A New Approach to Improving the Seismic Performance of Existing Reinforced Concrete Buildings Using Laminated Timber

Abstract

Following recent earthquakes in Van, Istanbul, Izmir, and Kahramanmaraş, concerns have once again been raised regarding whether existing buildings possess adequate seismic performance and the necessity of strengthening those that do not. A common theme in all related discussions is how to improve the seismic resilience of the existing building stock most efficiently and cost-effectively. In particular, seismic retrofitting efforts should be accelerated for residential buildings in areas where urban transformation has not been feasible due to low added value, as well as for public buildings in smaller settlements and school or dormitory structures in rural towns and villages. In this study, the seismic performance of a reinforced concrete (RC) frame was evaluated using the nonlinear single-mode pushover analysis method in accordance with the Turkish Building Earthquake Code (TBEC). For frames with inadequate performance, a retrofitting method was proposed using glued laminated timber (glulam), a renewable and sustainable material, as diagonal bracing. This intervention aimed to improve the structural performance to an acceptable level specified by the code. The results indicated that glulam braces can effectively enhance the seismic performance of RC buildings and may be considered a viable solution for this purpose.

1. Introduction

In countries with high seismic risks, such as Turkey, a significant portion of the existing building stock consists of RC buildings with weak structural systems that have not received engineering services. Therefore, strengthening solutions are vital to increase the seismic safety of these structures. To date, traditional strengthening techniques, such as reinforced concrete jacketing, steel bracing, and shear wall addition methods, have been widely used.

A fundamental vulnerability of frame systems and one of the primary reasons for building collapse during earthquakes is inter-story drift. In braced frame systems, these inclined elements are subjected to tension and compression, depending on the design and construction details, thereby helping to reduce the relative story drifts [1]. Although braced frame systems generally offer lower strength than shear wall systems, they tend to provide superior ductility [2]. Strengthening RC buildings with bracing elements is a common practice. Since it is subsequently added to an existing structure, the steel bracing method is generally preferred. In some cases, RC buildings are also strengthened using precast RC bracing elements [3,4,5]. Another method, the application of reinforced concrete jacketing to strengthen existing columns, can significantly improve the compressive behavior of these elements [6,7,8,9,10]. However, this method has some disadvantages, such as a significant increase in structural weight and occupied area, and it requires a complex construction process. In situations where the load-bearing capacity of damaged columns must be significantly increased in a short time, traditional strengthening techniques may be insufficient to meet these requirements. Another traditional strengthening method involves the use of RC shear walls, which play a fundamental role in the structural system design of buildings, especially in seismic regions [11,12]. These walls are critically important for resisting horizontal loads and enhancing the structural integrity and safety of buildings during earthquakes [13,14]. Although traditional strengthening methods, such as steel braces, fiber-reinforced polymers, and ultra-high-performance concrete, have been applied to improve the seismic performance of these structures, these techniques have limitations, such as durability, application difficulties, and cost [15,16,17,18,19,20].

Traditional strengthening methods often involve long application times, add extra weight to the structure, and are costly and labor-intensive. Due to these limitations, modern strengthening techniques have been developed. Energy dissipators (liquid viscous dampers), buckling-restrained braces (BRBs), and fiber-reinforced polymer (FRP) composites are notable examples in this regard. With advances in research on controlling seismic vibrations, the addition of external control systems has emerged as a prominent solution for reducing the impact of earthquake vibrations on structures [21,22,23]. Passive energy dissipation devices are an effective solution that provides additional damping to structures without the need for an external energy source. The addition of passive energy dissipation devices reduces damage to the main structural system by decreasing the need for inelastic energy dissipation, rather than increasing the strength of the structure [24,25,26,27]. Significant developments, including viscoelastic, liquid viscous, frictional, and metallic dampers, have occurred in the application of passive devices to mitigate severe earthquake and wind effects [28]. In addition to passive damping systems, alternative strengthening methods that act as part of the structural system also exist. One such method, BRBs, not only increases the energy dissipation capacity of the structural system but also offers ductile behavior by eliminating the risk of buckling. Frame systems strengthened with BRBs can significantly reduce seismic structural demands and residual displacements compared with conventional moment frames [29,30,31,32,33,34,35]. Furthermore, many studies have shown that the residual displacements occurring in BRB-strengthened frames are well below the limit values that would allow the repair of the structure [36,37,38,39,40]. In essence, the collapse resistance capacity and seismic reliability of traditional moment frame systems can be significantly enhanced using BRBs.

However, increasing sustainability goals have encouraged a shift towards environmentally friendly materials in the construction sector. In this context, engineered wood, such as glued laminated timber, stands out due to its environmental and structural advantages. The prominent characteristics of wood are its renewability, low carbon footprint, lightness, and workability. Wood has a lower embodied impact than concrete during production and construction processes. Replacing concrete with wood can reduce a building’s carbon footprint by 25–75% [41,42]. Shin B. and Kim S. stated that wood is more advantageous than concrete structures in reducing environmental impacts and suitability for building reuse, utilizing the building circularity method (BCI) [43]. Existing research has highlighted the sustainability of using wood. It has been determined that converting the original structural system to a cross-laminated timber (CLT) structural system can reduce lifecycle sustainability impacts by over 51% [42]. In addition to these benefits, wood can be sourced sustainably from nature and is easier to process than other materials, making it an inherently sustainable construction material. Structurally, wood possesses a higher strength-to-weight ratio than concrete and has a density that is about one-fifth that of concrete [44]. In recent years, the development of engineered wood (EW), also known as mass timber, such as glulam or CLT, with high structural rigidity, has enabled its diverse use in mid- and high-rise buildings [44,45]. Jayalath et al. [46] demonstrated that CLT mid-rise residential buildings in Australia could reduce life cycle greenhouse gas emissions by 30% compared to RC structures. Pierobon et al. [41] reported that in commercial buildings, a CLT hybrid building reduced the Global Warming Potential (GWP) by an average of 26.5% when compared to RC structures.

Various experimental and numerical studies have been conducted on timber elements and timber connections. Chen et al. [47] presented a novel approach for using laminated wood as a filler material within the square steel tube of the core of BRBs, replacing mortar or concrete. Their study shaped this new BRB design based on various parameters and evaluated its cyclic behavior (mechanical properties, fatigue performance, and energy dissipation capacity) through experimental tests. They suggested that while glulam may not have the same high strength as concrete, it could offer a suitable, economical, and sustainable alternative, especially for laminated timber frame structures or low-rise, earthquake-resistant structures subjected to vertical loads. Dorn et al. [48] conducted experiments on 64 steel-wood single-dowel connections. Connections using high-density wood showed a higher load-bearing capacity but also exhibited more brittle behavior. Meng et al. [49] revealed the significant role of gravitational potential energy in the seismic performance of traditional timber structures, stating that this energy conversion mechanism enables traditional timber structures to resist large earthquakes. Chen and Popovski [50] mathematically demonstrated the effect of connection properties on the system performance in braced timber frames, highlighting that factors such as connection design and column stiffness play a crucial role in system ductility. In a study by Sustersic and Dujic, the seismic performance of a previously full-scale modeled and dynamically analyzed RC structure was improved by applying CLT panels to its exterior walls. The study revealed that these panels significantly increased the structural rigidity and strength of the building [51]. An experimental study by Juhász et al. on the damage behavior of laminated timber-concrete composite beams showed that such composite systems allow for spanning long spans while maintaining sustainability and improving structural efficiency [52]. Selçukoglu and Zwicky emphasized that composite slabs with a concrete top layer and laminated timber bottom layer exhibit better structural performance and vibration behavior than traditional timber slabs, specifically highlighting the significant ductility of laminated timber under compression [53]. A study published by Öztürk et al. stated that structural system elements produced with laminated timber technology are components of a modern and advanced building system, further emphasizing that these elements can be produced in Turkey using local timber and adhesives [54]. Similarly, Sandoli et al.’s work stated that CLT structures offer a strong alternative to heavier structural systems in terms of seismic resistance and environmental sustainability [55]. Furthermore, Furukawa and his team evaluated whether the flexural stiffness and load-bearing capacity of composite beams formed from H-section steel beams, using CLT floor panels with high-strength friction-type bolted connections, could be simply predicted from a design perspective based on the properties of individual components and connection details [56].

In recent years, various studies have explored the use of glued laminated timber elements to strengthen existing RC buildings. However, the literature in this field is still limited, and there is a shortage of practical application examples. This study aims to develop an alternative strengthening method to improve the seismic performance of existing RC buildings with inadequate earthquake resistance. Additionally, it seeks to present a sample approach that may pave the way for future research exploring the use of timber elements in this field, offering both aesthetic value and ease of application. Within this scope, the seismic performance level of a two-dimensional RC frame without shear walls was first assessed using a nonlinear pushover analysis method. Subsequently, the system was retrofitted with pinned glued-laminated timber braces in various configurations. The seismic performance of the strengthened system was re-evaluated, and the contribution of the glulam braces to overall structural performance was examined. Although numerous studies in the literature focus on the comparative performance analyses of RC structures and the use of materials such as fiber-reinforced polymers or steel braces for seismic strengthening, research addressing the use of laminated timber elements to enhance the seismic performance of RC buildings remains limited.

2. Materials

2.1. Timber

Timber primarily consists of cellulose (≈60%), lignin (≈30%), and other sugar-based compounds. Its load-bearing capacity stems from longitudinally aligned cellulose fibers bonded by lignin [57]. Glued laminated timber, one of the earliest engineered wood products, is produced by gluing timber laminations in the same direction. Glulam can be classified as homogeneous (“h”) if all laminations have similar strength, or combined (“c”) if laminations of different strength classes are used.

2.1.1. Strength and Stiffness of Timber

Timber is an orthotropic material with distinct mechanical properties in three principal directions: longitudinal (L), radial (R), and tangential (T) directions. Its compressive strength is significantly higher parallel to the grain (L) than perpendicular to it, making loading direction a critical factor in design. While radial and tangential differences are often negligible in structural applications, accurate modeling requires the elastic moduli (E_L, E_R, E_T), shear moduli (G_LR, G_LT, G_RT), and Poisson’s ratios (ν_LR, ν_RL, etc.) for these directions [58].

Considering the similarity between radial and tangential directions and assuming equal Poisson’s ratios, the 12 orthotropic parameters can be reduced to six: $E_{//},E_{\perp },G_{//},G_{\perp },{\upsilon }_{//},{\upsilon }_{\perp }$. In this study, the full orthotropic properties of glulam were defined for completeness; however, since the braces were modeled as axial link elements, only the axial behavior governed by the fiber direction properties was relevant. Orthotropic parameters were used solely for capacity checks under axial loading.

2.1.2. Timber Material Model

Since timber is an anisotropic material, it is challenging to accurately model its mechanical behavior. In this study, the glulam braces to be used will be modeled to carry only axial forces. Therefore, the material model shown in Figure 1 (Elastic Perfectly Plastic) will be used, with the mechanical properties of timber in the direction parallel to the fibers, specifically the modulus of elasticity and characteristic strengths.

2.2. Concrete and Reinforcement Steel

For the material models of concrete and reinforcing steel, the material models provided in Appendix 5A of the “Principles for the Design of Buildings Under Earthquake Effects” annexed to the Turkish Building Earthquake Code (TBEC 2018) are used [59].

2.2.1. Confined and Unconfined Concrete Material Models

The Poisson’s ratio for concrete, υ_c, is assumed to be 0.2. The uniaxial compressive strength of unconfined concrete and its corresponding strain are denoted as f_c and ε_c, respectively. The value of ${\mathsf{\epsilon }}_{\mathrm{c}}$ typically, it ranges from 0.002 to 0.003 [60]. When concrete is subjected to lateral confining pressure, its uniaxial compressive strength, f_cc, and the corresponding strain, ${\mathsf{\epsilon }}_{\mathrm{c}\mathrm{c}}$, become significantly higher compared to unconfined concrete. The compressive strengths of confined and unconfined concrete, f_c and f_cc, can be calculated using the formulas provided in Equation (5)A-1 and Equation (5)A-2 of TBEC-2018 [59].

2.2.2. Reinforcement Steel Material Model

The stress-strain curve of reinforcing steel has been assumed to be elastic-perfectly plastic. The elastic modulus of reinforcing steel, E_S, is taken as 200 GPa. To be used in performance assessment under nonlinear analysis based on displacement demands, the stress–strain relationships for reinforcing steel are defined according to Equation (1) [59].

$$f_s=E_s.{\epsilon }_s\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}({\epsilon }_s\le {\epsilon }_{sy})$$

$$f_s=f_{sy}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}({\epsilon }_s<{\epsilon }_{sy}\le {\epsilon }_{sh})$$

(1)

$$f_s=f_{su}-\left(f_{su}-f_{sy}\right){\displaystyle \frac{{({\epsilon }_{su}-{\epsilon }_s)}^2}{{({\epsilon }_{su}-{\epsilon }_{sh})}^2}} \hspace{1em}\hspace{1em}\hspace{1em} ({\epsilon }_{sh}<{\epsilon }_s\le {\epsilon }_{su})$$

3. Methods

3.1. Determination of Analysis Models

In the analyses, a 2D existing RC frame consisting of a ground floor + 4 normal floors with a 3 m story height and a 5 m beam span, and reinforced models created by adding glulam braces with a central diagonal and inverted V arrangement to the edge spans of the RC frame (without earthquake shear walls) were used.

In the reinforced models, the effect of using diagonally placed braces and braces with an inverted V arrangement on the increase in rigidity and the resulting changes in the system was investigated. An example of an inverted V-glulam brace arrangement is shown in Figure 2.

3.2. Determination of Earthquake Performance by Nonlinear Analysis

Using the nonlinear analysis method, specifically single-mode pushover analysis, the 2D existing frame was analyzed to determine the damage zones, earthquake performance demand, and earthquake performance level based on this demand.

Subsequently, glulam braces were added to the edge spans of the frame system, which were subjected only to axial loads, and the nonlinear single-mode pushover analysis was repeated. As a result, the damage zones, earthquake performance demands, and the earthquake performance level based on this demand were determined for the reinforced frame.

For the performance analysis, a plastic hinge model based on accumulated plastic behavior was used for the RC frame elements, while for the glulam braces, brittle (force-based) hinges were defined to check the axial compression/tension capacity.

3.3. Evaluation of System Performance

The calculation principles to be applied in the evaluation of the performance of existing buildings and building-type structures under earthquake effects are defined in Chapter 15 of TBEC-2018. Within the scope of this study, the principles in this chapter were used for the frame models, whose performance under earthquake effects was evaluated. In cases where no specific information was available, the closest applicable conditions were approximated using generally accepted approaches or methods, in accordance with the principles of this chapter.

3.3.1. Knowledge Level

Depending on the scope of information obtained from the assessment of the existing condition of buildings, knowledge level coefficients defined in Section 15.2.12 of TBEC-2018 are used [59].

Within the scope of this study, considering disadvantaged structures such as residential buildings in regions where urban transformation projects cannot be implemented due to low added value, public buildings in small settlements, and schools and dormitories in rural or town areas, the limited knowledge level coefficient (0.75) was used. This coefficient was applied to the material strengths and incorporated into the capacity calculations of the structural-system elements.

3.3.2. Damage Boundaries and Damage Zones

For ductile elements, the section damage state and damage limits are defined as Limited Damage (LD), Controlled Damage (CD), and Pre-Collapse Damage (PCD), along with their corresponding threshold values. However, these classification states and limit values are not applicable to elements that fail in a brittle manner. The damage limits and damage zones are illustrated in Figure 3.

3.3.3. General Principles and Rules Regarding Earthquake Calculations

In TBEC-2018, both linear and nonlinear analysis methods can be used to evaluate the seismic performance of existing structures. Although it is stated that both analysis methods are applicable, it should not be expected that these fundamentally different approaches will yield similar results.

The principles and rules to be applied for both linear and nonlinear methods are outlined in Section 15.4 of TBEC-2018 [59]. In this study, the Nonlinear Static Single-Mode Pushover Method was used.

3.4. Design of Structural Timber Elements

As only glulam braces subjected solely to axial tension or compression loads are used in this study, only the effects of axial loads are addressed in this section. Calculations will be carried out in accordance with Eurocode 5: Design of Timber Structures [61].

3.4.1. Force Limits for Laminated Timber Braces

For the glulam braces under axial loading, force-controlled brittle hinges will be defined. These hinges will be used to control both the axial tension and axial compression capacities under seismic effects by setting force control limits at 50%, 75%, and 100% of their capacities.

These defined force limits allow the capacity states of the glulam braces to be checked at the performance point of the system.

3.4.2. Ultimate Modulus of Elasticity

In structural analysis, when stiffness plays a critical role, the influence of load duration and moisture content on deformations must be considered. To account for these effects, the final (adjusted) modulus of elasticity is used in both the serviceability and ultimate limit states [61].

In this study, a reduction factor was applied to the moment of inertia instead of directly modifying the modulus of elasticity (E). This approach preserves the inherent properties of the material while realistically reducing the section stiffness for an accurate analysis.

$$E_{mean,fin}= {\displaystyle \frac{E_{mean}}{{1+{\Psi }_2 . k}_{def}}}$$

(2)

Here;

$E_{mean,fin}$: Ultimate modulus of elasticity,

$E_{mean}$: Average modulus of elasticity,

${\Psi }_2$: Semi-permanent load combination factor,

$k_{def}$: It is the adjustment factor to take into account the effect of humidity on deformation.

4. Analysis

Within the scope of this study, SAP2000 V.23, a widely used finite element-based analysis and design program in structural engineering, was utilized. It allows the modeling of RC, steel, and composite systems, as well as the performance of linear/nonlinear and static/dynamic analyses. The structural behavior under loads, such as earthquakes, wind, and temperature, can be examined in detail [62].

Analyses were conducted on a 2D RC frame with a floor height of 3 m and a beam span of 5 m, consisting of a ground floor plus 4 normal floors without seismic shear walls. To enhance the system, glulam braces with a central diagonal and reverse V arrangement were added to the edge spans of the frame. Glulam of GL24H strength class with dimensions of 20 × 20 cm was used for the braces.

As a result of all the analyses, the changes induced by the glulam braces and the different bracing configurations were examined and reported.

4.1. Analysis Models

The names of the analysis models are listed in

Table 1. Naming of analysis models.

Number of Floors	Unbraced Frame Model	Diagonal Braced Frame Model	Inverted V Braced Frame Model
Ground + 4 Normal Floors	Model 01	Model 01D	Model 01V

. The framework models are shown in Figure 4, Figure 5 and Figure 6.

4.2. Material Properties

The material properties of the concrete (C16/20) and reinforcement steel (S420) used in the frames are shown in

Table 2. Material properties of concrete.

Property	Value
$\mathrm{E}(\mathrm{k}\mathrm{N}/{\mathrm{m}}^2)$	$27\times {10}^6$
$\mathsf{\upsilon }$	$0.2$
${\mathrm{f}}_{\mathrm{c}}(\mathrm{k}\mathrm{N}/{\mathrm{m}}^2)$	$16\times {10}^3$
${\mathsf{\epsilon }}_{\mathrm{c}\mathrm{o}}$	$2\times {10}^{-3}$
${\mathsf{\epsilon }}_{\mathrm{c}\mathrm{u}}$	$5\times {10}^{-3}$

and

Table 3. Material properties of the reinforced steel.

Property	Value
$\mathrm{E}(\mathrm{k}\mathrm{N}/{\mathrm{m}}^2)$	$2\times {10}^8$
${\mathrm{f}}_{\mathrm{y}}(\mathrm{k}\mathrm{N}/{\mathrm{m}}^2)$	$420\times {10}^3$
${\mathrm{f}}_{\mathrm{u}}(\mathrm{k}\mathrm{N}/{\mathrm{m}}^2)$	$550\times {10}^3$
${\mathsf{\epsilon }}_{\mathrm{s}\mathrm{h}}$	$8\times {10}^{-3}$
${\mathsf{\epsilon }}_{\mathrm{s}\mathrm{u}}$	$0.08$

. The strength values and properties of the existing concrete and reinforcement steel have been reduced by considering the information level factor (0.75). This ensures that the capacities of the elements are determined according to the information level.

The unit deformations for compression and tension capacities of GL24H have been calculated according to the material model in Section 2.1.2, and the properties of GL24H are shown in

Table 4. Material properties of GL24H laminated timber.

Property	Value
${\mathrm{f}}_{\mathrm{t},0,\mathrm{k}}(\mathrm{N}/{\mathrm{m}\mathrm{m}}^2)$	$19.20$
${\mathrm{f}}_{\mathrm{c},0,\mathrm{k}}(\mathrm{N}/{\mathrm{m}\mathrm{m}}^2)$	$24.00$
${\mathrm{E}}_{0.05}(\mathrm{N}/{\mathrm{m}\mathrm{m}}^2)$	$9600.00$
${\mathrm{G}}_{0.05}(\mathrm{N}/{\mathrm{m}\mathrm{m}}^2)$	$540.00$
${\mathrm{E}}_{0,\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}(\mathrm{N}/{\mathrm{m}\mathrm{m}}^2)$	$\mathrm{11,500}.00$
${\mathrm{E}}_{90,\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}(\mathrm{N}/{\mathrm{m}\mathrm{m}}^2)$	$300.00$
${\mathrm{G}}_{0,\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}(\mathrm{N}/{\mathrm{m}\mathrm{m}}^2)$	$650.00$
${\mathrm{G}}_{90,\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}(\mathrm{N}/{\mathrm{m}\mathrm{m}}^2)$	$65.00$
${\mathsf{\rho }}_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}(\mathrm{k}\mathrm{g}/{\mathrm{m}}^3)$	$420.00$
${\mathsf{\epsilon }}_{\mathrm{t},0}$	$1.7\times {10}^{-3}$
${\mathsf{\epsilon }}_{\mathrm{c},0}$	$2.1\times {10}^{-3}$

.

4.3. Section Properties

The section definitions for the concrete and reinforcement steel have been created using the Section Designer tool in SAP2000 V.23. Thus, all stress-strain relationships, moments, curvatures, and rotation values for the relevant materials have been obtained using the program.

4.3.1. Reinforced Concrete Column and Beam Sections

All frame columns have the same reinforcement arrangement and dimensions (40 × 40 cm). The column section is modeled with a 2.5 cm unwrapped shell concrete outside and a 35 × 35 cm confined core concrete inside, with 12Φ14 reinforcement. The column confinement reinforcement has a diameter of Φ8, and the spacing between the confinement reinforcement is 20 cm.

All frame beams also have the same reinforcement arrangement and dimensions (25 × 50 cm). The beam section is modeled with a 2.5 cm unwrapped shell concrete outside and a 20 × 45 cm confined core concrete inside, with 6Φ12 reinforcement. The beam confinement reinforcement has a diameter of Φ8, and the spacing between the confinement reinforcement is 20 cm. The cross sections of the columns and beams are shown in Figure 7.

4.3.2. Glulam Cross Sections

Timber cross sections are defined as 20 × 20 cm in size according to the properties of laminated timber of GL24H strength class. The effective cross-sectional area value multiplier mentioned in Section 3.4.2 is calculated as follows:

$$E_{mean,fin}={\displaystyle \frac{E_{mean}}{{1+{\Psi }_2.k}_{def}}}={\displaystyle \frac{\mathrm{11,500.00}}{1+0.3\times 0.8}}=9274.19\mathrm{N}/{\mathrm{m}\mathrm{m}}^2$$

$$Effective section area multiplier={\displaystyle \frac{E_{mean,fin}}{E_{mean}}}={\displaystyle \frac{9274.19}{\mathrm{11,500.00}}}\cong 0.81$$

4.4. Load and Mass Source

The fixed and live distributed loads from the floors and walls applied to the frame beams are shown in

Table 5. Dead and live loads act on the beams.

Type of Load	Value
$\mathrm{G}(\mathrm{k}\mathrm{N}/\mathrm{m})$	$25.00$
$\mathrm{Q}(\mathrm{k}\mathrm{N}/\mathrm{m})$	$5.00$

. The material unit weights were included in the calculations with a unit weight multiplier of 1.0 when defining fixed loads in SAP2000 V.23.

The mass source is defined with the G + 0.3Q combination, where the dynamic load mass participation factor is taken as 0.3.

4.5. Earthquake Load Parameters

The earthquake load parameters used in the analyses are shown in

Table 6. Earthquake load parameters.

Soil Class	${\mathbf{S}}_{\mathbf{S}}$	${\mathbf{S}}_1$	${\mathbf{S}}_{\mathbf{D}\mathbf{S}}$	${\mathbf{S}}_{\mathbf{D}1}$	$\mathbf{P}\mathbf{G}\mathbf{A}$	$\mathbf{P}\mathbf{G}\mathbf{V}$	${\mathbf{T}}_{\mathbf{L}}$
ZC	1.957	0.517	2.348	0.767	0.065	0.327	6.00

.

4.6. Definition of Force Limits for Glulam Cross-Braces

The calculated axial tension and compression capacity values for the 20 × 20 cm glulam cross-braces under axial load are shown in

Table 7. Axial tension and compression capacities of glulam cross-braces.

Values	Diagonal Brace (GL24H)	Inverted V Brace (GL24H)
${\mathrm{f}}_{\mathrm{t},0,\mathrm{d}}(\mathrm{N}/{\mathrm{m}\mathrm{m}}^2)$	16.90
${\mathrm{f}}_{\mathrm{c},0,\mathrm{d}}(\mathrm{N}/{\mathrm{m}\mathrm{m}}^2)$	21.12
${\mathsf{\epsilon }}_{\mathrm{t}}$	0.0017
${\mathsf{\epsilon }}_{\mathrm{c}}$	0.0021
${\mathrm{N}}_{\mathrm{t},0,\mathrm{R}\mathrm{d}}(\mathrm{N}/{\mathrm{m}\mathrm{m}}^2)$	675.84	675.84
${\mathrm{N}}_{\mathrm{c},0,\mathrm{R}\mathrm{d}}(\mathrm{N}/{\mathrm{m}\mathrm{m}}^2)$	305.84	595.22

. To verify the calculated axial tension and compression capacities, the acceptance criteria were defined at 50%, 75%, and 100% of their capacities, and force-controlled (force-controlled) hinges were defined for the glulam cross-braces in SAP2000 V.23.

4.7. Analysis with Constant Single Mode Pushover Method

According to TBEC-2018, Section 15, the application principles for Nonlinear Analysis Methods, specifically the Single Mode Pushover Method, used in the evaluation of existing buildings, are defined in Section 5.6. Analyses were conducted following these principles.

The displacements and internal force demands obtained from the analyses were compared with the displacement and internal force capacities to perform a structural performance assessment at the section and frame levels. Based on this, the performance level was determined.

4.8. Validation

Obtaining the Performance Point and Capacity Curve of the System

Using the methods defined in Annex 5B of the TBEC 2018 for the fixed single-mode pushover analysis, the performance point and capacity curve of Model 01 were calculated, and the results are presented below. The linear earthquake spectrum for the system was obtained based on the spectral values provided in Table 6. According to the modal analysis performed in SAP2000 V.23, the period of the first mode of vibration is 1.168 s.

The maximum displacement of the modal single-degree-of-freedom system (nonlinear spectral displacement) was obtained by superimposing the modal capacity curve and the linear earthquake spectrum, as shown in Figure 8.

Using the maximum displacement, the system’s peak displacement (the peak displacement demanded by the earthquake) was determined to be 0.278 m.

$$u_{Nx1}^{\left(p\right)}={\varphi }_{Nx1}^{\left(1\right)} . d_{1,max}^{\left(X\right)}. {\Gamma }_1^{(X,1)}=0.278 \mathrm{m}$$

The peak displacement of the system can be obtained by plotting the linear earthquake spectrum and modal capacity diagram together, or it can be directly calculated using the following equations:

$$d_{1, max}^{\left(X\right)}=S_{di}\left(T_1\right)=C_R. S_{de}\left(T_1\right)$$

$$T_1>T_B \text{since} \mathrm{it} \mathrm{is} C_R=1$$

In this case, the maximum displacement is equal to the elastic design spectral displacement.

$$d_{1, max}^{\left(X\right)}=S_{di}\left(T_1\right)=1\times S_{de}\left(T_1\right)={\displaystyle \frac{T^2}{4{\pi }^2}}.g.S_{ae}\left(T\right)$$

Horizontal elastic design spectral acceleration,

$$T_B\le T\le T_L \text{since} \mathrm{it} \mathrm{is} S_{ae}\left(T\right)={\displaystyle \raisebox{1ex}{$S_{D1}$}\!\left/ \!\raisebox{-1ex}{$T_1$}\right.}$$

is calculated as.

$$d_{1, max}^{\left(X\right)}={\displaystyle \frac{T^2}{4{\pi }^2}}.g.S_{ae}\left(T\right)={\displaystyle \frac{{1.142}^2}{4{\pi }^2}}\times 9.80665\times {\displaystyle \frac{0.767}{1.142}}\cong 0.218 m$$

And as a result, the top displacement of the system is,

$$u_{Nx1}^{\left(p\right)}={\varphi }_{Nx1}^{\left(1\right)} . d_{1,max}^{\left(X\right)}. {\Gamma }_1^{(X,1)}=0.0772\times 0.218\times 16.51=0.278 m$$

is found as.

The system was pushed again to the obtained peak displacement value, and a capacity curve consisting of displacement–base shear force coordinates was obtained. The performance point of the system was determined as the intersection point of the peak displacement and base shear force.

According to the “ATC-40: Seismic Evaluation and Retrofit of Concrete Buildings” guideline [63] available in SAP2000 V.23, it is possible to obtain performance point and capacity curve values close to those of TBEC-2018 using the capacity spectrum method.

For a peak displacement of 0.278 m, the base shear force obtained using TBEC-2018 is 272.29 kN. According to the adapted ATC-40 guideline, the base shear force corresponding to a peak displacement of 0.289 m is calculated by the program as 271.60 kN. The base shear forces are 99.75% close to each other. In the performance comparisons of the models, a high correlation was observed between the performance points and capacity curve values obtained from SAP2000 V.23 and those calculated using the TBEC-2018 design principles.

5. Findings

As a result of the analyses and calculations, the peak displacement and base shear force values at the performance point for Models 01, 01D, and 01V are provided in

Table 8. Peak displacement—base shear force values at the performance point.

Model Nu.	Peak Displacement (m)	Base Shear Force (kN)
Model 01	0.289	272.37
Model 01D	0.106	1017.98
Model 01V	0.087	913.76

.

The damage zones at the performance point are shown in Figure 9, Figure 10 and Figure 11.

The numerical distributions of the column and beam damage regions are presented in

Table 9. Numerical distribution of column-damage regions at the performance point.

Model Nu.	The Number of Columns in the Damage Regions (Number)
	LDZ (Gray)	SDZ (Green)	ADZ (Blue)	CDZ (Red)
Model 01	20	5	0	0
Model 01D	20	5	0	0
Model 01V	18	4	3	0

and

Table 10. Numerical distribution of beam-damage regions at the performance point.

Model Nu.	The Number of Beams in the Damage Regions (Number)
	LDZ (Gray)	SDZ (Green)	ADZ (Blue)	CDZ (Red)
Model 01	0	8	12	0
Model 01D	0	20	0	0
Model 01V	4	14	2	0

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In the Figure 9, the tilting and displacement of the structure towards the upper floors demonstrate the effect of lateral displacement. Looking at the color distribution, the vast majority of the system remains within the IO (Immediate Occupancy) and LS (Life Safety) performance levels. This indicates that the structure behaves safely under the influence of an earthquake and does not carry a serious risk of collapse. None of the laminated timber braces, as shown in Figure 10 and Figure 11, reached their full capacity at the performance point. Therefore, the strengths and dimensions of the selected laminated braces were sufficient. The numerical distribution of the laminated timber braces according to their capacity regions is shown in

Table 11. Numerical distribution of laminated timber braces according to axial load capacity ratios.

Model Nu.	Number of Braces According to Capacity Regions
	Number of Braces	%0–50	%50–75	<%100
Model 01D	10	2	0	8
Model 01V	20	6	6	8

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According to the principles specified in Section 15.8 of TBEC-2018, performance level checks were carried out by progressing from the cross-section to the structural elements, and from the structural elements to the entire structural system. The performance levels of the systems are presented in

Table 12. Performance levels of frame models.

Model Nu.	Performance Level
Model 01	Collapse Prevention
Model 01D	Controlled Damage
Model 01V	Collapse Prevention

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The performance level of the existing structural system (Model 01) is Collapse Prevention. According to TBEC–2018, at this performance level, the current condition and use of a building pose safety concerns for life and property.

As specified in TBEC–2018 Section 15.8.1, under the DD-2 earthquake ground motion level, the Building Performance Target for the existing structural system is the Controlled Damage performance level, as shown in

Table 13. Performance targets for the existing structural system (Model 01).

Building Use Category (TBEC-2018 Table 3.1)	Earthquake Design Class (TBEC-2018 Table 3.2)	Building Height Class (TBEC-2018 Table 3.3)	Normal Performance Target (TBEC-2018 Table 3.4.c)	Evaluation Approach
BUC = 3	EDC = 1	BHC = 6	LD	DDM (Deformation Design Method)

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The strengthening approach using laminated timber cross braces in Model 01D successfully raised the system performance level to the controlled damage performance level.

However, in Model 01V, the use of reverse V braces, which are both more numerous and have a higher axial compression capacity, made the structure more rigid. As a result, during the push to the peak displacement, the base shear force reached 1592.88 kN by the 6th step, and due to the high plastic rotations in the ground floor columns, the load-carrying capacities of the columns significantly decreased. Along with these sudden capacity losses, by the 11th step of the push, the base shear force dropped to 913.76 kN at the peak displacement value.

This situation is illustrated by the system capacity curve in Figure 12. In such a case, if the push steps were continued, the system capacity would rapidly deplete, and after reaching the maximum peak displacement, collapse would occur. The system then collapses entirely while still carrying a small amount of load through forces.

The capacity curves of Models 01, 01D, and 01V are shown together in Figure 13. While the frame is quite ductile in its initial state, adding laminated timber cross-braces results in a significant reduction in ductility, accompanied by a considerable increase in the base shear force. In Model 01D with diagonal cross-braces, which successfully achieves the targeted performance level, the optimal performance point is reached under the current conditions with minimal section damage.

The story displacements of the frames are shown in Figure 14. Without laminated timber braces (Model 01), the peak displacement of the system is approximately 2% of the total height. Models 01D and 01V exhibit similar displacements, with the peak displacements for the two models being approximately 0.7% and 0.6% of the total height, respectively.

6. Conclusions and Recommendations

In this study, a 2D frame with a height of 3 m per story and a 5 m beam span, lacking earthquake shear walls, with insufficient seismic performance, consisting of a Ground + 4 Normal Floors, was analyzed. To improve the seismic performance, diagonal and reverse V-arrangement laminated glued-timber braces were added at the edge openings. The performance of the created models was examined according to TBEC-2018, and the controlled damage performance level requested by the regulation for the existing load-bearing system at the DD-2 earthquake ground motion level was achieved using Model 01D.

As a result of the analyses, the following observations were made:

a.

To improve the seismic performance of structures in disadvantaged areas, laminated glued timber braces can be used due to their speed and ease of application.

b.

Glued laminated timber has a high potential to restrict the displacements and increase the strength of reinforced concrete systems.

c.

For buildings with inadequate seismic performance, the rigidity of the glued-laminated timber braces used in strengthening works should be compatible with the system rigidity. Therefore, repeated analyses may be required.

d.

If glued laminated timber braces or a brace arrangement with higher rigidity than the existing system’s rigidity is applied, the base shear force is resisted through the columns, which could lead to the system reaching a collapse mechanism, particularly in the ground floor columns, after a sudden loss of strength, without achieving the desired performance target. Therefore, in addition to adding laminated braces to the system, column strengthening may also be necessary.

e.

In the future, further integration of glulam systems with performance criteria such as energy efficiency, thermal comfort, and structural strength holds great potential for sustainable architectural and engineering practices.

f.

Glued laminated timber is a significant structural material in sustainable building design due to its high load-bearing capacity, low density, and suitability for prefabrication. Compared to concrete and steel, glulam has a significantly lower embodied energy, which substantially reduces its carbon footprint.

Furthermore, its environmental impact is minimized because its production process consumes less energy and is derived from renewable resources. Glulam’s ability to enhance the energy efficiency of buildings throughout their lifecycle makes it an advantageous choice, especially for projects developed with low-carbon targets in mind. Considering all these aspects, glulam offers a strong and viable alternative for designing sustainable structural systems and excels in both environmental and structural performance.

Additionally, studies on the connections of glued laminated timber braces with reinforced concrete frames would be beneficial for the development of this type of strengthening approach.