beams and the beam-column joints. Therefore, major conclusions are summarized herein: The vulnerability is increased gradually with the increment of the number of stories due to the reduction of the overall stiffness of the structure. It is decreased with the increment of the number of bays because of increasing lateral stiffness of structures. So, a 15-storied structure with 3 bays shows more vulnerability and a 4-storied structure with 5 bays expresses less vulnerability. This phenomenon is seen in both seismic vulnerability assessing procedures. According to the nonlinear static analysis, the ranges of the normalized roof displacements for the lower and higher vulnerabilities are found to be (0.87 ~ 1.0) and (0.38 ~ 0.56), respectively. Similarly, the ranges of the peak ground accelerations for the higher and lower vulnerabilities are obtained to be (0.05 ~ 0.09) g and (0.45 ~ 0.5) g, respectively, based on the incremental dynamic analysis. There is a scope to further extend this research by considering the variable geometry of structures and individual haunch beams, adding more plastic hinges over the beam, taking different conditions for choosing the plastic hinge rotation according to the code, including material anisotropy, etc. Declarations Conflict of Interest There is no conflict of interest to conduct this research. Author Contribution Md. Foisal Haque: Conceptualizations, Methodology, Software Analysis, Writing, Editing, Resources, Reviewing.Md. Mozammel Hoque: Resources. Data Availability No data are available in this research. References 318-05, A. (2014). Building Code Requirements for Structural Concrete and Commentary. USA: American Concrete Institute. Ahmad, N., Akbar, J., Rizwan, M., Alam, B., Khan, A. N., & Lateef, A. (2019). Haunch retroftting technique for seismic upgrading defcient RC frames. Bulletin of Earthquake Engineering , 1-38. Retrieved from https://doi.org/10.1007/s10518-019-00638-9 Akbar, J., Ahmad, N., Rizwan, M., Javed, S., & Alam, B. (2020). Response Modification Factor of RC Frames Strengthened with RC Haunches. Shock and Vibration , 1-18. Retrieved from https://doi.org/10.1155/2020/3835015 Albegmprli, H. M., Gülşan, M. E., & Cevik, A. (2019). Comprehensive experimental investigation on mechanical behavior for types of reinforced concrete Haunched beam. Advances in Concrete Construction, 7 (1), 39-50. Retrieved from https://doi.org/10.12989/acc.2019.7.1.039 Aljawhari, K., Gentile, R., Freddi, F., & Galasso, C. (2021). Efects of ground‑motion sequences on fragility and vulnerability of case‑study reinforced concrete frames. Bulletin of Earthquake Engineering , 6329–6359. Retrieved from https://doi.org/10.1007/s10518-020-01006-8 Aziz, A. H., Hassan, H. F., & Razzaq, F. M. (2016). Experimental Study on Shear Behavior of Reinforced Self-Compacted Concrete Tapered Beams. Civil and Environmental Research, 8 (8), 11-22. BNBC. (2020). Bangladesh National Building Code. Chen, M., Liang, X., Yang, Z., Ge, X., & Xu, C. (2023). Analytical Study on the Random Seismic Responses of an Asymmetrical Suspension Structure. buildings , 1-19. Retrieved from https://doi.org/10.3390/buildings13061435 Colunga, A., Archundia-Aranda, H., Grande-Vega, A., & González-Cuevas, O. (2007). Cyclic Shear Behavior of Reinforced Concrete Haunched Beams. Ninth Canadian Conference on Earthquake Engineering , (pp. 1127-1137). Ottawa, Ontario, Canada. Colunga, A., Urbina-Californias, L. A., & Archundia-Aranda, H. (2017). Assessment of the shear strength of continuous reinforced concrete haunched beams based upon cyclic testing. Journal of Building Engineering, 11 , 187-204. Retrieved from https://doi.org/10.1016/j.jobe.2017.04.018 Dang, C.-T., & Dinh, N.-H. (2017). Experimental Study on Structural Performance of RC Exterior Beam-Column Joints Retrofitted by Steel Jacketing and Haunch Element under Cyclic Loading Simulating Earthquake Excitation. Advances in Civil Engineering , 1-11. Retrieved from https://doi.org/10.1155/2017/9263460 Elsanadedy, H., Sezen, H., Abbas, H., Almusallam, T., & Al-Salloum, Y. (2022). Progressive collapse risk of steel framed building considering column buckling. Engineering Science and Technology, an International Journal , 1-15. Retrieved from https://doi.org/10.1016/j.jestch.2022.101193 ETABS. (2020). CSI Analysis Reference Manual (Version 18 ed.). United States of America: Computers & Structures, Inc. Fakharifar, M., Chen, G., Dalvand, A., & Shamsabadi, A. ( 2015). Collapse Vulnerability and Fragility Analysis of Substandard RC Bridges Rehabilitated with Different Repair Jackets Under Post-mainshock Cascading Events. International Journal of Concrete Structures and Materials , 345–367. FEMA 273. (1997). NEHRP Guidelines for the Seismic Rehabilitation of Buildings. Washington, D.C.: FEDERAL EMERGENCY MANAGEMENT AGENCY. Ferreira, T. M., Rodrigues, H., & Vicente, R. (2020). Seismic Vulnerability Assessment of Existing Reinforced Concrete Buildings in Urban Centers. Sustainability , 1-20. doi:10.3390/su12051996 Fotopoulou, S., Karapetrou, S., & Pitilakis, K. (2012). Seismic vulnerability of RC buildings considering SSI and aging effects. 15 WCEE , (pp. 1-10). Lisboa. Godínez-Domínguez, E. A., Tena-Colunga, A., & Juárez-Luna, G. (2015). Nonlinear finite element modeling of reinforced concrete haunched beams designed to develop a shear failure. Engineering Structures, 105 , 99–122. Retrieved from http://dx.doi.org/10.1016/j.engstruct.2015.09.023 Kalantari, H., Nasserasadi, K., & Arjmandi, S. A. (2018). Seismic vulnerability study of Soltaniyeh dome using nonlinear static and dynamic analyses. International Journal of Advanced Structural Engineering , 367–380. Retrieved from https://doi.org/10.1007/s40091-018-0203-3 Luca, F. D., & Verderame, G. M. (2021). Seismic Vulnerability Assessment: Reinforced Concrete Structures. Encyclopedia of Earthquake Engineering , 1-31. doi:10.1007/978-3-642-36197-5_252-1 Moniri, H. (2017). Evaluation of seismic performance of reinforced concrete (RC) buildings under near-field earthquakes. Int J Adv Struct Eng , 13–25. doi:10.1007/s40091-016-0145-6 Mosleh, A., Razzaghi, M. S., Jara, J., & Varum, H. (2016). Int J Adv Struct Eng , 1–9. doi:10.1007/s40091-016-0108-y Naser, M., Hawileh, R. A., & Abdalla, J. (2021). Modeling Strategies of Finite Element Simulation of Reinforced Concrete Beams Strengthened with FRP: A Review. Compos. Sci. , 1-15. Retrieved from https://doi.org/10.3390/jcs5010019 Shafaei, J., Hosseini, A., Marefat, M. S., & Ingham, J. M. (2016). Experimental Evaluation of Seismically and Non-Seismically Detailed External RC Beam-Column Joints. Journal of Earthquake Engineering . doi:10.1080/13632469.2016.1185052 SUPARP, S., & JOYKLAD, P. (2021). Flexural Behavior of Hollow Reinforced Concrete Haunched (RCH) Beams. Journal of Engineering Science and Technology, 16 (4), 3267 – 3282. Tena-Colunga, A. (1994). Concerns Regarding the Seismic Design of Reinforced Concrete Haunched Beams. ACI Structural Journal , 287-293. Vamvatsikos, D., & Cornell, C. A. (2002). Incremental Dynamic Analysis. Earthquake Engng Struct. Dyn. , 1-21. Xu, Z., & Yan, S. (2023). Progressive-Collapse Mechanism of Suspended-Dome Structures Subjected to Sudden Cable Rupture. buildings , 1-21. Retrieved from https://doi.org/10.3390/buildings13061533 Zabihi, A., Tsang, H.-H., Gad, E. F., & Wilson, J. L. (2016). Retrofitting RC Beam-Column Joint in Australia using Single Diagonal Haunch. Australian Earthquake Engineering Society 2016 Conference (pp. 1-9). Melbourne: Australian Earthquake Engineering Society. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 07 Jul, 2024 Reviews received at journal 07 Jul, 2024 Reviewers agreed at journal 07 Jul, 2024 Reviews received at journal 03 Jul, 2024 Reviewers agreed at journal 02 Jul, 2024 Reviewers invited by journal 06 Jun, 2024 Editor assigned by journal 31 May, 2024 Submission checks completed at journal 30 May, 2024 First submitted to journal 29 May, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4497972","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":313271200,"identity":"5a782cef-0770-4558-ad14-920cbb03db07","order_by":0,"name":"Md. Foisal Haque","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAzElEQVRIiWNgGAWjYDAC5jNAwoCBh4+9AcSwIEILWw5ECxvPARBDglgtIFoiAUQRoUW3jfcAw4+CwzJsks+vbvhRIMHA396dgFeL2TG+BMYeg8M8bNI5ZTd7gA6TOHN2A34t93sMmBkM0kBa0m7wALUYSOQS0HKMB6pF8kzazT8kaLHhYZNgP3abaFsO9oC08OSw3ZYxkOAh7JdjPIYPfvyRsOdnP/7s5ps/NnL87b34tYDAAQjFYwAmCSpHAuwPSFE9CkbBKBgFIwgAAPDePECqDO+VAAAAAElFTkSuQmCC","orcid":"","institution":"Dhaka University of Engineering \u0026 Technology","correspondingAuthor":true,"prefix":"","firstName":"Md.","middleName":"Foisal","lastName":"Haque","suffix":""},{"id":313271201,"identity":"d98fc3b0-3287-4e50-a6b9-548062bb869a","order_by":1,"name":"Md. Mozammel Hoque","email":"","orcid":"","institution":"Dhaka University of Engineering \u0026 Technology","correspondingAuthor":false,"prefix":"","firstName":"Md.","middleName":"Mozammel","lastName":"Hoque","suffix":""}],"badges":[],"createdAt":"2024-05-29 15:06:28","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4497972/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4497972/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":58190974,"identity":"c94a846e-29dd-4900-892a-124d12b41ffc","added_by":"auto","created_at":"2024-06-12 08:26:20","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":417898,"visible":true,"origin":"","legend":"\u003cp\u003eGeometry of the Ohio Union building: (a) longitudinal section, and (b) plan (after, Elsanadedy et al., 2022).\u003c/p\u003e","description":"","filename":"1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4497972/v1/0c3d977b66cdaba923be47c0.jpeg"},{"id":58191642,"identity":"34a18b8d-19cb-4f6f-ae9e-7965999d8ee0","added_by":"auto","created_at":"2024-06-12 08:34:20","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":14579,"visible":true,"origin":"","legend":"\u003cp\u003eDifferent bays of various storied structures.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-4497972/v1/ce64aa55111ce499c69bb125.png"},{"id":58190971,"identity":"1a26ad0b-61f3-4ce9-aff1-62ed10b51ecc","added_by":"auto","created_at":"2024-06-12 08:26:20","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":48497,"visible":true,"origin":"","legend":"\u003cp\u003eSectional elevation of various storied structures.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-4497972/v1/fda182aa2294e8058e7f0a2c.png"},{"id":58192444,"identity":"595e1b5e-b43b-47ac-9036-bf557197ab6d","added_by":"auto","created_at":"2024-06-12 08:42:20","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":77541,"visible":true,"origin":"","legend":"\u003cp\u003eArrangement of plastic hinges for the vulnerability analysis.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-4497972/v1/3a16e77ac1306b1da083a89a.png"},{"id":58190976,"identity":"adcf3676-3b54-4a0b-92f1-d25f2d1173ab","added_by":"auto","created_at":"2024-06-12 08:26:20","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":2547641,"visible":true,"origin":"","legend":"\u003cp\u003eFragility curves for assessing vulnerability by nonlinear static analysis.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-4497972/v1/d2e4489eae153c0216b6318f.png"},{"id":58191643,"identity":"95c3d1b5-bfc1-4d6f-8172-5330f610c126","added_by":"auto","created_at":"2024-06-12 08:34:20","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":2396166,"visible":true,"origin":"","legend":"\u003cp\u003eFragility curves for assessing vulnerability by incremental dynamic analysis.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-4497972/v1/0c8b53bb8e806ecebbc27099.png"},{"id":58192964,"identity":"277035cd-eb74-411a-a344-48f3e94f973f","added_by":"auto","created_at":"2024-06-12 08:50:24","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":6479539,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4497972/v1/5edfaba0-0311-4ca9-b620-9c411e382cf7.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Seismic Vulnerability Assessment of Reinforced Concrete Haunch Beam By Nonlinear Static and Incremental Dynamic Analyses","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eSeismic vulnerability analysis of reinforced concrete haunch beam in terms of the plastic hinge rotation is scarce in the literature. Many studies were completed to evaluate the vulnerability of the reinforced concrete structure using nonlinear static (Kalantari \u003cem\u003eet al.\u003c/em\u003e, 2018) and incremental dynamic (Elsanadedy \u003cem\u003eet al.\u003c/em\u003e, 2022; Fakharifar \u003cem\u003eet al.\u003c/em\u003e, 2015; Xu and Yan, 2023; Moniri, 2017; Kalantari \u003cem\u003eet al.\u003c/em\u003e, 2018; Mosleh \u003cem\u003eet al.\u003c/em\u003e, 2016) analyses. Rectangular beams may behave as more vulnerable than haunch beams because of inadequate depth at support. The haunch mechanism gives extra shear resistance capacity to the beam because of the additional depth at support. The additional depth can be capable of keeping the incremental length of stirrups. This incremental length increases the additional shear capacity. In some of the cases (Zabihi \u003cem\u003eet al.\u003c/em\u003e, 2016; Ahmed \u003cem\u003eet al.\u003c/em\u003e, 2019), a steel haunch mechanism was used to retrofit the rectangular reinforced concrete (RC) beam of the existing RC structure. So, the RC haunch mechanism is a novel technique to evaluate the performance and vulnerability of new and retrofitted RC structures under seismic loadings.\u003c/p\u003e \u003cp\u003eThe seismic performance of the RC structure can be evaluated by the nonlinear static analysis (NSA). The largest brick dome of Soltaniyeh in the world according to UNESCO\u0026rsquo;s world heritage site in Iran was studied by using the finite element method (FEM) considering nonlinear static analysis (NSA) and nonlinear dynamic analysis (NDA) methods (Kalantari \u003cem\u003eet al.\u003c/em\u003e, 2018). All elements of that dome were modeled to consider 10-nodded tetrahedron. The maximum dimension of the mesh element was considered to be 300 mm. The natural frequencies of X-directional, Y-directional, and torsional modes in the Soltaniyeh dome were found to be 3.341 Hz, 3.57 Hz, and 4.93 Hz, respectively. The maximum base shear in the X-direction of the Soltaniyeh dome was obtained to be 29892 kN with a dome tip displacement of 200 mm from the NSA. Similarly, it was found to be 31885 kN with a dome tip displacement of 155 mm in the Y-direction. The dome, second, and third stories failed when the dome tip displacement/pushover stage exceeded 400 mm. The seven-time history records including three components were chosen for the NDA. Three assumptions were considered for the NDA: a) the duration of excitation must be exceeded 3 times of structure\u0026rsquo;s period or 10 seconds, b) the magnitude of the earthquake must be greater than 6.5, and c) the original record peak acceleration must be greater than 0.2g. The damping ratio of that structure was considered to be 5%. It seemed that the crack was propagated to the dome and first story.\u003c/p\u003e \u003cp\u003eAnother study (Elsanadedy \u003cem\u003eet al.\u003c/em\u003e, 2022) was performed to evaluate the progressive collapse risk of a five-storied steel moment-resistant framed building in Ohio Union considering column buckling to use NDA. They studied the nine numbers of columns and beams. The NDA was performed by using the LS-DYNA package. Beams and columns were assumed to be 2-nodded Hughes-Liu beam elements. All connections were considered to be fully rigid. All slabs were modeled to be 4-nodded quadrilateral shell elements. The maximum rotation in the beam-column connection from NDA was found to be 0.018 rad at the location of the missing column from the exterior on the short side. So, the dynamic increase factor was recommended to be 1.5 and 1.8 for the force and deformation-controlled action of the NSA.\u003c/p\u003e \u003cp\u003eThe vulnerability study was performed for the two-span highway Reinforced Concrete (RC) Bridge due to the main and aftershocks (Fakharifar \u003cem\u003eet al.\u003c/em\u003e, 2015). The circular column was used with a height of 6.7 m. The 25 mm diameter longitudinal bar was used as reinforcement. The diameter of the transverse reinforcement was used to be 12 mm with a spacing of 102 mm. The design yield strength of steel and compressive strength of concrete used to be 300 MPa and 28 MPa, respectively. The RC bridge pier was subjected to six incremental ground motions. The damage was observed in terms of concrete spalling, concrete cracking, longitudinal bar buckling, and longitudinal bar fracture in the plastic hinge region. The incremental dynamic analysis (IDA) was used to overcome the limitations of the NSA. The IDA was first proposed by Vamvatsikos and Cornell (2002).\u003c/p\u003e \u003cp\u003eThe progressive collapse mechanism of a suspended dome structure subjected to cable rupture was studied experimentally and numerically (Xu and Yan, 2023). The dome structure was solved by the explicit dynamic finite element program ABAQUS. The span and rise were considered 4.2 m and 0.6 m, respectively. The roof dead and live loads were considered to be 0.8 kPa and 0.5 kPa, respectively. Analytically, the Clough-Penzien spectrum excitation was used to evaluate the seismic responses of an asymmetrical suspension structure (Chen \u003cem\u003eet al.\u003c/em\u003e, 2023). The largest suspended span was capable of consuming more seismic energy based on the previous study. So, the smaller horizontal displacements and accelerations were obtained from the test results. The seismic performance of the reinforced concrete (RC) building was evaluated to consider the near-field earthquakes by using incremental dynamic analysis (IDA) (Moniri, 2017). Three categories of models were studied such as 6, 10, and 15-storied. The compressive strength of concrete and the yield strength of steel were used to be 30 MPa and 400 MPa, respectively. For performing IDA, 14 numbers of earthquake records of near-field ground motions were considered for the analysis. Based on the numerical analysis result, it is seen that overall and relative displacements increased along with the building height.\u003c/p\u003e \u003cp\u003eThe non-linear dynamic time history analysis was performed to predict the seismic vulnerability of typical pre-1990 bridges (Mosleh \u003cem\u003eet al.\u003c/em\u003e, 2016). The elastic behaviors were considered for the superstructure. Also, the non-linear behavior in piers was modeled by assigning plastic hinges in columns. The bridges were modeled and analyzed with the SAP2000. The fragility curve was drawn based on the damage states of slight, moderate, extensive, and complete damage. The fragility curves were generated by the lognormal distribution function considering median and dispersion. The 70 number of earthquake records were considered for the non-linear dynamic analysis.\u003c/p\u003e \u003cp\u003eIn the previous study (Luca and Verderame, 2021), a framework was proposed to assess the seismic vulnerability of reinforced concrete structures. All typical modes of failure of reinforced concrete elements were considered in the vulnerability analysis (Luca and Verderame, 2021). The seismic vulnerability of reinforced concrete buildings was studied to consider a group of 91 buildings affected by the macro seismic excitations (Ferreira \u003cem\u003eet al.\u003c/em\u003e, 2020). Four positions of the building were considered to assess various vulnerability classes. Also, four confidence factors were selected for the assessment of vulnerability such as elevated, medium, low, and absent. A higher vulnerability index was observed for getting higher levels of damage.\u003c/p\u003e \u003cp\u003eA shake table test was performed for the two-storied structure to predict the deficiency of the reinforced concrete structure for proposing the hunch mechanism in the beam to overcome the deficiency by using the hunch retrofitting technique (Ahmad \u003cem\u003eet al.\u003c/em\u003e, 2019). They conducted four haunch retrofitted models. Also, special moment resisting frame (SMRF) was considered for the analysis using UBC (Uniform Building Code) 1997. The partition wall load was considered to be 1.915 kPa. Similarly, the live loads for the floor and roof were considered to be 2.873 kPa and 1.915 kPa, respectively. The compressive strength of concrete and the tensile strength of steel were considered to be 24 MPa and 414 MPa, respectively. The beam and column sizes were taken to be 300 mm x 450 mm and 300 mm x 300 mm, respectively. The retrofit technique of the haunch mechanism increased the strength and stiffness of the structure based on the previous study (Ahmad \u003cem\u003eet al.\u003c/em\u003e, 2019). However, the vulnerability study of reinforced concrete haunch beams is limited based on the previous literature. Although, the vulnerability study of the reinforced concrete structure is available in the literature.\u003c/p\u003e \u003cp\u003eThe main goal of this research is the assessment of the vulnerability of reinforced concrete haunch beams to consider the probability of exceedance of the plastic hinge rotations of the collapse prevention performance level of beams and the life safety performance level of joints due to the seismic excitations by the non-linear static and incremental dynamic analyses. For this reason, seven numbers of earthquake records are selected to perform the vulnerability analysis. This is an innovative technique to predict the vulnerability of the reinforced concrete haunch beam. The several categorized reinforced concrete structures are considered in this research. The previous literature on the haunch beam is addressed in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e to understand the general information, which helps to consider the geometry of the haunch and other properties. The vulnerability of reinforced concrete haunch beams is evaluated by satisfying the acceptance criteria of collapse prevention (CP) for beam and life safety (LS) for the beam-column joint.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExperimental test records of haunch beam from previous literature.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSL\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eReferences\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTest ID / Remarks\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eLoadings\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eHaunch Length (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eHaunch Thickness (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eMid-span Depth (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMid-span Displacement (mm)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eShear Reinforcement (%) at support\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAlbegmprli \u003cem\u003eet al.\u003c/em\u003e, 2019\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eC2-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStatic (Two Points)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.625\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.250\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e5.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.67\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDang and Dinh, 2017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSteel Haunch\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCyclic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.424\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.440\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAziz \u003cem\u003eet al.\u003c/em\u003e, 2016\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTB-1S-WC\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStatic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.750\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e8.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eColunga \u003cem\u003eet al.\u003c/em\u003e, 2007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTASCα1-R1-c\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCyclic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.933\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.050\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eColunga \u003cem\u003eet al.\u003c/em\u003e, 2017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTASCV3α1-R1c\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCyclic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.125\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.007\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.038\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e25.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.37\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSuparp and Joyklad, 2021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHB-01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStatic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e1.200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.460\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e62.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.24\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNaser \u003cem\u003eet al.\u003c/em\u003e, 2021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eHB-900\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eStatic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.064\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.204\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"2. Numerical Study","content":"\u003cp\u003eThe numerical study is conducted by ETABS (Version 18.1.1) (ETABS, 2020). ETABS is finite element-based software. The numerical study is performed for the nonlinear static and incremental dynamic analyses. 70 numbers of seismic excitations are applied in the numerical model. Each excitation carries various PGA (Peak Ground Acceleration). The PGA is started from 0.05g (\"g\" is the gravitation acceleration) to 0.5g with an incremental interval of 0.05. The finite element-based numerical code of ETABS is validated with the previous experimental works before the start of this study. In the previous study (Elsanadedy et al., 2022) was used ETABS to predict progressive collapse of the frame structure.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Validation of Numerical Analysis\u003c/h2\u003e \u003cp\u003eThe validation of the numerical analysis of ETABS 18.1.1 is performed for the previous (Elsanadedy et al., 2022) numerical analysis of the five-story moment resisting framed Ohio Union building. The previous nonlinear dynamic analysis was conducted by the LS-DYNA package (Elsanadedy et al., 2022). All columns and beams were modeled as 2-nodded Hughes-Liu beam elements. In ETABS, all beams and columns are modeled as 2-nodded line elements. The slab was modeled as a 4-nodded quadrilateral element. The same element of the slab is considered during modeling in ETABS 18.1.1. The total number of elements of beams and columns is the same as the present and previous studies. The masonry walls are applied as loads on the structure to avoid the complexity of numerical analysis. The building longitudinal section and plan are presented in Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e (a), and (b), respectively. The beam-column joint was used as the moment connection. The bottom of the column was used to be the pin support. The gravity load was considered a ramp function, and it was taken at a constant value at the period of 2 seconds. The displacement of the top node of the column was maintained to be 10 mm for the time history of 10 seconds. The material properties were considered from the concrete Eurocode EC2 (type 172). The column and beam sections of the Ohio Union building are shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The same material properties and sections are considered for the analysis in ETABS. The ramp function is input as a time-history function in the ETABS. The basement column axial load-carrying capacity is shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e for the previous (Elsanadedy et al., 2022) and present studies. The difference in results between the two studies is varied within 5%, which may inform a good agreement of validation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBeams and Columns geometry of the Ohio Union building (Elsanadedy et al., 2022).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eColumn ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eColumn Size\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eBeam ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBeam Size\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWF10 x 72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eB24 x 74\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWF12 x 133\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eB20 x 68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWF12 x 120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eB16 x 58\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWF10 x 100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWF21 x 62\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWF10 x 89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWF18 x 50\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWF10 x 54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eB14 x 17.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWF10 x 112\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eB14 x 22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWF10 x 60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWF24 x 76\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWF10 x 33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eB9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eWF10 x 21\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eValidation results of the axial load of the basement columns.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eColumn ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003eUltimate Axial Loads (kN)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eDifference in Results (%)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eP\u003csub\u003eLS\u0026minus;DYNA\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(Elsanadedy et al., 2022)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eP\u003csub\u003eETABS\u003c/sub\u003e\u003c/p\u003e \u003cp\u003e(Present Research)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4162\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4143\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e7962\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e7890\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.9\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e7236\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e7115\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5690\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5482\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.7\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5056\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4887\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e3.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Numerical Models\u003c/h2\u003e \u003cp\u003eThe numerical models are performed for the 4, 6, 9, 12, and 15-storied buildings considering the number of bays of 3, 4, and 5 for each category of structure. The widths of each bay are used to be 5, 6, and 8 m. All beams are considered to be the reinforced concrete haunch. Details of geometric and material considerations are shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e with valid reasons. The plans of the various storied structures are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Also, the sectional elevations of all storied structures are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. In this research, the finite element-based software ETABS 18.1.1 (ETABS 2020) is used for the nonlinear static and nonlinear dynamic analyses. The ETABS was used for the linear static analysis of the Ohio Union building (Elsanadedy et al., 2022). Also, the ETABS was used for the haunch retrofitting technique of the reinforced concrete frame (Ahmad et al., 2019). The beams and columns are considered to be 2-nodded line elements as previously (Elsanadedy et al., 2022; Ahmad et al., 2019) published works. The slab is assumed to be a 4-nodded quadrilateral element the same as the previous (Elsanadedy et al., 2022) study. The floor finish and roof live load are considered to be 1.2 kN/m\u003csup\u003e2\u003c/sup\u003e and 1.5 kN/m\u003csup\u003e2\u003c/sup\u003e, respectively, according to the BNBC (2020). The partition and live loads of all floors are taken to be 2.873 kN/m\u003csup\u003e2\u003c/sup\u003e based on the previous (Ahmad et al., 2019) study. The 5% viscous damping is considered for the analysis according to the previous (Moniri 2017; Aljawhari et al., 2020) similar types of study. The P-Δ effect is included in the geometric nonlinear analysis. Recently (Fakharifar et al., 2015; Akbar et al., 2020), the P-Δ effect was considered for the vulnerability and fragility analysis to include the geometric nonlinearity impact on the structures. The seven numbers of selected seismic excitations are applied at the base of each structure during the nonlinear dynamic analysis. These excitations are listed in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. The incremental dynamic analysis was first proposed by Vamvatsikos and Cornell (2002). Several (Fakharifar et al., 2015; Mosleh et al., 2016; Moniri 2017; Ahmad et al., 2019; Akbar et al., 2020) vulnerability and fragility studies were performed to consider the incremental dynamic analysis. The vulnerability was assessed by the fragility curve to consider the probability of damage (Fakharifar et al., 2015) and exceedance (Mosleh et al., 2016) with the PGA range of (0\u0026thinsp;~\u0026thinsp;1) g and (0\u0026thinsp;~\u0026thinsp;2) g. In this research, the vulnerability is assessed by the fragility function to consider the probability of exceedance of CP and LS levels of haunch beams and joints under various seismic excitations with PGAs (peak ground accelerations) of 0.05g, 0.10g, 0.15g, 0.20g, 0.25g, 0.30g, 0.35g, 0.40g, 0.45g, and 0.50g. The CP and LS levels are ensured by the plastic hinge rotation. This rotation is evaluated from the analysis of several numerical models.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eGeometric and material properties for the numerical analysis.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSL No.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eItems\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eValues with Units\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSpecific Information, if any (References)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNumber of Stories\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4, 6, 9, 12, and 15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6, 15 (Moniri, 2017); 4 (Fotopoulou et al., 2012; Aljawhari et al., 2020); 12 (Tena-Colunga, 1994)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNumber of Bays\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3, 4, and 5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3 (Moniri, 2017; Fotopoulou et al., 2012; Shafaei et al., 2016); 4 (Aljawhari et al., 2020)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eBays Width\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5 m, 6 m, and 8 m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5 m (Fotopoulou et al., 2012; Shafaei et al., 2016); 6 m (Moniri, 2017);\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInter-Storey Height\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3 m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMoniri, 2017; Fotopoulou et al., 2012; Zabihi et al., 2016; Aljawhari et al., 2020\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSupport Conditions at Base\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFixed\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMoniri, 2017; Shafaei et al., 2016; Aljawhari et al., 2020\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSize of Column\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e300 mm x 300 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAhmed et al., 2019; Akbar et al., 2020; Aljawhari et al., 2020\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eWidth of Beam\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e300 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFotopoulou et al., 2012; Ahmed et al., 2019; Akbar et al., 2020; Zabihi et al., 2016; Shafaei et al., 2016; Aljawhari et al., 2020\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDepth of Beam\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e400 mm (Support)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eZabihi et al., 2016; Shafaei et al., 2016\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHaunch Depth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e100 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAkbar et al., 2020\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eHaunch Length\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.933L\u003csup\u003e1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eColunga et al., 2007\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSlab Thickness\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e150 mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBNBC 2020; ACI 318-05\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCylindrical Compressive Strength of Concrete\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e21 MPa\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAhmed et al., 2019\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYield Strength of Steel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e414 MPa\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eAhmed et al., 2019\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"4\"\u003eNote: L\u003csup\u003e1\u003c/sup\u003e is the beam length.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eVarious earthquake records for the nonlinear time history analysis.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSL No.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eYear\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eEarthquake Name\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eMoment Magnitude, Mw\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePGA (g)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eReference\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1971\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSan Fernando\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.699\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eMosleh et al., 2016\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1987\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSuperstition Hills\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.793\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1989\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eLoma Prieta\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.644\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1994\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNorthridge\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e6.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.871\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\" morerows=\"2\" rowspan=\"3\"\u003e \u003cp\u003eMoniri 2017\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1999\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eChi-Chi\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.568\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1999\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eKocaeli\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e7.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.415\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1998\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUmbria\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e4.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.240\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eFotopoulou et al., 2012\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Nonlinear Static Analysis Procedure\u003c/h2\u003e \u003cp\u003eThe displacement control nonlinear static analysis is performed in ETABS considering the P-Δ effect. The displacement is monitored on the roof. The target displacement and approximate fundamental time of all structures are calculated based on the given formulae in the BNBC (2020). The normalized acceleration response spectrum is calculated according to the BNBC (2020) for the definition of earthquake force in ETABS for linear static analysis. The importance factor and zone coefficient of all structures are considered to be 1 and 0.20g, respectively, based on the BNBC (2020). It is assumed that all structures stand on the loose to medium cohesionless soil. The response reduction factor is considered for the special moment resisting frame according to the BNBC (2020). These above-describing factors are taken for the seismic force consideration of the linear static analysis, which is defined as the load during the nonlinear static analysis. The nonlinear static analysis is continued until the control point (roof) displacement is reached at least 1.5 times the target displacement. The plastic hinges are provided in the beams and beam-column joints before starting the analysis. In the beam, the plastic hinge is provided at the both supports and the middle. In the case of the support, it is placed at a relative length factor of 0.05. The iterative analysis procedure is followed to consider the Newton-Raphson method. The implicit analysis is continued until convergence is achieved.\u003c/p\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e2.3.1 Details of Plastic Hinge for Beam\u003c/h2\u003e \u003cp\u003eThe shear and flexural hinges are used in the reinforced concrete haunch beam at the support and middle, respectively. The relative length is maintained to be 19.4% of the total center-to-center length in the case of the support hinge. This relative length is the average value of the shear hinge location based on the experimental (God\u0026iacute;nez-Dom\u0026iacute;nguez et al., 2015) study. The plastic hinge rotation represents the performance of beams as well as overall structures. The shear plastic hinge rotation in the case of the collapse prevention (CP) level is considered to be 0.01 radians according to the standard (FEMA 273) to assume the stirrup spacing is greater than half of the effective depth. The flexural hinge of the beam is provided in the middle. Some assumptions are assumed for the flexural hinge consideration such as (a) balance reinforcement ratio, (b) transverse reinforcement, and (c) shear demand and capacity ratio of 3 (three). The plastic hinge rotation is considered to be 0.05 radians in the case of the CP level of acceptance criteria for the secondary component. Details mechanism to define the shear and flexural plastic hinge of the beam in ETABS are shown in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e2.3.2 Details of Plastic Hinge for Joint\u003c/h2\u003e \u003cp\u003eThe joint performance is considered to be the life safety (LS) level in the case of the exterior and interior. For this reason, some assumptions are considered to evaluate the performance of joints such as (a) axial load capacity of 1% of the gross area of the concrete, (b) confirmation of the transverse reinforcement, and (c) demanding shear of 1.2 times of shear capacity. The plastic hinge rotations at the LS level of the interior and exterior joints in the case of the secondary component are found to be 0.02 and 0.015 radians according to FEMA (273). The joint plastic hinge is provided at the beam-column joint of each structure. The definition information of the joint plastic hinge in ETABS is presented in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDetails information of various plastic hinges for defining in ETABS.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eItems\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eShear Plastic Hinge of Beam at Support\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFlexural Plastic Hinge of Beam at Middle\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003ePlastic Hinge at the Beam-Column Joint\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHinge Type\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eShear\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eInteracting M2-M3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eInteracting P-M2-M3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHinge Specification Type\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eMoment-Curvature\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eMoment-Curvature\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHinge Rotation Representation Type\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eForce-Displacement\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBackbone Curve Type\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSymmetric\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDouble Symmetry\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eDouble Symmetry\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLoad Carrying Capacity\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDrops to Zero\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDrops to Zero\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eDrops to Zero\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eImmediate Occupancy (IO)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eI\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eO\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLife Safety (LS)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.005\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.015\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCollapse Prevention (CP)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eHysteresis Type\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eIsotropic\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInteraction Surface\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eDefault from Material Property of Associated Frame Object\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eDefault from Material Property of Associated Frame Object\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAxial Load \u0026ndash; Displacement Relationship\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003eElastic-Perfectly Plastic\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAxial Force Associated with M2-M3 Curve\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSelect it after the end of the Linear Static Analysis\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003eNote: (i) \u0026ldquo;/\u0026rdquo; means that not necessary; (ii) O\u0026thinsp;=\u0026thinsp;Other; (iii) I\u0026thinsp;=\u0026thinsp;Interior.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Incremental Dynamic Analysis Procedure\u003c/h2\u003e \u003cp\u003eIn this research, the incremental dynamic analysis is related to the nonlinear dynamic as well as time history analysis. The reinforced concrete haunch and structural responses are recorded for variable PGA with a specific earthquake record. This seismic excitation is input in ETABS as a time history function. For the nonlinear time history analysis, the response reduction and structural importance factors are considered to be the unit (BNBC 2020) value according to the BNBC (2020). The nonlinear direct time integration considering the Hilber-Hughes-Taylor method (Elsanadedy et al., 2022) is followed to predict the performance of the structure. The seismic excitation is applied from the two orthogonal directions of each structure.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Vulnerability Analysis","content":"\u003cp\u003eEach structure is divided into four categories based on the arrangement of plastic hinges such as normal beam at support (NBS), haunch beam at support (HBS), haunch beam at support and middle (HBSM), and haunch beam at support-middle-joint (HBS-M-J). Figure\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e depicts the various plastic hinge arrangements at the beams and joints of structures. The probability of exceedance of the plastic hinge rotation with the help of the fragility function assesses the vulnerability. Collapse prevention (CP) and life safety (LS) performance levels are controlled by beams and joints, respectively. The mean (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\theta\\)\u003c/span\u003e\u003c/span\u003e) of the exceedance of CP or LS levels depends on the total (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({n}_{i}\\)\u003c/span\u003e\u003c/span\u003e) and failure (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({r}_{i}\\)\u003c/span\u003e\u003c/span\u003e) beams and joints. Failure means the exceedance of CP and LS levels of plastic hinge rotation. The mean, standard deviation (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\beta\\)\u003c/span\u003e\u003c/span\u003e), and probability of exceedance (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({p}_{i}\\)\u003c/span\u003e\u003c/span\u003e) are expressed in Eqs.\u0026nbsp;(1), (2), and (\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e), respectively, according to the FEMA (273).\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\theta =\\frac{1}{{n}_{i}}\\sum _{i=1}^{{n}_{i}}ln\\left({r}_{i}\\right) \\left(1\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\beta =\\sqrt{\\frac{1}{\\left({n}_{i}-1\\right)}\\sum _{i=1}^{{n}_{i}}{\\left\\{ln\\left(\\raisebox{1ex}{${r}_{i}$}\\!\\left/ \\!\\raisebox{-1ex}{$\\theta $}\\right.\\right)\\right\\}}^{2}} \\left(2\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$${p}_{i}=\\varphi \\left(\\frac{ln\\left(\\raisebox{1ex}{${r}_{i}$}\\!\\left/ \\!\\raisebox{-1ex}{$\\theta $}\\right.\\right)}{\\beta }\\right) \\left(3\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Assessment of Vulnerability by Nonlinear Static Analysis\u003c/h2\u003e \u003cp\u003eThe roof displacement is monitored in the nonlinear static analysis. It depends on the plastic hinge rotations of beams and joints. The roof displacement is normalized by dividing the target displacement. The probability of exceedance in terms of plastic hinge rotations of beams and joints is a new insight. Another novelty is the representation of the probability of exceedance in terms of the normalized roof displacement. These variations for all structures including bays and plastic hinge placement conditions are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. The plastic hinges of both opposite supports of the beam exceed the CP level, then the middle hinge exceeds the CP level. Finally, the beam-column joint exceeds the LS level. The vulnerability rate increment means the exceedance of the CP and LS levels within the shorter range of the normalized roof displacement. The vulnerability increases with the increment of the number of stories due to the decrement of the overall structural stiffness to hamper the individual beam stiffness to cause an exceedance of CP level within the shorter normalized roof displacement. The normal or rectangular beam is more vulnerable than the haunch beam because of the lower stiffness. The HBS-M-J shows less vulnerability because of controlling the joint performance level. In addition, the HBS-M-J is the critical condition for all structures due to the plastic hinge formation of beams and adjacent joints under successive seismic excitation. The normalized roof displacement range for the probability of exceedance of the HBS-M-J condition is (0.4\u0026thinsp;~\u0026thinsp;0.8) considering all structures with 3 bays. The probability of exceedance considering all structures and bays is performed for the bay width of 5 m because the higher width shows more vulnerability than the lower. The vulnerability reduces gradually with the increment of the number of bays due to the increment of the structural stiffness reducing the achievement of plastic hinge rotation of CP and LS levels. The higher vulnerability shows the 15-storied structure of 3 bays for the placement condition of the plastic hinge of NBS. The lower vulnerability shows the 4-storied structure of 5 bays for the placement condition of the plastic hinge of HBS-M-J. The ranges of the normalized roof displacements in the case of the higher and lower vulnerabilities are (0.38\u0026thinsp;~\u0026thinsp;0.56) and (0.87\u0026thinsp;~\u0026thinsp;1.0), respectively.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Assessment of Vulnerability by Incremental Dynamic Analysis\u003c/h2\u003e \u003cp\u003eThe incremental dynamic analysis is performed based on the probability of exceedance of the plastic hinge rotation. This is a new insight into the vulnerability evaluation considering successive variations of the PGA. The incremental dynamic analysis was performed to consider the probability of exceedance of various types of damage such as slight, moderate, extensive, and complete damage states (Mosleh et al., 2016). Also, it was conducted to predict the probability of exceedance of several parameters such as idealized yield, code drift limit, and incipient collapse (Ahmad et al., 2019). In this research, the plastic hinge rotation is controlled by the exceedance of the CP and LS performance levels of beams and joints. For the incremental dynamic analysis, the HBS-M-J is the critical condition because of the exceedance of the CP level of the beam at the support and middle and LS levels of the joint. So, the higher value of the PGA is required to satisfy the condition of HBS-M-J. The lower value of the PGA is required to satisfy the condition of NBS. The incremental vulnerability rate is NBS\u0026thinsp;\u0026gt;\u0026thinsp;HBS\u0026thinsp;\u0026gt;\u0026thinsp;HBSM\u0026thinsp;\u0026gt;\u0026thinsp;HBS-M-J according to the probability of exceedance as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The incremental dynamic analysis results are listed in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e to consider the maximum value of PGA among the seven earthquake records. Structures are shown to be more vulnerable to the maximum intense earthquake. The vulnerability rate increases gradually with the increment of the number of stories due to the reduced stiffness increasing plastic hinge rotation under seismic excitations. The vulnerability rate gradually decreased with the increment of the number of bays because of the increment of overall structural stiffness. The lower and higher vulnerabilities show the 4-storied structure with 5 bays and the 15-storied structure with 3 bays as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e (a) and (m). The incremental dynamic analysis is performed for the bay width of 5 m because the lower width shows less vulnerability than the higher one. The PGA ranges of lower and higher vulnerabilities are found to be (0.45\u0026thinsp;~\u0026thinsp;0.5) g and (0.05\u0026thinsp;~\u0026thinsp;0.09) g, respectively. The NBS condition shows a higher vulnerability, and the HBS-M-J represents a lower vulnerability.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eThis research evaluates the seismic vulnerability of the reinforced concrete haunch beam by the nonlinear static analysis considering roof displacement and incremental dynamic analysis considering various peak ground accelerations. For this reason, several numerical analyses have been performed by ETABS considering various structures with variable bays. The seven numbers of seismic excitations are chosen for the nonlinear time history analysis. Each structure is classified into four categories based on the plastic hinge location and beam types. The probability of exceedance of the plastic hinge rotation of the collapse prevention performance level of beams and the life safety performance level of joints assesses the vulnerability. The roof displacement controls the vulnerability of reinforced concrete rectangular and haunch beams based on the nonlinear static analysis. The new insight in this research is the assessment of the seismic vulnerability in terms of the plastic hinge rotations of beams and the beam-column joints. Therefore, major conclusions are summarized herein:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eThe vulnerability is increased gradually with the increment of the number of stories due to the reduction of the overall stiffness of the structure. It is decreased with the increment of the number of bays because of increasing lateral stiffness of structures. So, a 15-storied structure with 3 bays shows more vulnerability and a 4-storied structure with 5 bays expresses less vulnerability. This phenomenon is seen in both seismic vulnerability assessing procedures.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eAccording to the nonlinear static analysis, the ranges of the normalized roof displacements for the lower and higher vulnerabilities are found to be (0.87\u0026thinsp;~\u0026thinsp;1.0) and (0.38\u0026thinsp;~\u0026thinsp;0.56), respectively. Similarly, the ranges of the peak ground accelerations for the higher and lower vulnerabilities are obtained to be (0.05\u0026thinsp;~\u0026thinsp;0.09) g and (0.45\u0026thinsp;~\u0026thinsp;0.5) g, respectively, based on the incremental dynamic analysis.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eThere is a scope to further extend this research by considering the variable geometry of structures and individual haunch beams, adding more plastic hinges over the beam, taking different conditions for choosing the plastic hinge rotation according to the code, including material anisotropy, etc.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eConflict of Interest\u003c/h2\u003e \u003cp\u003eThere is no conflict of interest to conduct this research.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eMd. Foisal Haque: Conceptualizations, Methodology, Software Analysis, Writing, Editing, Resources, Reviewing.Md. Mozammel Hoque: Resources.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e \u003cp\u003eNo data are available in this research.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003e318-05, A. (2014). \u003cem\u003eBuilding Code Requirements for Structural Concrete and Commentary.\u003c/em\u003e USA: American Concrete Institute.\u003c/li\u003e\n \u003cli\u003eAhmad, N., Akbar, J., Rizwan, M., Alam, B., Khan, A. N., \u0026amp; Lateef, A. (2019). Haunch retroftting technique for seismic upgrading defcient RC frames. \u003cem\u003eBulletin of Earthquake Engineering\u003c/em\u003e, 1-38. Retrieved from https://doi.org/10.1007/s10518-019-00638-9\u003c/li\u003e\n \u003cli\u003eAkbar, J., Ahmad, N., Rizwan, M., Javed, S., \u0026amp; Alam, B. (2020). Response Modification Factor of RC Frames Strengthened with RC Haunches. \u003cem\u003eShock and Vibration\u003c/em\u003e, 1-18. Retrieved from https://doi.org/10.1155/2020/3835015\u003c/li\u003e\n \u003cli\u003eAlbegmprli, H. M., G\u0026uuml;lşan, M. E., \u0026amp; Cevik, A. (2019). Comprehensive experimental investigation on mechanical behavior for types of reinforced concrete Haunched beam. \u003cem\u003eAdvances in Concrete Construction, 7\u003c/em\u003e(1), 39-50. Retrieved from https://doi.org/10.12989/acc.2019.7.1.039\u003c/li\u003e\n \u003cli\u003eAljawhari, K., Gentile, R., Freddi, F., \u0026amp; Galasso, C. (2021). Efects of ground‑motion sequences on fragility and vulnerability of case‑study reinforced concrete frames. \u003cem\u003eBulletin of Earthquake Engineering\u003c/em\u003e, 6329\u0026ndash;6359. Retrieved from https://doi.org/10.1007/s10518-020-01006-8\u003c/li\u003e\n \u003cli\u003eAziz, A. H., Hassan, H. F., \u0026amp; Razzaq, F. M. (2016). Experimental Study on Shear Behavior of Reinforced Self-Compacted Concrete Tapered Beams. \u003cem\u003eCivil and Environmental Research, 8\u003c/em\u003e(8), 11-22.\u003c/li\u003e\n \u003cli\u003eBNBC. (2020). \u003cem\u003eBangladesh National Building Code.\u003c/em\u003e\u0026nbsp;\u003c/li\u003e\n \u003cli\u003eChen, M., Liang, X., Yang, Z., Ge, X., \u0026amp; Xu, C. (2023). Analytical Study on the Random Seismic Responses of an Asymmetrical Suspension Structure. \u003cem\u003ebuildings\u003c/em\u003e, 1-19. Retrieved from https://doi.org/10.3390/buildings13061435\u003c/li\u003e\n \u003cli\u003eColunga, A., Archundia-Aranda, H., Grande-Vega, A., \u0026amp; Gonz\u0026aacute;lez-Cuevas, O. (2007). Cyclic Shear Behavior of Reinforced Concrete Haunched Beams. \u003cem\u003eNinth Canadian Conference on Earthquake Engineering\u003c/em\u003e, (pp. 1127-1137). Ottawa, Ontario, Canada.\u003c/li\u003e\n \u003cli\u003eColunga, A., Urbina-Californias, L. A., \u0026amp; Archundia-Aranda, H. (2017). Assessment of the shear strength of continuous reinforced concrete haunched beams based upon cyclic testing. \u003cem\u003eJournal of Building Engineering, 11\u003c/em\u003e, 187-204. Retrieved from https://doi.org/10.1016/j.jobe.2017.04.018\u003c/li\u003e\n \u003cli\u003eDang, C.-T., \u0026amp; Dinh, N.-H. (2017). Experimental Study on Structural Performance of RC Exterior Beam-Column Joints Retrofitted by Steel Jacketing and Haunch Element under Cyclic Loading Simulating Earthquake Excitation. \u003cem\u003eAdvances in Civil Engineering\u003c/em\u003e, 1-11. Retrieved from https://doi.org/10.1155/2017/9263460\u003c/li\u003e\n \u003cli\u003eElsanadedy, H., Sezen, H., Abbas, H., Almusallam, T., \u0026amp; Al-Salloum, Y. (2022). Progressive collapse risk of steel framed building considering column buckling. \u003cem\u003eEngineering Science and Technology, an International Journal\u003c/em\u003e, 1-15. Retrieved from https://doi.org/10.1016/j.jestch.2022.101193\u003c/li\u003e\n \u003cli\u003eETABS. (2020). \u003cem\u003eCSI Analysis Reference Manual\u003c/em\u003e (Version 18 ed.). United States of America: Computers \u0026amp; Structures, Inc.\u003c/li\u003e\n \u003cli\u003eFakharifar, M., Chen, G., Dalvand, A., \u0026amp; Shamsabadi, A. ( 2015). Collapse Vulnerability and Fragility Analysis of Substandard RC Bridges Rehabilitated with Different Repair Jackets Under Post-mainshock Cascading Events. \u003cem\u003eInternational Journal of Concrete Structures and Materials\u003c/em\u003e, 345\u0026ndash;367.\u003c/li\u003e\n \u003cli\u003eFEMA 273. (1997). \u003cem\u003eNEHRP Guidelines for the Seismic Rehabilitation of Buildings.\u003c/em\u003e Washington, D.C.: FEDERAL EMERGENCY MANAGEMENT AGENCY.\u003c/li\u003e\n \u003cli\u003eFerreira, T. M., Rodrigues, H., \u0026amp; Vicente, R. (2020). Seismic Vulnerability Assessment of Existing Reinforced Concrete Buildings in Urban Centers. \u003cem\u003eSustainability\u003c/em\u003e, 1-20. doi:10.3390/su12051996\u003c/li\u003e\n \u003cli\u003eFotopoulou, S., Karapetrou, S., \u0026amp; Pitilakis, K. (2012). Seismic vulnerability of RC buildings considering SSI and aging effects. \u003cem\u003e15 WCEE\u003c/em\u003e, (pp. 1-10). Lisboa.\u003c/li\u003e\n \u003cli\u003eGod\u0026iacute;nez-Dom\u0026iacute;nguez, E. A., Tena-Colunga, A., \u0026amp; Ju\u0026aacute;rez-Luna, G. (2015). Nonlinear finite element modeling of reinforced concrete haunched beams designed to develop a shear failure. \u003cem\u003eEngineering Structures, 105\u003c/em\u003e, 99\u0026ndash;122. Retrieved from http://dx.doi.org/10.1016/j.engstruct.2015.09.023\u003c/li\u003e\n \u003cli\u003eKalantari, H., Nasserasadi, K., \u0026amp; Arjmandi, S. A. (2018). Seismic vulnerability study of Soltaniyeh dome using nonlinear static and dynamic analyses. \u003cem\u003eInternational Journal of Advanced Structural Engineering\u003c/em\u003e, 367\u0026ndash;380. Retrieved from https://doi.org/10.1007/s40091-018-0203-3\u003c/li\u003e\n \u003cli\u003eLuca, F. D., \u0026amp; Verderame, G. M. (2021). Seismic Vulnerability Assessment: Reinforced Concrete Structures. \u003cem\u003eEncyclopedia of Earthquake Engineering\u003c/em\u003e, 1-31. doi:10.1007/978-3-642-36197-5_252-1\u003c/li\u003e\n \u003cli\u003eMoniri, H. (2017). Evaluation of seismic performance of reinforced concrete (RC) buildings under near-field earthquakes. \u003cem\u003eInt J Adv Struct Eng\u003c/em\u003e, 13\u0026ndash;25. doi:10.1007/s40091-016-0145-6\u003c/li\u003e\n \u003cli\u003eMosleh, A., Razzaghi, M. S., Jara, J., \u0026amp; Varum, H. (2016). \u003cem\u003eInt J Adv Struct Eng\u003c/em\u003e, 1\u0026ndash;9. doi:10.1007/s40091-016-0108-y\u003c/li\u003e\n \u003cli\u003eNaser, M., Hawileh, R. A., \u0026amp; Abdalla, J. (2021). Modeling Strategies of Finite Element Simulation of Reinforced Concrete Beams Strengthened with FRP: A Review. \u003cem\u003eCompos. Sci.\u003c/em\u003e, 1-15. Retrieved from https://doi.org/10.3390/jcs5010019\u003c/li\u003e\n \u003cli\u003eShafaei, J., Hosseini, A., Marefat, M. S., \u0026amp; Ingham, J. M. (2016). Experimental Evaluation of Seismically and Non-Seismically Detailed External RC Beam-Column Joints. \u003cem\u003eJournal of Earthquake Engineering\u003c/em\u003e. doi:10.1080/13632469.2016.1185052\u003c/li\u003e\n \u003cli\u003eSUPARP, S., \u0026amp; JOYKLAD, P. (2021). Flexural Behavior of Hollow Reinforced Concrete Haunched (RCH) Beams. \u003cem\u003eJournal of Engineering Science and Technology, 16\u003c/em\u003e(4), 3267 \u0026ndash; 3282.\u003c/li\u003e\n \u003cli\u003eTena-Colunga, A. (1994). Concerns Regarding the Seismic Design of Reinforced Concrete Haunched Beams. \u003cem\u003eACI Structural Journal\u003c/em\u003e, 287-293.\u003c/li\u003e\n \u003cli\u003eVamvatsikos, D., \u0026amp; Cornell, C. A. (2002). Incremental Dynamic Analysis. \u003cem\u003eEarthquake Engng Struct. Dyn.\u003c/em\u003e, 1-21.\u003c/li\u003e\n \u003cli\u003eXu, Z., \u0026amp; Yan, S. (2023). Progressive-Collapse Mechanism of Suspended-Dome Structures Subjected to Sudden Cable Rupture. \u003cem\u003ebuildings\u003c/em\u003e, 1-21. Retrieved from https://doi.org/10.3390/buildings13061533\u003c/li\u003e\n \u003cli\u003eZabihi, A., Tsang, H.-H., Gad, E. F., \u0026amp; Wilson, J. L. (2016). Retrofitting RC Beam-Column Joint in Australia using Single Diagonal Haunch. \u003cem\u003eAustralian Earthquake Engineering Society 2016 Conference\u003c/em\u003e (pp. 1-9). Melbourne: Australian Earthquake Engineering Society.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"asian-journal-of-civil-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Asian Journal of Civil Engineering](https://www.springer.com/journal/42107)","snPcode":"42107","submissionUrl":"https://submission.nature.com/new-submission/42107/3","title":"Asian Journal of Civil Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Incremental Dynamic Analysis, Nonlinear Static Analysis, Reinforced Concrete Haunch Beam, Seismic Vulnerability","lastPublishedDoi":"10.21203/rs.3.rs-4497972/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4497972/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis research presents a novel technique of the seismic vulnerability assessment of the reinforced concrete haunch beams in terms of the probability of exceedance of the plastic hinge rotations. For this reason, the nonlinear static and incremental dynamic analyses of various structures with bays have been conducted by the ETABS. The plastic hinge rotation is controlled by the collapse prevention and life safety performance levels of beams and joints, respectively. The roof displacement controls the probability of exceedance of the plastic hinge rotations of beams and joints based on the nonlinear static analysis, which is a new insight of this research. The numerical analysis of ETABS is validated with the previously published work to obtain a good agreement of validation results. The 15-storied structure with 3 bays shows a higher vulnerability and the 4-storied structure shows a lower vulnerability according to the numerical analysis. The ranges of the normalized roof displacement and the peak ground acceleration for higher vulnerability are found to be (0.38\u0026thinsp;~\u0026thinsp;0.56) and (0.05\u0026thinsp;~\u0026thinsp;0.09) g, respectively, based on the nonlinear static and incremental dynamic analyses.\u003c/p\u003e","manuscriptTitle":"Seismic Vulnerability Assessment of Reinforced Concrete Haunch Beam By Nonlinear Static and Incremental Dynamic Analyses","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-12 08:26:15","doi":"10.21203/rs.3.rs-4497972/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-07-07T14:36:49+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-07T14:29:02+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"199686641999039408051930811786387193829","date":"2024-07-07T14:12:09+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-07-03T11:34:47+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"43918802175337170361061375615803453439","date":"2024-07-02T08:41:37+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-06-06T18:06:15+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-05-31T08:27:56+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-05-31T00:10:29+00:00","index":"","fulltext":""},{"type":"submitted","content":"Asian Journal of Civil Engineering","date":"2024-05-29T15:03:05+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"asian-journal-of-civil-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Asian Journal of Civil Engineering](https://www.springer.com/journal/42107)","snPcode":"42107","submissionUrl":"https://submission.nature.com/new-submission/42107/3","title":"Asian Journal of Civil Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"11a8954b-1e7c-492c-a8cd-4eebe5be3969","owner":[],"postedDate":"June 12th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2024-07-09T05:36:29+00:00","versionOfRecord":[],"versionCreatedAt":"2024-06-12 08:26:15","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4497972","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4497972","identity":"rs-4497972","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}