A Comparison Analysis of Buildings as per Norwegian and Ethiopia ES-EN1998-1 Seismic Code

Abstract

An earthquake is one of the most significant and shocking natural disasters ever documented anywhere on the planet. Throughout history, it has claimed millions of lives and wreaked devastation on infrastructure. Because earthquake forces are spontaneous and unpredictable, engineering methods must be honed to investigate buildings under the impact of these forces. The dynamic and static computations of four RC multistory structure prototypes with various elevations in a high seismic zone are compared in this paper. The project under review is modeled as a 3, 6, 12, and 18-story establishment, and it is analyzed employing ETABS vs. 2019. The Equivalent Lateral Force (ELF) Procedure is used for static experimentation, while the Response Spectrum (RS) Procedure is employed for dynamic investigation. Both calculations are performed as per the EUROCODE 8-2004 recommendation. The ELF seismic load practice utilized was for the country of Norway, which has similar parameters to the ES-EN 8-15 seismic regulation Type I target RS, with ag/g = 0.1, spectrum type = I, soil factor S = 1.3 ground type, spectrum period (Tb, Tc, and Td) 0.1 s, 0.25 s, and 1.5 s. For the RS investigation, the parameters employed are as per ESEN-2015, ag/g = 0.1, and the spectrum type = I and ground type = B parameters were involved in the same manner for the RS analysis. The soil factor was set to 1.35; the spectrum period was set to (Tb, Tc, and Td) 0.05 s, 0.25 s, and 1.2 s. The behavior factor = 3.8, the lower bound factor = 0.2, and the damping ratio = 0.05. The results are then compared by employing different components such as displacement, story drift, story stiffness, base story shear, and story moment. Ultimately, a comparison of static and dynamic investigations has been carried out. Compared to the RS approach, the ELF technique produces more additional displacement, total drift, and base shear. As per the findings of this paper, for high-rise and tall buildings, dynamic analysis such as RS should be used rather than static analysis (ELF).

1. Introduction

Due to the world’s growing population, creating low- to high-rise structures that can withstand lateral dynamic stresses induced by earthquakes is becoming more fashionable. The impacts of earthquakes are more potent than the effects of wind. Many buildings have been destroyed as a result of natural and unexpected earthquakes that induce tremendous ground shaking, as shown by previous severe disasters. As a result, tremor analysis and design are critical in today’s society. The ELF and RS techniques used in this investigation were performed following EUROCODE 8-2004 and the Norwegian building code.

2. Literature Review

This research includes an investigation of the seismic behavior of high-rise structures, such as the Fortune One Tower, which is approximately twenty-two stories with four basements and is found in Jinnah Avenue (Sector F-9), Islamabad. (Zone-2B) [1,2,3]. The project aims to specify the most cost-effective structural component sizes while providing the suggested structure’s safety, stability, and serviceability. ETABS 2016 was utilized to model the structure [4,5,6,7]. The chosen design was subjected to linear static and linear dynamic investigations. A static study used the ELF approach, whereas a dynamic investigation was conducted using RSA. The structure was designed utilizing the Pakistan Building Code (BCP), the UBC-97, and the ACI 318-14 conditions [8,9,10]. The cost-effective sizes of structural components are the result of this study. The response spectrum analysis procedure was authenticated to be better than the equivalent lateral force method [11,12,13,14,15,16,17,18].

The location of an earthquake at a multi-story building clearly illustrates that buildings built poorly and without abundant strength will fall apart when the earthquake happens [19,20,21,22,23]. To ensure the safety of multi-story structures against seismic forces, the seismic investigation must be studied, and earthquake-resistant systems must be developed [24]. In structural seismic investigation, the response spectrum analysis approach is applied. The seismic investigation used was a residential building with G+13 stories in zone III [24]—the STAAD. The Pro V8i program analyzes the complete structure [24]. This work investigates the effect of a significant number of vertically displaced, geometrically imperfect components on the seismic response of a structure [25]. For this project, the primary purpose is to use the RSA on RC buildings with inconsistent vertical frames and design methods/standards based on IS 13920 to perform RSA design using the ductility procedure [26]. The findings from analyzing the irregular structure are contrasted with those from the study of the regular structure [24]. “The researchers examined three forms of irregularities: mass irregularity, stiffness irregularity, and stiffness and mass irregularity” [27]. According to the observations, the maximum story shear force was found to be highest in the first story and lowest in the top story in all illustrations [28]. The base shear in mass irregular structures was shown to be more significant than in identical regular structures [24]. The stiff, uneven structure had higher inter-story drifts and survived less base shear [24].

The New Zealand Building Code’s current dynamic moment and shear force magnification requirements in cantilever wall constructions are scrutinized [29]. Higher mode effects are insufficiently captured by either the relative ELF or modal RS design procedures, according to time–history assessments of six wall constructions ranging in height from two to twenty stories [30]. According to the time–history data, dynamic amplification depends on both starting periods and predicted displacement ductility levels. Using two alternative methodologies, higher mode properties in cantilever walls are considered [31]. The first is based on a straightforward adaptation of the modal RS method, while the second is appropriate for single-mode design methods like the ELF method. Both provide a good characterization of the predicted reaction [32]. It is revealed that providing capacity protection at the design seismic intensity does not promise that undesired catastrophe modes will not happen at intensities larger than the design level. This has consequences for the design of crucial infrastructure, such as hospitals [33].

In another study, the building was planned according to code requirements, which imposed several limits while analyzing dynamic loads [34]. This time-consuming and complicated analytical technique takes a long time to complete. As a result, most structures are constructed on the premise of static loading [35]. In the event of a disaster, such as an earthquake, overlooking the dynamic forces may collapse the whole building. Recent earthquakes have shown the importance of dynamic analysis [36]. Most research is now being accomplished on dynamic analysis to ensure that structures can sustain earthquake-induced strains. Several theoretical formulae exist in various nations’ seismic regulations that relate the building’s height to the building’s omega, or natural period of vibration [37,38]. The lateral forces are predicted using the acceleration spectrum in this technique. The displacement demand provides a detailed estimate of the damage to be expected [39]. The essential periods of a case study of a low-rise structure are examined in this research utilizing the ELF and RS, all of which are based on IS 1893 (Part 1), as well as FEM in seism structure [40]. These techniques’ basic periods correspond to 0.39 s, 0.14 s, and 0.178 s. The components determining a structure’s fundamental period are explained [41]. The findings, however, demonstrate an appropriate error in the range (1–30%), and the seism struct provided genuine natural frequency calculations since the Indian code has a regular mode shape. This work also examines the limits of doing modal analysis [42].

All structures are directly affected by earthquakes. The consequences vary depending on the zone where earthquakes occur. The state and varieties of medium, hard, and soft soil impact how buildings react to earthquake loads. Because the soil grades of these soils’ conditions are so variable, seismic waves flow through the strata in different ways [43,44]. During earthquakes, the foundations of structures interact with the soil underneath. In conclusion, the type of soil and building directly disturb the ground structure and the consequences of the earthquake it experiences [45]. As a result, several evaluations of the same building in diverse seismic zones are carried out by changing the soil type for each simulation among hard, medium, and soft. Responses such as tale drift and displacement are shown for various zones and soil types [46]. The RS requirements for simulations in these different soil types are provided in IS 1893:2016, “Criteria for Earthquake Resistant Design of Structures”. This study has significant implications for structural design and geotechnical engineering [47].

As the world’s population continues to rise, there is an excellent demand for high-rise construction [48]. All across the globe, these establishments are utilized for residential, commercial, and industrial motivations [49]. Because natural catastrophes such as earthquakes are unexpected, the seismic resilience of these buildings is critical [50]. Bracings are essential to neutralize lateral loads, which may boost a building’s earthquake resistance capability [49]. “Using STAAD Pro V8i and the response spectrum and analogous static methods, this paper investigated the seismic manners of a G+41 story steel frame with concrete slab under X, K, and V bracings” [49]. All of the frames were tested for story displacement and base shear. V bracing, out of all the analyzed bracings, provided the structure with the most effective seismic protection [50].

In urban India, reinforced concrete frame structures are the most common building [51]. A structure is subjected to various static and dynamic forces during its existence [52]. The self-weight of the building is the primary source of static forces, which are time-independent. Dynamic forces, which include earthquake forces, are, on the other hand, time-dependent [53]. Both static and dynamic procedures may be used to conduct seismic analysis on RC structures. “The static technique assumes that the rate at which the load is applied is too sluggish to create substantial inertia forces in the structure, whereas the dynamic method considers inertia forces” [54]. Static approaches can only serve the purpose for low- to medium-rise structures, while dynamic analysis becomes critical for high-rise buildings, which are the most impacted by earthquake forces [55]. Buildings are increasingly becoming higher and thinner as demand grows and land availability shrinks [51]. As a result, dynamic analysis has generated vitality in a nation like India, which has been severely discouraged by strong earthquakes in the past, inflicting significant harm to infrastructure and human lives [51]. The ELF and the RS, both dynamic and static methods, are the most broadly used seismic analysis methods [56]. The equivalent static method is appropriate for typical structures under 15 m in height in seismic zone II. At the same time, the linear dynamic method is recommended for all other buildings, as per Indian standard regulations [57]. However, it has been noticed that the ELF method is also used in design practice for structures of more than 15 m in different seismic zones [54]. Using ETABS v. 2019 structural analysis software, this paper employs the ELF and RS methods to analyze multi-story framed structures of varying heights across different seismic zones. A comparative assessment is conducted between the outcomes of both methods, focusing on responses like bending moments, axial forces, and nodal displacements [57]. The most suitable and precise of the two ways of analyzing RC structure is selected based on the comparisons [58].

Using the force-based design technique (FBD) and the direct displacement-based design approach, this research investigates the seismic behavior of low-, medium-, and high-rise RC-framed building models (DDBD) [52]. Four-story, eight-story, and twelve-story RC-framed building models were used in the inquiry as low-, medium-, and high-rise structures, respectively [50]. The program ETABS was employed to model, analyze, and design the buildings [28]. For the building models, criteria such as base shear, story displacement, story drift, hinge formation, and reinforcing needs were explored and compared [48]. The analysis and design results revealed that the latter method is more cost-effective than the FBD method [28]. The DDBD is more conformed for medium-rise structures than low-, medium-, and high-rise buildings under consideration [28].

According to another investigation in the early days of civil engineering, buildings were continually constructed with the static load factor in mind. Subsequently, advancements in civil engineering studies showed that structures are subject to a collection of additional loads, enclosing seismic forces, wind pressures, snow loads, and various others, contingent upon factors such as the structure’s sizes, geographical placement, soil conditions, and other pertinent variables. “As a result, the procedure of assessing a design for many types of loads and designing the system for the essential load requirement was presented, with the dynamic load standing as one of the major loads for which the system should be evaluated and developed”. The preliminary objective of this investigation is to examine the seismic persistence of a multistory RC moment-resistant articulated structure under static and dynamic hurdles by BNBC, 2006 [10,43]. The structure was subjected to a static seismic load using the equivalent static force (ESF) technique. Nevertheless, the response spectrum (RS) approach implemented dynamic loading [41]. “The current investigation examines the divergences in story displacement and drift for each story, as well as base shear, story stiffness, bending moments, and story shear forces in columns at various story levels” [40]. Finally, a comparison of static and dynamic analysis has been carried out [20]. According to computational modeling output data, the base shear obtained by RS analysis is smaller than that obtained from the ESF procedure [39]. The maximum story displacement obtained from dynamic response spectrum analysis is approximately 78% of that obtained from static analysis [15,59]. Simultaneously, an internal column’s dynamic maximum bending moment is approximately 87% of its static counterpart [60].

Furthermore, in another study [15], the most favored kinds of construction in urban India are reinforced concrete (RC) building frames. During their lifespan, they are exposed to various forces, including static forces from DL and LL as well as dynamic forces from earthquakes [15]. In this investigation, two towering construction methods, G+10 and +25, in seismic zone III are analyzed, employing two different strategies: ELF and RS, both of which are performed in ETABS 15 [15]. “For comparison investigation, factors such as story drift, story displacement, axial load, and bending moments are calculated from the analytical findings. The response spectrum approach was better than the equivalent static analysis method” [15].

For structural design and evaluation, numerous seismic analysis methodologies have been defined in the most current standards. Because various techniques have varied benefits and disadvantages, a thorough comparison is necessary to determine which is most successful [30]. The numerous ordinary methods are the ELF procedure, the modal response MRS, and the LRH investigation [29]. This research intends to provide a comparative analysis of various approaches using ETABS v. 2019 software by the ASCE 7-16 standard. Six different types of buildings designed as per ACI 318-19 norms were investigated in terms of base shear and the allocation of story shear forces [58]. In areas prone to high seismic activity, building code specifications for reinforced concrete buildings equipped with a dual lateral force-resisting system undergo scrutiny [61]. Compared to the MRS or LRH analyses, the ELF procedure’s base shear for the building under investigation is conservative [61]. The ELF procedure’s vertical distribution is simply a function of the structure’s basic period; however, the MRS and LRH analyses have the advantage of exposing how a structure’s mass and stiffness distribution affects member forces and displacements [61,62,63].

2.1. Gap in the Literature

Following an extensive literature review, research was conducted globally on equivalent lateral force (ELF) and response spectrum (RS) analyses. However, to our knowledge, there is a lack of comparable studies on ELF and RS calculations for 3-, 6-, 12-, and 18-story moment-resisting frame systems in the chosen design region of Ethiopia. This comparative analysis holds significance due to adherence to the Type I response spectrum outlined in the Ethiopian Building Code ES EN 1989-1:2015 and the Norwegian Building Code. Various parameters, encompassing both local and global structural responses, are included in the comparison.

2.2. The Objective of the Research

This study compares structures under earthquake motions, employing static (ELF) and dynamic (RS) analyses. The analysis focuses on reinforced concrete framed structures with varying story heights in a high seismicity zone, adhering to EUROCODE 8-2004 standards. The ELF seismic load pattern utilized corresponds to that of Norway, which shares parameters similar to those of the Building Code of Ethiopia ESEN-2015, as depicted in Figure A1 and Figure A2,

Table A1. Elastic response spectra as per ES EN 1998-1:2015.

Ground Type	S	TB (S)	TC (S)	TD (S)
A	1.0	0.05	0.25	1.2
B	1.35	0.05	0.25	1.2
C	1.5	0.10	0.25	1.2
D	1.8	0.10	0.30	1.2
E	1.6	0.05	0.25	1.2

and

Table A2. Values of the parameters describing the recommended Type II elastic response spectra as per ES EN 1998-1:2015.

Ground Type	S	TB (S)	TC (S)	TD (S)
A	1.0	0.15	0.4	2.0
B	1.2	0.15	0.5	2.0
C	1.15	0.20	0.6	2.0
D	1.35	0.20	0.8	2.0
E	1.4	0.15	0.5	2.0

. To achieve this, four models with different heights were created and analyzed using ETABS 2019, with results compared across five parameters: story moment, displacement, story shear, story drift, and base shear.

3. Case Study—Description

This study focuses on a standard reinforced concrete building, depicted in

Table 1. Sample RC buildings detail.

Property for 3-, 6-, 12-, and 18-Story RC Sample Building	Description
Height for 3-, 6-, 12-, and 18-story RC Structure’s type	9, 18, 36, 54 m Multi-story moment-resisting frame (3, 6, 12, and 18 story)
Floor-to-floor height	3 m
Soil type	B
Damping	0.05
Support	Fixed support
Importance factor	1
R factor	3.8
Beam section	500 × 350 mm
Column section	400 × 400 mm
Wall section	300 mm
Slab section	200 mm
Seismic zone	3 (Addis Ababa)
Concrete quality	C-30
Steel	G-60

, Figure 1, Figure 2 and Figure 3a–d. The floor area of the structure spans 900 square meters, measuring 30 m by 30 m, and includes five bays along each side, with individual spans measuring 6 m. The structure is modeled in three variations: 3, 6, 12, and 18 stories, each with a height of 3.20 m.

Different loads operating on a building play an essential role in its design. The failure of a structure may be caused by a mistake in estimating these loads. As a result, a thorough examination of the loads operating on the structure is required. The loads in a particular region must be carefully chosen, and the worst possible combination of these loads must be assessed. The weight of all walls, partitions, floors, and roofs, as well as the weight of any other permanent structures in the building, should be included in the dead load. The dead load (DL) is computed as 2 kN/m² based on the materials used in the construction. The live load (LL) is measured at 3 kN/m². The construction is said to be in a seismically active location near Addis Ababa, Ethiopia.

Table 2. Loading Detail.

Dead load	2 kN/m2
Live load	3 kN/m2
Wall load on beam	12 kN/m2
ELF and RS procedure	ES8-15 corresponds to Eurocode 8-2004 standards (based on EN1998-1) and Norwegian Building Code

shows the seismic parameters employed in this research, which are based on ES8-15, corresponding to Eurocode 8-2004 standards (based on EN1998-1) and the Norwegian Building Code.

4. Modeling and Analysis

Various configurations with different dimensions were simulated and assessed using ETABS 2019, employing ELF for static analysis and RS for dynamic investigation following ES8-15 and the Norwegian Building Code, adhering to Eurocode 8-2004 standards. The modeling of different systems in the software v. 19 is depicted in Figure 2.

5. Results and Discussion

Ultimately, the internal forces calculated from the static and dynamic analysis of the structures at different heights were compared for all five criteria: displacement, story drift, base shear, story shear, and story moment.

5.1. Three-Story Building

Table 3. CM displacement for diaphragm D1 for three-story structure by static and dynamic analysis.

		ELF X-Y Axis Output		RS X-Y Axis Output		X-Y Axis Output
		CM Displacement for Diaphragm D1		CM Displacement for Diaphragm D1		CM Displacement for Diaphragm D1
Elevation	Location	X-Dir	Y-Dir	X-Dir	Y-Dir	ELF vs. RS X-Dir	ELF vs. RS Y-Dir
m		mm	mm	mm	mm	%	%
9	Top	1.313	1.189	1.794	1.619	73.188	73.440
6	Top	0.871	0.774	1.186	1.05	73.440	73.714
3	Top	0.38	0.331	0.516	0.446	73.643	74.215
0	Top	0	0	0	0	0	0

, Figure A3a, Figure A7a, Figure A9b and Figure 4 illustrate the three-story CM displacement for diaphragm D1 by dynamically and statically analyzing the sample structure results. It can be seen that the maximum SMD obtained by RS is higher than that obtained by ELF for all the stories. The ELF result indicated 73.188% in the X-axis and 73.44% in the Y-axis of the RS results. It can be observed that the difference in CMD generated by both methods decreased from the bottom to the top of the structure in both X and Y directions.

Table 4. Comparison of static and dynamic analysis results for CM drifts for diaphragm D1 for three-story structures.

		ELF X-Y Axis Output		RS X-Y Axis Output		X-Y Axis Output
		Drifts for Diaphragm D1		Drifts for Diaphragm D1		Drifts for Diaphragm D1
Elevation	Location	X-Dir	Y-Dir	X-Dir	Y-Dir	ELF vs. RS X-Dir	ELF vs. RS Y-Dir
m						%	%
9	Top	0.000154	0.000138	0.000218	0.000191	70.642	72.251
6	Top	0.00017	0.000148	0.000238	0.000202	71.428	73.267
3	Top	0.000131	0.00011	0.000182	0.000149	71.978	73.825
0	Top	0	0	0	0	0	0

, Figure A3b, Figure A7b, Figure A10a and Figure 5 illustrate the three-story drift for diaphragm D1 by dynamically and statically analyzing the sample structure results. It can be seen that the maximum DFD obtained by RS is higher than that obtained by ELF for all the stories. The ELF result indicated 71.97% in X—the X-axis and 73.82% in the Y-axis of the RS results. It has been observed that the difference in DFD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

Table 5. Comparison of static and dynamic analysis results in max story displacement for three-story structures.

		ELF X-Y Axis Output		RS X-Y Axis Output		X-Y Axis Output
		Max Story Displacement		Max Story Displacement		Max Story Displacement
Elevation	Location	X-Dir	Y-Dir	X-Dir	Y-Dir	ELF vs. RS X-Dir	ELF vs. RS Y-Dir
m		mm	mm	mm	mm	%	%
9	Top	1.362	1.189	1.903	1.623	71.571	73.259
6	Top	0.9	0.774	1.255	1.052	71.713	73.574
3	Top	0.392	0.331	0.545	0.447	71.926	74.049
0	Top	0	0	0	0	0	0

, Figure A4a, Figure A8a, Figure A11a and Figure 6 illustrate the three-story max story displacement by dynamically and statically analyzing the sample structure results. It can be seen that the maximum MSD obtained by RS is higher than that obtained by ELF for all the stories. The ELF result indicated 71.92% in the X-axis and 74.04% in the Y-axis of the RS results. It can be observed that the difference in MSD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

Table 6. Comparison of static and dynamic analysis results for max story drifts for three-story structures.

		ELF X-Y Axis Output		RS X-Y Axis Output		X-Y Axis Output
		Max. Story Drifts		Max. Story Drifts		Max. Story Drifts
Elevation	Location	X-Dir	Y-Dir	X-Dir	Y-Dir	ELF vs. RS X-Dir	ELF vs. RS Y-Dir
m						%	%
9	Top	0.000154	0.000138	0.000218	0.000191	70.642	72.251
6	Top	0.00017	0.000148	0.000238	0.000202	71.428	73.267
3	Top	0.000131	0.00011	0.000182	0.000149	71.978	73.825
0	Top	0	0	0	0	0	0

, Figure A4b, Figure A10b and Figure 7 illustrate the three-story max story drifts by dynamically and statically analyzing the sample structure results. It can be seen that the maximum MSD obtained by RS is higher than that obtained by ELF for all the stories. The ELF result indicated 71.97% in the X-axis and 73.82% in the Y-axis of the RS results. It can be observed that the difference in MSD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

Table 7. Comparison of static and dynamic analysis results in story shears for three-story structures.

ELF X-Y Axis Output				RS X-Y Axis Output		X-Y Axis Output
Story Shears				Story Shears		Story Shears
Elevation	Location	X-Dir	Y-Dir	X-Dir	Y-Dir	ELF vs. RS X-Dir	ELF vs. RS Y-Dir
m		kN	kN	kN	kN	% kN	% kN
9	Top	−4684.32	−4684.3181	6634.351	6656.891	−70.607	−70.367
	Bottom	−4684.32	−4684.3181	6634.351	6656.891	−70.607	−70.367
6	Top	−8049.99	−8049.9904	11053.03	11028.78	−72.830	−72.990
	Bottom	−8049.99	−8049.9904	11053.03	11028.78	−72.830	−72.990
3	Top	−9732.83	−9732.8265	13209.4	13116.83	−73.681	−74.201
	Bottom	−9732.83	−9732.8265	13209.4	13116.83	−73.681	−74.201
0	Top	0	0	0	0	0	0

, Figure A5a, Figure A8b, Figure A12b and Figure 8 illustrate the three-story max story shear by dynamically and statically analyzing the sample structure results. It can be seen that the maximum MSD obtained by RS is higher than that obtained by ELF for all the stories. The ELF results indicated 73.68% on the X-axis and 74.20% on the Y-axis of the RS results. It can be observed that the difference in MSD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

Table 8. Comparison of static and dynamic analysis results for overturning moment for three-story structures.

		ELF X-Y Axis Output		RS X-Y Axis Output		X-Y Axis Output
		Overturning Moment		Overturning Moment		Overturning Moment
Elevation	Location	X-Dir	Y-Dir	X-Dir	Y-Dir	ELF vs. RS X-Dir	ELF vs. RS Y-Dir
m		kN-m	kN-m	kN-m	kN-m	% kN-m	% kN-m
9	Top	0	0	0	0	0	0
6	Top	14052.95	−14052.9544	19970.67	19903.05	70.367	−70.607
3	Top	38202.93	−38202.9256	52741.39	52730.14	72.434	−72.449
0	Top	67401.41	−67401.4051	91389.9	91625.96	73.751	−73.561

, Figure A6a,b, Figure A11b and Figure 9 illustrate the three-story max overturning moment by dynamically and statically analyzing the sample structure results. It can be seen that the maximum MOM obtained by RS is higher than that obtained by ELF for all the stories. The ELF result indicated 73.75% on the X-axis and 73.56% on the Y-axis of the RS results. It can be observed that the difference in MOM generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

5.2. Six Story Building

Table 9. Comparison of static and dynamic analysis results for CM displacement for diaphragm D1 for six-story structures.

			ELF X-Y Axis Output		RS X-Y Axis Output		X-Y Axis Output
			CM Displacement for Diaphragm D1		CM Displacement for Diaphragm D1		CM Displacement for Diaphragm D1
Story	Elevation	Location	X-Dir	Y-Dir	X-Dir	Y-Dir	ELF vs. RS X-Dir	ELF vs. RS Y-Dir
	m		mm	mm	mm	mm	%	%
Story6	18	Top	6.129	6.13	10.32	10.349	59.389	59.232
Story5	15	Top	5.003	4.944	8.394	8.316	59.602	59.451
Story4	12	Top	3.806	3.709	6.358	6.21	59.861	59.726
Story3	9	Top	2.599	2.492	4.325	4.151	60.092	60.033
Story2	6	Top	1.477	1.385	2.452	2.299	60.236	60.243
Story1	3	Top	0.555	0.504	0.922	0.835	60.195	60.359
Base	0	Top	0	0	0	0	0	0

, Figure A13a, Figure A16b, Figure A20a and Figure 10 illustrate the six-story CM displacement for diaphragm D1 by dynamically and statically analyzing the sample structure results. It can be seen that the maximum SMD obtained by RS is higher than that obtained by ELF for all the stories. The ELF result indicated 60.19% in the X-axis and 60.35% in the Y-axis of the RS results. It can be observed that the difference in CMD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

Table 10. A comparison of static and dynamic analysis results in drifts for diaphragm D1 for six-story structures.

			ELF X-Y Axis Output		RS X-Y Axis Output		X-Y Axis Output
			Drifts for Diaphragm D1		Drifts for Diaphragm D1		Drifts for Diaphragm D1
Story	Elevation	Location	X-Dir	Y-Dir	X-Dir	Y-Dir	ELF vs. RS X-Dir	ELF vs. RS Y-Dir
	m						%	%
Story6	18	Top	0.000397	0.000395	0.000705	0.000685	56.312	57.664
Story5	15	Top	0.000421	0.000412	0.000745	0.000711	56.510	57.946
Story4	12	Top	0.000423	0.000406	0.000741	0.000694	57.085	58.501
Story3	9	Top	0.000392	0.000369	0.000679	0.000623	57.731	59.229
Story2	6	Top	0.000321	0.000294	0.000551	0.000491	58.257	59.877
Story1	3	Top	0.000192	0.000168	0.000329	0.00028	58.358	60
Base	0	Top	0	0	0	0	0	0

, Figure A13b, Figure A17a, Figure A20b and Figure 11 illustrate the six-story drift for diaphragm D1 by dynamically and statically analyzing the sample structure results. It can be seen that the maximum DFD obtained by RS is higher than ELF for the whole story. The ELF result indicated 59.38% in the X-axis and 60% in the Y-axis of the RS results. It can be observed that the difference in DFD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

Table 11. Comparison of static and dynamic analysis results in max story displacement for six-story structures.

			ELF X-Y Axis Output		RS X-Y Axis Output		X-Y Axis Output
			Max Story Displacement		Max Story Displacement		Max Story Displacement
Story	Elevation	Location	X-Dir	Y-Dir	X-Dir	Y-Dir	ELF vs. RS X-Dir	ELF vs. RS Y-Dir
	m		mm	mm	mm	mm	%	%
Story6	18	Top	6.439	6.13	11.175	10.393	57.619	58.982
Story5	15	Top	5.248	4.944	9.077	8.352	57.816	59.195
Story4	12	Top	3.985	3.709	6.864	6.236	58.056	59.477
Story3	9	Top	2.715	2.492	4.66	4.169	58.261	59.774
Story2	6	Top	1.538	1.385	2.634	2.309	58.390	59.982
Story1	3	Top	0.575	0.504	0.986	0.839	58.316	60.071
Base	0	Top	0	0	0	0	0	0

, Figure A14, Figure A17b, Figure A21a and Figure 12 illustrate the six-story max story displacement by dynamically and statically analyzing sample structure results. It can be seen that the maximum MSD obtained by RS is higher than that obtained by ELF for all the stories. The ELF result indicated 58.31% in the X-axis and 60% in the Y-axis of the RS results. It can be observed that the difference in MSD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

Table 12. A comparison of static and dynamic analysis results in max story drifts for six-story structures.

			ELF X-Y Axis Output		RS X-Y Axis Output		X-Y Axis Output
			Max. Story Drifts		Max. Story Drifts		Max. Story Drifts
Story	Elevation	Location	X-Dir	Y-Dir	X-Dir	Y-Dir	ELF vs. RS X-Dir	ELF vs. RS Y-Dir
	m						%	%
Story6	18	Top	0.000397	0.000395	0.000705	0.000685	56.312	57.664
Story5	15	Top	0.000421	0.000412	0.000745	0.000711	56.510	57.946
Story4	12	Top	0.000423	0.000406	0.000741	0.000694	57.085	58.501
Story3	9	Top	0.000392	0.000369	0.000679	0.000623	57.731	59.229
Story2	6	Top	0.000321	0.000294	0.000551	0.000491	58.257	59.877
Story1	3	Top	0.000192	0.000168	0.000329	0.00028	58.358	60
Base	0	Top	0	0	0	0	0	0

, Figure A14b, Figure A18a, Figure A22b and Figure 13 illustrate the six-story max story drifts by dynamically and statically analyzing the sample structure results. It can be seen that the maximum MSD obtained by RS is higher than that obtained by ELF for all the stories. The ELF result indicated 58.35% in the X-axis and 60% in the Y-axis of the RS results. It can be observed that the difference in MSD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

A comparison of the static and dynamic analysis results in story shears for six-story structures in Figure A14a, Figure A19a, Figure A21b and Figure 14 illustrates the six-story max story shear by dynamically and statically analyzing the sample structure results. It can be seen that the maximum MSD obtained by RS is higher than that obtained by ELF for the whole story. The ELF result indicated 59.51% in the X-axis and 59.42% in the Y-axis of the RS results. It can be observed that the difference in MSD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

Table 13. Comparison of static and dynamic analysis results for overturning moment for six-story structures.

			ELF X-Y Axis Output		RS X-Y Axis Output		X-Y Axis Output
			Overturning Moment		Overturning Moment		Overturning Moment
Story	Elevation	Location	X-Dir	Y-Dir	X-Dir	Y-Dir	ELF vs. RS X-Dir	ELF vs. RS Y-Dir
	m		kN-m	kN-m	kN-m	kN-m	%	%
Story6	18	Top	0	0	0	0	0	0
Story5	15	Top	9514.703	−9514.7029	19,215.76	18,903.87	49.515	−50.332
Story4	12	Top	27,574.77	−27574.7721	52,198.28	51,543.4	52.826	−53.498
Story3	9	Top	52,471.13	−52,471.1343	94,172.54	93,324.97	55.718	−56.224
Story2	6	Top	82,494.72	−82,494.7162	142,497.3	141,612.1	57.892	−58.254
Story1	3	Top	115,936.4	−115936.445	195,544.3	194,684.7	59.289	−59.550
Base	0	Top	151087.2	−151,087.246	251,666.4	250,831.2	60.034	−60.234

, Figure A15a, Figure A18b, Figure A23a and Figure 15 illustrate the six-story max overturning moment by dynamically and statically analyzing the sample structure results. It can be seen that the maximum MOM obtained by RS is higher than that obtained by ELF for the whole story. The ELF result indicated 60.03% in the X-axis and 60.23% in the Y-axis of the RS results. It can be observed that the difference in MOM generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

Table 14. Comparison of static and dynamic analysis results in story stiffness for six-story structures.

			ELF X-Y Axis Output		RS X-Y Axis Output		X-Y Axis Output
			Story Stiffness		Story Stiffness		Story Stiffness
Story	Elevation	Location	X-Dir	Y-Dir	X-Dir	Y-Dir	ELF vs. RS X-Dir	ELF vs. RS Y-Dir
	m		kN/m	kN/m	kN/m	kN/m	%	%
Story6	18	Top	2,817,990	2,674,783.212	3,243,421	3,124,450	86.883	85.608
Story5	15	Top	5,027,595	4,874,996.691	5,324,604	5,206,412	94.421	93.634
Story4	12	Top	6,878,333	6,815,751.587	6,945,641	6,899,407	99.030	98.787
Story3	9	Top	8,914,755	9,043,683.932	8,885,015	9012666	100.334	100.344
Story2	6	Top	12,086,256	12,647,605.41	12,136,646	12,703,461	99.584	99.560
Story1	3	Top	21,111,590	23,265,933.05	21,330,620	23,552,992	98.973	98.781
Base	0	Top	0	0	0	0	0	0

, Figure A16a, Figure A9b, Figure A22a and Figure 16 illustrate the six-story story stiffness by dynamically and statically analyzing the sample structure results. It can be seen that the maximum SS obtained by RS is higher than that obtained by ELF for all the stories. The ELF result indicated 98.97% in the X-axis and 98.78% in the Y-axis of the RS results. It can be observed that the difference in SS generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

5.3. Twelve-Story Building

Table 15. Comparison of static and dynamic analysis results in CM displacement for diaphragm D1 for 12-story structures.

			ELF X-Y Axis Output		RS X-Y Axis Output		X-Y Axis Output
			CM Displacement for Diaphragm D1		CM Displacement for Diaphragm D1		CM Displacement for Diaphragm D1
Story	Elevation	Location	X-Dir	Y-Dir	X-Dir	Y-Dir	ELF vs. RS X-Dir	ELF vs. RS Y-Dir
	m		mm	mm	mm	mm	%	%
Story12	36	Top	35.003	36.847	30.282	31.18	115.590	118.175
Story11	33	Top	31.577	33.133	27.213	27.938	116.036	118.594
Story10	30	Top	28.069	29.347	24.103	24.663	116.454	118.992
Story9	27	Top	24.497	25.514	20.987	21.394	116.724	119.257
Story8	24	Top	20.895	21.668	17.902	18.169	116.718	119.258
Story7	21	Top	17.313	17.865	14.888	15.028	116.288	118.878
Story6	18	Top	13.817	14.174	11.982	12.01	115.314	118.018
Story5	15	Top	10.486	10.678	9.221	9.159	113.718	116.584
Story4	12	Top	7.412	7.475	6.651	6.528	111.441	114.506
Story3	9	Top	4.697	4.675	4.336	4.188	108.325	111.628
Story2	6	Top	2.461	2.401	2.365	2.231	104.059	107.619
Story1	3	Top	0.833	0.785	0.856	0.778	97.3130	100.899
Base	0	Top	0	0	0	0	0	0

, Figure A24a, Figure A27b, Figure A31a and Figure 17 illustrate the 12-story CM displacement for diaphragm D1 by dynamically and statically analyzing the sample structure results. It can be seen that the maximum SMD obtained by RS is higher than that obtained by ELF for all the stories. The ELF result indicated 97.31% in the X-axis and 100.8997% in the Y-axis of the RS results. It can be observed that the difference in CMD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

The comparison of the static and dynamic analysis results of drifts for diaphragm D1 for 12-story structures in Figure A24b, Figure A28a, Figure A31b and Figure 18 illustrates the 12-story drift for diaphragm D1 by dynamically and statically analyzing the sample structure results. It can be seen that the maximum DFD obtained by RS is higher than that obtained by ELF for all the stories. The ELF result indicated 93.83% in the X-axis and 100.3831% in the Y-axis of the RS results. It can be observed that the difference in DFD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

The comparison of the static and dynamic analysis results of max story displacement for 12-story structures in Figure A25a, Figure A28b, Figure A32a and Figure 19 illustrates the 12-story max story displacement by dynamically and statically analyzing the sample structure results. It can be seen that the maximum MSD obtained by RS is higher than that obtained by ELF for the whole story. The ELF result indicated 94.04% in the X-axis and 100.2554% in the Y-axis of the RS results. It can be observed that the difference in MSD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

The comparison of the static and dynamic analysis results of max story drifts for 12-story structures in Figure A25b, Figure A29a, Figure A32b and Figure 20 illustrates the 12-story max story drifts by dynamically and statically analyzing the sample structure results. It can be seen that the maximum MSD obtained by RS is higher than that obtained by ELF for the whole story. The ELF result indicated 93.83% in the X-axis and 100.38% in the Y-axis of the RS results. It can be observed that the difference in MSD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

The comparison of static and dynamic analysis results of story shears for 12-story structures in Figure A26b, Figure A30a, Figure A34 and Figure 21 illustrates the 12-story max story shear by dynamically and statically analyzing the sample structure results. It can be seen that the maximum MSD obtained by RS is higher than that obtained by ELF for the whole story. The ELF result indicated 79.98% in the X-axis and 80.08% in the Y-axis of the RS results. It can be observed that the difference in MSD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

The comparison of the static and dynamic analysis results of the overturning moment for 12-story structures in Figure A26a, Figure A29b, Figure A33a and Figure 22 illustrates the 12-story max overturning moment by dynamically and statically analyzing the sample structure results. It can be seen that the maximum MOM obtained by RS is higher than that obtained by ELF for all the stories. The ELF result indicated 116.83% in the X-axis and 115.34% in the Y-axis of the RS results. It can be observed that the difference in MOM generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

The comparison of the static and dynamic analysis results of story stiffness for 12-story structures in Figure A27a, Figure A30b, Figure A33b and Figure 23 illustrates the 12-story story stiffness by dynamically and statically analyzing the sample structure results. It can be seen that the maximum SS obtained by RS is higher than ELF for all the stories. The ELF result indicated 82.32% in the X-axis and 79.62% in the Y-axis of the RS results. It can be observed that the difference in SS generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

5.4. Eighteen-Story Building

Figure A35a, Figure A38b and Figure A42a illustrate the 18-story CM displacement for diaphragm D1 by dynamically and statically analyzing the sample structure results. It can be seen that the maximum SMD obtained by RS is higher than that obtained by ELF for all the stories. The ELF result indicated 123.87% in the X-axis and 129.35% in the Y-axis of the RS results. It can be observed that the difference in CMD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

Figure A35b, Figure A39a and Figure A42b illustrate the 18-story drift for diaphragm D1 by dynamically and statically analyzing the sample structure results. It can be seen that the maximum DFD obtained by RS is higher than ELF for the whole story. The ELF result indicated 119.4% in the X-axis and 128.68% in the Y-axis of the RS results. It can be observed that the difference in DFD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

Figure A36b, Figure A39b and Figure A43a illustrate the 18-story max story displacement by dynamically and statically analyzing the sample structure results. It can be seen that the maximum MSD obtained by RS is higher than that obtained by ELF for the whole story. The ELF result indicated 119.539% in the X-axis and 128.51% in the Y-axis of the RS results. It can be observed that the difference in MSD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

Figure A36a, Figure A40a and Figure A43b illustrate the 18-story max story drifts by dynamically and statically analyzing the sample structure results. It can be seen that the maximum MSD obtained by RS is higher than that obtained by ELF for all the stories. The ELF result indicated 119.407% in the X-axis and 128.68% in the Y-axis of the RS results. It can be observed that the difference in MSD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

Figure A37b, Figure A41a and Figure A44b illustrate the 18-story max story shear by dynamically and statically analyzing sample structure results. It can be seen that the maximum MSD obtained by RS is higher than that obtained by ELF for all the stories. The ELF result indicated 97.09% in the X-axis and 36.05% in the Y-axis of the RS results. It can be observed that the difference in MSD generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

Figure A37a, Figure A40b and Figure A44a illustrate the 18-story max overturning moment by dynamically and statically analyzing the sample structure results. It can be seen that the maximum MOM obtained by RS is higher than that obtained by ELF for the whole story. The ELF result indicated 157.115% in the X-axis and 154.47% in the Y-axis of the RS results. It can be observed that the difference in MOM generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

Figure A38a, Figure A41b and Figure A45a illustrate the 18-story story stiffness by dynamically and statically analyzing the sample structure results. It can be seen that the maximum SS obtained by RS is higher than ELF for the whole story. The ELF result indicated 78.53% on the X-axis and 76.07% on the Y-axis of the RS results. It can be observed that the difference in SS generated by both methods decreases from the bottom to the top of the structure in both X and Y directions.

6. Conclusions

From the extensive data, we concluded that the CM displacement for diaphragm D1 for a three-story structure by static and dynamic analysis shows that the maximum SMD obtained by RS is higher than that obtained by ELF for all the stories. The ELF results indicated 73.188% in the X-axis and 73.44% in the Y-axis of the RS results. We concluded that CM drifts for diaphragm D1 for a three-story structure by static and dynamic analysis show that the maximum DFD obtained by RS is higher than ELF for the whole story. The ELF results indicated 71.97% in the X-axis and 73.82% in the Y-axis of the RS results. In addition, it has been concluded that the max story displacement for a three-story structure by static and dynamic analysis shows that the maximum MSD obtained by RS is higher than that obtained by ELF for all stories. The ELF results indicated 71.92% in the X-axis and 74.04% in the Y-axis of the RS results. From the extensive data, we concluded that max story drifts for a three-story structure by static and dynamic analysis show that the MSD obtained by RS is higher than ELF for the whole story. The ELF results indicated 71.97% in the X-axis and 73.82% in the Y-axis of the RS results. From the extensive data, we concluded that max story shears for a three-story structure by static and dynamic analysis show that the MSD obtained by RS is higher than ELF for the whole story. The ELF results indicated 73.68% in the X-axis and 74.20% in the Y-axis of RS. From the extensive and wide range of data, we concluded that the overturning moment for a three-story structure by static and dynamic analysis shows that the MOM obtained by RS is higher than ELF for the whole story. The ELF results indicated 73.75% on the X-axis and 73.56% on the Y-axis of the RS results.

From extensive data, it can be concluded that CM displacement for diaphragm D1 for a six-story structure by static and dynamic analysis shows that the maximum SMD obtained by RS is higher than that obtained by ELF for all the stories. The ELF results indicated 60.19% in the X-axis and 60.35% in the Y-axis of the RS results. We concluded that CM drifts for diaphragm D1 for a six-story structure by static and dynamic analysis show that the maximum DFD obtained by RS is higher than ELF for the whole story. The ELF results indicated 59.38% in the X-axis and 60% in the Y-axis of the RS results. In addition, we concluded that max story displacement for a six-story structure by static and dynamic analysis shows that the maximum MSD obtained by RS is higher than that obtained by ELF for all stories. The ELF results indicated 58.31% in the X-axis and 60% in the Y-axis of the RS results. From the extensive data, we concluded that the max story drifts for a six-story structure by static and dynamic analysis show that the MSD obtained by RS is higher than ELF for the whole story. The ELF results indicated 58.35% in the X-axis and 60% in the Y-axis of the RS results. From the extensive data, we concluded that max story shears for a six-story structure by static and dynamic analysis show that the MSD obtained by RS is higher than ELF for the whole story. The ELF results indicated 59.51% in the X-axis and 59.42% in the Y-axis of the RS results. From the extensive and wide range of data, we concluded that the overturning moment for a six-story structure by static and dynamic analysis shows that the MOM obtained by RS is higher than ELF for the whole story. The ELF results indicated 60.03% in the X-axis and 60.23% in the Y-axis of the RS results.

From the extensive data, we concluded that CM displacement for diaphragm D1 for a 12-story structure by static and dynamic analysis shows that the maximum SMD obtained by RS is higher than that obtained by ELF for all the stories. The ELF results indicated 97.31% in the X-axis and 100.8997% in the Y-axis of the RS results. We concluded that CM drifts for diaphragm D1 for a 12-story structure by static and dynamic analysis show that the maximum DFD obtained by RS is higher than ELF for the whole story. The ELF results indicated 93.83% in the X-axis and 100.3831% in the Y-axis of the RS results. In addition, we concluded that the max story displacement for a 12-story structure by static and dynamic analysis shows that the maximum MSD obtained by RS is higher than that obtained by ELF for all stories. The ELF results indicated 94.04% in the X-axis and 100.2554% in the Y-axis of the RS results. From the extensive data, we concluded that max story drifts for a 12-story structure by static and dynamic analysis show that the MSD obtained by RS is higher than ELF for the whole story. The ELF results indicated 93.83% in the X-axis and 100.38% in the Y-axis of the RS results. From the extensive and wide range of data, we concluded that max story shears for a 12-story structure by static and dynamic analysis show that the MSD obtained by RS is higher than ELF for the whole story. The ELF results indicated 79.98% in the X-axis and 80.08% in the Y-axis of the RS results. From the extensive and wide range of data, we concluded that the overturning moment for a 12-story structure by static and dynamic analysis shows that the MOM obtained by RS is higher than ELF for the whole story. The ELF results indicated 116.83% in the X-axis and 115.34% in the Y-axis of the RS results.

From the extensive and wide range of data, we concluded that CM displacement for diaphragm D1 for an 18-story structure by static and dynamic analysis shows that the maximum SMD obtained by RS is higher than that obtained by ELF for all the stories. The ELF results indicated 123.87% in the X-axis and 129.35% in the Y-axis of the RS results. We concluded that CM drifts for diaphragm D1 for an 18-story structure by static and dynamic analysis show that the maximum DFD obtained by RS is higher than ELF for the whole story. The ELF results indicated 119.4% in the X-axis and 128.68% in the Y-axis of the RS results.

In addition, we concluded that the max story displacement for an 18-story structure by static and dynamic analysis shows that the maximum MSD obtained by RS is higher than that obtained by ELF for all stories. The ELF results indicated 119.539% in the X-axis and 128.51% in the Y-axis of the RS results. From the extensive data, we concluded that max story drifts for an 18-story structure by static and dynamic analysis show that the MSD obtained by RS is higher than ELF for the whole story. The ELF results indicated 119.407% in the X-axis and 128.68% in the Y-axis of the RS results. From the extensive data, we concluded that the max story shears for an 18-story structure by static and dynamic analysis show that the MSD obtained by RS is higher than the ELF for the whole story. The ELF results indicated 97.09% in the X-axis and 36.05% in the Y-axis of the RS results. From the extensive and wide range of data, we concluded that the overturning moment for an 18-story structure by static and dynamic analysis shows that the MOM obtained by RS is higher than the ELF for the whole story. The ELF results indicated 115.115% in the X-axis and 154.47% in the Y-axis of the RS results.

According to the research findings, response spectrum analysis emerges as a crucial dynamic method, offering superior results without requiring extensive modeling compared to static analysis. While engineers and researchers generally favor RS analysis over ELF for its accuracy, it is essential to acknowledge its limitations, as it relies solely on linear elastic analysis. Advanced dynamic analysis tools like non-linear time–history analysis can be employed to produce more precise results despite being more complex and time-consuming. For practical applications, utilizing dynamic analysis (RS) is recommended over static analysis (ELF), especially in high-rise structures, as it delivers comparable outcomes with less computational effort, ensuring a cost-effective and safe design.