Experimental Research on the Seismic Ductility Performance of Wavy Web PEC Beams

Abstract

To improve the out-of-plane stability of partially encased composite (PEC) beam webs and enhance the synergy between concrete and section steel, a new type of wavy web PEC beam was designed and fabricated. In this study, the flange thickness and shear–span ratio were varied as key parameters. Low-cycle reversed loading tests were conducted to investigate the effects of these variables on the load-bearing capacity, failure patterns, deformation capacity, hysteretic energy dissipation capacity, and stiffness degradation of the wavy web PEC beams. Numerical simulations were performed using ABAQUS CAE2023, a finite element analysis (FEA) software, under low-cycle reversed loading conditions. The applicability of the ABAQUS software CAE2023 for the corrugated web PEC beam model was validated by comparing test results with finite element analysis results. A detailed parametric analysis was then carried out using the finite element model to further investigate the mechanical properties of the wavy web PEC beams. The research findings are as follows: the wavy web PEC beams exhibited good ductility; a larger shear–span ratio led to a transition in the failure pattern from shear failure to flexural failure; varying the flange thickness significantly affected the failure location and characteristics; and reducing the flange thickness could limit the propagation of concrete cracks, thereby improving toughness and energy dissipation capacity.

1. Introduction

The sinusoidal corrugated web PEC beam is a new type of composite structure beam that combines the features of corrugated steel webs with partially encased composite (PEC) structures. Replacing the flat web of the I-shaped steel in the PEC component with a corrugated web effectively addresses the weak out-of-plane stability of the beam during the bending moment [1]. The strong mechanical interlock between the corrugated web and concrete reduces the need for longitudinal reinforcement, stirrups, and shear studs in the PEC cross-section, thereby simplifying construction [2]. Meanwhile, the undulating shape of the corrugated web enhances its resistance to shear deformation and allows for the even distribution of stresses, resulting in increased overall bending stiffness and a reduction in stress concentrations. This can delay the onset of fatigue in structures and materials, particularly in seismic applications [3,4,5].

Current research on corrugated plates typically uses sinusoidal, folded, and trapezoidal corrugations, primarily focusing on I-shaped beams [6], shear walls [7], and T-shaped composite box beams [8] in building and bridge structures, all of which have exhibited good structural performance and economic benefits. Morkhade et al. [9] conducted an extensive parametric study on corrugated web steel beams with web openings, investigating key variables such as corrugation angle, web thickness, and opening diameter. Their findings indicated that the height-to-thickness ratio of the steel beam is the primary parameter influencing the buckling performance of corrugated web steel beams. Chen et al. [10] proposed a new type of composite box beam incorporating a corrugated steel web and truss. Bending tests revealed that, in the elastic stage, the strains were primarily observed in the concrete roof and bottom steel tube, which adhered to the plane section assumption and exhibited good ductility. Jiang et al. [11] validated the reliability of a new type of wavy web beam–column node with end plate bolt connections under seismic conditions.

Extensive theoretical and experimental research on PEC components has been conducted both within China and abroad [12,13,14]. Chen Y et al. [15], through monotonic and cyclic loading tests on PEC beams, concluded that these beams exhibit excellent ductility and energy dissipation capacity, and that the cross-section classification recommended in Eurocode 4 is often overly conservative. Ahmad et al. [16], through comparative tests, found that openings in the webs of PEC beams can effectively improve their bending capacity and energy absorption, thereby reducing the structural self-weight while still meeting design requirements. Feng et al. [17] presented a theoretical model for calculating the plastic bending of PEC beams, incorporating the results from four-point bending tests and taking into consideration both precast and cast-in-place components. Yicong X et al. [18] proposed a new shear strength model that decouples the shear contributions of steel and concrete by applying the principle of strain compatibility, which enabled more accurate predictions of the shear strength of PEC beams. Wang Wei et al. [19] applied the corrugated web to PEC columns and found that, under weak-axis bending, the load-bearing capacity of corrugated web PEC columns is greater than that of flat web PEC columns, while maintaining similar seismic performance. However, the accordion effect of the corrugated web under strong-axis bending is unfavorable for the PEC column after concrete crushing.

The wavy web PEC beam addresses several issues associated with traditional T-shaped wavy web composite beams, such as insufficient web constraint, poor fire resistance, and fully encased flanges, which are not ideal for the assembly of prefabricated building components [20,21]. Existing studies have found that under monotonic static loading, the sinusoidal wavy web PEC beam performs exceptionally well in bending and shear tests, with its actual load-bearing capacity exceeding theoretical predictions. Tests have also demonstrated its good ductility and joint action [22,23], indicating its significant potential for seismic resistance.

In this study, to further investigate the seismic performance of the wavy web PEC beam, sinusoidal wavy web PEC beam components with various parameters were designed and fabricated, and quasi-static tests were conducted on them. The load-bearing capacity, failure patterns, seismic energy dissipation capacity, and damage assessment of the specimens under cyclic loading were explored. This helps to validate the applicability of the finite element model and provides an experimental foundation for the application of wavy web PEC components in engineering practice.

2. Test Proposal

2.1. Specimen Fabrication

In this test, four wavy web PEC beam components were designed with varying shear–span ratios and flange thicknesses. Each beam segment is connected to base segments and node stiffeners of the same dimensions. The upper and lower flanges of the main steel components are made from Q355B steel, while the wavy web, with a 10 mm wave amplitude and a 155 mm wavelength, is constructed from Q235 steel, as shown in the Figure 1. The longitudinal reinforcement consists of 48, and the tie reinforcement is 4@100, with all reinforcements made from HRB400 steel. For all specimens, the concrete used is of strength grade C30. The basic parameters of the specimens are shown in

Table 1. Design parameters of wavy web PEC beam specimens.

No.	Length (mm)	Height (mm)	Width (mm)	Shear–Span Ratio	Flexural Capacity (kN·m)	Shear Capacity (kN)	Steel Ratio (%)
L–8–2	1000	400	100	2	95.65	146.66	6.4
L–6–2	1000	400	100	2	72.1	146.66	5.4
L–8–4	1800	400	100	4	95.65	146.66	6.4
L–6–4	1800	400	100	4	72.1	146.66	5.4

and Figure 1. The numbering rule of the test beam is L-flange thickness (mm)-shear–span ratio; for example, L–8–2 represents a beam member with a flange thickness of 8 mm and a shear–span ratio of 2. The flexural and shear capacities were calculated with reference to the T/CECS 719-2020 Technical Specification for Partially-Encased Composite Structures of Steel and Concrete [24].

The flange plates are connected to the wavy web through double-sided fillet welds. The transverse tie reinforcement is welded to the upper and lower flanges, while the longitudinal reinforcement is tied to the transverse tie reinforcement. At the ends, the reinforcement is welded to the base and end plates, forming a reinforcement mesh. Photographs of the main steel components are shown in Figure 2. After embedding the strain gauges, the concrete is cast in two stages, one on each side.

2.2. Material Properties Test

The compressive strength of the concrete cube is shown in

Table 2. Measured compressive strength of concrete cube.

Batch No.	fcu (MPa)	fc (MPa)	Ec (MPa)
First	30.6	20.5	27,235
Second	33.3	24.2	28,965

. The material properties of the steel materials were determined in accordance with GB/T228.1-2021 Metallic Materials—Tensile Testing—Part 1: Method of Test at Room Temperature [25]. The results from the steel tensile tests are shown in

Table 3. Tensile test results of steel.

Sampling Location	Thickness/Diameter (mm)	Yield Strength, fy (MPa)	Ultimate Strength, fu (MPa)	Elastic Modulus, Ea (MPa)
Web	2.5	347.05	473.54	269,639
Flange plate	6	356.99	488.86	233,630
	8	352.84	487.35	227,092
Connecting plate	10	401.50	518.33	214,013
Cover plate	14	433.81	568.77	205,440
Reinforcement	4	816.43	904.5	240,570
	8	458.76	584.99	219,878

.

2.3. Loading Scheme

An electro-hydraulic servo-actuator system was used for the test loading. The horizontal actuator has a maximum push/pull force capacity of 150 t and a travel range of ±250 mm. During the test, the beam specimen was rotated 90° and placed vertically. Since the actual axial force on the beam component is minimal, no vertical axial force was applied. Instead, the specimen was only subjected to a low-cycle reversed loading test using the horizontal actuator, as shown in Figure 3. The specimen’s base was fixed to the test platform, and the actuator loading head was pin-connected, simulating the actual conditions during an earthquake, where there is no bending moment at the midspan of the beam.

A graded quasi-static cyclic loading protocol was employed in the test. Before the formal loading, preloading was conducted by applying a cyclic load at the beam ends twice, with the preload value set at 20% of the estimated load-bearing capacity. The formal loading followed the Specification for Seismic Test of Buildings (JGJ101-1996) [26], using a combined force–displacement control loading protocol. During the initial stage of small deformation, before the specimen reached its calculated yield load, load control was employed. After the specimen yielded, displacement control was adopted, taking the horizontal displacement Δ at both ends of the steel beam at the yield point as the initial displacement control loading level. Each displacement level was cycled three times until the specimen completely failed (i.e., when the bearing capacity dropped to 85% of the ultimate load).

3. Phenomena and Failure Patterns

Table 4. Load–displacement curve feature points and failure characteristics.

No.	Initial Cracking Point of Concrete		Yield Point of Steel Flange		Ultimate Point		Failure Characteristics
	Displacement (mm)	Load (kN)	Displacement (mm)	Load (kN)	Displacement (mm)	Load (kN)
L–8–2	−5.59	−80.0	−5.59	−80.0	27.95	134.1	The maximum crack width on the south side is 0.2 mm, and on the north side, it is 0.25 mm. Large-scale concrete spalling is observed on the west side of the north side.
L–6–2	−4.91	−49.2	7.37	78.2	29.48	104.7	The maximum crack widths on both the south and north sides are 3 mm. Concrete spalling is present, along with severe buckling of the steel flanges and tearing of the west flange on the north side.
L–8–4	−6.55	−18.2	−12.67	−44.0	—	—	The maximum crack widths on the south and north sides are 2.6 mm and 3.2 mm, respectively. There is severe concrete cracking at the beam root and minor spalling in some locations. The welded joints are also cracked.
L–6–4	5.53	30.0	12.10	33.1	48.40	56.88	Numerous diagonal cracks have appeared, accompanied by concrete spalling and audible cracking sounds, with the maximum crack width on the south side reaching 5 mm.

—: Not reached.

presents the key points of the load–displacement curves and the failure characteristics of the four specimens during the loading process. The final failure patterns are illustrated in Figure 4. The concrete cracking displacement and load for Specimen L–8–2 were significantly larger than those for Specimen L–6–2, whereas the maximum width and number of cracks at final failure were smaller in Specimen L–8–2 compared to Specimen L–6–2. This indicates that appropriately increasing the flange thickness can enhance the flange’s constraint on the concrete, thereby improving crack control capacity. The initial damage to the components manifested as concrete cracks at the beam root. In beam sections with a shear–span ratio of 2, diagonal cracks appeared first. Due to the small shear–span ratio and relatively high shear stress, the failure of these beams was primarily characterized by shear failure with prominent cross-diagonal cracks. In beam sections with a shear–span ratio of 4, the earliest cracks were horizontal cracks, and failure was dominated by flexural failure, with horizontal cracks as the main feature. Beams with a flange thickness of 8 mm experienced failure through concrete crushing and spalling, while the flange itself did not show significant failure. For beams with a flange thickness of 6 mm, the flange exhibited buckling or tearing in addition to concrete crushing and spalling, indicating that the flange’s strength was fully utilized, resulting in more pronounced ductility. As the load size and the number of cycles increased, both diagonal and horizontal cracks in the concrete continued to increase in number, lengthen, and widen. The flanges at the ends of the beams tended to buckle or tear where the corrugated web is recessed (where the local flange width-to-thickness ratio is largest), and the concrete near the flanges showed signs of crushing and spalling, resulting in a significant decline in the beam’s load-bearing capacity. This indicates a complete failure of the beam. In this test, the weld at the beam–column (base) connection experienced large loads, and tearing of the beam-end weld was observed in the first loaded specimen, Specimen L–8–4. This prevented the beam from full failure and energy dissipation capacity from being fully utilized. However, the other three components did not experience this failure after weld reinforcement.

Due to the asymmetric constraint of the wavy web at specific sections of the flanges, particularly at the peaks and troughs of the web, the outward projection width of the flange reached its maximum on one side. This resulted in the largest flange width-to-thickness ratio, making it more susceptible to buckling. During testing, flange buckling was observed at the troughs of the wavy web in all components. Therefore, it is recommended to provide transverse reinforcement at these troughs to enhance the constraint on the flanges, thereby improving their local stability and further enhancing the seismic performance of the component.

4. Test Results and Analysis

4.1. Hysteresis Curves

The hysteresis curves for each specimen are illustrated in Figure 5. During the loading process, the weld between the flange at the Specimen L–8–4 beam root and the base fractured, resulting in incomplete test data. The figure shows that: (1) The ultimate ring stiffness is greater than that of the failure ring (the first hysteresis loop with a bearing capacity lower than 85% of the peak value), but the failure ring is fuller and has a stronger energy dissipation capacity. This indicates that after reaching the peak load, the energy dissipation capacity of the component continues to increase with further deformation, demonstrating a strong energy dissipation reserve after the peak. (2) For components with a shear–span ratio of 2, the hysteresis loops for those with a flange thickness of 8 mm still exhibit significant pinching at the peak, and failure is primarily manifested as concrete cracking and crushing. Due to the large cross-section of the steel sections, there is no significant buckling or yielding, meaning that its energy dissipation capacity is not fully utilized. In contrast, the hysteresis loops for components with a flange thickness of 6 mm are relatively full at the peak, and the corresponding phenomena show that the failure of these components is manifested as concrete cracking, crushing, and steel flange buckling or tensile yielding. At this stage, the energy dissipation capacity of the component has been exploited to a certain extent. (3) For components with a flange thickness of 6 mm and the same cross-sectional size, the lateral stiffness of beams varies significantly with different shear–span ratios. A smaller shear–span ratio results in greater stiffness. However, the components have similar energy dissipation (hysteresis loop area) at the ultimate state, and the component with a shear–span ratio of 2, due to its higher load-bearing capacity, exhibits slightly higher cumulative energy dissipation than the component with a shear–span ratio of 4 at the point of final failure.

4.2. Skeleton Curves

The skeleton curves are plotted by connecting the peak load–deformation points from the first loading cycle at each level, as shown in Figure 6. All the specimens’ skeleton curves display an oblique S-shape, effectively representing the four stages of elastic, plastic, ultimate, and failure experienced by the specimens throughout the loading process.

(1)

By comparing the skeleton curves of Specimen L–X–2, we observe that Specimen L–8–2 shows a more rapid decline in load-bearing capacity after reaching its peak, which is consistent with its failure characteristics dominated by shear action and concrete crushing and spalling. For components with the same shear–span ratio, those with thicker flanges exhibit a faster decline in load-bearing capacity after the peak, especially when the failure is dominated by concrete.

(2)

Compared to Specimen L–6–2, Specimen L–6–4 experienced a 26.3% and 48.3% decrease in yield load and peak load, respectively, but its yield displacement and peak displacement increased by 68% and 65.4%, respectively. The component with a shear–span ratio of 4 exhibits very low load-bearing capacity but has a significantly greater peak displacement compared to the component with a shear–span ratio of 2. Additionally, the decline in load-bearing capacity after the peak is more gradual, particularly under reversed loading conditions. This is in line with the observation that both the concrete and steel flanges have been relatively fully exploited during failure. The component with a shear–span ratio of 2 has higher stiffness and load-bearing capacity than its counterpart, but its small peak displacement and rapid decline in load-bearing capacity after reaching the peak limit its energy dissipation capacity.

4.3. Ductility Coefficient

In the test, the displacement ductility coefficient, µ_Δ is used to evaluate the ductility performance of the components. It is defined as µ_Δ = Δ_y/Δ_u, where Δ_y is the beam-end displacement at the component’s yield point, also known as the yield displacement, and Δ_u is the beam-end displacement at which the maximum load-bearing capacity has decreased to 85%, referred to as the failure displacement. During testing, the criterion for determining the component’s yield and the shift in loading mode is based on the flanges reaching their yield strain. After obtaining the component’s skeleton curve, the actual yield point is determined using the energy equivalence method, and then the ductility coefficient is calculated, as shown in Figure 7.

Based on the aforementioned method, the ductility coefficients for various components are presented in

Table 5. Ductility coefficient of specimens.

Component No.	Positive			Negative
	Yield Displacement	Ultimate Displacement	Ductility Coefficient	Yield Displacement	Ultimate Displacement	Ductility Coefficient
L–8–2	13.94	28.03	2.01	14.73	33.54	2.28
L–6–2	13.94	29.48	2.11	13.78	29.02	2.11
L–6–4	13.31	48.43	3.64	14.29	60.6	4.24

. The loading displacements at the components’ yield points, calculated using the energy equivalence method, are approximate, possibly due to the calculation method itself. Additionally, there is no significant correlation between the positive and negative ductility coefficients of the components and the flange thickness. However, due to variations in ultimate displacements, the positive and negative ductility coefficients of the components increase significantly as the shear–span ratio increases; the average ductility coefficient increases by 86.7%. Components with a shear–span ratio of 2 have ductility coefficients ranging from 2.01 to 2.28, which are relatively low due to the shear failure pattern.

4.4. Energy Dissipation Performance

The equivalent viscous damping coefficient is used to evaluate the energy dissipation capacity of beams under cyclic loading. The schematic diagram for calculating the energy dissipation coefficient of a single hysteresis loop of the component is shown in Figure 8, and the equivalent viscous damping coefficient he is calculated according to Equation (1).

$$h_{\mathrm{e}}={\displaystyle \frac{1}{2\mathsf{\pi }}}{\displaystyle \frac{S_{\left(\mathrm{A}\mathrm{BC}+\mathrm{ADC}\right)}}{S_{\left(\mathrm{O}\mathrm{BE}+\mathrm{ODF}\right)}}}$$

(1)

Figure 9 illustrates the curves of the damping coefficients at both the peak and critical failure states of the components. Specifically, it shows the relationship between the equivalent viscous damping coefficient and flange thickness for components with a shear–span ratio of 2, and the relationship between the equivalent viscous damping coefficient and shear–span ratio for components with a flange thickness of 6 mm. It can be seen from the figure that the calculated equivalent viscous damping coefficient for beams with a flange thickness of 8 mm is smaller than that for beams with a flange thickness of 6 mm, indicating that the energy dissipation capacity of the 8 mm beam is not fully utilized. This is primarily because the section steel is relatively stronger compared to the concrete, resulting in less significant damage to the steel itself during failure, thus limiting the steel’s ability to fully exploit its energy dissipation capacity. In contrast, beams with a flange thickness of 6 mm experience adequate plastic deformation in both steel and concrete during failure. The shear–span ratio significantly affects the damping coefficient, with beams having larger shear–span ratios exhibiting better energy dissipation performance and higher damping coefficients. Furthermore, as the beam approaches the failure state, the damping coefficient increases more rapidly. At the ultimate load, the equivalent viscous damping coefficient of Specimen L–6–2 is 25.7% higher than Specimen L–8–2 but 5.3% lower than Specimen L–6–4. At the failure load, the equivalent viscous damping coefficient of Specimen L–6–2 is 28.6% higher than Specimen L–8–2 but 22.3% lower than Specimen L–6–4.

4.5. Stiffness Degradation

The stiffness of the specimens is represented by the secant stiffness K_i, which is calculated using Equation (2). This value is determined as the ratio of the sum of the absolute values of the load to the sum of the absolute values of the displacement for both positive and negative loading directions during the same loading process.

$$K_i={\displaystyle \frac{\left|+F_i\right|+\left|-F_i\right|}{\left|+X_i\right|+\left|-X_i\right|}}$$

(2)

where +F_i and −F_i are the positive and negative peak load values at the i-th loading, respectively, and +X_i and −X_i are the positive and negative peak displacement values at the i-th loading, respectively. Figure 10 illustrates the comparison of stiffness degradation curves, from which the following can be seen:

(1)

The initial stiffness of Specimen L–8–2 is 40.3% greater than that of Specimen L–6–2, and the initial stiffness of Specimen L–6–2 is 50.3% greater than that of Specimen L–6–4. Components with a shear–span ratio of 2 have significantly higher absolute stiffness compared to those with a shear–span ratio of 4. With all other conditions being equal, a thicker flange results in greater component stiffness.

(2)

Overall, the stiffness degradation follows the pattern of initially occurring rapidly and then slowing down. However, components with a shear–span ratio of 2 experience faster stiffness degradation, with the relationship between stiffness and displacement development appearing nearly linear. For components with a shear–span ratio of 4, the pattern of rapid initial stiffness degradation followed by a slower rate is quite pronounced. As displacement increases, the stiffness degradation becomes increasingly gradual, reflecting their relatively higher ductility.

5. Finite Element Analysis

5.1. Material Constitutive Model

5.1.1. Concrete Constitutive Model

This study adopts the uniaxial compressive and tensile stress–strain relationship curves for concrete as outlined in the Code for Design of Concrete Structures (GB50010-2010) [27]. Based on these curves, the parameters for the concrete damage plasticity model are calculated. The parameters for the concrete material are detailed in

Table 6. Concrete damage plasticity model parameters.

Expansion Angle	Offset	σb0/σc0	Kc	Coefficient of Viscosity (μ)
30°	0.1	1.16	2/3	0.0005

. Among them, σ_b0/σ_c0 and K_c are the ratios of the initial yield strength of biaxial and uniaxial and the second stress invariant of the tensile compressive meridian plane, respectively. They are used to determine the shape of the yield surface on the plane stress and off plane [28].

5.1.2. Steel Constitutive Model

In this study, the built-in elastic-plastic model in ABAQUS is used to define the material constitutive behavior of section steel beams, links, and longitudinal reinforcements. Based on experimental data, the steel constitutive model is defined as a bilinear model using the Mises yield criterion and the kinematic hardening criterion. This model assumes that the flow potential function is identical to the yield surface function, and it treats the tensile and compressive elastic moduli as equal. After yielding, the steel’s elastic modulus Es’ = 0.01 Es, and the stress–strain relationship remains linear. The Poisson’s ratio is consistently assumed to be 0.3 for all steel materials.

5.2. Geometric Model Establishment

5.2.1. Element Selection and Mesh Division

In the PEC beam cross-section, steel reinforcements and links are modeled using the T3D2 element, a two-node three-dimensional truss element, while concrete and steel beams are modeled using the C3D8R element, which is an eight-node three-dimensional solid hexahedral element with linear reduced integration. A structured mesh division technique is applied, with an element size of 40 mm for the steel beam flanges, wavy web, and concrete, and 20 mm for concrete links, longitudinal load-bearing reinforcements, and longitudinal tie reinforcements.

5.2.2. Contact Settings

In the test, the steel flanges exhibited buckling, and the concrete web developed significant cracks. To simulate these phenomena, the finite element model uses a paired contact model between the concrete and the steel beam. Tangential contact is modeled using Coulomb friction with a friction coefficient of 0.4, while normal contact is modeled using hard contact, allowing the flanges to detach from the concrete but preventing them from penetrating it. The links are rigidly connected to the steel beam flanges at both ends, with the remainder of each link embedded in the concrete. The longitudinal reinforcements are also rigidly connected at the end plates, with the rest embedded in the concrete.

5.2.3. Hysteresis Curves Comparison of Hysteresis Curves

Figure 11 shows a comparison of the hysteresis curves obtained from numerical simulations and experimental tests for the wavy web PEC beam specimen. It can be seen that the test and simulation curves align closely, especially at the peak load points. The slight irregularities in the test curve could be attributed to internal defects, inelastic deformation, minor cracking in the concrete material, and friction between the steel and concrete.

5.2.4. Skeleton Curves Comparison of Skeleton Curves

Figure 12 illustrates a comparison between the tested and simulated skeleton curves. In Figure 12c, for the tested skeleton curve of Specimen L–8–4, data from Specimen L–6–4 was used, resulting in the test curve being lower than the simulated skeleton curve. For the other specimens, the tested and simulated curves show good agreement during the early loading stages, with only slight deviations observed in the later stages, which are not significant.

5.2.5. Stress and Damage Analysis

Figure 13 shows the stress distribution in the steel and the concrete damage contour of the wavy web PEC beam at the ultimate load, as derived from the numerical simulation. High-stress areas in the steel section are primarily located near the bottom support of the specimen, with a similar pattern observed in the distribution of concrete damage. The yielding regions of the steel and the distribution of concrete plastic strain are generally consistent with theoretical expectations and test results. However, it is important to note that, during testing, some specimens exhibited partial buckling of the steel flanges due to insufficient confinement when concrete spalling occurred, which was not present in the simulation. This requires further discussion and improvement of the modeling details, such as component modeling, mesh discretization, constitutive model selection, and failure characteristics.

5.3. Parametric Analysis

The analysis above demonstrates that the numerical model effectively captures the stress and damage conditions of actual concrete. To further investigate the relationship between the load-bearing performance of the wavy web PEC beam and relevant parameters, we established nine models with varying flange thicknesses (6, 8, and 10 mm) and shear–span ratios (2, 3, and 4), and simulated the load-bearing performance of each specimen under unidirectional lateral loading. The specimen naming convention is the same as before. Figure 14 shows the section steel stress and concrete damage contours at the peak points for the analyzed specimens. The results indicate that as the shear–span ratio increases, the peak steel stress becomes more concentrated at the beam root. Conversely, for smaller shear–span ratios, the high-stress region in the steel extends over a larger area. This suggests that for larger shear–span ratios, the bending moment is the dominant factor, allowing a distinct plastic hinge to form at the beam root. In contrast, for smaller shear–span ratios, the shear force becomes more significant, resulting in a less pronounced plastic hinge region at the root. With other conditions being equal, an increase in flange thickness results in a decrease in peak steel stress, indicating that stronger steel leads to a failure pattern characterized by concrete crushing or cracking. However, this characteristic is less evident in specimens with a shear–span ratio of 2, as the shear is primarily supported by the web and the adjacent concrete, making the variation in flange thickness a secondary factor. The damage patterns in concrete tension and compression closely resemble the stress distributions in the steel. For larger shear–span ratios, concrete damage is more concentrated at the beam root, while for smaller shear–span ratios, the damage is more widespread. Increasing the flange thickness results in more severe concrete damage at the peak point. Conversely, specimens with thinner flanges exhibit less concrete damage at the peak point, suggesting that failure is triggered by steel tensile rupture or compressive buckling, as observed in the component test.

5.3.1. Influence of Flange Thickness

Figure 15 shows the load–displacement curves for different flange thicknesses. The flange thickness has little effect on the initial stiffness, but as the flange thickness increases, both the yield strength and peak load increase significantly. Compared to the L–6–2 beam model with a shear–span ratio of 2, the peak loads of the L–8–2 and L–10–2 beam models increase by 11.5% and 19.5%, respectively. For a shear–span ratio of 3, the peak loads of the L–8–3 and L–10–3 models increase by 17.3% and 38.6%, respectively. For a shear–span ratio of 4, the peak loads of the L–8–4 and L–10–4 models increase by 16.3% and 39.4%, respectively. This demonstrates that flange thickness has a significant positive effect on the peak load. Considering the steel ratio limitations of the specimens, it is recommended to use a flange thickness between 6 mm and 8 mm.

5.3.2. Influence of Shear–Span Ratio

The analysis results for components under the influence of the shear–span ratio are shown in Figure 16 and

Table 7. Load-bearing characteristics of components with different shear span ratios.

Flange Thickness (mm)	Shear–Span Ratio	Yielding Moment (kN·m)	Ultimate Moment (kN·m)
6	2	85.6	147.7
	3	82.7	142.6
	4	73.8	126.6
8	2	101.7	164.6
	3	102.1	167.3
	4	92.9	147.3
10	2	111.3	176.4
	3	126.8	198.5
	4	125.2	176.4

. As the shear–span ratio increases, both the initial stiffness and load-bearing capacity increase significantly. For a flange thickness of 6 mm, increasing the shear–span ratio from 2 to 3 and 4 results in a reduction of the yield moment by 3.4% and 13.8%, respectively, and a reduction of the ultimate bending moment by 3.5% and 14.2%, respectively, indicating a relatively minor impact of the shear–span ratio on these parameters. However, for flange thicknesses of 8 mm and 10 mm, the components with a shear–span ratio of 3 exhibit the highest flexural capacity.

6. Damage Assessment

The damage assessment model adopts the improved Park–Ang model, and the damage index is calculated using the equation as follows [29].

$$D={\displaystyle \frac{{\delta }_{\mathrm{m}}-{\delta }_{\mathrm{y}}}{{\delta }_{\mathrm{u}}-{\delta }_{\mathrm{y}}}}+\beta {\displaystyle \frac{E_{\mathrm{h}}}{Q_{\mathrm{y}}{(\delta }_{\mathrm{u}}-{\delta }_{\mathrm{y}})}}$$

(3)

where δ_m is the maximum displacement achieved during the cyclic loading process; δ_u is the ultimate displacement under the monotonic static loading; Q_y and δ_y are the average yield strength and displacement in the two loading directions of the specimen, respectively. The hysteretic energy E_h is obtained by integrating force and deformation up to the ultimate state. In the ultimate state, it is assumed that the damage index for Specimen L–6–4 is 1 (D = 1). Using the experimentally determined combined coefficient β, the final damage indices for Specimens L–8–2 and L–6–2 are then calculated to be 1.05 and 1.09, respectively. This shows that the combined coefficient can be applied to the calculation and seismic damage assessment of wavy web PEC beams. The progression of the damage index is as shown in Figure 17.

As can be seen from Figure 17, the damage index development trends for specimens with different flange thicknesses are similar. Increasing the shear–span ratio effectively delays the damage development rate. The curves accurately reflect the progression of slight damage, moderate damage, severe damage, and collapse in the specimens, aligning with observed test phenomena. After the onset of numerous concrete cracks and significant yielding of the steel flanges, the damage index shows a slight acceleration in growth.

7. Conclusions

Through quasi-static tests and numerical simulations, this study investigates the effects of shear–span ratio and flange thickness on the seismic load-bearing capacity, ductility, stiffness degradation, and energy dissipation performance of wavy PEC beams. Based on the test results and numerical analysis, the following conclusions can be made:

• The failure pattern results show that specimens with shear–span ratios of 2 and 4 exhibit shear failure and flexural failure, respectively. The equivalent viscous damping coefficients at beam failure are 0.26, 0.34, and 0.44, demonstrating good energy dissipation performance;
• Increasing the shear–span ratio significantly improves displacement ductility and energy dissipation capacity. The stiffness degradation trend initially accelerates and then slows down; however, the ultimate bearing capacity under cyclic loading is relatively reduced. The average ductility coefficient of Specimen L–6–4 is 86.7% higher than that of Specimen L–6–2, while the average bearing capacity is reduced by about 48.3%;
• Flange thickness has little effect on the ductility coefficient. Specimens with a flange thickness of 6 mm have relatively lower stiffness and ultimate bearing capacity, but reducing the flange thickness allows the flanges and concrete to fully utilize their energy dissipation capacity;
• The results from the numerical simulation closely match the experimental failure patterns, and the calculated ultimate bearing capacities of the specimens are within 10% of the test values. The parametric analysis indicates that the shear–span ratio significantly influences the failure pattern of the beam, while the flange thickness affects the failure location. When the flange is thick, failure occurs in the concrete portion; otherwise, it occurs in the steel flange section. A comprehensive analysis indicates that a specimen with a flange thickness of 8 mm and a shear–span ratio of 3 has better mechanical properties;
• The parametric analysis results show that the shear–span ratio significantly influences the failure pattern of the beam. When the shear–span ratio is large, the bending moment becomes the dominant factor, leading to the formation of a significant plastic hinge at the beam root, where concrete damage is also concentrated. When the shear–span ratio is reduced, shear force becomes the dominant factor, resulting in a less pronounced plastic hinge area at the steel root and a larger range of tensile and compressive damage in the concrete. Under otherwise identical conditions, as the flange thickness increases, failure shifts from steel buckling or rupture to concrete crushing or cracking. However, this characteristic is not significant for specimens with a shear–span ratio of 2;
• By incorporating the combined coefficient β, the improved Park–Ang model can effectively evaluate the damage of wavy web PEC beams.

During testing, it was found that the side of the flange trough is prone to buckling. It is recommended to place transverse reinforcement at the cross-section location corresponding to the trough of the wavy web, where the flange overhang width is the greatest.