1.Introduction

The concentrically braced frames (CBFs) have accepted system with high lateral strength and stiffness but suffered from low ductility. To address these shortcomings, researchers have explored various strategies, with passive energy dissipation devices, specifically metallic dampers, emerging as an effective solution to enhance CBF performance. Researchers have discovered various approaches to overcome these shortcomings, with metallic dampers, emerging as an effective solution to enhance CBF performance.

Various dampers have been presented to enhance the CBF’s behavior. The diagonal components of CBFs tend to buckle under compressive forces, which dwindled their ability to dissipate energy. This buckling issue is a significant limitation regarding the CBFs performance. Utilizing shear damper proposed by Ghamari et al. [1], this problem was solved. Their design featured a shear plate enclosed within a cylindrical casing, offering improved ductility and energy dissipation. The shear damper was more economical and easier to produce in comparing with other famuse damper such as ADAS [2], TADAS [3], shear panels [4], slit dampers [5], and buckling-restrained braces (BRBs) [6]. Expanding on this concept, Jeong, Ghamari et al. [7, 8] suggested an octagonal cover instead of the cylindrical one, which showed effective performance under shear, flexural, and combined shear-flexural conditions. However, the octagonal configuration increased the damper’s weight, making manufacturing and installation more challenging. Drawing inspiration from the effective shear link behavior in eccentrically braced frames (EBFs) [9–19], researchers proposed integrating an I-shaped shear element directly into CBFs. Experimental studies [20–31] confirmed that I-shaped dampers enhance CBF performance by improving ductility, preventing brace buckling, and simplifying fabrication and installation compared to other dampers. These studies showed that I-shaped dampers increase overstrength and ductility but often reduce the system’s overall stiffness and strength. The influence of the I-shaped damper’s flange on system behavior was also evaluated.

Despite their benefits, I-shaped dampers, like other directly attached CBF dampers, tend to compromise the system’s ultimate strength and stiffness. Two common approaches to address this issue include: a) using an I-shaped section with a thicker web or b) increasing the number of dampers and braces. However, thickening the damper web has a limited impact on stiffness and can elevate stresses in surrounding brace elements, potentially leading to buckling. In such cases, the damper may fail to perform effectively, resulting in reduced strength, stiffness, and brittle behavior. Similarly, adding more dampers to restore stiffness introduces higher construction costs and architectural constraints.

A promising alternative is the incorporation of stiffeners into the I-shaped damper design. Stiffeners require minimal material and are straightforward to implement, as illustrated in Fig. 1. This idea successfully compensates for lacks in stiffness and ultimate strength, offering a practical solution to enhance the seismic behavior of CBFs.

Figure 1. Strengthening of I-shaped damper with stiffeners.

2.Methods and Materials

To ensure that the damper yields prior to other structural components, the elements outside the damper must be designed to withstand forces exceeding the damper’s capacity. This force denoted as  which is calculated using the following expression:

                                              (1)

where  is the ratio of ultimate stress of the materials to the yielding stress. Also,  represents the overstrength factor, a critical parameter explored in this study, and  denotes the nominal strength of the damper. The overstrength factor,  is determined by evaluating the ratio of the nominal strength  to the strength, at which the first plastic hinge forms,  as expressed in:

                                                                              (2)

According to the AISC 341-16 [32] standard for shear links with I-shaped cross-sections, the shear strength  is calculated as:

                                                                    (3)

where  is the yield stress of the web plate, and  and  represent the width and thickness of the web plate, respectively. The standard specifies that a shear-dominated mechanism governs when the ratio  defined as:

                                                                         (4)

where  is less than 1.6. For dampers equipped with X-shaped stiffeners, the nominal strength  is computed as:

                                                              (5)

where  is the number of web plates,  is the shear strength contributed by the X-shaped stiffeners, and  is the shear strength of the flange plates. The flange plate’s contribution to shear strength  is derived from the formation of flexural hinges at both ends of the flange plates. Using plastic theory, the maximum strength of the flange plate is achieved when the plastic moment  is reached, and  is calculated as:

                                                                       (6)

where  is the effective height of the damper, and the plastic moment  is determined using plate-shell theory as:

                                                                   (7)

Here,  and  represent the width, thickness, and yield stress of the flange plate, respectively.

At the onset of hinge formation, the strength  accounts for contributions from the web plate, flange plate, and stiffeners, and is expressed as:

                                                                (8)

where  is web plate stiffness that calculated as  Accordingly,  is the plastic deformation, and  and  are the stiffness contributions of the flange plates and stiffeners, respectively. This formulation ensures a comprehensive assessment of the damper’s behavior under seismic loading, enabling robust and resilient structural performance.

3.Results and Discussion

Numerical Models

In this study, a numerical analysis is conducted to evaluate the performance of a metallic damper, with a focus on the influence of the flange plate and its properties on the damper’s behavior. The numerical studies are performed using the finite element (FE) method with simulations performed using ANSYS. The damper’s components were modeled using the SHELL181 element, which is well-suited for capturing large displacements and buckling while ensuring convergence during nonlinear simulations.

The FE models were defined with consistent geometric parameters: a web plate thickness  of 6 mm, damper height  of 140 mm, stiffener width  of 160 mm, and flange width  of 160 mm. The variables examined include the web plate thickness  and stiffener thickness  which result in variations in shear strength  and stiffness ratio  A36 steel, characterized by a yield strength of 235 MPa and a Young’s modulus of 200 GPa, was used for all damper components.

Lateral loading was applied to the damper using simplified boundary conditions, as depicted in Fig. 2. Given the pinned connections between the beam and columns, the main frame is assumed to have no influence on the damper’s behavior, and vice versa. Since the primary objective of this study is to assess the damper’s performance and validate proposed analytical relationships, only the damper itself is analyzed. The interaction between the damper and a diagonally braced frame will be explored in future research.

Figure 2. Boundary conditions of simplified damper.

Validation of Finite Element Results

According to Fig. 3, the FE results were validated against the experimental results of the I-shaped shear damper detailed in [33] through FE simulation. As can be seen from Fig. 3, the FE simulation is relatively compatible with the experimental results on predicting the hysteresis curve and the yielding state of the damper.

a)

b)

c)

Figure 3. Comparing the experimental test and FE results in a) hysteresis curve; b) the tested damper [33]; c) simulated the damper.

4.Discussion

Comparing the Curves of Stiffened/Unstiffened Dampers

As discussed in Section 1, the shear capacity, stiffness, and overstrength of the damper are closely tied to the properties of the web plates. As a result, the adoption of low-yield-point (LYP) steel is expected to significantly enhance the damper’s performance under shear loading. To explore this further, Fig. 4 illustrates both the load-rotation relationship and the stiffness versus rotation behavior, plotted for a range of ρ values to provide a comprehensive view of the damper’s response under varying conditions.

The load-rotation graph serves as a valuable tool for evaluating the overall performance of different damper configurations. As shown in the figure, the addition of stiffeners to create a reinforced I-shaped damper shifts the curve upward, indicating improvements in key mechanical properties. Specifically, this modification leads to a noticeable increase in elastic stiffness, ultimate strength, and energy dissipation capacity, all of which are critical for effective seismic performance. These enhancements suggest that the stiffened damper can better withstand cyclic loading, making it a promising option for structures in earthquake-prone regions.

To further contextualize these findings, the results suggest that design decisions regarding stiffener placement and material selection should prioritize the intended loading conditions. For applications where elastic stiffness is paramount, such as in structures requiring minimal deformation under moderate loads, the reinforced I-shaped damper offers clear advantages. However, in scenarios where the damper is expected to undergo significant nonlinear deformation, alternative approaches such as optimizing the web plate geometry or exploring hybrid material combinations may be necessary to achieve the desired performance. These insights provide a foundation for tailoring damper designs to specific structural demands, balancing cost, complexity, and seismic resilience.

Figure 4. Comparing the curves of the I-shaped and stiffened dampers.

Stiffness

Fig. 5 illustrate the stiffness of the I-shaped and stiffened dampers. Referring to Figure 5, either damper with and without stiffeners have no degradation in stiffness. Also, adding stiffeners improve the stiffness considerably. By increasing the thickness of the stiffeners, the stiffness has raised. So, the stiffeners affect the stiffness in elastic and inelastic zones.

Figure 5. Comparing the stiffness of the I-shaped and stiffened dampers.

Overstrength

Given that elements external to the damper must be designed to withstand amplified forces based on the overstrength factor  the values of  for various dampers are presented Fig. 6. Also, the  of stiffened dampers are divided by the I-shaped dampers in Fig. 6 to consider the effect of the X-stiffeners on  of the damper. Results indicated that have  > 1.5, which exceeds the AISC-recommended value of 1.5. Consequently, it is advised to adopt an  of 2.0 for damper design since its average is 1.97.

Figure 6. The Ω of the dampers with X-stiffeners.

Referring to Fig. 7, the  values for dampers with different flange plate thicknesses are normalized against those with a flange thickness  of 10 mm. The data suggest that thicker flange plates result in higher  values. Similarly, the seventh column compares the  of stiffened dampers to unstiffened I-shaped dampers with identical  With the exception of the damper at  = 0.25, the addition of stiffeners increases  by 2 % to 19 %.

To better evaluate the influence of various parameters on overstrength, Fig. 5 plots  against different variables. The results indicate that increasing the ratios  and  leads to a higher  though this relationship is nonlinear. Conversely, increasing the slenderness of stiffeners, as represented by the ratios  and  tends to decrease  To mitigate significant reductions in  it is recommended to limit  to 35 and  to 50.

Figure 7. Comparing the Ω of the I-shaped and stiffened dampers.

Limitation of Stiffeners Slenderness to Achieve Suitable Overstrength

To evaluate the appropriateness of the proposed constraints of  = 40 and  = 60, Fig. 8 presents a detailed analysis by plotting ultimate strength and stiffness against these variables. Consistent with the behavior observed for overstrength, the data reveal that both ultimate strength and stiffness diminish as the slenderness of the stiffeners, represented by  and  increases. This trend highlights the sensitivity of the damper’s performance to geometric configurations, particularly in terms of how slender stiffeners can compromise structural efficiency.

At the specific thresholds of  = 40 and  = 60, the graphs indicate a notable shift: the rate of reduction in both stiffness and ultimate strength begins to stabilize, transitioning to a more gradual decline. This leveling-off suggests that these limits mark a practical boundary where further increases in slenderness yield diminishing negative impacts on performance. Consequently, adopting  = 40 and  = 60 as design constraints appears to be a well-founded and robust recommendation, balancing structural integrity with practical implementation.

These findings have broader implications for damper design optimization. By adhering to the proposed limits, engineers can ensure that the damper maintains adequate overstrength that represent the stiffness, strength, and economic aspect under anticipated loading conditions, particularly in seismic applications where energy dissipation is critical. Moreover, the data in Fig. 6 underscore the importance of carefully calibrating stiffener geometry to avoid excessive slenderness, which could lead to premature degradation of performance. To further validate these limits, future studies could explore their applicability across a wider range of damper configurations and loading scenarios, potentially refining the thresholds for specific use cases. For now, these constraints offer a reliable guideline for achieving efficient and resilient damper designs.

Figure 8. The ultimate strength and stiffness versus slenderness.

5.Conclusions

This study numerically and parametrically explored the performance of an I-shaped damper enhanced with stiffeners, confirming its effective behavior. The key findings are outlined below:

The stiffened I-shaped damper functions as a ductile fuse, efficiently absorbing energy imposed on structures during loading. Incorporating stiffeners into the I-shaped damper significantly improves its elastic stiffness, ultimate strength, and energy dissipation capacity. However, their impact on stiffness in the nonlinear deformation phase remains minimal. The average overstrength factor,  for both stiffened and unstiffened I-shaped dampers was calculated as 1.97, surpassing the AISC-recommended value of 1.5. As a result, a design value of  = 2.0 is suggested for practical applications. The characteristics of the flange plates and stiffeners influence  Thicker flange plates lead to an increase in  Additionally, with the exception of the damper at  = 0.25, stiffeners contribute to a 2 % to 19 % rise in Increasing the slenderness ratios of stiffeners (  and ) results in a reduction of  To counteract significant declines, it is recommended to limit  to 35 and  to 50. At the proposed limits of  = 35 and  = 50, the decline in stiffness and strength stabilizes, indicating a more gradual reduction. These thresholds are therefore considered a reliable and effective design guideline.