The Impact of Bracing System Distribution and Location on Seismic Performance Enhancement of Multi-Story Steel Buildings

Earthquakes are ground vibrations encompassing a wide spectrum of frequencies, triggered by various phenomena such as tectonic shifts, volcanic activity, landslides, rock bursts, and human-induced explosions. Among these, tectonic-induced earthquakes are the most prevalent and impactful, resulting from the fracturing and shifting of rocks along faults within the Earth's crust [1].

In the era preceding modern engineering, traditional materials like timber, clay brick, and stone dominated architecture. However, these materials proved to be highly susceptible to damage in earthquake-prone regions. The recognition of steel's resilient behavior during several earthquakes led to its emergence as a promising structural material, especially for buildings in seismic zones. This preference was predicated on two factors: firstly, steel's inherent properties of exceptional strength and ductility—specifically, its ability to endure substantial inelastic deformation without significant loss of strength, and secondly, the successful performance of steel structures in numerous earthquakes throughout the past century, during which the principles of seismic design were entrenched [2].

In terms of strength, steel buildings have typically exhibited commendable performance during earthquakes. Yield strength and elastic stiffness—two inherent properties of steel—contribute to the elastic resistance of steel structures during moderate earthquakes. However, during more substantial seismic events, a structure may undergo inelastic deformations and rely on its ductility and hysteresis energy dissipation capacity to prevent collapse. Steel, being a ductile material equally strong in tension and compression, is superbly suited for earthquake-resistant structures. Its ductility allows the structure to experience large plastic deformations with minimal loss of strength [3].

Damage to steel buildings observed in previous earthquakes has predominantly been induced by ground movements. This includes damage to beam-to-column connections caused by severe ground motion, buckling of diagonal braces, cracking of the concrete at the column base, and yielding and fracturing of anchor bolts. Nonstructural damage was also extensive in buildings with large open sections, such as gymnasiums and industrial facilities, particularly in ceilings and claddings. Additionally, widespread damage was observed in external finishes composed of mortar over light-gauge metal lath [4].

In this study, the focus will be on the bracing system, one of the various strategies employed to enhance the seismic performance of steel buildings, alongside shear walls and dampers [5]. The concentrically braced frame is a preferred type of bracing system due to its high elastic stiffness and is extensively used as a lateral force-resisting system. This setup comprises horizontal and vertical framing elements interconnected by a diagonal brace member, with intersecting axes. The concentric brace is available in several configurations, including the X-brace, multistory X-brace, inverted V-brace, V-brace, and multibay X-brace [6].

Previous research on the bracing system has been extensive. For instance, Tafheem and Khusru [7] modeled a six-story steel building and assessed its response to wind, earthquake, dead, and live loads using various types of bracing, such as X-bracing and V-bracing with HSS bracing. They analyzed the building's lateral story displacement, story drift, axial force, and bending moment at different levels. Their study showed that X-bracing significantly reduces lateral and inter-story displacement while increasing lateral stiffness.

In their study, Di Sarno and Elnashai [8] scrutinized the seismic behavior of steel moment-resisting frames (MRFs) initially designed with inadequate lateral stiffness but later retrofitted with various bracing systems. The study's focus was on three bracing systems: buckling-restrained braces (BRBFs), special concentric braces (SCBFs), and mega-braces (MBFs). The researchers used non-linear time-history analysis to evaluate these systems' structural performance during earthquake-induced ground motions. The study found that the MBFs exhibited 70% less maximum story drift than the MRFs and about 50% less than the SCBFs. Furthermore, the quantity of steel used for structural parts and connections in the mega-brace configurations was 20% less than that in the SCBFs. This reduction could potentially lower construction costs, making the MBFs an appealing choice for seismic retrofitting applications. Consequently, the results suggest that retrofitting with MBFs can considerably enhance the seismic performance of existing MRFs while also reducing construction costs.

Nassani et al. [9] undertook a comparative study on the seismic response of steel frames featuring different types of bracing systems. The systems under investigation were X-braced frames, V-braced frames, inverted V-braced frames, knee-braced frames, and zipper-braced frames. The study employed nonlinear static and dynamic analyses to evaluate the structural response of the frames, considering parameters like capacity curve, drift ratio, global damage index, base shear, story displacements, roof displacement time history, and plastification. The findings revealed that the bracing systems significantly curtailed inter-story drifts, with an average reduction of 58% compared to unbraced frames. Moreover, the incorporation of steel braces substantially decreased the global damage index of the frames.

The objective of this research is to explore the influence of bracing distribution and forms on a building's seismic performance. This study sets itself apart from previous research by considering various patterns of bracing and distribution, while standardizing the weight of the bracing on each floor across all models.

3.1 Effective seismic weight

According to (ASCE 7-16), the load considered in the seismic analysis is defined as a mass, equal to all dead load (including self-weight) above the building's foundation plus 25% of the live load (dead load+0.25*live load) [11].

3.2 Free vibration analysis

The established methods of mechanics are used to perform an undamped free-vibration analysis of the entire building. This analysis utilizes the appropriate masses and elastic stiffness of the structural system to determine the natural periods (T_n) and mode shapes (ɸ) of the relevant vibration modes that must be considered [13].

The research employs free-vibration analysis to determine the natural periods (T_n) for the first and second modes of each model. T_n has various applications; firstly, it can be used to identify whether a building is rigid or flexible, where a small T_n indicates a rigid building and a large T_n indicates a flexible building. Secondly, in non-linear time history analysis, it is necessary to determine the first and second natural periods for each model.

The results of free-vibration analysis by SAP 2000 v20 are summarized in Table 7.

Table 7. Free vibration result

3.3 Non-linear time history analysis by SAP 2000 v20

Non-linear time history analysis by program sap2000 v20 is used to investigate the response of steel structures under the El-Centro earthquake with a duration of 12.1 sec and time step equal to 0.02 sec, with a damping ratio equal to 0.02 for steel structure [14].

The most intricate method for the dynamic analysis of buildings is the Time History Analysis (THA) technique. This approach involves subjecting the mathematical model of the building to accelerations from earthquake records that simulate the anticipated earthquake at the base of the structure. The technique involves a sequential direct integration over a time period and can be used for both elastic and inelastic analysis. However, in the case of inelastic analysis, the stiffness is presumed to be constant only during each incremental time [13].

There are many parameters to compare between different models such as max roof displacement, max inter-story drift ratio, max base shear, and max base bending moment.

3.3.1 Maximum roof displacement

In the x-direction, a non-linear time history analysis of a sixteen-story steel building indicates that the maximum roof displacement of Model 1 (without bracing) is exceeded by Model 2, Model 3, Model 4, and Model 5 by 4.08%, 9.7%, 21.6%, and 24.73%, respectively. Conversely, for Model 6, Model 7, Model 8, Model 9, and Model 10, the roof displacements are less than Model 1 by 41.84%, 42.57%, 43.48%, 48.2%, and 47.9%, respectively.

In the Y-direction, the maximum roof displacement for Model 1 is surpassed by Model 2, Model 3, Model 4, and Model 5 by 9.5%, 11.72%, 28.2%, and 30.5%, respectively. Conversely, for Model 6, Model 7, Model 8, Model 9, and Model 10, the roof displacements are less than Model 1 by 43.34%, 37.22%, 39.7%, 44%, and 43.6%, respectively. These results suggest that Model 9 and Model 10 perform better in improving the steel building's performance than the other models. Table 8 and Figure 5 show the results of maximum roof displacement.

Table 8. Maximum roof displacement

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Figure 5. Max. roof displacement

3.3.2 Max-inter story drift ratio

The drift ratio is the ratio of the horizontal displacement at vertically aligned points between the top and bottom of a story, divided by the story height [11].

During an earthquake, a base shear force is generated at the base of a building. This force is distributed in the vertical direction at each level, taking into account the weight and height of each story in relation to the other stories. The shear force is then transferred to story shear at each story, which causes displacement in each story. The amount of displacement is dependent on the stiffness of the element designed to withstand seismic forces [11].

According to ASCE 7-16 there is a limit for drift ratio depending on the risk category of the building describe in Table 9.

Table 9. Allowable drift [11]

*h_sx is the story height below level x

For this research, the risk category of the building is assumed to be IV.

In this research, the maximum inter-story drift ratio (max IDR) was determined by calculating the drift ratio of each story every 0.02 seconds during the earthquake duration. The maximum drift ratio was then selected from among the other drift ratios recorded during the entire duration of the earthquake.

The results of the analysis for ten models in two directions are summarized as follows:

In the Y-direction, as described in Figure 6 and Figure 7 maximum inter-story drift ratio increases in Model 2, Model 3, Model 4, and Model 5 concerning Model 1 by 10.2%, 20.47%, 30.77%, and 36.25% respectively, while for Model 6, Model 7, Model 8, Model 9 and Model 10 the maximum inter-story drift decreases by 34%, 35.5%, 34.54%, 41.15%, and 39% respectively.

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Figure 6. Max. drift ratio in Y-direction

In the X-direction, as described in Figure 8 and Figure 9 maximum inter-story drift ratio increased in Model 2, Model 3, Model 4, and Model 5 concerning Model 1 by 6.76%, 15.56%, 24.1%, and 31.2% respectively, while for Model 6, Model 7, Model 8, Model 9 and Model 10 the maximum inter-story drift decreases by 35.07%, 35.21%, 37.25%, 44.01%, and 43.73%, respectively.

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Figure 7. Max. drift ratio in Y-direction

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Figure 8. Max. drift ratio in X-direction

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Figure 9. Max. drift ratio in X-direction

Based on the results, it appears that Model 9 outperforms the other models in terms of improving performance. Specifically, it reduces the maximum inter-story drift by 41.15% for the Y-direction and 44.01% for the X-direction, which is within the code limit as indicated in Table 9.

3.3.3 Maximum base shear and maximum base moments

It is the maximum lateral force that acts at the level at which the horizontal seismic ground motion is considered to be transported to the structure [11].

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Figure 10. Maximum base shear (KN)

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Figure 11. Maximum base moment (KN.m)

The results of the analysis as described in Figure 10 for maximum base shear and Figure 11 for maximum base moments show that Model 9 has the minimum value for max base shear and max base moments in the X-direction and y-direction concerning other models. And the maximum base shear at Model 3 and Model 5 is the worst, so the best model among the nine suggested models is Model 9 because it has the minimum base shear to reduce possible damage to the structure.

During the occurrence of an earthquake, the acceleration of the earthquake is transformed into a shearing force that affects the base of the structure. By using relationships from the Pseudo-acceleration, principle as mentioned below we can conclude some facts from the analysis [14].

$V_{\text {peak }}=\stackrel{\mathrm{A}}{g} * W$             (3)

$\mathrm{A}=\left(\frac{2 \pi}{T_n}\right)^2 * \mathrm{D}$        (4)

$T_n=2 \pi * \sqrt{\frac{m}{k}}$              (5)

By adding bracing to the structure, the natural period of the structure is reduced. This indicates that the structure becomes more rigid, and the stiffness increases as well. According to formula (5), the acceleration at the base will increase when the natural period (T_n) is reduced, as per formula (4). This results in a greater base shear than the case without bracing.