Prestressed Steel-Concrete Composite I-Beams with Single and Double Corrugated Web

: Composite steel girders with concrete have been used for many years and advances in structural and fabrication technology have established their optimization. One of the changes in structural steel I-beams during the past few years has been the availability of web corrugation. The economic design of steel girders normally requires thin webs. Moreover, using externally prestressed tendons as a strengthening technique controls deﬂections and stresses. However, this strengthening technique causes shear buckling of the steel beams. In this study, the ﬂexural behavior of externally prestressed composite steel-concrete I-beams with a single and double corrugated web was experimentally and numerically investigated. Three simply supported prestressed steel-concrete composite I-beams with single corrugated web (SCW) and double corrugated web (DCW) were tested under four-point loading. The tested beams were externally prestressed by using straight tendons along the full length. The experimental results showed that using SCW was more efﬁcient in shear buckling resistance than DCW with the same equivalent web thickness. The ABAQUAS package was used to simulate the nonlinear behavior of the tested beams. The developed model was validated against the experimental results to carry out a parametric study in order to investigate the effect of various parameters on the behavior of the composite beams with SCW and DCW. Using stiffeners at the loading points as deviators to maintain the prestressed tendon positions increased the beam capacity and improved the beam performance.


Introduction
Steel-concrete composite beams present a popular and economical form of construction in both buildings and bridges. Advances in structural and fabrication technology have established the optimization of steel girders. The idea of using corrugated webs in steel structures to increase buckling resistance was first tried out as early as 1924, but due to difficulties in fabrication, its use was limited until further technical development [1,2]. As part of a national French project, a search for lighter and stronger girders took place, which could be achieved by external prestressing and corrugated web (CW). A large-scale test model was built by Campenon Bernard in 1983 and was externally prestressed. Afterwards, they built the first ever corrugated steel web bridge, Cognac Bridge, which was constructed in France between June 1985 and July 1986 [2,3]. Many advantages can be gained from using external prestressing [4]. Prestressing can increase the beam capacity and reduce the serviceability deflection. It can also improve the behavior of the beam against fatigue and increase the elastic behavior zone. The first ever corrugated steel-built web bridge was the stiffness of the prestressed composite beams increased by about 20% to 25% compared with the non-prestressed. Lee et al. [20] studied two new specimens to investigate the effect of the welding method and concluded that the use of partial welding can reduce time and cost and give the required performance, compared with gross welding. Xu, Zhang [21] investigate the reliability of the ABAQUS finite element model that was used to simulate the external prestressed concrete composite beam with CW after its verification in the work of Song, Zhang [22], who found that the consideration of secondary effects for externally prestressed tendons in the calculation is irrational. Motlagh and Rahai investigated numerically the long-term losses of prestressed composite beams with CW. Decreasing the corrugation depth could decrease the prestressing losses [23]. The structural performance and cost-effectiveness of a composite beam with CSW for an extradosed cable-stayed bridge were investigated [24]. Three different prestressed steel-concrete composite beams with corrugated web were investigated experimentally and numerically by Zhou et al. [25] under fire conditions, the first beam without encased web, the second encased with concrete from one side, and the third encased on two sides. The failure of the first beam was the buckling of the web. The beam with one-sided concrete between the flanges experienced horizontal deflection, and shear centers move in the direction of the coldest side of the web. Numerical analyses showed that the failure appears to have been caused by cable strands rupturing inside of concrete enclosure.
An overview of the different contributions of different types of prestressed composite steel-concrete I-beams that have been investigated in the literature is presented in Table 1.
In light of the previous discussion, ample research has been focused on the use of composite flat web beams and their behavior under external prestressing, but utilizing corrugated web in buildings and bridges has also increased in recent years. There is also an urgent need to strengthen these types of beams, which can be achieved by using external prestressing. A small amount of research has been conducted on the full and partially encased prestressed I-beam with CW, based on information available to the authors. Additionally, no studies have investigated the behavior of the externally prestressed steel Ibeam with a single or double corrugated web. Therefore, the flexural behavior of externally prestressed composite steel-concrete I-beams with a single and double corrugated web was experimentally and numerically investigated in this paper. Three simply supported prestressed steel-concrete composite I-beams with single corrugated web (SCW) and double corrugated web (DCW) were tested under four-point loading. The tested beams were externally prestressed by using straight tendons along the full length. The ABAQUAS package was used to simulate the nonlinear behavior of the tested beams. The developed model was validated against experimental results to carry out a parametric study to investigate the effect of various parameters on the behavior of the composite beams with SCW and DCW.

Experimental Test Program
Three simply supported prestressed steel-concrete composite I-beams with SCW and DCW were tested in this experimental program. The tested beams were externally prestressed by using straight tendons along the full length. The experimental program was conducted at the Housing and Building National Research Center (HBRC), Egypt. Table 2 lists a summary of the tested beams.

Test Specimens and Fabrication
As shown in Figure 1, the total length of the beams was 4150 mm and the clear span was 3900 mm. The overall height of the beams was 316 mm. The beam with DCW was designed to have an equivalent thickness and corrugation depth to the beams with SCW.
The top and bottom flanges of the steel beams had a total length of 4100 mm and a thickness of 8 mm. The widths of these flanges were 180 mm and 200 mm, respectively. The dimensions of the single and double corrugated web plates were 4100 mm in outer length and 220 mm in depth. The plate thicknesses were 6 mm and 3 mm for the SCW and DCW, respectively. Figure 2 illustrates the geometry and corrugation dimensions of the single and double corrugated webs. The nominal and measured thicknesses of the different steel parts are listed in Table 3. Two pairs of vertical stiffeners with thicknesses of 25 mm and 15 mm were welded to the steel web of each beam at the beam ends and support locations, respectively. Holes with a 20 mm diameter were created in each of the vertical stiffeners at the intersection with the prestressed strands. Moreover, horizontal stiffeners with a 10 mm thickness were welded between the vertical stiffeners. The steel I-beam parts were welded and assembled in a workshop and then the concrete slabs were cast and cured in the laboratory, as shown in Figure 3.
The concrete slabs were compositely connected to the steel beams using high-strength bolts of grade 8.8 as shear connectors (see Figure 3). These bolts were 12 mm in diameter and 50 mm in height. The shear connectors were welded to the top steel flange at the interface with the concrete slab in two rows with transverse and longitudinal spacing of 80 mm and 200 mm, respectively. The Shear connectors were designed to obtain a full interaction between the concrete slab and steel beam. The concrete slabs of dimensions 4100 mm in length, 80 mm in thickness, and 600 mm in width were reinforced with steel rebars of 10 mm and 8 mm in diameter (see Figure 1b).

Test Specimens and Fabrication
As shown in Figure 1, the total length of the beams was 4150 mm and the clear span was 3900 mm. The overall height of the beams was 316 mm. The beam with DCW was designed to have an equivalent thickness and corrugation depth to the beams with SCW. The top and bottom flanges of the steel beams had a total length of 4100 mm and a thickness of 8 mm. The widths of these flanges were 180 mm and 200 mm, respectively. The dimensions of the single and double corrugated web plates were 4100 mm in outer length and 220 mm in depth. The plate thicknesses were 6 mm and 3 mm for the SCW and DCW, respectively. Figure 2 illustrates the geometry and corrugation dimensions of the single and double corrugated webs. The nominal and measured thicknesses of the different steel parts are listed in Table 3. Two pairs of vertical stiffeners with thicknesses of 25 mm and 15 mm were welded to the steel web of each beam at the beam ends and support locations, respectively. Holes with a 20 mm diameter were created in each of the vertical stiffeners at the intersection with the prestressed strands. Moreover, horizontal stiffeners with a 10 mm thickness were welded between the vertical stiffeners. The steel I-beam parts were welded and assembled in a workshop and then the concrete slabs were cast and cured in the laboratory, as shown in Figure 3.   The concrete slabs were compositely connected to the steel beams using highstrength bolts of grade 8.8 as shear connectors (see Figure 3). These bolts were 12 mm in diameter and 50 mm in height. The shear connectors were welded to the top steel flange at the interface with the concrete slab in two rows with transverse and longitudinal spacing of 80 mm and 200 mm, respectively. The Shear connectors were designed to obtain a full interaction between the concrete slab and steel beam. The concrete slabs of dimensions 4100 mm in length, 80 mm in thickness, and 600 mm in width were reinforced with steel rebars of 10 mm and 8 mm in diameter (see Figure 1b).   The top and bottom flanges of the steel beams had a total length of 4100 mm and a thickness of 8 mm. The widths of these flanges were 180 mm and 200 mm, respectively. The dimensions of the single and double corrugated web plates were 4100 mm in outer length and 220 mm in depth. The plate thicknesses were 6 mm and 3 mm for the SCW and DCW, respectively. Figure 2 illustrates the geometry and corrugation dimensions of the single and double corrugated webs. The nominal and measured thicknesses of the different steel parts are listed in Table 3. Two pairs of vertical stiffeners with thicknesses of 25 mm and 15 mm were welded to the steel web of each beam at the beam ends and support locations, respectively. Holes with a 20 mm diameter were created in each of the vertical stiffeners at the intersection with the prestressed strands. Moreover, horizontal stiffeners with a 10 mm thickness were welded between the vertical stiffeners. The steel I-beam parts were welded and assembled in a workshop and then the concrete slabs were cast and cured in the laboratory, as shown in Figure 3.   The concrete slabs were compositely connected to the steel beams using highstrength bolts of grade 8.8 as shear connectors (see Figure 3). These bolts were 12 mm in diameter and 50 mm in height. The shear connectors were welded to the top steel flange at the interface with the concrete slab in two rows with transverse and longitudinal spacing of 80 mm and 200 mm, respectively. The Shear connectors were designed to obtain a full interaction between the concrete slab and steel beam. The concrete slabs of dimensions After reaching the full strength of the concrete slabs, the prestressing forces were applied to the composite beams. Each composite beam was designed to have two seven-wire low relaxation strands with 5500 mm in length, 15.24 mm in diameter, and 140 mm 2 as the nominal area. The tendons were anchored to the end stiffener plates and prestressed to an initial prestressing force of N i = 90 kN. This level of prestressing was chosen so that the tensile stress in the top concrete fiber does not exceed the allowable tensile strength of concrete according to ACI [26]. The prestressing force was applied using a hydraulic jack with a capacity of 200 kN by Specialized Construction Company, Egypt (see Figure 4). In beam SW4150-S, each of the tendons was restrained by the two stiffener plates under the loading points (Saddle Points, S) (see Table 2). However, the prestressed tendons were free and there were no saddle points in the other two beams (SW4150-N and DW4150-N).
Buildings 2023, 13, x FOR PEER REVIEW 6 of 22 nominal area. The tendons were anchored to the end stiffener plates and prestressed to an initial prestressing force of Ni = 90 kN. This level of prestressing was chosen so that the tensile stress in the top concrete fiber does not exceed the allowable tensile strength of concrete according to ACI [26]. The prestressing force was applied using a hydraulic jack with a capacity of 200 kN by Specialized Construction Company, Egypt (see Figure 4). In beam SW4150-S, each of the tendons was restrained by the two stiffener plates under the loading points (Saddle Points, S) (see Table 2). However, the prestressed tendons were free and there were no saddle points in the other two beams (SW4150-N and DW4150-N).

Steel
Coupon specimens were cut out from the flanges and corrugated web plates of the steel beams and were tested to obtain the mechanical properties of steel according to EN 1993-1-2 [27]. Moreover, tension tests were conducted to obtain the mechanical properties of the steel rebars according to EN 1992-1-1 [28]. The material properties of the tendons were provided by the manufacturer (United Wires Company Elsewedy, Egypt). The mechanical properties of the different steel components are summarized in Table 4.

Concrete
Portland Pozzolana cement grade 42.5 was used in the concrete mix. Locally available crushed coarse and fine aggregates were used. Clean drinking tap water was used for the casting and curing of the tested specimens. A superplasticizer additive was used in the mixture to reduce the required water content. The concrete mix proportions are listed in Table 5. Nine concrete cubes, 150 mm × 150 mm × 150 mm, were prepared and tested according to BS EN 12390-3 [29]. The cubic compressive strength results were 50.1 MPa, 49.5 MPa, and 41.7 MPa for the beams SW4150-N, DW4150-N, and SW4150-S.

Steel
Coupon specimens were cut out from the flanges and corrugated web plates of the steel beams and were tested to obtain the mechanical properties of steel according to EN 2 January 1993 [27]. Moreover, tension tests were conducted to obtain the mechanical properties of the steel rebars according to EN 1992-1-1 [28]. The material properties of the tendons were provided by the manufacturer (United Wires Company Elsewedy, Cairo, Egypt). The mechanical properties of the different steel components are summarized in Table 4.

Concrete
Portland Pozzolana cement grade 42.5 was used in the concrete mix. Locally available crushed coarse and fine aggregates were used. Clean drinking tap water was used for the casting and curing of the tested specimens. A superplasticizer additive was used in the mixture to reduce the required water content. The concrete mix proportions are listed in Table 5. Nine concrete cubes, 150 mm × 150 mm × 150 mm, were prepared and tested according to BS EN 12390-3 [29]. The cubic compressive strength results were 50.1 MPa, 49.5 MPa, and 41.7 MPa for the beams SW4150-N, DW4150-N, and SW4150-S.

Instrumentation
Three linear variable differential transducers (LVDTs) were installed on each beam. The first LVDT was installed at the interface between the concrete slab and steel beam to measure the relative slippages between the two parts. The second and third LVDTs were installed at the middle span to measure the vertical and out of plane displacements, as shown in Figure 5a. Strain gauges were installed on various locations of the steel web and flanges at the mid-span of each tested beam, as shown in Figure 5b. The incremental prestressing forces in each of the strands were monitored by strain gauges attached to the tendons during the test.

Instrumentation
Three linear variable differential transducers (LVDTs) were installed on each beam. The first LVDT was installed at the interface between the concrete slab and steel beam to measure the relative slippages between the two parts. The second and third LVDTs were installed at the middle span to measure the vertical and out of plane displacements, as shown in Figure 5a. Strain gauges were installed on various locations of the steel web and flanges at the mid-span of each tested beam, as shown in Figure 5b. The incremental prestressing forces in each of the strands were monitored by strain gauges attached to the tendons during the test.  Figure 6 shows the upward camber while applying the initial prestressing force for the tested beam SW4150-S. The initial prestressing force was applied alternately in four stages for each tendon to minimize the undesired torsional stresses Table 6 lists the effective initial prestressing force versus the initial upward camber in each beam.  Figure 6 shows the upward camber while applying the initial prestressing force for the tested beam SW4150-S. The initial prestressing force was applied alternately in four stages for each tendon to minimize the undesired torsional stresses Table 6 lists the effective initial prestressing force versus the initial upward camber in each beam.

Tendon Eccentricity
As the tendons are placed outside the composite beam, the connection to the beam will be through deviators along the beam length and anchorages at the beam end. Between such points, the tendons are free to move up and down relative to the beam cross-section. If the deviators are not used, the second-order effects due to changing tendon eccentricity during deflection lead to a lower load-carrying capacity [30]. The use of deviators along the span of the beams can effectively reduce those effects. The main reason for using deviators is to maintain the tendon position with respect to the steel beam section during loading and to avoid the p-δ effect.
The change in tendon eccentricities was explored by measuring the distance from the top surface of the steel flange and the center of the tendons (e f ) at the mid-span. The profile of the prestressed tendons was straight and anchored only at the beam ends of beams DW4150-N and SW4150-N. The tendons were free to move up or down relative to the beam cross-section (see Figure 7). The value of e f changed during the test when the beams were deflected downward while the tendons were straight. On the other hand, the prestressed tendons were restrained by two stiffener plates under the loading points in beam SW4150-S to maintain the eccentricity in place during the deflection of the tested beam.

Tendon Eccentricity
As the tendons are placed outside the composite beam, the connection to the beam will be through deviators along the beam length and anchorages at the beam end. Between such points, the tendons are free to move up and down relative to the beam cross-section. If the deviators are not used, the second-order effects due to changing tendon eccentricity during deflection lead to a lower load-carrying capacity [30]. The use of deviators along the span of the beams can effectively reduce those effects. The main reason for using deviators is to maintain the tendon position with respect to the steel beam section during loading and to avoid the p-δ effect.
The change in tendon eccentricities was explored by measuring the distance from the top surface of the steel flange and the center of the tendons (ef) at the mid-span. The profile of the prestressed tendons was straight and anchored only at the beam ends of beams DW4150-N and SW4150-N. The tendons were free to move up or down relative to the beam cross-section (see Figure 7). The value of ef changed during the test when the beams were deflected downward while the tendons were straight. On the other hand, the prestressed tendons were restrained by two stiffener plates under the loading points in beam SW4150-S to maintain the eccentricity in place during the deflection of the tested beam.   Figure 6. Stages of introducing the initial prestressing force for beam SW4150-S.

Tendon Eccentricity
As the tendons are placed outside the composite beam, the connection to the beam will be through deviators along the beam length and anchorages at the beam end. Between such points, the tendons are free to move up and down relative to the beam cross-section. If the deviators are not used, the second-order effects due to changing tendon eccentricity during deflection lead to a lower load-carrying capacity [30]. The use of deviators along the span of the beams can effectively reduce those effects. The main reason for using deviators is to maintain the tendon position with respect to the steel beam section during loading and to avoid the p-δ effect.
The change in tendon eccentricities was explored by measuring the distance from the top surface of the steel flange and the center of the tendons (ef) at the mid-span. The profile of the prestressed tendons was straight and anchored only at the beam ends of beams DW4150-N and SW4150-N. The tendons were free to move up or down relative to the beam cross-section (see Figure 7). The value of ef changed during the test when the beams were deflected downward while the tendons were straight. On the other hand, the prestressed tendons were restrained by two stiffener plates under the loading points in beam SW4150-S to maintain the eccentricity in place during the deflection of the tested beam.

Deformations and Modes of Failure
The load vs. deflection relationships for the tested beams are compared in Figure 8. First, the beams with SCW showed better behavior and larger capacity over the beam with DCW. According to these relationships, the initial upward movement of the prestressed beams was considered the same and their behaviors were very close during the elastic region. The beam SW4150-N obtained a higher yielding load in comparison to beam SW4150-S. However, the ultimate load capacities were the same for the two beams. The peak loads for the tested beams were 362.3 kN, 379.1 kN, and 383.2 kN for beams DW4150-N, SW4150-S, and SW4150-N, respectively.
The beam with double web DW4150-N failed due to shear buckling near the hinged support accompanied with separation and cracking due to tension at the bottom face of the concrete slab (see Figure 9a). Due to concrete separation, the concrete slab started to behave away from the steel beam and subsequently tension cracks were formed at the bottom surface. For beam SW4150-S, longitudinal cracks were observed on the bottom surface of the concrete slab starting at the loading level of 330 kN. The concentrations of the longitudinal shear forces at the shear connectors led to higher levels of damage in concrete around the headed stud connectors and formed such cracks during loading. The failure mode was local buckling in the steel top flange and concrete slab crushing, as shown in Figure 9b. The beam SW4150-N failed due to crushing in the concrete slab near the loading points accompanied by local buckling in the steel top flange (see Figure 9c). The local buckling mode of failure caused the tested beams to exhibit the same behavior and a slight difference in the load-deflection curves was obtained.

Deformations and Modes of Failure
The load vs. deflection relationships for the tested beams are compared in Figure 8. First, the beams with SCW showed better behavior and larger capacity over the beam with DCW. According to these relationships, the initial upward movement of the prestressed beams was considered the same and their behaviors were very close during the elastic region. The beam SW4150-N obtained a higher yielding load in comparison to beam SW4150-S. However, the ultimate load capacities were the same for the two beams. The peak loads for the tested beams were 362.3 kN, 379.1 kN, and 383.2 kN for beams DW4150-N, SW4150-S, and SW4150-N, respectively.
The beam with double web DW4150-N failed due to shear buckling near the hinged support accompanied with separation and cracking due to tension at the bottom face of the concrete slab (see Figure 9a). Due to concrete separation, the concrete slab started to behave away from the steel beam and subsequently tension cracks were formed at the bottom surface. For beam SW4150-S, longitudinal cracks were observed on the bottom surface of the concrete slab starting at the loading level of 330 kN. The concentrations of the longitudinal shear forces at the shear connectors led to higher levels of damage in concrete around the headed stud connectors and formed such cracks during loading. The failure mode was local buckling in the steel top flange and concrete slab crushing, as shown in Figure 9b. The beam SW4150-N failed due to crushing in the concrete slab near the loading points accompanied by local buckling in the steel top flange (see Figure 9c). The local buckling mode of failure caused the tested beams to exhibit the same behavior and a slight difference in the load-deflection curves was obtained.   Figure 10 presents the relationships between the incremental increase in the prestressing force and vertical deformation of the tested beams. The maximum prestressing forces were 181 kN, 164 kN and 148 kN for the beams SW4150-S, SW4100-N and DW4150-N; respectively. The highest level of prestressing force was recorded in the tendons of beam SW4150-S where the eccentricity was constant and maintained through the loading stages. Maintaining the tendon position with respect to the steel beam section during loading resulted in more stretching and then higher incremental increase in the prestressing force.

Slippages, out of Plane Deflections, and Strains
The relation between the applied load and relative slippage between the concrete slab and steel beam for the tested beams is illustrated in Figure 11a. The slippage for the beams was very similar during loading up to the yield of the steel beam, and then the slippage for the beam SW4150-S became higher than that for the other beams up to ultimate load. The slippages at the ultimate loads were 13 mm, 1.  Figure 10 presents the relationships between the incremental increase in the prestressing force and vertical deformation of the tested beams. The maximum prestressing forces were 181 kN, 164 kN and 148 kN for the beams SW4150-S, SW4100-N and DW4150-N; respectively. The highest level of prestressing force was recorded in the tendons of beam SW4150-S where the eccentricity was constant and maintained through the loading stages. Maintaining the tendon position with respect to the steel beam section during loading resulted in more stretching and then higher incremental increase in the prestressing force.    Figure 10 presents the relationships between the incremental increase in the prestressing force and vertical deformation of the tested beams. The maximum prestressing forces were 181 kN, 164 kN and 148 kN for the beams SW4150-S, SW4100-N and DW4150-N; respectively. The highest level of prestressing force was recorded in the tendons of beam SW4150-S where the eccentricity was constant and maintained through the loading stages. Maintaining the tendon position with respect to the steel beam section during loading resulted in more stretching and then higher incremental increase in the prestressing force.  The applied load-strain relationships for the tested beams are shown in Figure 12. The effect of the prestressed tendons generated compressive strains in the bottom steel flange before loading owing to its upward reverse effect, which reduced the net tensile strain induced during loading. which stabilized the beam at the loading region. The out of plane deflections (d out) at failure were 1.27 mm, 15.1 mm, and 24.5 mm for the beams DW4150-N, SW4150-N, and SW4150-S; respectively.

Incremental Increases in the Prestressing Force
The applied load-strain relationships for the tested beams are shown in Figure 12. The effect of the prestressed tendons generated compressive strains in the bottom steel flange before loading owing to its upward reverse effect, which reduced the net tensile strain induced during loading. which stabilized the beam at the loading region. The out of plane deflections (d out) at failure were 1.27 mm, 15.1 mm, and 24.5 mm for the beams DW4150-N, SW4150-N, and SW4150-S; respectively. The applied load-strain relationships for the tested beams are shown in Figure 12. The effect of the prestressed tendons generated compressive strains in the bottom steel flange before loading owing to its upward reverse effect, which reduced the net tensile strain induced during loading.

FE Models
ABAQUAS [31] package was used to simulate the nonlinear behavior of the tested beams.

Element Selection
The model has ten parts. The steel beam web and flanges were modeled using linear quadrilateral shell elements (S4R). Triangular shell elements (S3) were used in the steel flanges at the intersections with the inclined parts of the steel web. The prestressed tendons, anchors, and concrete slab were simulated by linear hexahedral elements (C3D8R). The shear connectors and steel rebars were modeled linear beam element (B31) and truss elements (T3D2), respectively. Figure 13 shows the various element types used in the FE model.

FE Models
ABAQUAS [31] package was used to simulate the nonlinear behavior of the tested beams.

Element Selection
The model has ten parts. The steel beam web and flanges were modeled using linear quadrilateral shell elements (S4R). Triangular shell elements (S3) were used in the steel flanges at the intersections with the inclined parts of the steel web. The prestressed tendons, anchors, and concrete slab were simulated by linear hexahedral elements (C3D8R). The shear connectors and steel rebars were modeled linear beam element (B31) and truss elements (T3D2), respectively. Figure 13 shows the various element types used in the FE model. The model has ten parts. The steel beam web and flanges were modeled using linear quadrilateral shell elements (S4R). Triangular shell elements (S3) were used in the steel flanges at the intersections with the inclined parts of the steel web. The prestressed tendons, anchors, and concrete slab were simulated by linear hexahedral elements (C3D8R). The shear connectors and steel rebars were modeled linear beam element (B31) and truss elements (T3D2), respectively. Figure 13 shows the various element types used in the FE model.

Part Assembly and Interaction
The sketched corrugated web with stiffeners, shear connectors and top and bottom steel flanges were assembled in the position and then merged into a new part called steel beam. The prestressed tendons and anchors were merged into one part. The embedded region constraint was used to simulate the interaction between the concrete slabs (host region) and both the slab reinforcement and studs (embedded region). The surface-tosurface contact was used to simulate the interaction between the concrete slab and steel beam, the loading beam and concrete slab, and the prestressed tendons with stiffeners. The tie constraint was used to model the interaction between the anchors and the end stiffeners of the steel beams. The rigid body constraint was applied between the loading beam and reference point at the top center of this beam.

Part Assembly and Interaction
The sketched corrugated web with stiffeners, shear connectors and top and bottom steel flanges were assembled in the position and then merged into a new part called steel beam. The prestressed tendons and anchors were merged into one part. The embedded region constraint was used to simulate the interaction between the concrete slabs (host region) and both the slab reinforcement and studs (embedded region). The surface-tosurface contact was used to simulate the interaction between the concrete slab and steel beam, the loading beam and concrete slab, and the prestressed tendons with stiffeners. The tie constraint was used to model the interaction between the anchors and the end stiffeners of the steel beams. The rigid body constraint was applied between the loading beam and reference point at the top center of this beam.

Boundary Conditions and Steps of Solution
The analyzed beams were supported by two supports (hinge and roller supports). For the hinged support, the three translation degrees of freedom were restrained, whereas the two translation degrees of freedom were restrained in the roller supports (Y and Z directions). Two solution steps were used in the analysis. The first step was used to apply the prestressing force, whereas step two was to simulate the loading stage. The loads were applied as displacements, which were assigned to the reference point on the loading beam.

Steel Model
The nominal values of stresses and strains, which were obtained from the tension coupon tests, were translated to true stress and logarithmic strain that were used by ABQUAS. The stress-strain relationship of steel parts was established using the bi-linear elastic-plastic model.

Concrete Model
The concrete damage plasticity (CDP) model was adopted in this analysis. Two mechanisms of concrete failure were considered: tensile cracking and compressive crushing [32][33][34]. The inelastic strain in compression and cracking strain in tension were used instead of the total strains that were calculated from the concrete constitutive models. The damage parameters that were used in simulation were the program default values except for the dilation angle of 32 • and viscosity parameters of 0.001. These adopted values provided accurate results and reduced the time of the analyses without any convergence problems.
The linear elastic, perfectly plastic stress-strain curve that was used by Kachlakev et al. [35] was selected to model the stress-strain curve of concrete in compression. In this relationship, the descending portion was ignored. The simplified model consists of a few points, as shown in Figure 14. The first point was located at 0.3 of the compressive strength (f c ' ) and the corresponding strain was calculated by Equation (1). Equation (2) was used to calculate the stress at points (2), (3), and (4) for any corresponding strain (ε). Point (5) is located at the compressive strength and the strain (ε o ) calculated according to Equation (3). The concrete modulus of elasticity (E c ) was calculated according to the ACI-318 code [36].

Validation of the FE Results
Three finite element models were analyzed to validate the tested beams in terms of the deformation, prestressing force, and mode of failure as shown in Figures 15-17 and Table 7. Figure 15 shows that the FE results agreed closely with the experimental results for the load-deflection responses. In the linear range, the FE load-deflection response coincides with that from the experimental results. When the load-deflection curve transitioned from linear to nonlinear, the yielding of the beam began. After this point, a slight difference in stiffness was obtained owing to the difference in the behavior of the shear connection between the concrete slab and steel beam in the experimental and FE model, which caused a difference in slippage behavior. Moreover, this difference in behavior could be attributed to the used constitutive models for materials and the full bond assumed between the concrete and steel rebars. The descending portion of the load-deflection curves was not well represented because of the assumed constitutive model of concrete. The descending portion of the stress-strain curve was not simulated and subsequently affected the analyzed beam behavior after reaching the peak loads. There was an un-convergence issue that stopped the solution at this loading level. The load step size was reduced and the element size was refined to avoid this problem. However, the solution continued until the beam showed good deformation behavior relative to the experimental results.
As listed in Table 7, the maximum loads predicted by the FE model were 382.5 kN, 379 kN, and 362.75 kN, which showed a −0.9%, +9.7%, and +1.2% difference to the experimental load capacities, for beams SW4150-N, SW4150-S, and DW4150-N, respectively. Figure 16 shows comparison of deflection versus prestressing force in the prestressed tendons between the experimental and numerical results. The two curves for each beam were offset from the origin by an initial prestressing force of 90 kN. The prestressing force increased as the loading on the beam increased. Figure 17 shows the shear buckling of the beam DW4150-N in both experimental and finite element models. The developed FE models were able to capture the experimental mode of failure as well as the flexural behavior of prestressed steel-concrete composite beams with single and double corrugated web. Therefore, the verified model was used to conduct a parametric study to investigate different parameters that affect the beam behavior.

Validation of the FE Results
Three finite element models were analyzed to validate the tested beams in terms of the deformation, prestressing force, and mode of failure as shown in Figures 15-17 and Table 7. Figure 15 shows that the FE results agreed closely with the experimental results for the load-deflection responses. In the linear range, the FE load-deflection response coincides with that from the experimental results. When the load-deflection curve transitioned from linear to nonlinear, the yielding of the beam began. After this point, a slight difference in stiffness was obtained owing to the difference in the behavior of the shear connection between the concrete slab and steel beam in the experimental and FE model, which caused a difference in slippage behavior. Moreover, this difference in behavior could be attributed to the used constitutive models for materials and the full bond assumed between the concrete and steel rebars. The descending portion of the load-deflection curves was not well represented because of the assumed constitutive model of concrete. The descending portion of the stress-strain curve was not simulated and subsequently affected the analyzed beam behavior after reaching the peak loads. There was an un-convergence issue that stopped the solution at this loading level. The load step size was reduced and the element size was refined to avoid this problem. However, the solution continued until the beam showed good deformation behavior relative to the experimental results.
As listed in Table 7, the maximum loads predicted by the FE model were 382.5 kN, 379 kN, and 362.75 kN, which showed a −0.9%, +9.7%, and +1.2% difference to the experimental load capacities, for beams SW4150-N, SW4150-S, and DW4150-N, respectively. Figure 16 shows comparison of deflection versus prestressing force in the prestressed tendons between the experimental and numerical results. The two curves for each beam were offset from the origin by an initial prestressing force of 90 kN. The prestressing force increased as the loading on the beam increased. Figure 17 shows the shear buckling of the beam DW4150-N in both experimental and finite element models. The developed FE models were able to capture the experimental mode of failure as well as the flexural behavior of prestressed steel-concrete composite beams with single and double corrugated web. Therefore, the verified model was used to conduct a parametric study to investigate different parameters that affect the beam behavior.

Parametric Study
The investigated parameters included the effect of the initial prestressing force, deviators to maintain the tendon position, stiffness of the steel beam, and using double corrugated web. The same material properties and beam dimensions in the experimental work were used in this parametric study.

Effect of the Initial Prestressing Force
The effect of using different initial prestressing force levels of 0 kN, 30 kN, 60 kN, 80 kN, 100 kN, and 120 kN was explored on the composite beam SW4150-N. Moreover, the steel cross-section parameters such as the steel flange width, web thickness, and flange thickness were investigated at these levels of prestressing force. The beams were compared with a conventional beam without any tendons. Figure 18 and Table 8 illustrate the effect of the initial prestressing force level (Ni) on the ultimate capacity (Pult) as a ratio to

Parametric Study
The investigated parameters included the effect of the initial prestressing force, deviators to maintain the tendon position, stiffness of the steel beam, and using double corrugated web. The same material properties and beam dimensions in the experimental work were used in this parametric study.

Effect of the Initial Prestressing Force
The effect of using different initial prestressing force levels of 0 kN, 30 kN, 60 kN, 80 kN, 100 kN, and 120 kN was explored on the composite beam SW4150-N. Moreover, the steel cross-section parameters such as the steel flange width, web thickness, and flange thickness were investigated at these levels of prestressing force. The beams were compared with a conventional beam without any tendons. Figure 18 and Table 8 illustrate the effect of the initial prestressing force level (Ni) on the ultimate capacity (Pult) as a ratio to

Parametric Study
The investigated parameters included the effect of the initial prestressing force, deviators to maintain the tendon position, stiffness of the steel beam, and using double corrugated web. The same material properties and beam dimensions in the experimental work were used in this parametric study.

Effect of the Initial Prestressing Force
The effect of using different initial prestressing force levels of 0 kN, 30 kN, 60 kN, 80 kN, 100 kN, and 120 kN was explored on the composite beam SW4150-N. Moreover, the steel cross-section parameters such as the steel flange width, web thickness, and flange thickness were investigated at these levels of prestressing force. The beams were compared with a conventional beam without any tendons. Figure 18 and Table 8 illustrate the effect of the initial prestressing force level (Ni) on the ultimate capacity (Pult) as a ratio to

Parametric Study
The investigated parameters included the effect of the initial prestressing force, deviators to maintain the tendon position, stiffness of the steel beam, and using double corrugated web. The same material properties and beam dimensions in the experimental work were used in this parametric study.

Effect of the Initial Prestressing Force
The effect of using different initial prestressing force levels of 0 kN, 30 kN, 60 kN, 80 kN, 100 kN, and 120 kN was explored on the composite beam SW4150-N. Moreover, the steel cross-section parameters such as the steel flange width, web thickness, and flange thickness were investigated at these levels of prestressing force. The beams were compared with a conventional beam without any tendons. Figure 18 and Table 8 illustrate the effect of the initial prestressing force level (N i ) on the ultimate capacity (P ult ) as a ratio to the capacity of the conventional composite beam (P o ) and incremental increase in the prestressing force (∆ N). To consider the effect of the steel flange width beside the initial prestressing level, three different widths of 200 mm, 240 mm, and 280 mm were investigated (see Figure 18a). The results revealed that effectiveness of increasing the external prestressing force in improving the beam capacity decreased as the steel flange width increased. However, the incremental increase in the prestressing force was reduced. When the steel flange width increased, the neutral axis (NA) approached to the bottom flange of the steel beam and the eccentricity (e) between the prestressed tendons and the NA decreased. Consequently, the prestressed tendons can be used effectively when they are moved away from the NA or increase the initial prestressing force to give the same percentage increase in the ultimate load.
Changing the steel web thickness did not change the position of the NA. Therefore, a slight effect on the values of the beam capacity and ∆N was obtained. Figure 18b shows that beams with web thicknesses of 6 mm and 7 mm exhibited nearly identical behavior with different N i values. The web thickness of 5 mm provided a better performance at N i of 0 kN. The drop in the beam capacity occurred along with increased N i due to the premature occurrence of web buckling. The beams at a web thickness of 4 mm failed at a lower value of P ult, as web buckling occurred with all levels of the N i and the maximum value of the %P ult /P o increased by only 11.43% at N i of 120 kN. However, this improvement was 23.3% for the beam with 6 mm thickness.
Three different bottom flange thicknesses of 8 mm, 10 mm, and 12 mm were investigated with two different web thicknesses of 8 mm and 10 mm, as shown in Figure 18c. Increasing the flange thickness decreased the values of the ∆N and % P ult /P o due to changing the position of the NA.

Effect of Deviators to Maintain the Tendon Position
The effect of deviators to maintain the tendon position with respect to the steel beam section during loading was introduced by comparing the stiffened beams at the loading points (SW-S) and the beams without these stiffeners (SW-N) using four different beam lengths (4100 mm, 5300 mm, 6100 mm, and 7100 mm). The results showed that using stiffeners at the loading points increased the ultimate loads. However, this improvement in the beam capacity decreased as the beam length increased, as shown in Figure 19. The behavior of the beams was nearly the same in the elastic stage due to the smaller deflection before yielding, which caused smaller changes in eccentricity. After yielding and larger deformations, the p-δ effect was avoided by maintaining the positions of the prestressed tendons, and subsequently enhanced the beam behavior and capacity.

Effect of Stiffenes of the Steel Beam
The CW behaves differently than the FW because of the lower axial rigidity, which makes it easier to stretch and contract; this is called the "accordion effect" [37]. The accordion effect can maximize the effectiveness of prestressing force; otherwise, a drop in the beam capacity can be observed compared with the FW. The accordion effect depends on various parameters, including not only the corrugation shape but also the stiffness of the steel beam. Both the beam depth and length are two major parameters in determining the beam stiffness. Three different beam lengths (L c ) of 5100 mm, 5900 mm, and 6900 mm were used with different web thicknesses (t w ) and steel beam heights (d s ). To determine the accordion effect, each composite beam with SCW was compared with the same beam with flat web (FW). The ratio between the ultimate load of the beam with SCW (P ult ) and the ultimate load of the beam with FW (P f ) is presented as β. This ratio can represent the accordion effect for each beam. Increasing this ratio means less accordion effect and vice versa.    lengths (4100 mm, 5300 mm, 6100 mm, and 7100 mm). The results showed that using stiffeners at the loading points increased the ultimate loads. However, this improvement in the beam capacity decreased as the beam length increased, as shown in Figure 19. The behavior of the beams was nearly the same in the elastic stage due to the smaller deflection before yielding, which caused smaller changes in eccentricity. After yielding and larger deformations, the p-δ effect was avoided by maintaining the positions of the prestressed tendons, and subsequently enhanced the beam behavior and capacity. Figure 19. Comparisons between the SW-N and SW-S beams for different beam lengths. Figure 19. Comparisons between the SW-N and SW-S beams for different beam lengths.
The results showed that increasing the beam length decreased the β ratio, which means an increase in the accordion effect. Shear buckling started to appear clearly with the beam with flat webs FW6100-ds400-tw4, FW5300-ds400-tw4, and FW5300-ds400-tw5. The same beams with corrugated web did not buckle and the β ratio increased in comparison to the peer beams with FW. Beam SW5300-ds400-tw4 exhibited a β ratio bigger than 1, where the capacity of the beam with SCW was greater than the peer beam with FW (see Figure 20a). For a small web thickness, more buckling resistance can be gained from the CW than the FW due to the premature shear buckling failure. Increasing the steel beam height decreased the β ratio, as shown in Figure 20b for the beam length of 6900 mm. The beam SW7100-ds500 obtained the lowest β value for the t w of 6 mm and the highest value of β for the t w of 4 mm. This behavior could be attributed to the shear buckling failure. Except for the beams that failed in shear buckling, increasing the web thickness could decrease the β ratio.

Effect of Using Double Corrugated Web
Although the tested beam with DCW showed a drop in the beam capacity due to buckling of the web when compared to the beam with SCW, the FE models showed good performance of the DCW in the absence of shear buckling. FE models with different web thicknesses are compared in Figure 21a. Moreover, the effect of changing the beam length with the web thickness are shown in Figure 21b. The results showed that increasing the web thickness and beam length improved the performance of the beams with DCW. The maximum ratio of increase in the ultimate load was about 4.22% for the beam DW6100-tw (4-4) relative to the same beam with SCW. This increase in the ultimate load could be attributed to the fact that each web in the beam with DCW has a corrugation depth (d r ) of 40 mm. Figure 21c shows the effect of using two corrugations with a depth of 40 mm and 80 mm for SCW and 80 mm (40 + 40) for DCW. The results showed better performance for the beam with a single web. Due to the buckling shear failure of the steel beams with a smaller web thickness of 4 mm (2 + 2) and 5 mm (2.5 + 2.5), the beam with a SCW showed a better performance than the DCW. The maximum decrease in the ultimate load of the DCW was about 20% for beam DW4100-tw (2 + 2). Moreover, changing the closer distance between the two web sheets (CL) of the DW beams has no effect on the results (see Figure 21d). 1, where the capacity of the beam with SCW was greater than the peer beam with FW (see Figure 20a). For a small web thickness, more buckling resistance can be gained from the CW than the FW due to the premature shear buckling failure. Increasing the steel beam height decreased the β ratio, as shown in Figure 20b for the beam length of 6900 mm. The beam SW7100-ds500 obtained the lowest β value for the tw of 6 mm and the highest value of β for the tw of 4 mm. This behavior could be attributed to the shear buckling failure. Except for the beams that failed in shear buckling, increasing the web thickness could decrease the β ratio.

Effect of Using Double Corrugated Web
Although the tested beam with DCW showed a drop in the beam capacity due to buckling of the web when compared to the beam with SCW, the FE models showed good performance of the DCW in the absence of shear buckling. FE models with different web thicknesses are compared in Figure 21a. Moreover, the effect of changing the beam length with the web thickness are shown in Figure 21b. The results showed that increasing the web thickness and beam length improved the performance of the beams with DCW. The maximum ratio of increase in the ultimate load was about 4.22% for the beam DW6100tw (4-4) relative to the same beam with SCW. This increase in the ultimate load could be attributed to the fact that each web in the beam with DCW has a corrugation depth (dr) of 40 mm. Figure 21c shows the effect of using two corrugations with a depth of 40 mm and 80 mm for SCW and 80 mm (40 + 40) for DCW. The results showed better performance for the beam with a single web. Due to the buckling shear failure of the steel beams with a smaller web thickness of 4 mm (2 + 2) and 5 mm (2.5 + 2.5), the beam with a SCW showed a better performance than the DCW. The maximum decrease in the ultimate load of the DCW was about 20% for beam DW4100-tw (2 + 2). Moreover, changing the closer distance between the two web sheets (CL) of the DW beams has no effect on the results (see Figure  21d).

Conclusions
In this paper, the flexural behavior of externally prestressed composite steel-concrete I-beams with a single and double corrugated web was experimentally and numerically investigated. Three simply supported prestressed steel-concrete composite I-beams with single corrugated web (SCW) and double corrugated web (DCW) were tested under fourpoint loading. The tested beams were externally prestressed by using straight tendons

Conclusions
In this paper, the flexural behavior of externally prestressed composite steel-concrete I-beams with a single and double corrugated web was experimentally and numerically investigated. Three simply supported prestressed steel-concrete composite I-beams with single corrugated web (SCW) and double corrugated web (DCW) were tested under fourpoint loading. The tested beams were externally prestressed by using straight tendons along the full length. The ABAQUAS package was used to simulate the nonlinear behavior of the tested beams. The developed model was validated against the experimental results to carry out a parametric study to investigate the effect of various parameters on the behavior of the composite beams with SCW and DCW. The following conclusion can be drawn from this study:

•
The experimental and FE results confirmed a higher shear buckling resistance for the composite beams with SCW, with the same equivalent web thickness relative to the DCW.

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The failure mechanism was a yielding in the steel bottom flange, followed by crushing of concrete under the loading points for SCW beam without saddle points, local buckling and crushing under the loading points for SCW beam with saddle points, and shear buckling for DCW beam without saddle points. • Using stiffeners at the loading points as deviators to maintain the prestressed tendon positions increased the beam capacity and improved the beam performance.

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Increasing the initial prestressing force improved the beam capacity relative to unstrengthened beams. However, reductions in the incremental increase of the prestressing force were obtained. • Greater accordion effect can be gained with increasing beam length, web thickness, and steel beam depth.

•
The FE models demonstrated better behavior for the DCW when compared to SCW when the equivalent web thickness and (or) beam length was increased.