A Parametric Study on the Behavior of Arch Composite Beams Prestressed with External Tendons

Abstract

Arch beams are widely used in bridge construction due to their ability to withstand much greater loads than horizontal beams. The utilization of composite construction has also increased due to its tendency to optimize the utilization of construction materials, leading to significant savings in steel costs. In this research, a detailed experiment work on a simply supported arch composite beam under a positive moment was presented; then, a numerical model was created using ABAQUS to simulate its nonlinear behavior. The beams were formed from a concrete slab attached to steel beams by means of perfobond shear connectors (PSCs). A good agreement between the model and experiment was obtained. A parametric study was developed to identify the influence of the initial prestressing, rise to span ratio, and beam length on the behavior of the arch composite beam. It was found that the presence of tendons enhances the serviceability behavior, increases the ultimate load by 40% compared to the control beam, and equilibrates the horizontal thrust of the arch, even in the absence of initial prestressing. In addition, the beam exhibits a clear tied arch behavior due to the large eccentricity as the rise-to-depth ratio increases. Furthermore, the prestress force was found to be more effective in the longer span and the incremental stress in tendons more remarkable.

1. Introduction

Historically, arch bridges are among the oldest bridge types, featuring extended spans compared to conventional horizontal beam bridges. Technically, an arch bridge generates vertical reaction forces and a horizontal thrust when subject to vertical loads, which minimizes the bending moment and optimizes the material strength within the main arch’s section [1]. In contemporary bridge engineering, arch designs have gained popularity owing to their remarkable load-bearing capacity and the material’s strength optimization in the main section [2]. A substantial thrust is characteristic of an arch, whose in-plane strength correlates with its support’s stiffness due to the dominant role of compressive stresses [3]. The horizontal component acts as a tension tie, mitigating the arch support’s horizontal displacement. The optimal rise-to-span ratios for a structural arch vary between 5 and 6 [4]. However, as the support spreads further, the arch members dramatically weaken, potentially leading to extremely high vertical displacements at the peak or even total collapses. Meanwhile, a steel–concrete composite structure combines the high compressive strength and stiffness of concrete with the tensile strength and ductility of steel. Owing to their enhanced performance and bearing capacity, these composite structures are particularly effective in bridge constructions to address modern transportation demands [5,6].

Numerous works have been reported in the literature on the efficacy of steel–concrete composite horizontal beams in post-tensioning and prestressing conditions. The comparison to steel bridges has shown a significant reduction in prestress losses in post-tensioned composite structures, with long-term losses of around 7% after 30 years, which increases their durability and enhances their cost efficiency [7]. Experiments have shown that prestressing improves yields and ultimate loads, increasing the moment resistance and decreasing the deflections under service loads. Moreover, draped tendons were found to offer superior ductility compared to straight tendons [8].

Chen et al. [9] examined two prestressed composite beams and calculated the ultimate incremental tendon force. They showed that prestressing contributes to the yield and ultimate load’s improvement, driving an up to 25% enhancement in the ultimate moment resistance and decreasing the deflection under service loads. Their analytical model accurately predicted the final moment resistance.

Craine and Uy [10] tested steel–concrete composite horizontal beams with and without post-tensioning, and established a calibrated finite element model using test data from load–deflection curves. Zona et al. [11] suggested a simpler approach (i.e., not using nonlinear analysis) to evaluate the increase in the tendon force at failure and the general flexural strength of a horizontal beam, yielding reasonable approximations when compared to a nonlinear FE model and experimental data. Chen et al. [12] and Nie et al. [13] examined the initial imperfections, residual stresses, and overall design techniques for prestressed continuous composite beams, highlighting their influence on the ultimate strength and load capacity.

Finite elements method (FEM)-based investigations have been extensively reported on externally prestressed steel–concrete composite beams. Advanced FEM studies have shown that the flexural stiffness of a post-tensioned beam increases by 33% and ultimate strength by 25% when post-tension is added to areas with positive moments [14]. Lou et al. [15] conducted a nonlinear FEM analysis for externally prestressed steel–concrete composite beams under short-term and long-term loading conditions. Morsch et al. [16] developed a three-dimensional finite element model for steel–concrete composite beams and calculated the cracking lengths and the ultimate moment resistance. Sousa et al. suggested an FEM-based equation for the nonlinear analysis of prestressed composite beams, considering the shear connection flexibility [17]. El-Zohairy et al. [18] experimentally studied the fatigue behavior of beams, showing that post-tensioning decreases strains in studs, steel beams, and concrete slabs, but increases longitudinal fatigue cracks in the concrete slab. Furthermore, Kim et al. investigated the improvements in the prestress efficiency, deflection control, and shear buckling capability through research on corrugated web beams [19]. Recently, Nawar et al. demonstrated that single corrugated web (CGW) composite beams exhibit a higher shear buckling resistance compared to double corrugated webs (DCW) beams [20].

The effects of prestressing in beams have been abundantly explored in the literature. Ribeiro et al. showed that prestressing improves the bending resistance in beams with symmetrical steel profiles, despite potentially large compression stresses [21]. Similarly, in prestressed steel–concrete composite beams with profiled steel decking, Moreira et al. showed that prestressing improves the ultimate moment resistance by up to 19% and reduces deflections. Nonetheless, design adjustments remain necessary for addressing localized slab failures [22]. Hu et al. demonstrated that the cracking load and girder optimization in hogging moment areas are intimately related to the settings of prestressed reinforcement in beams [23].

Recent research has contributed significantly to the understanding of prestressed steel–concrete composite beams, with an emphasis on their structural behavior, design optimization, and performance under changing conditions. Carbon fiber polymer (CFRP) reinforcement has been shown to minimize interface slip in composite beams [24]. Reviews have highlighted the importance of considering time-dependent effects to guarantee durability [25]. The development of prestressed steel–concrete composite beams and unique pouring molds has enhanced structural performance and construction efficiency. Furthermore, new information on the characteristics and development of steel and composite prestressed tendons has offered critical recommendations for materials selection [26].

While prestressing has been thoroughly studied in straight composite beams, its implications in arch beams remains insufficiently explored. The unique structural mechanics of arches, characterized by horizontal thrusts and a reliance on support stiffness, present particular challenges not addressed in straight beam models. Since prestressing was demonstrated to enhance the strength, stiffness, and deflection control in steel–concrete composite beans, incorporating it into composite arches may hold promising improvement in their load-bearing capacity and materials’ efficiency. However, comprehensive theoretical, numerical, and experimental investigations of prestressed composite arches are remarkably scarce in the current literature. Therefore, the combined experimental and numerical investigation in this study is expected to offer new perspectives on the improvement in the arches’ structural performances, particularly for applications requiring great strength, durability, and load-bearing capacity, such as bridges and long-span roofs.

This study seeks to examine the behavior of prestressed arch steel–concrete composite beams under four-point bending. The methodology includes experimental testing, numerical modeling using ABAQUS, a comparison between the experimental and numerical results, and a parametric analysis to assess the impact of several parameters. The successful execution of the study necessitates the availability of resources such as testing facilities, materials, software, specialized expertise, and financial support.

2. Experiment

A three-meter-span fully composite prestressed arch beam (B0) was fabricated. Its structural performance was assessed under a four-point bending test, using a hydraulic jack by apply incremental loads. For control, a push-out test, and six cylinders were fabricated using the same concrete as in the arch beam and tested on the same day of the arch beam bending experiments.

2.1. Beam Design

The bending moment resistance of the composite section at mid-span was computed using a plastic rectangular stress pattern according to Eurocode 4 [27], and applying the following materials’ properties:

• Structural steel yield strength (230 MPa);
• Concrete grade C45/50;
• Prestressing strand of 1860 MPa strength;
• Reinforcement bars with diameters of 8 mm and 10 mm, and a yield strength of 400 MPa.

By using an initial 380 MPa prestress, stress increments of up to 1000 MPa were predicted, with an ultimate designed load of 150 kN.

2.2. Beam Fabrication

Figure 1a,b show the steel web cutting process using a laser cutter machine and the shape curving of the flange using pyramidal roll bending, respectively. The latter process was iterated until the desired radius of curvature was reached. The web and flange were welded together along the full span, as shown in Figure 1c. The geometry of the beam is depicted in Figure 2a. The upper part of the web forms the perfobond shear connectors (PSC), consisting of 100 mm spaced steel plates with holes for inserting steel-reinforcing dowels (Figure 2b) [28]. PSC resist horizontal shears and vertical uplift pressures using concrete end-bearing zones, concrete dowels, and transverse rebar in the rib holes [29]. The final fully composite 3 m structure of the arch beam was made by covering the steel structure with 90 mm-thick and 480 mm-wide concrete slabs (Figure 2c), with their top and bottom surfaces reinforced using four 10 mm rebars (Figure 2d).

Following the slabs’ curing, a prestress was applied to the arch beam, which was anchored using two 25 mm plates welded at both of its ends and positioned 35 mm above the bottom flange. The tendons, composed of 7-wire strands, used in this experiment have a nominal diameter (D) of 12 mm and a cross-sectional area of 100 mm². Strands were alternately tied using one mono jack to prevent beam horizontal bending.

2.3. Material Properties

The concrete mix was obtained from ready mix concrete plant (Betomix, Tripoli, North Lebanon). To assess the compressive strength of the concrete used in the fabrication of the beam, four cylinders (15 × 30) cm made of the same concrete were tested following the ASTM C39 procedure [30]. The mean compressive strength was measured at 47 MPa (designed value: 45 MPa) and the modulus of elasticity at 29 GPa. For the design of prestressing, a 3 MPa tensile strength was applied to the concrete for its cracking control. The steel was provided by local supplier and fabricated in china (Shangang metal group, Jinan, China). The properties of steel were determined through a tensile strength test conducted on specimens cut from the steel plate. The yield and ultimate stresses were measured at 230 and 320 MPa, respectively. The modulus of elasticity was found equal to 206 GPa. For post-tensioning, a 7-wire strand cable was used, having a tensile strength of 1860 MPa, nominal diameter of 12.7 mm, and a section of 100 mm². The mechanical characteristics are given by the standard grade of the strand.

2.4. Instrumentation

During the test, the vertical deflection was measured using a linear variable transducer (LVDT) that is positioned at the middle of the beam under the lower steel flange, as illustrated in Figure 3a. A second horizontal LVDT was utilized at the beam’s ends to measure the displacement between the concrete slab and the steel beam. A strain gauge with 100 mm length and a resistance of 350 Ohm was used to measure the strains at the top of the concrete at mid-span (Figure 3b), and a second strain gauges with 2 cm length was bonded at the bottom of the steel flange at mid-span. A fundamental manual technique was used to regulate the tension in the prestressed strands of the composite beam. Rather than using sophisticated hydraulic systems, the tension was assessed by simply monitoring the movement between two markers positioned along the cable The map of the installation of LVDT and strain gauge is presented in Figure 3c.

2.5. Loading

Four-point bending tests were performed on all beams. An electro-hydraulic testing machine of 500 kN capacity was used to apply a monotonic vertical load at mid-span, which was then distributed to two-point loads. The beam rested on cylindrical support as shown in Figure 4. The beam was carefully positioned within the loading frame to ensure precise alignment of the specimen and hydraulic jack centerline. Prior to load application, all strain gauges underwent calibration. A small preload, not exceeding 5% of the anticipated ultimate load, was incrementally applied and released to eliminate system slack and secure specimen seating. This procedure was repeated to verify the proper functioning of dial gauges. In the experiment’s description, the vertical load acting on the beam is denoted F, and the force in a single jack is F/2.

2.6. Shear Connectors

Push-out tests (POTs) are commonly used to assess the shear load between the steel and concrete in composite beams. POT is a destructive test in which a specimen of the steel beam (i.e., the PSC described above) is held upright between two concrete slabs and fixed to them through bolts, as shown in Figure 5a,b. The test aims to reproduce the structural setting between the concrete slab and the steel flange in the actual arch beam.

A vertical load is applied to the whole structure, creating a shear load through the interface between the concrete slabs and the steel on both sides.

The push-out test outcomes are used to evaluate the ductility of the connector, in accordance with Eurocode requirements that the ultimate slip exceeds 6 mm, to verify the connector’s capacity for full composite action of the beam, and to generate the load–slip curve for use in modeling the beam’s behavior. The test outcomes reveal the force–displacement relationship (i.e., load–slip curve in Figure 6a) and the ultimate load (206 kN) measured before structural cracking (Figure 6a). Visual inspection shows the initial crack appearing on the lower longitudinal surface of the outer concrete slab in the two opposite sides of the PSC (Figure 6b). As the crack starts propagating through the slab, the load starts diminishing as the test continues further.

2.7. Beam Results

The load–deflection curve for the beam and the load–strain curve measured for the steel flange are shown in Figure 7a,b, respectively. The beam’s deflection varies linearly with the applied load up until 117 kN, where nonlinear variation indicates non-elastic behavior. This load defines the elastic limit of the beam deflection (i.e., F_y = 117 kN). Interestingly, the elastic limit of the beam matches the value of the load at which the steel flange yields, as observed in Figure 7b. As the load increases further, the beam’s load–deflection curve become strongly nonlinear until the ultimate load (i.e., P_u = 165 kN) is reached, at which the concrete slab fails, resulting in its fracture (Figure 8).

Figure 9 shows the variation in the tension stresses (σ_p) measured during the bending test as a function of the applied vertical load. The tension stresses exhibit a linear increase between 380 MPa and 600 MPa as the load increases below its elastic limit value, Fy. Beyond that limit, the tension undergoes a much sharper variation, approaching 900 MPa as the ultimate load F_u is reached. Visual inspection reveals no slippage between concrete and steel near the beam’s ends after the bending test. This observation highlights the role of cables acting as tension ties during bending, preventing arch spreading. During the collapse, a significant portion of the slab’s cross-section was crushed.

3. Finite Element Modeling

A numerical methodology that is used in engineering design and analysis is known as the finite element method (FEM), which is a very effective tool. Engineers are able to build better structures with the aid of finite element modeling since it enables them to study complicated forms and predict how the structure will react to various effects. When it comes to constructions that are both complicated and huge in size, this strategy is particularly significant since typical methods are not enough. In recent years, there has been a growing need for analytic methods that are both more exact and quicker. As a consequence, new FEM approaches have been developed that are suitable for complex structures that include a large number of components. This is due to the fact that it is necessary to guarantee safety and optimize designs, both of which often require a great deal of analysis.

Nonlinear finite element research was conducted using the ABAQUS software package V2017. A 3D finite element model was created for the purpose of simulating the nonlinear behavior of composite beams with external post-tensioned tendons in terms of the geometry and material. The finite element models for several components of the concrete–steel composite beam are shown thereafter

3.1. Element Type

The C3D8R solid elements were used to model the slab. The solid element in question is composed of eight nodes, and each of those nodes has three degrees of freedom, which allow for translations in the x, y, and z dimensions, and one reduced integration point situated in the middle of the element. In order to simulate the steel web and flange, an S4R, or quadrilateral shell element, was used. Two-node linear three-dimensional truss elements (T3D2) were used to simulate the tendon’s transversal and longitudinal reinforcement elements. T3D2 is a three-dimensional structural analysis tool in ABAQUS that has two linear beam nodes. It shows straight-line beam members that can support axial, bending, and torsional loads, with six degrees of freedom at each node (three translations and three rotations). This element is appropriate for simulating thin structural components such as trusses, frames, and beams, when deformation and force interactions are important.

3.2. Shear Connectors Modeling

The shear connector model used in this research adheres to the methodology outlined by Wang et al. (2022) [31]. The Cartesian connector, one of several available connectors in ABAQUS, establishes a link between two nodes with three specified local connection directions. It may act like a spring in both the elastic and inelastic domains. The nonlinear connections take their input data from a table that shows forces as a function of displacement (slip). A table of forces vs displacement was generated using the load–slip curve obtained from the push-out test. These data were then utilized to model the behavior of the perfobond shear connections that were tested. The load–slip curve of shear connectors based on the experimental push-out test was shown in Figure 6a. This Cartesian connector is used to simulate the PSC.

3.3. Meshing

To find the optimal mesh size, various refinement levels were evaluated during model assembly. Through a comparison with the experimental data, a 10 mm mesh for the steel beam and a 20 mm mesh for the concrete elements were determined to provide satisfactory results. The 3D model with the appropriate mesh is displayed in Figure 10.

3.4. Contact Properties and Boundary Conditions

The interaction between the longitudinal, transversal reinforcement, and concrete slab was defined using the embedded constraint. This method constrains the nodes of the embedded components inside the host element, assuming perfect bonding between them. The tie constraint was used to simulate the welded connections between the web and bottom flange; it enforces a perfect compatibility between the connected elements. It was also used to simulate contact between the tendons and the extreme plates of the steel beam, where the tendons are anchored. The connection between the stiffeners and web are simulated with the same method. The relationship between the concrete slab and the upper edge of the steel shape was modeled using surface-to-surface contact. A rigid property was presumed in the normal direction, whereas a penalty property was assumed in the tangential direction with a friction value of 0.4. Regarding the boundary conditions, the beams are simply supported.

3.5. Loading Steps

The procedure of applying the load consisted of three steps that preceded one another. The model was first established by defining the boundary conditions that would limit its behavior in the initial step. This was the first phase in the process. In the subsequent phase, the stress was transferred in the tendon in a step-by-step manner by means of the predetermined field command. Through the contact interaction that takes place at the anchoring, stress is transferred from the tendons to the composite arch beam during the contact interaction. The third phase included applying the external load to the beam in a progressive manner.

3.6. Material Modeling

3.6.1. Steel

The stress–strain curve for structural steel is derived from experimental tests as shown in Figure 11. The relationship exhibits linear elasticity until yielding occurs, followed by perfect plasticity from the elastic limit to the onset of strain hardening. The nominal static stress–strain curves were transformed into true stress and logarithmic plastic true strain curves, using following Equations (1) and (2) as given by ABAQUS V2017:

$${\sigma }_{true}=\sigma (1+\epsilon ).$$

(1)

$${\epsilon }_{p{l}_{true}}=\ln (1+\epsilon )-{\displaystyle \raisebox{1ex}{${\sigma }_{true}$}\!\left/ \!\raisebox{-1ex}{$E_0$}\right.}$$

(2)

E₀ represents the initial Young’s modulus, while σ and ε denote the measured nominal (engineering) stress and strain values, respectively.

3.6.2. Concrete

The concrete damage plasticity (CDP) model built-in in the ABAQUS program was used to simulate the concrete slab. The CDP material model is an effective instrument for modeling the nonlinear behavior of concrete under diverse stress conditions. In contrast to more basic material models, CDP integrates specialized features to accurately represent the essential characteristics of concrete behavior: damage plasticity, concrete compression hardening, and concrete tension stiffening. ABAQUS improves the precision of the CDP model by enabling the calibration of its parameters to align with the distinct qualities of the concrete being modeled. This calibration method enables a more accurate depiction of the material’s behavior, resulting in more trustworthy simulations. The failure modes used by the CDP are compressive crushing and tensile cracking. In order to employ the CDP model, it is imperative that we establish the stress–strain relationship for the material based on stress versus inelastic strain. The compressive stress–strain relationship from the model established by Saenz [32] was employed in this research. Furthermore, the degradation of concrete’s stiffness during compression and tension is described by two isotropic damage factors, “d_c” and “d_t”, respectively. The parameters are determined as the concrete is deformed beyond its elastic limit. The damage parameters possess a maximum value of 1, indicating that the material has attained complete damage [33,34,35,36,37]. Equations (3) and (4) provide the damage parameters for compression and tension, respectively.

$$d_t=1-{\displaystyle \frac{{\sigma }_t}{E_0({\epsilon }_t-{\epsilon }_t^{pl})}}$$

(3)

$$d_c=1-{\displaystyle \frac{{\sigma }_c}{E_0({\epsilon }_c-{\epsilon }_c^{pl})}}$$

(4)

The damage parameters are used to convert the inelastic and crack stresses into plastic strains under compression “${\epsilon }_c^{pl}$” and tension “${\epsilon }_t^{pl}$” as follows, Equations (5) and (6).

$${\epsilon }_c^{pl}={\epsilon }^{in}-\left({\displaystyle \frac{d_c}{1-d_c}}\right)\left({\displaystyle \frac{{\sigma }_c}{E_0}}\right)$$

(5)

$${\epsilon }_t^{pl}={\epsilon }^{ck}-({\displaystyle \frac{d_t}{1-d_t}})({\displaystyle \frac{{\sigma }_t}{E_0}})$$

(6)

The mechanical parameters of concrete used in CDP are listed in

Table 1. Parameters of CDP used in the model.

Parameter	Elastic modulus E (MPa)	Poisson’s ratio ᶹυ	Density (Kg/m3)	Eccentricity ε
	39,725	0.2	2400	0.1
	Compressive strength (MPa)	Peak compressive strain ἑc (mm/m)	Tensile strength ft	Bi-axial to uni-axial strength ratio fb0/ft0
	40	2.3	3.86	1.16
	Peak compressive strain ἑc (mm/m)	Tensile strength ft	Dilation angle Ψ	Second stress invariant ratio K
	2.3	3.86	36	0.667

.

3.7. Finite Element Validation

To verify the precision of the numerical model, the beam was simulated. The contrasts between the numerical model and the actual data are shown in Figure 12. The coefficient of determination (R²) was exceptionally high, with values reaching 0.984, demonstrating that the numerical model well-represented the experimental behavior. The modeling approach will be used to conduct a parametric investigation.

4. Parametric Study

In the proposed parametric study, the influence of several factors on the ultimate resistance and serviceability behavior of arch steel concrete composite beams were analyzed. The beams were designed considering the full shear connection, regardless of prestressing. The analyzed parameters were the initial prestressing stress (σ_i), rise-to-span ratio (Ha/L), and beam length (L). The beams were subjected to positive bending moments, simulating four bending tests. The parametric study consists of 35 beams divided into three groups with different span lengths. Each group is divided into three subgroups. The first group consists of 11 beams with a 3000 mm length. The first subgroup of group 1 consists of five beams with Ha/L (rise to span ratio) = 0.05, one reference without a cable and four others with different initial prestress. The second subgroup consists of three beams with Ha/L = 0.1, one without prestress and two with different prestress. The third subgroup consists of three beams with Ha/L = 0.16. The second group consists of 12 beams with a 6000 mm length, divided into three subgroups: the first subgroup has four beams with Ha/L = 0.05, including one reference without prestress and three with varying prestress; the second subgroup has four beams with Ha/L = 0.1, consisting of one unprestressed beam and three with different prestress levels; and the third subgroup has four beams with Ha/L = 0.16, featuring one beam without prestress and three others with increasing prestress. The third group consists of 12 beams with a 9000 mm length and is divided in the same manner as Group 2, with subgroups defined by Ha/L ratios of 0.05, 0.09, and 0.16, each containing one unprestressed beam and three with varying levels of prestress. The characteristics of the models is presented in

Table 2. Characteristics of the models.

Group	Sub Group	Model	L (mm)	Hb (mm)	Hc (mm)	Hs (mm)	Ha (mm)	Hs-Ha (mm)	bc (mm)	Ha/L	tw (mm)	tf (mm)	D (mm)	σi (MPa)
G1	S1	1	3000	285	90	187	135	52	480	0.05	8	8	-	0
		2	3000	285	90	187	135	52	480	0.05	8	8	12	0
		3	3000	285	90	187	135	52	480	0.05	8	8	17	0
		4	3000	285	90	187	135	52	480	0.05	8	8	12	190
		5	3000	285	90	187	135	52	480	0.05	8	8	12	380
	S2	6	3000	438	90	348	296	52	480	0.10	8	8	-	0
		7	3000	438	90	348	296	52	480	0.10	8	8	12	0
		8	3000	438	90	348	296	52	480	0.10	8	8	12	380
	S3	9	3000	633	90	543	491	52	480	0.16	8	8	0	0
		10	3000	633	90	543	491	52	480	0.16	8	8	12	0
		11	3000	633	90	543	491	52	480	0.16	8	8	12	380
G2	S1	12	6000	465	90	375	270	105	960	0.05	8	8	-	0
		13	6000	465	90	375	270	105	960	0.05	8	8	12	0
		14	6000	465	90	375	270	105	960	0.05	8	8	12	190
		15	6000	465	90	375	270	105	960	0.05	8	8	12	380
	S2	16	6000	735	90	645	540	105	960	0.09	8	8	-	0
		17	6000	735	90	645	540	105	960	0.09	8	8	12	0
		18	6000	735	90	645	540	105	960	0.09	8	8	12	190
		19	6000	735	90	645	540	105	960	0.09	8	8	12	380
	S3	20	6000	1155	90	1065	960	105	960	0.16	8	8	-	0
		21	6000	1155	90	1065	960	105	960	0.16	8	8	12	0
		22	6000	1155	90	1065	960	105	960	0.16	8	8	12	190
		23	6000	1155	90	1065	960	105	960	0.16	8	8	12	380
G3	S1	24	9000	696	90	606	450	156	1440	0.05	8	8	-	0
		25	9000	696	90	606	450	156	1440	0.05	8	8	12	0
		26	9000	696	90	606	450	156	1440	0.05	8	8	12	190
		27	9000	696	90	606	450	156	1440	0.05	8	8	12	380
	S2	28	9000	1146	90	1056	900	156	1440	0.10	8	8	-	0
		29	9000	1146	90	1056	900	156	1440	0.10	8	8	12	0
		30	9000	1146	90	1056	900	156	1440	0.10	8	8	12	190
		31	9000	1146	90	1056	900	156	1440	0.10	8	8	12	380
	S3	32	9000	1686	90	1596	1440	156	1440	0.16	8	8	-	0
		33	9000	1686	90	1596	1440	156	1440	0.16	8	8	12	0
		34	9000	1686	90	1596	1440	156	1440	0.16	8	8	12	190
		35	9000	1686	90	1596	1440	156	1440	0.16	8	8	12	380

σ_i = initial prestress; D = diameter of prestress cable; L = beam length.

. In the models, the section of the beams for each group at mid-span was the same. The arch rise varies from one subgroup to another. The details of the beams with and without tendons are presented in Figure 13. In the case of prestressed beams, the stiffeners are thick enough to anchor the tendons without any damage.

4.1. Results and Discussion

The parametric study investigated the following parameters: the initial prestressing stresses, rise-to-span ratio, and beam length. The results are presented and discussed in terms of ultimate load, yield load, and initial stiffness.

4.1.1. Influence of Initial Prestressing Stress

This investigation presents the influence of the initial prestressing stress. The initial prestressing degree is determined by the tendon resistance. Various prestressing stresses were assessed in beams of 3 and 9 m in length.

Effect on Initial Stiffness, Ultimate Load, and Yield Load

The relationship between the applied load and deflection at the midpoint for various prestressing stresses within subgroup S1 of group G1 are illustrated in Figure 14. The inclusion of a cable in Beam 2, without initial prestressing, significantly improved the ultimate load, yield load, and initial stiffness by 40%, 25%, and 23%, respectively, compared to the control Beam 1. The presence of this tie cable effectively mitigated support spreading, reducing it from 20 to 11 mm, thereby enabling the development of both the beam and arch action.

In Beam 3, replacing the 12 mm cable with a 17 mm cable, also without prestressing, further decreased support spreading and enhanced stiffness within the elastic zone. This modification resulted in a 15% increase in ultimate load, while the yield load improved by 6% compared to Beam 2.

For Beam 25, with a length of 9 m and a rise-to-span ratio (Ha/L) of 0.05 (Figure 15), the inclusion of a non-prestressed tendon anchored at the beam ends increased the ultimate load by 178%, enhanced the initial stiffness by 46%, and reduced support spreading at failure by 64% compared to the control Beam 24. In contrast, Beam 26, prestressed to 190 MPa, showed an improved initial stiffness but did not achieve a higher ultimate load compared to Beam 25. Longer beams, being inherently more flexible, experience larger deflections under load. This increased deflection generates higher strains in the prestressing tendons, resulting in a rise in tendon stress as the beam approaches its ultimate capacity. Consequently, the final stresses in the tendons converge to similar levels, regardless of the initial prestress, leading to the beams achieving the same ultimate load capacity despite the differences in the initial prestress.

Effect on Stresses in the Bottom Flange

The tensile stress in Beam 4 within the lower flange decreases from 77 to 0 MPa at a distance of L/6 from the support as shown in Figure 16. This is due to the fact that the post-tensioned tendons produce compressive stresses in the bottom flange prior to loading due to their upward reverse action, which decreases the net tensile stress experienced during loading. In the same context, Figure 17 displays the stress at failure in the bottom flange for Beam 1 (control beam) and for Beam 2 along the length of the beam. It was noticed that Beam 1 exhibited a yield plateau at mid-span at a distance equal 1 m. The steel in Beam 2 has a reserve of capacity since the yield plateau can extend further. Upon the application of the load, the supports of Beam 2 expanded horizontally. The non-prestressed tendons functioned as an arch tie, inhibiting additional spreading. This produced a secondary negative moment at the support, and the tensile stress in the lower steel flange was transformed into compressive stress near the support.

Effect on Increment Stresses in the Tendons

The relation between the applied vertical load and stresses in tendons was displayed in Figure 18. It was observed that, as the initial prestress increased, the slope of the incremental tendon stresses decreased after the yield load. This behavior can be attributed to the fact that a higher initial prestress pre-tensions the tendons to a greater extent, meaning that a larger portion of the tensile forces is already being resisted by the tendons before the external load is applied. As a result, the tendons are less susceptible to rapid stress increases once the yield load is reached. The initial prestress helps distribute the load more evenly across the tendons, reducing the need for them to carry additional tensile forces under load. This leads to a more gradual increase in tendon stress beyond the yield point, reflected in the flatter slope of the stress–strain curve in the post-yield region.

In contrast, when the initial prestress is lower, the tendons carry a larger portion of the tensile forces as the external load increases, resulting in a steeper rise in tendon stress after yielding. Thus, the initial prestress plays a critical role in controlling the rate at which tendon stresses increase beyond the yield load, and higher prestress values contribute to a more stable and controlled response of the beam under load.

The results on the effect of initial prestressing are consistent with those reported by Moreira et al. [22], who found that, for a 4500 mm-long beam, a higher initial prestressing stress led to a higher initial upward deflection, improved serviceability, and enhanced overall resistance when compared to a beam with lower initial prestressing. Furthermore, although the increase in tendon force was initially analogous in both situations, the beam with greater beginning prestressing showed a slower rate of force and an increase beyond the yield moment compared to the beam with lower initial prestressing. Similarly, the findings are consistent with those of Lorenc and Kubica [38], who reported that external prestressing greatly improves both the yield and ultimate load of composite beams exposed to sagging moments. Their findings demonstrated that the addition of prestressing tendons enhanced the ultimate load capacity by 25% when compared to beams without prestressing.

4.1.2. Influence of Rise-to-Span Ratio

Without Tendons

To assess the influence of the rise-to-span ratio on the behavior of the arch composite beam, three different rise-to-span ratios were selected, Ha/L = 0.5, 0.1, and 0.16. First, the behavior of Beam 1, Beam 6, and Beam 9 are compared as shown in Figure 19. They have the same initial stiffness, yield, and ultimate load, although they have different depths. This is due to the three beams having the same cross-section at mid-span and the failure is due to the bending moment in the three beams. The bending capacity are the same and the bending governs their behavior. The three beams behave as straight beams, no arch effect took place, and the beam with the higher depth has a high support spreading.

With Tendons

The load–deflection curve for subgroup S2 and S3 of group G1 are presented in Figure 20 and Figure 21, respectively. It is noticed that the beam with a higher arch-to-depth ratio has the higher support spreading. For Beam 7 with Ha/L = 0.1, the presence of a cable with no prestressing enhances the ultimate capacity by about 160%. The yield load was also improved by about 67% compared to control Beam 6. This significant improvement compared to subgroup S1 results from the fact that the tendons are far from the composite section so the level arm is higher. As the rise-to-depth ratio increases, the beam behaves clearly as a tied arch. For Beam 8 with a post-tension of 380 MPa, the ultimate and yield load were about 180% higher than those of beam 6. The ultimate load for Beam 10 with tendons is 185% higher than Beam 9. For subgroup S3 with a higher arch-to-depth ratio, the improvement is higher in terms of the stiffness and ultimate load.

4.1.3. Influence of Beam Length

Three different beam spans—3, 6, and 9 m—were investigated to assess the impact of the beam length on the behavior of arch composite beams. For all the beams, the tendons were positioned 35 mm above the bottom flange, meaning that, as the height of the beam increases, the distance between the tendons and the composite section also increases. For a rise-to-span ratio Ha/L = 0.05 and post-tensioning of 190 MPa, the ultimate load increased by 43% for the 3 m span compared to the reference beam. For the 6 m span, the increase was 100%, and, for the 9 m span, it was 190%. The increase in the prestressing efficiency is more pronounced in longer beams, even though the cross-sectional strength of the longer beams is higher, a trend not observed in straight beams, as reported by Moreira et al. [22]. This could be attributed to the more significant influence of eccentricity. Figure 22 and Figure 23 show the variation in ultimate load and initial stiffness, respectively, as a function of Ha/L for different beam lengths, with the ultimate load and initial stiffness of the control beam denoted F_uc and I_sc, respectively.

Moreira et al. found that longer beams require more prestressing to achieve equivalent improvements in overall performance and ultimate moment resistance [22]. This enhancement is typically achieved by increasing the tendon eccentricity and adding extra tendons, which better distribute the forces and optimize the beam’s structural behavior and bending resistance. However, the results of this study indicate that post-tensioning is more effective in longer beams, which contrasts with the findings of Moreira. This discrepancy may arise from the higher eccentricity associated with the arch beam design, which enhances the structural performance.

5. Conclusions

This research encompassed the fabrication and evaluation of a completely prestressed arch composite prestressed beam. A numerical model was subsequently introduced and juxtaposed with the experimental results. Parametric research was conducted, encompassing the initial prestressing effects, arch-to-depth ratio, and beam length. The study yielded the following conclusions:

• The numerical model created using ABAQUS successfully simulated the behavior of arch composites prestressed with external tendons, as demonstrated by the comparison between the numerical models and experimental data.
• The presence of tendons even without initial prestressing enhances the serviceability behavior, increases the ultimate load by 40%, and equilibrates the horizontal thrust of the arch.
• The findings indicate that the prestressed tendons enhanced the structural performance by augmenting its ultimate moment resistance by 80%, balancing the horizontal forces, reducing the support spreading, and diminishing the deflection of the arch beams by 60%, in comparison to non-prestressed beams.
• The increase in the initial prestressing stress has a significant effect on the overall behavior of the beams at the elastic stages for the evaluated models compared with control beam. When submitted to higher initial stresses, the tendons suffered lower stress increments due to the loading action. In tendons with lower initial stresses, the increments were higher. The total stresses are similar in both cases, which leads them to resemble the ultimate load.
• For shallower beams to achieve the same gain in overall behavior and an increased ultimate moment resistance, a higher prestressing setting is required than for deep beams.
• The prestress was found to be more effective in longer spans and the incremental prestress in tendons was found to be more remarkable.