# Seismic Evaluation of Advanced Reinforced Concrete Structures

Authors: Vijayakumar Arumugam; Lakshmi Keshav; Aravindan Achuthan; Somashekar Dasappa
Journal: Advances in Materials Science and Engineering
 (2022)

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## Abstract

Many reinforced concrete frame buildings were developed and constructed in Coimbatore zone III before 2002. In 2002, the seismic code IS 1893 was updated. As a result, structures constructed earlier in 2002 do not meet the codal criterion. The majority of structures through infilled walls were nondesigned with infills in consideration. This paper goals to appraise seismic exposure of an advanced reinforced present concrete building with infilled and without infilled frames. A pushover analysis was used to conduct this analysis. According to ATC40, the analysis shows the comportment levels of several building components for various stated concert objectives.


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## Body

## 1. Introduction

Because design code standards are regularly updated as engineering knowledge advances, existing buildings may become seismically weak. Furthermore, due to a lack of knowledge about the seismic behavior of structures, Indian buildings developed in the last two decades are seismically weak. The distribution of mass and stiffness is one of the most critical aspects in the seismic design of moderate- to high-rise buildings. These components invariably create coupling effects and nonlinearity in the system; thus, for seismic evaluation of structures, it is critical to adopt a nonlinear static analysis technique using specialized programs such as SAP2000, ETABS, and IDARC, among others.Coimbatore, India's fastest-growing city, is situated in seismic zone III. Many reinforced concrete frame buildings were developed and constructed in Coimbatore before 2002. In 2002, the seismic code IS 1893 was updated. As a result, structures constructed before 2002 do not meet the code’s requirements. The majority of structures with infilled walls were not designed with infills in mind. Furthermore, the structure chosen for analysis is located in zone III of the Coimbatore region. An existing structure in the Coimbatore region requires seismic evaluation for a variety of reasons, including noncompliance with code requirements, code updates, poor design practice, and changes in the building’s use. Existing defective structures in Coimbatore zone III, on the other hand, can be rehabilitated to maintain the projected recital level. Beforehand beginning the restoration effort, it is required to assess the current structure’s capability and determine whether it fulfills the desired performance level.The nonlinear static pushover analysis is highlighted in the publication [1]. It is a practical way of assessing the performance of a structure that is subjected to seismic loads. The capability curve, capability spectrum approach, and movement coefficient method are all steps in the pushover analysis process. This report is detailed with modeling components of the hinge behavior, taking criteria, and the location of the routine point employing these procedures. A pushover study [2, 3] involves exposing a building to a steadily increasing pattern of lateral stresses that replicate the inertial forces it would experience if it were subjected to ground shaking various structural parts which may yield consecutively under steadily increasing stresses. As a result, the structure loses rigidity as each event occurs. A characteristic of a nonlinear force-displacement relationship can be found via a pushover analysis. The pushover analysis is highlighted in reports [1, 2, 4]. It is a realistic way of assessing the recital of a structure that is exposed to seismic loads. The capacity curve, demand curve, and performance point are all determined by a step-by-step approach in the pushover analysis. These studies cover hinge behavior modeling, acceptability criteria, and methodologies for locating the performance point. The paper referred to in [3, 5] demonstrates how to perform a pushover study of 3D architecture using SAP2000. SAP2000 is a cutting-edge, all-purpose, 3D structural analysis application. SAP2000 includes fully integrated static pushover analysis capabilities that enable rapid and informal deployment of pushover procedures for both 2D and 3D frames. The reference [6] discusses the structural examination of RC buildings in various Indian zones. All seismic zones in India are subjected to response spectrum evaluations, both with and without infill stiffness. Pushover analysis, which comprises the capacity spectrum, demand spectrum, and performance point, is used to produce a pushover curve. The performance of building components as well as the structures’ maximum base shear carrying capacity for different zones are revealed through a pushover study. Succeeding steps will help you to achieve the goal of selecting a representative existing building with and without infill that was built before 2002 and for which data is available. Make a three-dimensional model of the structure, taking into account the infill influence of partitions, carrying out a pushover analysis of the with and without infilled structures. Based on the analysis, identify the hinge formation, base shear capacity, and performance of the building as per ATC40.


## 2. Description of the Frame Structures

The selected building’s three-dimensional frame has dissimilar kinds of earthquake weight battling systems with and without infilled frames, which are taken into account. Figure1 displays the building’s proposal of the structure and brace configuration model that represents infills that are used in the analysis. SAP2000 software is used for creating three-dimensional models and analysis of the existing building.Figure 1
The representation infills the frame with bracing in three dimensions.The structure is located in Coimbatore and is representative of several others in the area. M15 concrete and Fe415 steel were used to construct it. M20 [7, 8] is the concrete grade required by IS 456 : 2000 for structural purposes. Many structures in the Coimbatore region, on the other hand, were constructed using solely M15 grade concrete. The pushover analysis was performed to check the susceptibility of such structures using concrete and steel strength based on test results. Concrete strength was determined to be 16.5 N/mm2 for the example building, whereas steel strength was determined to be Fe 420 N/mm2 using the various NDT tests. In the pushover analysis, these values were employed. We chose G + 2 hostel buildings with reinforced concrete structures. The dimensions of all building components is in accordance with the existing framework.


### 2.1. Bare Frame Model

Beam and column members are frame elements that have the necessary proportions and steel. Slabs are defined as an area element with shell-like features and a specified thickness. Rigid diaphragms have been used to represent slabs [9, 10]. The following load cases are examined after the structural components have been modeled: beams, columns, slabs, and other permanent parts such as infills all contribute to the structure’s gravity stresses. The application automatically considers the individual mass of beams, columns (frame members), and slabs (area element).


#### 2.1.1. Seismic Weight of the Building

The deck, all gravity, and lateral members, and all walls all contribute to the structure’s self-weight. The column and wall weights in each story are evenly distributed to the floors above and below the story when estimating the seismic weight of each floor diaphragm. The total seismic mass of the building without infill is computed as 9966.418 kN as per IS code.Based on the building’s remaining functional life, the proposed methodology allows for a reduction in the design base shear [9, 11]. The reduced base shear was calculated as per modification formula 580 kN. U=Trem/Tdes0.5≥0.7.


### 2.2. Infill Frame Method (Equivalent Diagonal Strut Method)

Under seismic loads, the effects of infill walls might be advantageous or negative. The distribution of infill throughout the building floors, on the other hand, had a significant impact on this improvement. It is well known that the presence of infill walls boosts the lateral strength and stiffness of the frames significantly when compared to bare frames while lowering average drifts. However, depending on the situation, these consequences may or may not be beneficial. The parts that make up the infill walls are sturdy but fragile. Infill walls can produce unforeseen damages such as early column failures due to shear, compression, or tension failures if the surrounding structure is not robust enough. The growth of soft-story mechanisms in the structure could also have a detrimental impact. Structures lacking infill walls at the bottom storey are more likely to experience this process. Soft-story mechanisms, in particular, may emerge as a result of drift concentrations at lower stories. These negative impacts may be mitigated by an orderly stiffness distribution along with the structure’s height.Some methodologies for simulating the behavior of infilled structures are now available in the literature; experimental and numerical studies have shown that a diagonal strut with appropriate geometrical and mechanical characteristics could be a good solution for accounting for the influence of infills in seismic behavior. The most common way of researching infilled frame systems is to utilize a macro-model [12, 13] that substitutes a single equivalent-strut for the entire infill panel, as seen in Figure 2, and seismic mass of the building as 9966.418 kN and reduced base shear 580 kN.Figure 2
Brick infill panel as equivalent diagonal strut.
(a)(b)


## 2.1. Bare Frame Model

Beam and column members are frame elements that have the necessary proportions and steel. Slabs are defined as an area element with shell-like features and a specified thickness. Rigid diaphragms have been used to represent slabs [9, 10]. The following load cases are examined after the structural components have been modeled: beams, columns, slabs, and other permanent parts such as infills all contribute to the structure’s gravity stresses. The application automatically considers the individual mass of beams, columns (frame members), and slabs (area element).


### 2.1.1. Seismic Weight of the Building

The deck, all gravity, and lateral members, and all walls all contribute to the structure’s self-weight. The column and wall weights in each story are evenly distributed to the floors above and below the story when estimating the seismic weight of each floor diaphragm. The total seismic mass of the building without infill is computed as 9966.418 kN as per IS code.Based on the building’s remaining functional life, the proposed methodology allows for a reduction in the design base shear [9, 11]. The reduced base shear was calculated as per modification formula 580 kN. U=Trem/Tdes0.5≥0.7.


## 2.1.1. Seismic Weight of the Building

The deck, all gravity, and lateral members, and all walls all contribute to the structure’s self-weight. The column and wall weights in each story are evenly distributed to the floors above and below the story when estimating the seismic weight of each floor diaphragm. The total seismic mass of the building without infill is computed as 9966.418 kN as per IS code.Based on the building’s remaining functional life, the proposed methodology allows for a reduction in the design base shear [9, 11]. The reduced base shear was calculated as per modification formula 580 kN. U=Trem/Tdes0.5≥0.7.


## 2.2. Infill Frame Method (Equivalent Diagonal Strut Method)

Under seismic loads, the effects of infill walls might be advantageous or negative. The distribution of infill throughout the building floors, on the other hand, had a significant impact on this improvement. It is well known that the presence of infill walls boosts the lateral strength and stiffness of the frames significantly when compared to bare frames while lowering average drifts. However, depending on the situation, these consequences may or may not be beneficial. The parts that make up the infill walls are sturdy but fragile. Infill walls can produce unforeseen damages such as early column failures due to shear, compression, or tension failures if the surrounding structure is not robust enough. The growth of soft-story mechanisms in the structure could also have a detrimental impact. Structures lacking infill walls at the bottom storey are more likely to experience this process. Soft-story mechanisms, in particular, may emerge as a result of drift concentrations at lower stories. These negative impacts may be mitigated by an orderly stiffness distribution along with the structure’s height.Some methodologies for simulating the behavior of infilled structures are now available in the literature; experimental and numerical studies have shown that a diagonal strut with appropriate geometrical and mechanical characteristics could be a good solution for accounting for the influence of infills in seismic behavior. The most common way of researching infilled frame systems is to utilize a macro-model [12, 13] that substitutes a single equivalent-strut for the entire infill panel, as seen in Figure 2, and seismic mass of the building as 9966.418 kN and reduced base shear 580 kN.Figure 2
Brick infill panel as equivalent diagonal strut.
(a)(b)


## 3. Nonlinear Static Pushover Analysis

The NSP approach, also known as pushover analysis, or POA, is a technique in which a computer model of a structure is exposed to a preset lateral load pattern that approximates the relative inertia forces generated at significant mass positions. The lateral force is increased in intensity, causing the structure to be “pushed,” and the sequence of cracks, yielding, plastic hinge forms, and the load at which various structural components fail is recorded as a function of the growing lateral stress. This technique is repeated until a predefined displacement limit is reached.Nonlinear behavior inside frame elements is anticipated to occur at concentrated plastic hinges in SAP2000. Uncoupled moment hinges, uncoupled axial hinges, uncoupled shear hinges, coupled axial force, and biaxial bending moment hinges are the default types. The application of gravity loads and a realistic lateral load pattern are used in the pushover study. The applied lateral loads areX-axis accelerations that simulate the forces that the structures would feel if they were subjected to ground shaking. Some elements may yield sequentially under steadily increasing stresses. As a result, the structures’ stiffness changes at each event, as shown in Figure 3. The material model utilized in the static nonlinear pushover analysis is based on the processes described in the [1, 2] publications, which define force-deformation criteria for the pushover hinges. Figure 3 depicts the structure’s typical force-deformation relationship.Figure 3
Force-deformation for pushover analysis.The force-deflection behavior of the structure is defined by 5 points designated A, B, C, D, and E. A to B, elastic state; B to IO, below immediate occupancy; IO to LS, between immediate occupancy and life safety; LS to CP, between life safety and collapse prevention; CP to C, between collapse prevention and ultimate capacity; C to D, between C and residual strength; D to E, between D and collapse > E collapse.


## 4. Results and Discussion

### 4.1. General

The experiment used a three-story existing hostel reinforced concrete with and without an infill frame. The frame was exposed toX and Y earthquake loads, as stated by the IS code for zone III level. The reactions of the frames are discussed more below.


### 4.2. Base Shear

#### 4.2.1. Without Infill Frame

In both directions, the base shear was computed using IS 1893 (part-1)-2002 and SAP2000 software as 580 kN and 335 kN, respectively. The base shear as per IS 1893 (part-1)-2002 is 1.75 times higher as compared to SAP2000 in both directions. Based on the analysis, base shear values in theX direction are higher than in the Y direction because of the configuration of the building.


#### 4.2.2. Infill Frame

The base shear was computed as 580 kN and 446 kN in both directions using IS 1893 (part-1)-2002 and SAP2000 software. The base shear as per IS 1893 (part-1)-2002 is 1.3 times higher as compared to SAP2000 in both directions. Based on the analysis, base shear values in theX direction are higher than in the Y direction because of the configuration of the building.


### 4.3. Pushover Curve

#### 4.3.1. Without Infill Frame

Figures4 and 5 show the X and Y directions of the building’s pushover curves. These curves show the overall behavior of the frame in terms of stiffness and ductility. According to pushover studies, bare frame base shear at a displacement of 0.180 m in the X direction is 1288 kN. At a displacement of 0.030 m in the Y direction, pushover analysis provides a base shear of 2924 kN. The base shear in the Y direction is stronger than in the X direction due to the configuration of the columns in the frames.Figure 4
Bare frame in theX direction.Figure 5
Bare frame in theY direction.


#### 4.3.2. Infill Frame

Figures6 and 7 depict the building’s pushover curves in the X and Y orientations. Base shear from pushover analysis for the infilled frame is 1381 kN at a displacement of 0.36 m in the X direction and 3270 kN at a displacement of 0.023 m in the Y direction. As a result, infill frame stiffness will exceed bare frame stiffness in terms of earthquake resilience. The structure’s base shear performance has been improved thanks to the application of infill.Figure 6
Infill frame in theX direction.Figure 7
Infill frame in theY direction.


### 4.4. Capacity Spectrum

The main output of a pushover analysis is in terms of response demand versus capacity. If the demand curve intersects the capacity envelope near the elastic range, then the structure has good resistance. If the demand curve intersects the capacity curve with little reserve of strength and deformation capacity, then it can be concluded that the structure will behave poorly during the imposed seismic excitation and need to be retrofitted to avoid future major damage or collapse.


#### 4.4.1. Without Infill Frame

At a base shear level of 1016.436 kN and a displacement of 0.015 m in theX direction, the bare frame performance point is attained. The structure reached immediate occupancy at this point in its performance. At a base shear level of 1,330.743 kN and a displacement of 0.0044 m in the Y-direction, the performance point is reached. The structure had reached the level of collapse prevention at this stage in its performance. As a result, the structure appears to be more significant in the Y direction than in the X direction, as expected.


#### 4.4.2. Infill Frame

At a base shear level of 1090.675 kN and a displacement of 0.018 m in theX direction, the infill frame performance point is attained. At a base shear level of 1632.520 kN and a displacement of 0.005 m in the Y-direction, the performance point is attained. Based on failure mechanisms, the structure’s status at the performance point is discussed afterward [13, 14].


### 4.5. Plastic Hinges

The seismic response of RC structures is investigated using a G+2 RC existing frame structure with and without masonry infill walls. Nonlinear analysis for SAP2000 is used to obtain pushover curves for the structures. Maximum plastic rotations are calculated using the pushover curves and storey displacement. As a consequence of the analysis, the structural behavior under earthquake was identified. A nonlinear static pushover analysis was performed to evaluate the performance of framed buildings during future predicted earthquakes. In the event of a bare frame, the majority of the hinges developed in the beams, with a few in the columns sustaining minor damage. When contemplating the infilled frame, first consider the hinges generated in the column, then the beams. The following findings in terms of demand, capacity, and plastic hinges provide insight into structural behavior in real life.


#### 4.5.1. Without Infill Frame

At a load of 664.45 kN and a displacement of 0.007 m, the first hinge forms in theX direction. The idealized moment rotation curve of initial yielding, instantaneous occupancy, and collapse prevention is shown in Figure 8. For point B (yielding), the moment and rotation values are 1.5767 kN-m and 0.0017 radians, respectively. For point IO (immediate occupancy), the moment and rotation values are 1.5849 kN-m and 0.0254 radians, respectively. For point CP (collapse prevention), the moment and rotation values are 1.9344 kN-m and 0.0356 radians, respectively.Figure 8
Sequence of hinges formation in theX direction.The first hinge is formed in theY direction at a base shear and displacements of 596.41 kN and 0.002 m, respectively. The idealized moment rotation curve of initial yielding, collapse prevention, and the ultimate moment of resistance is depicted in Figure 9. For point B (yielding), the moment and rotation values are 7.34730 kN-m and 0.00146 radians, respectively. For point CP (collapse prevention), the moment and rotation values are 7.408 kN-m and 0.00156 radians, respectively. For point C (ultimate moment of resistance), the moment and rotation values are 8.00880 kN-m and 0.00251 radians, respectively. The beam first reaches its capacity and rotates 0.00156 radians at the performance point level, according to the analysis.Figure 9
Moment versus rotation curve.


#### 4.5.2. Infill Frame

Figure10 shows how the plastic hinge creation begins with infills, columns, and beams in the X direction. Columns fail before beams, hence this is unacceptable for design consideration. When the first hinge occurs in the infill, the base shear and displacement values are 733 kN and 0.0073 m in the X direction. At the performance level, the moment and rotation values for initial yielding are 52.785 kN-m and 0.0528 radians, respectively.Figure 10
Moment versus rotation curve.Figure11 shows how the plastic hinge development begins with infills, columns, and beams in the Y direction. Columns fail before beams, hence this is unacceptable for design consideration. When the first hinge occurs in the infill, the base shear and displacement values are 550 kN and 0.001 m in the X direction. The moment and rotation value for initial yielding are 106.434 kN-m and 0.0328 radians, respectively, at the performance level.Figure 11
Sequence of hinges formation in theY direction.The order in which the hinges form implies that the column hinge comes first, followed by the beam hinge. This is unacceptably bad. As a result, the columns in such a structure must be updated such that they do not reach capacity before the beams [15–17].


## 4.1. General

The experiment used a three-story existing hostel reinforced concrete with and without an infill frame. The frame was exposed toX and Y earthquake loads, as stated by the IS code for zone III level. The reactions of the frames are discussed more below.


## 4.2. Base Shear

### 4.2.1. Without Infill Frame

In both directions, the base shear was computed using IS 1893 (part-1)-2002 and SAP2000 software as 580 kN and 335 kN, respectively. The base shear as per IS 1893 (part-1)-2002 is 1.75 times higher as compared to SAP2000 in both directions. Based on the analysis, base shear values in theX direction are higher than in the Y direction because of the configuration of the building.


### 4.2.2. Infill Frame

The base shear was computed as 580 kN and 446 kN in both directions using IS 1893 (part-1)-2002 and SAP2000 software. The base shear as per IS 1893 (part-1)-2002 is 1.3 times higher as compared to SAP2000 in both directions. Based on the analysis, base shear values in theX direction are higher than in the Y direction because of the configuration of the building.


## 4.2.1. Without Infill Frame

In both directions, the base shear was computed using IS 1893 (part-1)-2002 and SAP2000 software as 580 kN and 335 kN, respectively. The base shear as per IS 1893 (part-1)-2002 is 1.75 times higher as compared to SAP2000 in both directions. Based on the analysis, base shear values in theX direction are higher than in the Y direction because of the configuration of the building.


## 4.2.2. Infill Frame

The base shear was computed as 580 kN and 446 kN in both directions using IS 1893 (part-1)-2002 and SAP2000 software. The base shear as per IS 1893 (part-1)-2002 is 1.3 times higher as compared to SAP2000 in both directions. Based on the analysis, base shear values in theX direction are higher than in the Y direction because of the configuration of the building.


## 4.3. Pushover Curve

### 4.3.1. Without Infill Frame

Figures4 and 5 show the X and Y directions of the building’s pushover curves. These curves show the overall behavior of the frame in terms of stiffness and ductility. According to pushover studies, bare frame base shear at a displacement of 0.180 m in the X direction is 1288 kN. At a displacement of 0.030 m in the Y direction, pushover analysis provides a base shear of 2924 kN. The base shear in the Y direction is stronger than in the X direction due to the configuration of the columns in the frames.Figure 4
Bare frame in theX direction.Figure 5
Bare frame in theY direction.


### 4.3.2. Infill Frame

Figures6 and 7 depict the building’s pushover curves in the X and Y orientations. Base shear from pushover analysis for the infilled frame is 1381 kN at a displacement of 0.36 m in the X direction and 3270 kN at a displacement of 0.023 m in the Y direction. As a result, infill frame stiffness will exceed bare frame stiffness in terms of earthquake resilience. The structure’s base shear performance has been improved thanks to the application of infill.Figure 6
Infill frame in theX direction.Figure 7
Infill frame in theY direction.


## 4.3.1. Without Infill Frame

Figures4 and 5 show the X and Y directions of the building’s pushover curves. These curves show the overall behavior of the frame in terms of stiffness and ductility. According to pushover studies, bare frame base shear at a displacement of 0.180 m in the X direction is 1288 kN. At a displacement of 0.030 m in the Y direction, pushover analysis provides a base shear of 2924 kN. The base shear in the Y direction is stronger than in the X direction due to the configuration of the columns in the frames.Figure 4
Bare frame in theX direction.Figure 5
Bare frame in theY direction.


## 4.3.2. Infill Frame

Figures6 and 7 depict the building’s pushover curves in the X and Y orientations. Base shear from pushover analysis for the infilled frame is 1381 kN at a displacement of 0.36 m in the X direction and 3270 kN at a displacement of 0.023 m in the Y direction. As a result, infill frame stiffness will exceed bare frame stiffness in terms of earthquake resilience. The structure’s base shear performance has been improved thanks to the application of infill.Figure 6
Infill frame in theX direction.Figure 7
Infill frame in theY direction.


## 4.4. Capacity Spectrum

The main output of a pushover analysis is in terms of response demand versus capacity. If the demand curve intersects the capacity envelope near the elastic range, then the structure has good resistance. If the demand curve intersects the capacity curve with little reserve of strength and deformation capacity, then it can be concluded that the structure will behave poorly during the imposed seismic excitation and need to be retrofitted to avoid future major damage or collapse.


### 4.4.1. Without Infill Frame

At a base shear level of 1016.436 kN and a displacement of 0.015 m in theX direction, the bare frame performance point is attained. The structure reached immediate occupancy at this point in its performance. At a base shear level of 1,330.743 kN and a displacement of 0.0044 m in the Y-direction, the performance point is reached. The structure had reached the level of collapse prevention at this stage in its performance. As a result, the structure appears to be more significant in the Y direction than in the X direction, as expected.


### 4.4.2. Infill Frame

At a base shear level of 1090.675 kN and a displacement of 0.018 m in theX direction, the infill frame performance point is attained. At a base shear level of 1632.520 kN and a displacement of 0.005 m in the Y-direction, the performance point is attained. Based on failure mechanisms, the structure’s status at the performance point is discussed afterward [13, 14].


## 4.4.1. Without Infill Frame

At a base shear level of 1016.436 kN and a displacement of 0.015 m in theX direction, the bare frame performance point is attained. The structure reached immediate occupancy at this point in its performance. At a base shear level of 1,330.743 kN and a displacement of 0.0044 m in the Y-direction, the performance point is reached. The structure had reached the level of collapse prevention at this stage in its performance. As a result, the structure appears to be more significant in the Y direction than in the X direction, as expected.


## 4.4.2. Infill Frame

At a base shear level of 1090.675 kN and a displacement of 0.018 m in theX direction, the infill frame performance point is attained. At a base shear level of 1632.520 kN and a displacement of 0.005 m in the Y-direction, the performance point is attained. Based on failure mechanisms, the structure’s status at the performance point is discussed afterward [13, 14].


## 4.5. Plastic Hinges

The seismic response of RC structures is investigated using a G+2 RC existing frame structure with and without masonry infill walls. Nonlinear analysis for SAP2000 is used to obtain pushover curves for the structures. Maximum plastic rotations are calculated using the pushover curves and storey displacement. As a consequence of the analysis, the structural behavior under earthquake was identified. A nonlinear static pushover analysis was performed to evaluate the performance of framed buildings during future predicted earthquakes. In the event of a bare frame, the majority of the hinges developed in the beams, with a few in the columns sustaining minor damage. When contemplating the infilled frame, first consider the hinges generated in the column, then the beams. The following findings in terms of demand, capacity, and plastic hinges provide insight into structural behavior in real life.


### 4.5.1. Without Infill Frame

At a load of 664.45 kN and a displacement of 0.007 m, the first hinge forms in theX direction. The idealized moment rotation curve of initial yielding, instantaneous occupancy, and collapse prevention is shown in Figure 8. For point B (yielding), the moment and rotation values are 1.5767 kN-m and 0.0017 radians, respectively. For point IO (immediate occupancy), the moment and rotation values are 1.5849 kN-m and 0.0254 radians, respectively. For point CP (collapse prevention), the moment and rotation values are 1.9344 kN-m and 0.0356 radians, respectively.Figure 8
Sequence of hinges formation in theX direction.The first hinge is formed in theY direction at a base shear and displacements of 596.41 kN and 0.002 m, respectively. The idealized moment rotation curve of initial yielding, collapse prevention, and the ultimate moment of resistance is depicted in Figure 9. For point B (yielding), the moment and rotation values are 7.34730 kN-m and 0.00146 radians, respectively. For point CP (collapse prevention), the moment and rotation values are 7.408 kN-m and 0.00156 radians, respectively. For point C (ultimate moment of resistance), the moment and rotation values are 8.00880 kN-m and 0.00251 radians, respectively. The beam first reaches its capacity and rotates 0.00156 radians at the performance point level, according to the analysis.Figure 9
Moment versus rotation curve.


### 4.5.2. Infill Frame

Figure10 shows how the plastic hinge creation begins with infills, columns, and beams in the X direction. Columns fail before beams, hence this is unacceptable for design consideration. When the first hinge occurs in the infill, the base shear and displacement values are 733 kN and 0.0073 m in the X direction. At the performance level, the moment and rotation values for initial yielding are 52.785 kN-m and 0.0528 radians, respectively.Figure 10
Moment versus rotation curve.Figure11 shows how the plastic hinge development begins with infills, columns, and beams in the Y direction. Columns fail before beams, hence this is unacceptable for design consideration. When the first hinge occurs in the infill, the base shear and displacement values are 550 kN and 0.001 m in the X direction. The moment and rotation value for initial yielding are 106.434 kN-m and 0.0328 radians, respectively, at the performance level.Figure 11
Sequence of hinges formation in theY direction.The order in which the hinges form implies that the column hinge comes first, followed by the beam hinge. This is unacceptably bad. As a result, the columns in such a structure must be updated such that they do not reach capacity before the beams [15–17].


## 4.5.1. Without Infill Frame

At a load of 664.45 kN and a displacement of 0.007 m, the first hinge forms in theX direction. The idealized moment rotation curve of initial yielding, instantaneous occupancy, and collapse prevention is shown in Figure 8. For point B (yielding), the moment and rotation values are 1.5767 kN-m and 0.0017 radians, respectively. For point IO (immediate occupancy), the moment and rotation values are 1.5849 kN-m and 0.0254 radians, respectively. For point CP (collapse prevention), the moment and rotation values are 1.9344 kN-m and 0.0356 radians, respectively.Figure 8
Sequence of hinges formation in theX direction.The first hinge is formed in theY direction at a base shear and displacements of 596.41 kN and 0.002 m, respectively. The idealized moment rotation curve of initial yielding, collapse prevention, and the ultimate moment of resistance is depicted in Figure 9. For point B (yielding), the moment and rotation values are 7.34730 kN-m and 0.00146 radians, respectively. For point CP (collapse prevention), the moment and rotation values are 7.408 kN-m and 0.00156 radians, respectively. For point C (ultimate moment of resistance), the moment and rotation values are 8.00880 kN-m and 0.00251 radians, respectively. The beam first reaches its capacity and rotates 0.00156 radians at the performance point level, according to the analysis.Figure 9
Moment versus rotation curve.


## 4.5.2. Infill Frame

Figure10 shows how the plastic hinge creation begins with infills, columns, and beams in the X direction. Columns fail before beams, hence this is unacceptable for design consideration. When the first hinge occurs in the infill, the base shear and displacement values are 733 kN and 0.0073 m in the X direction. At the performance level, the moment and rotation values for initial yielding are 52.785 kN-m and 0.0528 radians, respectively.Figure 10
Moment versus rotation curve.Figure11 shows how the plastic hinge development begins with infills, columns, and beams in the Y direction. Columns fail before beams, hence this is unacceptable for design consideration. When the first hinge occurs in the infill, the base shear and displacement values are 550 kN and 0.001 m in the X direction. The moment and rotation value for initial yielding are 106.434 kN-m and 0.0328 radians, respectively, at the performance level.Figure 11
Sequence of hinges formation in theY direction.The order in which the hinges form implies that the column hinge comes first, followed by the beam hinge. This is unacceptably bad. As a result, the columns in such a structure must be updated such that they do not reach capacity before the beams [15–17].


## 5. Conclusions

The pushover analysis is a useful method for evaluating the seismic performance of structures at various levels of shaking. The pushover analysis is a straightforward approach to investigating a building’s nonlinear behavior. The findings in terms of demand, capacity, and plastic hinges provided insight into how structures behave.The pushover analysis treating the structure as a bare frame shows that(i)
The performance point is reached in theX direction and permits immediate occupancy level, and at this stage, the critical beam rotation is 0.0254 radians.(ii)
However, the performance point reached in theY direction is only at a collapse prevention level; at this stage, the critical beam rotation is 0.00156 radians.At the initial hinge formation level, the base shear capacity in theY direction is lower than in the X direction.The pushover analysis treating the structure as an infill frame shows that(i)
The performance point in theX direction is reached, and at this stage, infills had collapsed and the column had reached yield and has a rotation of 0.0528 radians.(ii)
The behavior in theY direction is similar to X direction but at a higher base shear level. The critical column hinge reaches a rotation of 0.03284 radians.(iii)
To avoid premature column collapse, the columns must be refitted with sufficient strength so that they do not approach the yield level at the performance point [18–22].



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*Source: 4518848-2022-05-16.xml*