Seismic analysis of RC building with plan irregularity in Baghdad/Iraq to obtain the optimal behavior

Hussein Hakim Hasan; Weaam Majeed Arif; Emadaldeen Abdulameer Sulaiman

doi:10.1515/eng-2024-0003

Article Open Access

Seismic analysis of RC building with plan irregularity in Baghdad/Iraq to obtain the optimal behavior

Hussein Hakim Hasan , Weaam Majeed Arif and Emadaldeen Abdulameer Sulaiman

Published/Copyright: April 6, 2024

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From the journal Open Engineering Volume 14 Issue 1

Abstract

A study was conducted for four-story reinforced concrete (RC) structure existing in Baghdad-Iraq (residential building) to evaluate the accuracy and reliability of the equivalent lateral force procedure (ELFP) analysis and the response spectrum model (RSA) according to Iraqi seismic code (ISC 2016) for designing and analyzing irregular buildings. The building was classified as an irregular in plan according to American Society of Civil Engineers (ASCE 7-16). The seismic behavior of the building was investigated by verifying many parameters: the ratio of shear demand to shear strength on the columns ( V / V n ), internal force (bending moment, shear force, and axial force) for beams and columns, and the inter-story drift ratio (IDR) obtained from the (ELFP and RSA); then, the results were compared with the nonlinear static procedure (NSP) and the nonlinear dynamic procedure (NDP) according to ASCE 7-16. Also, this study investigated the effects of the higher modes in the plan (roof plan displacement). From the results, it can be concluded that ELFP and RSA are not a suitable analysis for asymmetric structures and should use appropriate methods such as the NSP and NDP.

Keywords: RC irregular buildings; equivalent lateral force procedure; response spectrum model; nonlinear static procedure; nonlinear dynamic procedure

1 Introduction

The main target of seismic engineering is to minimize the structural vulnerability against earthquakes. To achieve this objective, models that can precisely and reliably predict the nonlinear dynamic behavior of structures must be used to determine the safety margin against structural collapse [1].

The essential source of nonlinearity for low- and medium-rise buildings is material elasticity. Material nonlinearity arises when the force–displacement law or stress–strain is not linear, as well as changes the properties of a material with the applied loads [2]. Plain concrete has limited ductility and low tensile strength due to its brittle nature; therefore, concrete properties need to be improved in order to increase serviceability, and the steel reinforcement of members can change the behavior of the material [3]. The seismic response of reinforced concrete members can be controlled by bending or shear behavior, depending on the properties of geometric and detailing of reinforcement [4]. For seismic design, building structures are categorized as regular or irregular, based on their structural configurations. Nevertheless, not all sorts of irregularities are included in every construction code. Table 1 synthesizes the criteria for horizontal irregularities, according to American Society of Civil Engineers (ASCE 7-16) [5] code. It is worth noting that the new Iraqi seismic code (ISC) 2016 [6] has the same irregularity specifications for the ASCE 7-16 code completely.

Table 1

Irregularity limits prescribed by ASCE 7-16 and ISC 2016

Horizontal irregularity	ASCE 7-16
a) Torsional irregularity	d _max ≤ 1.2 d _avg, d _max ≤ 1.4 d _avg
b) Diaphragm discontinuity	O _A > 50%, S _dst > 50%
c) Re-entrant corners	R _i ≤ 15%

d _max and d _avg are the maximum drift computed at a specific story level, respectively, and average of drifts computed at both sides of a structure; O _A and S _dst are the open area in diaphragm and diaphragm stiffness; R _i is the Re-entrant corner irregularity limits.

To simulate reinforced concrete (RC) structures’ nonlinear behavior (material nonlinearity), several methods based on the finite element approach have been developed. One of the methods applied to reproduce the nonlinear behavior is to use a concentrated (or lumped) plasticity approach. These models were being studied by many researchers at the present, which are considered effective computationally [7,8,9,10]. Multi-story models of the lumped plasticity type were used in some recent researches [11,12,13] to study the influence of the torsional irregularity on seismic behavior. The concentrated plasticity is known also the plastic hinge approach, which is the common method that has been proposed in the federal emergency management agency (FEMA) P-695 guidelines [14]. Analysis methods are generally classified as linear static, nonlinear static, linear dynamic, and nonlinear dynamic methods. Among these methods, the first two are suitable when structural loads are small, or for buildings with no structural irregularities. Nonlinear static and nonlinear dynamic analysis have improved the capabilities to simulate seismic response compared to linear methods. Table 2 illustrates the detailed discrepancy between method analysis and method mentation previously. In this case, geometrical nonlinearities and material nonlinearities will be taken into account in the analysis. For irregular buildings located in areas with seismic activity, design and analysis becomes more difficult. Therefore, the response spectrum model (RSA) is a more advanced method compared to equivalent lateral force (ELF) method, as it includes the contribution of higher vibration modes and provides a better estimate of the actual force distribution in the elastic range.

Table 2

Detailed discrepancy between methods analysis methods

NDP	NSP	RSA	ELFP
Nonlinear dynamic	Nonlinear static	Linear dynamic	Linear static
Is the most reliable in evaluating the seismic performance of structures, especially for irregular structures	Adopted for the seismic assessment of regular structures or irregular structures that have the translational response primarily in the inelastic range	Suitable when structural loads are small, or for buildings with no structural irregularities	Suitable when structural loads are small, or for buildings with no structural irregularities
		The RSA modeled response spectrum method is a more advanced method compared to the ELFP method, as it includes the contribution of higher vibration modes and provides a better estimate of the actual force distribution in the elastic range
Design the elements in nonlinear range (geometry and material nonlinearity) with plasticity approach to prevent sudden failure and collapse of the building; this will lead to make the dimensions of the elements less than in the elastic range, low cost relatively, and high design flexibility	Design the elements in nonlinear range (geometry and material nonlinearity) with plasticity approach to prevent sudden failure and collapse of the building; this will lead to make the dimensions of the elements less than in the elastic range, low cost relatively, and high design flexibility	Design the elements in elastic range; therefore, this may lead to increase the dimensions of the elements exaggeratedly to avoid the brittle failure during seismic action, and this makes the design economically unacceptable	Design the elements in elastic range and to avoid the brittle failure during seismic action; this may led to increase the dimensions of the elements exaggeratedly, and this makes the design economically unacceptable
The NDP is better than NSP analysis for irregular building, with the disadvantage of being more demanding for the point of view of computer processing time	The NSP analysis is not quite efficient, even though it is less time-consuming and less computationally demanding. The response is not quite accurate when compared to the NDP results	The response of irregular building from elastic analysis (RSA) is lower than the nonlinear response (NSP and NDP) analyses	The response of irregular building from elastic analysis (ELFP) is lower than RSA and the nonlinear response analyses (NSP and NDP)

Modern earthquake design and estimate regulations specify two types of nonlinear analysis methods: (1) nonlinear static procedure (NSP) and (2) nonlinear dynamic procedure (NDP) – the second method allowing engineers to understand structural behavior and damage assessment in structural elements as the intensity of seismicity increases. Therefore, the NDP is the most reliable in evaluating the seismic performance of structures, especially for irregular structures. For irregular structures, the NSP is adopted in previous researchers for the seismic assessment of structures that have the translational response primarily [15,16,17,18,19,20,21,22,23]. The NDP is conducted along with the NSP to assess the seismic performance of structures [24,25,26,27,28,29,30,31,32]. Although Iraq rarely experienced seismic activity in the past, in recent years, seismic activity began to increase in parts of Iraq, including the eastern region bordering Iran, which led to its effects reaching Baghdad. The most important earthquakes that occurred in Iraq in the last 10 years were in the city of Halabjah in the Kurdistan Region of Iraq which is located in the north of Republic of Iraq in 2017 and 2023. Thus, there is an urgent need to adopt appropriate and more effective methods for designing and evaluating the performance of reinforced concrete buildings, because it is the most widely used type in Iraq. The research aims to highlight for methods of design and analysis of concrete buildings in Iraq according to the Iraqi earthquake code and the importance of taking into account dynamic methods in the design and structural analysis of buildings, which are adopted in the ASCE 7-16 code. The future prospects will be concentrated on the continuance of the research regarding of irregular buildings, such as irregular in elevation or different structural system like dual system or wall system.

The scope of this study is to apply linear and nonlinear analysis methods on RC multi-story building, which are classified as being irregular in plan and designed for earthquake-prone zones of Baghdad using ASCE 7-16. The NSP and the NDP are applied to building according to ASCE/SEI 41-13 [33], and the results are compared, where the seismic behavior of the building is assessed. From the linear and nonlinear methods applied, various parameters were investigated according to ASCE 7-16 code provisions for irregular in plan buildings, inter-story drift ratio (IDR) along with the building, the effects of the higher modes in plan (roof plan displacement), the ratio of shear demand to shear strength on the columns ( V / V n ), and internal force (bending moment, shear force, and exile force) for beams and columns.

2 Description of the building model

The building that will be studied is a reinforced concrete frame structure under construction. A 3-D structural model is shown in Figure 1; the elevation and plan of the building are shown in Figure 2, which is similar to the rest of the floors. The building is residential, and the building is located in Baghdad. The building consists of four floors above the ground level (base) (GF + 3S), the dimensions of the plan are 28.8 × 12 m, and the height of the floor is 3.0 m, the slab is 0.15 m thick, and the total height of the building is 12.0 m. The building has three bays in the Y direction and seven bays in the X direction. The bay width is 6.00, 3.60 and 2.40 m in the Y direction and 4.20, 3.60 and 4.80 m in the X direction. Concrete C25 MPa for columns, beams, and slabs are used, and the corresponding modulus of elasticity amounts to Ec (23,500 MPa) according to American concrete institute-ACI 318 (considered for design in Iraq). Steel S 414 Class C is used, and the corresponding modulus of elasticity amounts to Es (200,000 MPa). The cross-section of columns and beams is shown in Table 3. The design floor and roof live loads (LLs) are 2.4 and 1.0 KN/m², respectively. The gravitational load combination includes the LL ratio according to ISC 2016 (W = dead load, DL + 25 % of the floor LL). According to American concrete institute (ACI 318) is allowed to model the (beam-column) joints as rigid points.

Figure 1

3-D structural model and plan of the building.

Figure 2

Elevation of the building in X and Y directions.

Table 3

Dimensions of the beams and the columns

Story	Sections of columns and beams (mm)
Story	Column sections axis 1, 2, 3, 4	Column sections axis 1(D, E)	Beam sections axis 1, 2, 3, 4	Beam sections axis 3(D, E)	Beam sections axis A, B, C, F, G, H	Beam sections axis D, E
Ground floor	300 × 400	400 × 400	250 × 400	250 × 600	250 × 500	250 × 600
Level 1	300 × 400	400 × 400	250 × 400	250 × 600	250 × 500	250 × 600
Level 2	300 × 400	400 × 400	250 × 400	250 × 600	250 × 500	250 × 600
Level 3	300 × 400	400 × 400	250 × 400	250 × 550	250 × 500	250 × 600

3 Structural design considerations

According to the ISC 2016, there are four categories for seismic design classification (A, B, C, and D), while the ASCE/SEI 7-16 code specifies six seismic design classes (A, B, C, D, E, and F); the studied building (existing in Baghdad) is classified as class C, but if taking into account the system with irregularity in plan (according to ASCE/SEI 7-16, Table 12.3-2), the classification will be of class D. According to ISC 2016 and ASCE/SEI 7-16, all reinforced concrete frame buildings in class D must be of the special type, as no ordinary or intermediate concrete frames are allowed; therefore, the response reduction factor is equal to R = 8 for special RC moment frames (SMF). According to ASCE/SEI 7-16 and ISC 2016, the values of S _D1 (design spectral response acceleration parameter at a period of 1.0 s) and SDS (design spectral response acceleration parameter at short periods) are equal to 0.312 and 0.160, respectively; the over-strength factor is equal to Ω ₀ = 3; the deflection amplification factor is equal to C _d = 5.5.

4 Structural regularity

The irregularity in the plan is checked depending on ASCE 7-16 code, which are the same limits of irregularities in ISC 2016, four seismic load cases (2 in the X-direction E _xand 2 in the Y-direction E _y, with positive and negative eccentricity on each direction). The building does not fulfill the criteria of the code because re-entrant corner represents more than 15% of the structure’s plan dimension in the given direction, i.e., R _i > 15%.

In the Y -direction, R i ( A/L ) = 3.6 / 28.8 = 0.13 < 0.15

In the X -direction, R i ( A/L ) = 2.4 / 12 = 0.2 > 0.15 where A is the dimension of the re-entrant corner and L is the structure’s plan dimension in the given direction. Therefore, the building is categorized as having plan irregularity in the X-directions. In addition, the building does not meet the requirement of the torsional irregularity of structure (torsional irregularity δ _max > 1.2 δ _avg), and it is classified as plan-asymmetric in the Y-direction (Tables 4 and 5).

Table 4

Criteria for irregularity in X according to ASCE 7-16

Story	DX/m	E _x+/mm				E _x−/mm
Story	DX/m	δ _max	δ _avg	δ _max > 1.2 d _avg	CHECK	δ _max	δ _avg	δ _max > 1.2 δ _avg	CHECK
LEVEL 3	28.8	1.266	1.238	1.023	R	1.284	1.247	1.03	R
LEVEL 2	28.8	2.007	1.973	1.017	R	2.047	1.987	1.03	R
LEVEL 1	28.8	2.359	2.321	1.016	R	2.409	2.338	1.03	R
GROUND FLOOR	28.8	1.589	1.564	1.015	R	1.627	1.576	1.032	R

R: regular, IR: irregular, δ _max: maximum story drift, δ _avg: average story drift.

Table 5

Criteria for irregularity in Y according to ASCE 7-16

Story	DY/m	E _y+/mm				E _y−/mm
Story	DY/m	δ _max	δ _avg	δ _max > 1.2 d _avg	CHECK	δ _max	δ _avg	δ _max > 1.2 δ _avg	CHECK
LEVEL 3	12	1.107	0.881	1.256	IR	1.107	0.881	1.256	IR
LEVEL 2	12	1.761	1.433	1.229	IR	1.761	1.433	1.229	IR
LEVEL 1	12	2.077	1.694	1.227	IR	2.077	1.694	1.227	IR
GROUND FLOOR	12	1.429	1.166	1.226	IR	1.429	1.166	1.226	IR

R: regular, IR: irregular, δ _max: maximum story drift, δ _avg: average story drift.

5 Seismic response assessment procedures and modeling member’s nonlinearity

This section presents the procedures used to determine the seismic response for the building under consideration. Linear and nonlinear analysis methods were used on the model that was designed for seismic-prone zones of Baghdad city by using ISC 2016 and ASCE 7-16 code. The dynamic response of the building is estimated by ELF, RSA, NSP, and NDP analyses.

According to the FEMA 440, the modified coefficient method (which was adopted in ASCE/SEI 41-13) was utilized for the NSP, and the pushover curve was developed by applying the first mode distribution to determine the target displacement according to the FEMA 440 and ASCE/SEI 41-13.

For the NDP, according to the ASCE/SEI 7-16, 11 pairs of artificial ground acceleration were selected, which are scaled to match the elastic response spectrum specified for Baghdad (for a peak ground acceleration PGA = 0.125 g, according to the ISC 2016), which used as a target spectrum. Two orthogonal seismic actions were applied independently (in the X- and Y-directions). The PEER NGA-2022 strong motion database was applied to find the best matching (spectral matching with the target response) earthquake records.

The elements of the model are detailed for ductility according to the requirements of ASCE/SEI 7-16 as well as of ACI-318. The columns and the beams were modeled as elastic members with concentrated user-defined plastic hinges at each end according to the ASCE/SEI 41-13. The Mander stress–strain models for confined and unconfined concrete of a rectangular section were applied, and for rebars, a simple stress–strain curve was applied using ETAB-19.

6 Discussion of the analysis results

The comparison of global response results is presented in the following, for each excitation and analysis type:

The results of parameters in terms of periods and frequency showed that the first two modes of vibration are translational and the third is torsional. The vibration periods are T ₁ = 0.878, T ₂ = 0.679, and T ₃ = 0.643.
In RSA, all 12 vibration modes were taken into account (the sum of the effective modular masses amounts to more than 90% of the total mass of the structure). It should be noted that the first six modes were sufficient to meet the requirements in the code (the sum of the effective modular masses is at least 90% of the total mass).
The translation to rotation period (Ω ratio) of the model is investigated, assuming a rigid diaphragm. The building is characterized by a Ω ratio in the X- and the Y-directions equal to 1.36 and 1.06. respectively, with Ω > 1. As a consequence, the model is considered torsionally stiff, and the predominant response is the translational mode [34].
The IDR_x,y are computed for both directions. The maximum inter-story inelastic drift ratio (IDR_max) is the maximum IDR of all stories. The story drift limit is 2% for the risk category II building, according to ASCE 7-16. The IDRs should not exceed this limit. The IDR parameter is calculated, for the ith floor, with the following equations (1) and (2):

(1) IDR x i = ∆ xi hi ,

(2) IDR y i = ∆ yi hi ,

where ∆x _i is the drift in the X-direction for the ith and (i − 1)th story, ∆y _i is the drift in the Y-direction for the ith and (i − 1)th story, and i is the story height.

The story drifts are shown in Figure 3 for both directions for all analysis methods. It can be noted that the drift of floors for the NDP along the building height is greater than the drift for both analyses (ELFP and RSA). In addition, the drifts of the second and third floors are greater than the drift limit 2% for the NDP, and the drifts of the first and second floors for the NSP are greater than the drift limit 2%, while the drifts for ELF and RSA are much less than drift limit 2%. It can be noted that the drift for the NSP is greater than the drift for the NDP in the first and second floors and less than that in the third and fourth floors, and this is due to the effect of irregular torsion of the structure. The maximum inter-floor drift (IDR_max) for all analysis methods is shown in Figure 4.

The effects of the vibration higher modes in the plane (roof displacement) in the X- and Y-directions were evaluated. The roof displacements were determined for center of mass (CM), stiff edge (SE), and flexible edge (FE) obtained using NSP, NSP, ELFP, and RSA; the schematic plan of the buildings’ roof is shown in Figure 5. The values were normalized by the displacement of the roof at the center of mass. The normalized roof displacement (u/u _CM) is shown in the X- and Y-directions in Figure 6.

Figure 3

IDR_x,y along the height of model, for ELFP, RSA, NSP, and NDP.

Figure 4

IDR_max for ELFP, RSA, NSP, and NDP.

Figure 5

Schematic plan of the building (roof level).

Figure 6

Displacement of the roof in the horizontal plane in the X- and Y-directions.

From the results of u/u _CM for all methods of analysis, it shows a significant difference between the values obtained from the NDP compared to the NSP values, which confirms the importance of taking into account the influences of the torsional effects to simulate the real behavior of the irregular buildings. The results also show a large difference obtained from NDP compared with ELFP and RSA, especially for the FE in the Y-direction. As illustrated in Figure 6 for the NDP analysis, the torsional effects increase in the FE in the Y-direction, where the values are greater than in the SE by 56%, while in the X-direction by 5%, and this is due to the torsional effects of the building in the Y-direction, which are greater than in the X-direction because of the irregularity in the Y-direction.

Figure 8 summarizes the shear capacity ratio for columns, which represents the ratio of the shear demand on column V to the shear strength V n . In all analysis methods, the shear demand V is the maximum shear force that occurs in the columns of the story levels during the analyses. The shear force V n is calculated from the equation (3) according to ACI 318-19:

(3) V n = V c + V s ,

where V n is the nominal shear strength, V c is the nominal shear strength provided by concrete, and V s is the nominal shear strength provided by the shear reinforcement.

Figure 7 shows the corners of the building in which the results were compared, which represent the FE and the SE (Figure 5).

Figure 7

A 3-D structural model showing the corners of the building.

From the resulting values shown in Figure 8, it can be noted that the shear ratios for the NDP analysis are less than those corresponding ones for the NSP analysis, which indicates the inaccuracy of the NSP results for these type of irregular buildings, while the results for the NDP analysis are larger compared to ELFP and RSA. It is also clear from the comparison of the results in Figure 9 in the Y-direction that columns in H3, which is considered as a SE, have lower values than columns in H1, which is considered as a F) for all the studied analysis methods. This difference is clearly noted for the NDP analysis, where the values for this analysis for H1 are greater than the values of H3 along the height of the model about 17–141%, while in the X-direction, for columns in A1 which is considered and SE, which has lower values than column H1, which is considered as FE, the difference along the height of the model about 14–20%. Therefore, it can be concluded that the relatively higher values of the shear ratio occurred in the FE of all the studied analysis methods, and this difference appears clearly for the NDP analysis, with a decrease in the ratios in the SE, as well as the inaccuracy in the results of the ELFP, NSP and RSA. It is noteworthy that the shear capacity ratios remain less than 1.0 (in fact, they do not exceed 0.2); thus, the seismic performance of the columns under consideration is quite satisfactory.

Figures 9 and 10 show the structural elements that were taken into account in the evaluation; by comparing the internal forces (axial forces and moment) for the columns in H3 between all the analyzed methods, it can be noted that the internal forces of the ELFP analysis have slight differences compared to the results obtained from RSA. The axial force of the NDP is greater about 104–144% than the RSA and greater about 151–218% than the ELFP, and the moment of the NDP is greater about 207–253% than the RSA and greater about 440–640% than the ELFP. However, for the columns in H1, it can be noted that the internal forces of the ELFP analysis have also slight differences compared to the results obtained from the RSA. The axial force for the NDP analysis is greater about 140–461% than the RSA and greater about 152–253% than the ELFP, and the moment for the NDP analysis is greater about 156–243% than the RSA and greater about 248–438% than the ELFP. As for the columns in A1, it can be noted also that the internal forces of the ELFP analysis have slight differences compared to the results obtained from the RSA. The axial force of the NDP analysis is greater about 90–321% than the RSA and greater about 91–361% than the ELFP, and the moment for the NDP for the NDP analysis are greater about 152–250% than the RSA and greater about 144–325% than the ELF.

It is evident that the NSP results are higher than those of the NDP results, and this overestimation of the results is due to the NSP analysis’s inaccuracy and reliability. In addition, it can be noted that the values of the internal stresses (moment and axial force) of the elements in the FE are higher than those in the SE for all the studied analysis methods. This difference appears clearly for the NDP analysis, where the values of the moment in the FE along the height of the model are greater about 20–222% than the SE, while the values of axial forces in the FE are greater about 17–47% along the height of the model. The same for the columns in A1 that is considered as (SE) in the X-direction, have lower values than the columns in H1 that is considers as FE, for all the studied analysis methods. This difference is clear for the NDP analysis, where the values of the moment in the FE along the height of the model are greater about 8–3% than the SE, while the values of axial forces in the FE are greater about 12–22% along the height of the model. The difference along the height of the model is 8–13%. For the torque, the difference along the height of the model is 12–22% with respect to the vertical forces.
Additionally, the values of the internal stresses (moment and shear force) of the beams at first level as illustrated in Figures 11–13, which confirm the same previous observations, where the results at the FE are higher than those of the SE. Where the results of NDP analysis in the Flexible Edge (FE) are greater about (225–484)% than results of RSA analysis and are greater about (383–1227)% than results of ELFP analysis, while the results of NSP analysis alternate between the decrease and the increase compared to the results of NDP analysis.

Figure 8

Shear ratio for columns in H3 at SE in the Y-direction, columns in A1 at SE in the X-direction, and columns in H1 at FE in both X- and Y-directions.

Figure 9

Axial forces for columns in H3 at SE in the Y-direction, columns in A1 at SE in the X-direction, and columns in H1 at FE in both X- and Y-directions.

Figure 10

Moment for columns in H3 at SE in the Y-direction, columns in A1 at SE in the X-direction, and columns in H1 at FE in both X- and Y-directions.

Figure 11

Moment and shear force of the A1-B1 beam at first level, in SE for the X-direction.

Figure 12

Moment and shear force of the G3-H3 beam at first level, in SE for the Y-direction.

Figure 13

Moment and shear force of the G1-H1 beam at first level, in FE for the X- and Y-directions.

From the above, it can be concluded that the NDP results are most accurate to simulate the nonlinear behavior of the building. It can also be noted that the results of the elements in the FE are higher than those of the elements in SE due to the torsional effects causes by the irregularity in plane for the building.

7 Conclusion

In this study, the seismic response of multi-story RC building with plan irregularity, designed for Baghdad locations, is studied and analyzed by four different methods: the ELFP, RSA, the NSP (the load pattern distribution, first mode, was considered because it is the one governing), and the NDP. Several parameters were investigated (i.e., the inter-story drift, the torsional effects through the assessment of the effects of higher vibration modes and torsion in plan [roof displacement], the seismic performance of the structural members represented by the shear capacity ratio, i.e. the shear demand on the column, V, divided by the shear strength V n , internal forces [bending moments, axial force and shear forces]). The following observations were made.

The response of the building from the elastic analysis methods (RSA and ELFP) according to the Iraqi earthquake code, represented by the internal stresses and IDRs, is significantly less than the nonlinear analysis methods (NSP and NDP). This leads to a conclusion that the RSA and ELFP are inadequate methods. Therefore, appropriate methods should be adopted for designing, analyzing, and evaluating the performance of reinforced concrete buildings in Iraq.
For the nonlinear response of the building, torsional effects, represented by evaluating the effects of higher modes in the plane (roof displacement), were evident in the values obtained from NDP compared to those obtained with NSP especially in the FE. It demonstrates the inability of the NSP analysis to accurately and reliably represent the response and behavior of the building in the nonlinear domain.

Funding information: Authors declare that the manuscript was done depending on the personal effort of the author, and there is no funding effort from any side or organization.
Conflict of interest: The authors state no conflict of interest.
Data availability statement: Most datasets generated and analyzed in this study are comprised in this submitted manuscript. The other datasets are available on reasonable request from the corresponding author with the attached information.

References

[1] Domizio M, Ambrosini D, Curadelli O. Nonlinear dynamic numerical analysis of a RC frame subjected to seismic loading. J Eng Struct. 2017;13(8):410–42.10.1016/j.engstruct.2017.02.031Search in Google Scholar

[2] Antoniou S, Pinho R. Nonlinear seismic analysis of framed structures. In Chapter 8 of Engineering dynamics and vibrations. 2018, 1st edn. Boca Raton: CRC Press; 2018. p. 268–301.10.1201/9781315119908-8Search in Google Scholar

[3] Harba I, Abdulridha A, AL-Shaar A. Numerical analysis of high-strength reinforcing steel with conventional strength in reinforced concrete beams under monotonic loading. Open Eng. 2022;12(1):817–33. 10.1515/eng-2022-0365.Search in Google Scholar

[4] Rodrigues H, Varum H, Costa A. A simplified shear model for reinforced concrete elements subjected to reverse lateral loadings. Open Eng. 2012;2(1):136–45. 10.2478/s13531-011-0055-0.Search in Google Scholar

[5] American Society of Civil Engineers. ASCE/SEI 7-16: Minimum design loads and associated criteria for buildings and other structures. Virginia. 2016;7:95.Search in Google Scholar

[6] Central organization for standardization and quality control. ISC 2016: Iraqi seismic code requirements for buildings. 1st edn. Baghdad, Iraq. 2016.Search in Google Scholar

[7] Shayanfar J, Bengar HA, Niroomandi A. A proposed model for predicting nonlinear behavior of RC joints under seismic loads. J Mater Des. 2016;95:563–79.10.1016/j.matdes.2016.01.098Search in Google Scholar

[8] Lepage A, Hoppe MW, Delgado SA, Dragovich JJ. Best-fit models for nonlinear seismic response of reinforced concrete frames. J Eng Struct. 2010;32:2931–9.10.1016/j.engstruct.2010.05.012Search in Google Scholar

[9] Babazadeh A, Burgueño R, Silva PF. Evaluation of the critical plastic region length in slender reinforced concrete bridge columns. J Eng Struct. 2016;125:280–93.10.1016/j.engstruct.2016.07.021Search in Google Scholar

[10] Inel M, Ozmen HB. Effects of plastic hinge properties in nonlinear analysis of reinforced concrete buildings. J Eng Struct. 2006;28:1494–502.10.1016/j.engstruct.2006.01.017Search in Google Scholar

[11] De Stefano M, Galassi S, Lapi M, Orlando M. Evaluation of the American approach for detecting plan irregularity. J Adv Civ Eng. 2019;2019:1–10. article ID 2861093.10.1155/2019/2861093Search in Google Scholar

[12] Kosmopoulos AJ, Fardis MN. Estimation of inelastic seismic deformations in asymmetric multistorey RC buildings. J Earthq Eng Struct Dyn. 2007;36(9):1209–34.10.1002/eqe.678Search in Google Scholar

[13] Erduran E, Ryan KL. Effects of torsion on the behavior of peripheral steel-braced frame systems. J Earthq Eng Struct Dyn. 2011;40(5):491–507.10.1002/eqe.1032Search in Google Scholar

[14] Hanson D FEMA P-695: Quantification of seismic performance factors. Applied Technology Council 201 Redwood Shores Parkway, Suite 240 Redwood City, California 94065 www.ATCouncil.org; 2009 June. Sponsored by Federal Emergency Managency Management.Search in Google Scholar

[15] Bento R, Bhatt C, Pinho R. Verification of nonlinear static procedures for 3D irregular SPEAR building. J Earthq Eng. 2010;1(2):177–95.10.12989/eas.2010.1.2.177Search in Google Scholar

[16] Fajfar P, Marusic D, Perus I. Torsional effects in the pushover-based seismic analysis of buildings. J Earthq Eng. 2005;9(6):831–54.10.1080/13632460509350568Search in Google Scholar

[17] Park J, Towashiraporn P, Craig JI, Goodno BJ. Seismic fragility analysis of low-rise unreinforced masonry structures. J Earthq Eng. 2009;31(1):125–37.10.1016/j.engstruct.2008.07.021Search in Google Scholar

[18] Milutinovic Z, Mouroux P. Risk-UE project: An advanced approach to earthquake risk scenarios with applications to different European towns. Proceeding of the International Workshop on Safety and Emergency Management of Essential Facilities; 2003 June 19–21. Ohrid, Republic of Macedonia: SEMEF; 2003.Search in Google Scholar

[19] Ahamed S, Kori JG. Performance based seismic analysis of an unsymmetrical building using pushover analysis. Int J Eng Res. 2013;1(2):100–10.Search in Google Scholar

[20] Athanassiadou G. Seismic performance of R/C plane frames irregular in elevation. J Eng Struct. 2008;30:1250–61.10.1016/j.engstruct.2007.07.015Search in Google Scholar

[21] Merter O, Ucar T. A comparative study on nonlinear static and dynamic analysis of RC frame structures. J Civ Eng Sci. 2013;2(3):155–62.Search in Google Scholar

[22] Ravikumar CM, Babu Narayan KS, Sujith BV, Venkat D. Effect of irregular configurations on seismic vulnerability of RC buildings. J Archit Res. 2012;2(3):20–6.10.5923/j.arch.20120203.01Search in Google Scholar

[23] Valmundsson EV, Nau JM. Seismic response of building frames with vertical structural irregularities. J Struct Eng. 1997;123(1):30–41.10.1061/(ASCE)0733-9445(1997)123:1(30)Search in Google Scholar

[24] Köber D, Zamfirescu D. Simplified methods used for evaluation of the displacement gain due to general torsion. J Math Model Civ Eng. 2009;5(2):32–51.Search in Google Scholar

[25] Köber D, Zamfirescu D. Influence of general torsion on structural behaviour. J Math Model Civ Eng. 2011;9(1/2):166–74.Search in Google Scholar

[26] Magliulo G, Ramasco R. Seismic response of three‐dimensional R/C multi‐story frame building under uni‐and bi‐ directional input ground motion. J Earthq Eng Struct Dyn. 2007;36(12):1641–57.10.1002/eqe.709Search in Google Scholar

[27] Lucchini A, Mollaioli F, Monti G. Intensity measures for response prediction of a torsional building subjected to bi-directional earthquake ground motion. J Bull Earthq Eng. 2011;9(5):1499–518.10.1007/s10518-011-9258-2Search in Google Scholar

[28] Birzhandi MS, Halabian AM. Application of 2DMPA method in develpoing fragility curves of plan-asymmetric structures. J Eng Struct. 2017;153:540–9.10.1016/j.engstruct.2017.10.038Search in Google Scholar

[29] Chopra AK, Clough RP, Clough RW. Earthquake resistance of buildings with a ‘soft’ first storey. J Earthq Eng Struct Dyn. 1973;1(4):347–55.10.1002/eqe.4290010405Search in Google Scholar

[30] Das S, Nau JM. Seismic design aspects of vertically irregular reinforced concrete buildings. J Earthq Spectra. 2003;19(3):455–77.10.1193/1.1595650Search in Google Scholar

[31] Van Thuat D. Story strength demands of irregular frame buildings under strong earthquakes. J Struct Des Tall Spec Build. 2011;22(9):687–99. 10.1002/tal.713.Search in Google Scholar

[32] Bhosale AS, Davis R, Sarkar P. Vertical irregularity of buildings: Regularity index versus seismic risk, ASCE-ASME. J Risk UncertaEng Syst Part A: Civ Eng. 2017;3(3):1–10.10.1061/AJRUA6.0000900Search in Google Scholar

[33] American Society of Civil Engineers. ASCE/SEI 41-13: Seismic evaluation and retrofit of existing buildings. Reston, Virginia: American Society of Civil Engineers; 2014.Search in Google Scholar

[34] Anagnostopoulos SA, Kyrkos MT, Stathopoulos K. Earthquake induced torsion in buildings: Critical review and state of the art. J Earthq Struct. 2015;8(2):305–77.10.12989/eas.2015.8.2.305Search in Google Scholar

Received: 2024-01-09

Revised: 2024-02-25

Accepted: 2024-03-03

Published Online: 2024-04-06

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/eng-2024-0003

Keywords for this article

RC irregular buildings; equivalent lateral force procedure; response spectrum model; nonlinear static procedure; nonlinear dynamic procedure

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