Steel-Concrete Composite Beams with Precast Hollow-Core Slabs: A Sustainable Solution

: Industrialization of construction makes building operation more environmental friendly and sustainable. This change is necessary as it is an industry that demands large consumption of water and energy, as well as being responsible for the disposal of a high volume of waste. However, the transformation of the construction sector is a big challenge worldwide. It is also well known that the largest proportion of the material used in multistory buildings, and thus its carbon impact, is attributed to their slabs being the main contributor of weight. Steel-Concrete composite beams with precast hollow-core slabs (PCHCSs) were developed due to their technical and economic beneﬁts, owing to their high strength and concrete self-weight reduction, making this system economical and with lower environmental footprint, thus reducing carbon emissions. Signiﬁcant research has been carried out on deep hollow-core slabs due to the need to overcome larger spans that resist high loads. The publication SCI P401, in accordance with Eurocode 4, is however limited to hollow-core slabs with depths from 150 to 250 mm, with or without a concrete topping. This paper aims to investigate hollow-core slabs with a concrete topping to understand their effect on the ﬂexural behavior of Steel-Concrete composite beams, considering the hollow-core-slab depth is greater than the SCI P401 recommendation. Consequently, 150 mm and 265 mm hollow-core units with a concrete topping were considered to assess the increase of the hollow core unit depth. A comprehensive computational parametric study was conducted by varying the in situ inﬁll concrete strength, the transverse reinforcement rate, the shear connector spacing, and the cross-section of steel. Both full and partial interaction models were examined, and in some cases similar resistances were obtained, meaning that the same strength can be obtained for a smaller number of shear studs, i.e., less energy consumption, thus a reduction in the embodied energy. The calculation procedure, according to Eurocode 4 was in favor of safety for the partial-interaction hypothesis.


Introduction
Researchers have been studying the impact that civil construction causes on the environment. In this context, a concept that has been studied is embodied energy in materials of buildings [1]. In Whitworth and Tsavdaridis [2,3], optimization studies were presented in Steel-Concrete composite beams with the objective of presenting sustainable structural designs by minimizing the embodied energy. The study showed that it is possible to reduce the embodied energy of these structural systems, considering the design recommendations of Eurocode 4 [4].
Conventional Steel-Concrete composite beams have a concrete slab that is placed at the upper flange of the downstand steel profile. In this context, three types of slabs can be 1.
150 mm of HCU depth and 50 mm of concrete topping with a squared end ( Figure 1b); 3.
265 mm of HCU depth and 50 mm of concrete topping with a squared end (Figure 1c).
strength of the composite beams by at least 7%. As observed, few studie investigated the behavior of Steel-Concrete composite beams with PCHCS Tawadrous and Morcous [4] and El-Sayed et al. [5] showed that, due to the succes of PCHCSs, deeper HCUs were developed to resist higher loads and to support spans. In this scenario, some researchers carried out tests to investigate the beha deeper PCHCSs [12,13,[27][28][29][30][31][32]. However, these investigations did not consider com behavior, i.e., Steel-Concrete composite beams.

Numerical Model: Validation Study
In this section, the methodology of the validation study is described. The A software [33] was used. Three types of Steel-Concrete composite beams were m considering symmetry: 1. 150 mm of HCU depth with a chamfered end ( Figure 1a); 2. 150 mm of HCU depth and 50 mm of concrete topping with a squared end 1b); 3. 265 mm of HCU depth and 50 mm of concrete topping with a squared end 1c). Geometrical nonlinear analyses were processed using the Static Riks metho method was previously used in [25,[34][35][36][37][38][39][40] and is based on the arc-length method ual stresses were not considered. These stresses do not influence the ultimate stre composite beams subjected to only positive moments. The residual stresses incre effects of the negative moment [41,42].

Tests
The numerical models were calibrated considering tests on Steel-Concrete com beams with PCHCSs, at 150 mm and 265 mm of depth, and with or without a c topping. Figure 2 and Table 1 show the details of the tests [18,43], in which d is th beam depth, bf is the steel-flange width, tf is the steel-flange thickness, tw is the st thickness, b is the effective slab width, g is the gap, hc is the depth of the HCU, concrete-topping thickness, Le is the distance between the end of the beam and t port, Lp is the distance between the load application point and the support, Lb is th strained length, φ is the diameter of the transverse reinforcement, fy,f is the yield s of the flange, fy,w is the yield strength of the web, fy,s is the transverse reinforceme strength, fc,HCU is the HCU compressive strength, and fc,in is the in situ infill comp strength. Geometrical nonlinear analyses were processed using the Static Riks method. This method was previously used in [25,[34][35][36][37][38][39][40] and is based on the arc-length method. Residual stresses were not considered. These stresses do not influence the ultimate strength of composite beams subjected to only positive moments. The residual stresses increase the effects of the negative moment [41,42].

Tests
The numerical models were calibrated considering tests on Steel-Concrete composite beams with PCHCSs, at 150 mm and 265 mm of depth, and with or without a concrete topping. Figure 2 and Table 1 show the details of the tests [18,43], in which d is the steelbeam depth, b f is the steel-flange width, t f is the steel-flange thickness, t w is the steel-web thickness, b is the effective slab width, g is the gap, h c is the depth of the HCU, c is the concrete-topping thickness, L e is the distance between the end of the beam and the support, L p is the distance between the load application point and the support, L b is the unrestrained length, ϕ is the diameter of the transverse reinforcement, f y,f is the yield strength of the flange, f y,w is the yield strength of the web, f y,s is the transverse reinforcement yield strength, f c,HCU is the HCU compressive strength, and f c,in is the in situ infill compressive strength. thickness, b is the effective slab width, g is the gap, hc is the depth of the HCU, c is the concrete-topping thickness, Le is the distance between the end of the beam and the support, Lp is the distance between the load application point and the support, Lb is the unrestrained length, φ is the diameter of the transverse reinforcement, fy,f is the yield strength of the flange, fy,w is the yield strength of the web, fy,s is the transverse reinforcement yield strength, fc,HCU is the HCU compressive strength, and fc,in is the in situ infill compressive strength.

Materials
The concrete-damage plasticity (CDP) [44][45][46] model was used. This model is based on the plastic theory, and can be used to describe the irreversible damage that occurs during the fracture process [33], such as cracking and crushing. The concrete-damage plasticity model makes use of the yield function of Lubliner et al. [45], with modifications proposed by Lee and Fenves [46]. Concrete, as a brittle material, undergoes considerable volume change called dilatancy [47], which is caused by inelastic strains. The flow rule followed the Drucker-Prager model. The concrete-damage plasticity model can be regularized using viscoplasticity. The regularization of Duvaut-Lions [48] was used. The input parameters for defining the plastic behavior are presented in Table 2, in which ψ is the dilation angle, ξ is the eccentricity, σ b0 is the initial equibiaxial compressive yield stress, σ c0 is the initial uniaxial compressive yield stress, K c is the ratio of the second stress invariant on the tensile meridian to that on the compressive meridian, and µ is the viscosity parameter. The concrete model of Carreira and Chu [50,51] was used for both compression and tension Equations (1)- (3). For steel, the perfect elasto-plastic behavior was considered. where ε c is the strain corresponding to concrete compressive strength, ε t is the strain corresponding to concrete tensile strength, f c is the compressive concrete strength, f t is the concrete tensile strength, and β c is the stress-strain relationship form factor of concrete in compression. Figure 3 shows the pairs of interactions. The tie constraint technique allowed us to simulate the perfect bond between the contact surfaces. The contacts between the concrete and the transverse reinforcements were made through the embedded region [33]. The normal/tangential behavior was considered between the steel beam and PCHCS, the steel beam and gap, the actuator and concrete topping, and the shear stud and gap. The shear studs were located in the gap, using the same technique presented in [52]. The friction coefficient was based on the Coulomb friction model. The literature reports some values of the friction coefficient [53][54][55]. Friction coefficients of 0.2 and 0.3 were adopted for the gap and headed stud and the steel beam and slab interfaces, respectively [55]. 6 of 24 concrete tensile strength, and βc is the stress-strain relationship form factor of concrete in compression. Figure 3 shows the pairs of interactions. The tie constraint technique allowed us to simulate the perfect bond between the contact surfaces. The contacts between the concrete and the transverse reinforcements were made through the embedded region [33]. The normal/tangential behavior was considered between the steel beam and PCHCS, the steel beam and gap, the actuator and concrete topping, and the shear stud and gap. The shear studs were located in the gap, using the same technique presented in [52]. The friction coefficient was based on the Coulomb friction model. The literature reports some values of the friction coefficient [53][54][55]. Friction coefficients of 0.2 and 0.3 were adopted for the gap and headed stud and the steel beam and slab interfaces, respectively [55].

Boundary Conditions
The boundary conditions ( Figure 4) were applied considering the symmetry at midspan (Uz = URx = URy = 0) [25,[37][38][39][40]. The vertical displacement was restrained at the supports (Uy = 0) and the lateral displacement at the ends of the slab (Ux = 0). Displacement control was used. The difficulties with softening materials can be avoided by applying a simple form of displacement control [56,57]. The disadvantages in displacement control are related to the selection of the appropriate displacement variable [58]. Thus, the variable selected for the stopping criterion was the midspan vertical displacement.

Boundary Conditions
The boundary conditions ( Figure 4) were applied considering the symmetry at midspan (U z = UR x = UR y = 0) [25,[37][38][39][40]. The vertical displacement was restrained at the supports (U y = 0) and the lateral displacement at the ends of the slab (U x = 0). Displacement control was used. The difficulties with softening materials can be avoided by applying a simple form of displacement control [56,57]. The disadvantages in displacement control are related to the selection of the appropriate displacement variable [58]. Thus, the variable selected for the stopping criterion was the midspan vertical displacement.

Discretization
The discretization of the elements is shown in Figure 5. The dimension values of the elements were adopted according to the literature [28,53,54], and with respect to the master and slave surfaces. The S4R element was a quadrilateral element with four nodes. This element had reduced integration. According to the ABAQUS, Dassault Systèmes, software [33], the C3D8R element had eight nodes, reduced integration, supported plastic analysis with large deformations, and allowed the visualization of the crack in the CDP model. The T3D2 element had 2-node linear displacement.

Results
The results are presented in Figure 6 and Table 3, in which MFE is the bending moment of finite element model, MTest is the bending moment of experimental tests, δFE is the midspan vertical displacement of the finite element models, and δTest is the mid-pan vertical displacement of the tests. It was possible to observe the yielding at the lower flange, and in the CB1 and CB2 models, the cracking was observed in the lower part of the PCHCSs, according to Lam [17]. The behaviors of the CB3 and CB4 models were similar to those presented in Batista and Landesmann [18]; that is, there was a propagation of cracks that started in the central part of the PCHCS and extended over the entire width.

Discretization
The discretization of the elements is shown in Figure 5. The dimension values of the elements were adopted according to the literature [28,53,54], and with respect to the master and slave surfaces. The S4R element was a quadrilateral element with four nodes. This element had reduced integration. According to the ABAQUS, Dassault Systèmes, software [33], the C3D8R element had eight nodes, reduced integration, supported plastic analysis with large deformations, and allowed the visualization of the crack in the CDP model. The T3D2 element had 2-node linear displacement.

Discretization
The discretization of the elements is shown in Figure 5. The dimension values of the elements were adopted according to the literature [28,53,54], and with respect to the master and slave surfaces. The S4R element was a quadrilateral element with four nodes. This element had reduced integration. According to the ABAQUS, Dassault Systèmes, software [33], the C3D8R element had eight nodes, reduced integration, supported plastic analysis with large deformations, and allowed the visualization of the crack in the CDP model. The T3D2 element had 2-node linear displacement.

Results
The results are presented in Figure 6 and Table 3, in which MFE is the bending moment of finite element model, MTest is the bending moment of experimental tests, δFE is the midspan vertical displacement of the finite element models, and δTest is the mid-pan vertical displacement of the tests. It was possible to observe the yielding at the lower flange, and in the CB1 and CB2 models, the cracking was observed in the lower part of the PCHCSs, according to Lam [17]. The behaviors of the CB3 and CB4 models were similar to those presented in Batista and Landesmann [18]; that is, there was a propagation of cracks that started in the central part of the PCHCS and extended over the entire width.

Results
The results are presented in Figure 6 and Table 3, in which M FE is the bending moment of finite element model, M Test is the bending moment of experimental tests, δ FE is the midspan vertical displacement of the finite element models, and δ Test is the mid-pan vertical displacement of the tests. It was possible to observe the yielding at the lower flange, and in the CB1 and CB2 models, the cracking was observed in the lower part of the PCHCSs, according to Lam [17]. The behaviors of the CB3 and CB4 models were similar to those presented in Batista and Landesmann [18]; that is, there was a propagation of cracks that started in the central part of the PCHCS and extended over the entire width.

Numerical Model: Parametric Study
The following were the general considerations for the parametric study: 1.
The thickness of the concrete topping was 50 mm; 2.
The total transverse reinforcement length was 1000 + g, in mm; 3.
For the steel beam, the ASTM A572 Gr.50 steel was adopted (f y = 345 MPa). The Young's module and the Poisson's ratio were 200 GPa and 0.3, respectively; 6.
The composite beams were simply supported, and subjected to four-point bending.
The loads were spaced in L/4 from each support. Stiffeners were placed at the support and points of loads; 7.
The midspan vertical displacement of a maximum value equal to L/100 was adopted as a stopping criterion [25].

Results and Discussion
In this section, the results are discussed, according were analyzed. At the end of this section, the results are culation procedures for Steel-Concrete composite beams The studied parameters are shown in Table 4.

Results and Discussion
In this section, the results are discussed, according to the steel cross-sections that were analyzed. At the end of this section, the results are compared with the resistant calculation procedures for Steel-Concrete composite beams, as well as with the results presented in Ferreira et al. [25], considering a 150 mm depth of the PCHCS with concrete topping.

W360x51 Section
Considering a spacing between shear studs of 120 mm, for the midspan vertical displacement at 15

Results and Discussion
In this section, the results are discussed, according to the steel cross-sections that were analyzed. At the end of this section, the results are compared with the resistant calculation procedures for Steel-Concrete composite beams, as well as with the results presented in Ferreira et al. [25], considering a 150 mm depth of the PCHCS with concrete topping.

W360x51 Section
Considering a spacing between shear studs of 120 mm, for the midspan vertical displacement at 15   With the variation of the transverse reinforcement rate and in situ concrete strength, there were no differences in the shear-slip and moment-deflection relationships ( Figure  9). With the variation of the transverse reinforcement rate and in situ concrete strength, there were no differences in the shear-slip and moment-deflection relationships ( Figure 9). This can be explained as a function of the depth and area of the steel cross-section in relation to the depth and effective area of the PCHCS and concrete topping. Upon reaching the ultimate strength, as shown in Figure 8, the neutral plastic axis (NPA) was in the concrete topping, a factor that generates excessive tensile stresses in the PCHCS. This can be concluded since in the final configuration, the upper part of the PCHCS, which was in the region of pure bending, was damaged. Another important observation was the fragile behavior of the composite beams, since the slip values at the steel-concrete interface were less than 6 mm, a parameter that Eurocode 4 [4] considers to characterize the ductile behavior ( Figure 9). Due to this fragile behavior, with the variation of parameters, such as transverse reinforcement rate and in situ concrete strength, there were no significant differences in terms of stresses, both in the shear studs and in the transversal reinforcement, considering the ultimate strength. Some examples are illustrated in Figure 10. On the other hand, for the shear-stud spacing at 175 mm and 225 mm, for the midspan vertical displacement at 15 mm, the behavior was similar to the models with 120 mm of spacing. However, at the ultimate strength, the midspan vertical displacements were greater than in the previous situation, with the maximum value equal to 36 mm, considering φ = 16 mm, fc = 40 MPa, and 175 mm of spacing. For the situation in which the spacing was 225 mm, the midspan vertical displacement reached 42 mm, considering φ = 10 mm and fc = 25 MPa. Regarding the ultimate strength, the composite beams with shear-stud spacing of 175 mm and 225 mm made better use of the steel section; that is, approximately half the web depth reached plastification ( Figure 11). Then, the greater the spacing between the shear studs, the better the use of the steel section. On the other hand, for the shear-stud spacing at 175 mm and 225 mm, for the midspan vertical displacement at 15 mm, the behavior was similar to the models with 120 mm of spacing. However, at the ultimate strength, the midspan vertical displacements were greater than in the previous situation, with the maximum value equal to 36 mm, considering ϕ = 16 mm, f c = 40 MPa, and 175 mm of spacing. For the situation in which the spacing was 225 mm, the midspan vertical displacement reached 42 mm, considering ϕ = 10 mm and f c = 25 MPa. Regarding the ultimate strength, the composite beams with shear-stud spacing of 175 mm and 225 mm made better use of the steel section; that is, approximately half the web depth reached plastification ( Figure 11). Then, the greater the spacing between the shear studs, the better the use of the steel section. On the other hand, for the shear-stud spacing at 175 mm and 225 mm, for the midspan vertical displacement at 15 mm, the behavior was similar to the models with 120 mm of spacing. However, at the ultimate strength, the midspan vertical displacements were greater than in the previous situation, with the maximum value equal to 36 mm, considering φ = 16 mm, fc = 40 MPa, and 175 mm of spacing. For the situation in which the spacing was 225 mm, the midspan vertical displacement reached 42 mm, considering φ = 10 mm and fc = 25 MPa. Regarding the ultimate strength, the composite beams with shear-stud spacing of 175 mm and 225 mm made better use of the steel section; that is, approximately half the web depth reached plastification ( Figure 11). Then, the greater the spacing between the shear studs, the better the use of the steel section.  The variation in both the transverse reinforcement rate (Figures 12 and 13) and the in situ concrete strength showed significant differences in the shear-slip and momentdeflection relationships.  The variation in both the transverse reinforcement rate (Figures 12 and 13) and the situ concrete strength showed significant differences in the shear-slip and moment-defl tion relationships. As shown in the illustrations, even with the variation of the transverse reinforcement r and in situ concrete strength, the initial stiffnesses of the composite beams modeled were s ilar, showing that the differences of these relations were significant in the nonlinear bran Although the ultimate moment had an approximate value for the models illustrated (φ = mm, φ = 12.5 mm, and φ = 16 mm), the models with φ = 10 mm and φ = 12.5 mm show similar behavior in the shear-slip and moment-deflection relationships, and were differ from the model with φ = 16 mm (Figures 12 and 13). According to Lam et al. [22], with increase in the transverse reinforcement rate, the flexural strength capacity increases, but duces the ductility, leading to fragile rupture.
Another important observation was that in no model presented for the W360x51 s tion did the composite beams show ductile behavior. Thus, it was possible to conclu that in all models analyzed for W360x51 section, the ultimate strength was characteriz as fragile. In most observations for both 175 mm and 225 mm of spacing, the von Mi stresses in the shear studs were less than the models with 120 mm of spacing. For examp for fc = 25 MPa, considering the 175 mm and 225 mm models, the von Mises stresses in shear studs were lower than the model with 120 mm of spacing. A similar situation curred for fc = 30 MPa. On the other hand, for fc = 40 MPa, there were models in which von Mises stresses in the shear studs, considering 175 mm and 225 mm of spacings, w The variation in both the transverse reinforcement rate (Figures 12 and 13) and situ concrete strength showed significant differences in the shear-slip and moment-d tion relationships. As shown in the illustrations, even with the variation of the transverse reinforcemen and in situ concrete strength, the initial stiffnesses of the composite beams modeled wer ilar, showing that the differences of these relations were significant in the nonlinear br Although the ultimate moment had an approximate value for the models illustrated (φ mm, φ = 12.5 mm, and φ = 16 mm), the models with φ = 10 mm and φ = 12.5 mm sh similar behavior in the shear-slip and moment-deflection relationships, and were dif from the model with φ = 16 mm (Figures 12 and 13). According to Lam et al. [22], wi increase in the transverse reinforcement rate, the flexural strength capacity increases, b duces the ductility, leading to fragile rupture.
Another important observation was that in no model presented for the W360x5 tion did the composite beams show ductile behavior. Thus, it was possible to con that in all models analyzed for W360x51 section, the ultimate strength was characte as fragile. In most observations for both 175 mm and 225 mm of spacing, the von stresses in the shear studs were less than the models with 120 mm of spacing. For exa for fc = 25 MPa, considering the 175 mm and 225 mm models, the von Mises stresses shear studs were lower than the model with 120 mm of spacing. A similar situatio curred for fc = 30 MPa. On the other hand, for fc = 40 MPa, there were models in whic von Mises stresses in the shear studs, considering 175 mm and 225 mm of spacings, As shown in the illustrations, even with the variation of the transverse reinforcement rate and in situ concrete strength, the initial stiffnesses of the composite beams modeled were similar, showing that the differences of these relations were significant in the nonlinear branch. Although the ultimate moment had an approximate value for the models illustrated (ϕ = 10 mm, ϕ = 12.5 mm, and ϕ = 16 mm), the models with ϕ = 10 mm and ϕ = 12.5 mm showed similar behavior in the shear-slip and moment-deflection relationships, and were different from the model with ϕ = 16 mm (Figures 12 and 13). According to Lam et al. [22], with the increase in the transverse reinforcement rate, the flexural strength capacity increases, but reduces the ductility, leading to fragile rupture.
Another important observation was that in no model presented for the W360x51 section did the composite beams show ductile behavior. Thus, it was possible to conclude that in all models analyzed for W360x51 section, the ultimate strength was characterized as fragile. In most observations for both 175 mm and 225 mm of spacing, the von Mises stresses in the shear studs were less than the models with 120 mm of spacing. For example, for f c = 25 MPa, considering the 175 mm and 225 mm models, the von Mises stresses in the shear studs were lower than the model with 120 mm of spacing. A similar situation occurred for f c = 30 MPa. On the other hand, for f c = 40 MPa, there were models in which the von Mises stresses in the shear studs, considering 175 mm and 225 mm of spacings, were greater than the model with 120 mm of spacing. This was observed specifically for transversal-reinforcement diameters equal to 10 mm and 12.5 mm.

W460x74 Section
Considering 120 mm of spacing between the shear studs, for the midspan vertical

W460x74 Section
Considering 120 mm of spacing between the sh displacement at 15 mm, only the region in which th yield strength. The von Mises stresses in the lower 290 MPa, 290 MPa, and 120 MPa, respectively. When timate strength, the upper flange and approximatel plastic regime. The von Mises stresses in the upper strength was governed by excessive cracking of the P  With the transverse reinforcement rate variation and in situ concrete strength, there were no differences in the shear-slip and moment-deflection relationships ( Figure 15).
As noted, there were no significant differences in the behavior of these analyzed composite beams, because the ultimate strength was achieved by excessive cracking of the PCHCS, a situation analogous to the W360x51 section. Another important observation was the fragile behavior of the composite beams, a situation similar to the W360x51 section. Due to this fragile behavior, with the variation of the parameters such as transverse reinforcement rate and in situ concrete strength, there were small differences in the magnitude of the von Mises stresses, specifically in the shear studs. Some examples are illustrated in Figure 16. With the transverse reinforcement rate variation and in situ concrete strength, there were no differences in the shear-slip and moment-deflection relationships (Figure 15).  Considering the models with 175 mm and 225 mm of spacing, it was possible to observe two different situations. In relation to the 175 mm of spacing, for the midspan vertical displacement at 15 mm, the yield strength was not reached in any region of the steel profile. The maximum von Mises stresses in the lower flange, web, and upper flange were 290 MPa, 290 MPa, and 120 MPa, respectively. When the composite beams reached the ultimate strength, only part of the lower flange was in the plastic regime (Figure 17a). For 225 mm of spacing between shear studs, the ultimate strength was characterized with the lower flange, half the web depth, and part of the upper flange, which were in the region of the loading application point, in the plastic regime (Figure 17b). This was the model in which the composite action took advantage of the strength of the steel profile. the shear studs for fc = 25 MPa. A similar situation occurred for fc = 30 MPa models. Fo the fc = 40 MPa models, the von Mises stresses in the shear studs varied with the variation of the transverse reinforcement diameter. Unlike the fc = 25 MPa models, the smaller the transverse reinforcement diameter, the greater the von Mises stresses in the shear studs This variation reached approximately 20 MPa between φ = 10 mm and φ = 16 mm.
Considering the models with 175 mm and 225 mm of spacing, it was possible to ob serve two different situations. In relation to the 175 mm of spacing, for the midspan ver tical displacement at 15 mm, the yield strength was not reached in any region of the stee profile. The maximum von Mises stresses in the lower flange, web, and upper flange were 290 MPa, 290 MPa, and 120 MPa, respectively. When the composite beams reached the ultimate strength, only part of the lower flange was in the plastic regime (Figure 17a). Fo 225 mm of spacing between shear studs, the ultimate strength was characterized with the lower flange, half the web depth, and part of the upper flange, which were in the region of the loading application point, in the plastic regime (Figure 17b). This was the model in which the composite action took advantage of the strength of the steel profile. The variation in both the transverse reinforcement rate and the in situ concrete strength (Figures 18 and 19) showed significant differences in the shear-slip and momentdeflection relationships.  The variation in both the transverse reinforcement rate and the in situ concrete strength (Figures 18 and 19) showed significant differences in the shear-slip and momentdeflection relationships.  The variation in both the transverse reinforcement rate and the in situ concrete strength (Figures 18 and 19) showed significant differences in the shear-slip and momentdeflection relationships. These differences were observed for the concrete with the highest strength and transversal-reinforcement diameters equal to 12.5 mm and 16 mm. Figure 18 shows that the The variation in both the transverse reinforcement rate and the in situ concrete strength (Figures 18 and 19) showed significant differences in the shear-slip and momentdeflection relationships. These differences were observed for the concrete with the highest strength and transversal-reinforcement diameters equal to 12.5 mm and 16 mm. Figure 18 shows that the These differences were observed for the concrete with the highest strength and transversal-reinforcement diameters equal to 12.5 mm and 16 mm. Figure 18 shows that the greater the concrete strength, the greater the initial stiffness of the composite beam, although the values for the ultimate moment were analogous, since the ultimate strength was governed by the slab. However, as the spacing between the connectors increased; that is, the interaction degree was reduced, as illustrated in Figure 19, the model with f c = 30 MPa showed a different behavior in the shear-slip and moment-deflection relationships. This change in behavior was previously presented in Araújo et al. [20] and Ferreira et al. [25]. The authors reported that when the compressive strength of the in situ concrete was close to 40 MPa, the failure mode could occur in the shear stud, and for resistance values below 30 MPa, the failure could be governed by the in situ concrete.
Another important observation was that for models with 225 mm of spacing, considering the W460x51 section, the composite beams showed ductile behavior; that is, the slip at the steel-concrete interface was greater than 6 mm. Thus, it was possible to conclude that in all models analyzed for the W460x51 section and 225 mm of spacing, the behavior at the steel-concrete interface was characterized as ductile, according to prescriptions of Eurocode 4. For the f c = 25 MPa models, the von Mises stresses in the shear studs, considering 175 mm and 225 mm of spacing, were greater than the models with 120 mm of spacing. A similar behavior occurred for f c = 30 MPa models. For f c = 40 MPa, there were models in which the von Mises stresses in the shear studs, considering 175 mm and 225 mm of spacings, were much higher than the models with 120 mm of spacing. This was observed for all transverse reinforcement diameters analyzed.

W530x72 Section
Considering 120 mm of spacing, for the midspan vertical displacement at 15 mm, the region where the composite beam was supported and the lower flange reached the yield resistance. The maximum von Mises stresses in the lower flange, web, and upper flange were 345 MPa, 316 MPa, and 230 MPa, respectively. When the composite beam reached the ultimate strength (Figure 20), for the midspan vertical displacement at 22 mm, the lower flange and approximately 1/4 of the web depth were in the plastic regime. spacings, were much higher than the models with 120 mm of spacin for all transverse reinforcement diameters analyzed.

W530x72 Section
Considering 120 mm of spacing, for the midspan vertical displac region where the composite beam was supported and the lower flan resistance. The maximum von Mises stresses in the lower flange, w were 345 MPa, 316 MPa, and 230 MPa, respectively. When the com the ultimate strength (Figure 20), for the midspan vertical displace lower flange and approximately 1/4 of the web depth were in the pla The ultimate strength was governed by excessive cracking of th to note that in these models, there were a better use of the steel se with the previous cross-sections. This was due to the fact that the stee and area greater than the other steel sections studied. So, the NPA te direction of the steel section, a factor that favored the resistance of thus reducing tension stresses. With the variation of the transverse re in situ concrete strength, there were no differences in the shear-slip tion relationships (similar to previous situations). Regarding the von shear studs, there were no significant differences, reaching values b MPa. The ultimate strength was governed by excessive cracking of the slab. It is important to note that in these models, there were a better use of the steel section, in comparison with the previous cross-sections. This was due to the fact that the steel section had a depth and area greater than the other steel sections studied. So, the NPA tended to move in the direction of the steel section, a factor that favored the resistance of the hollow-core slab, thus reducing tension stresses. With the variation of the transverse reinforcement rate and in situ concrete strength, there were no differences in the shear-slip and moment-deflection relationships (similar to previous situations). Regarding the von Mises stresses in the shear studs, there were no significant differences, reaching values between 556 and 570 MPa.
On the other hand, considering 175 mm of spacing between the shear studs, for the midspan vertical displacement at 15 mm, only the support region reached the yield strength. The von Mises stresses in the lower flange, web, and upper flange were 316 MPa, 288 MPa, and 116 MPa, respectively. At the ultimate strength (Figure 21a), the midspan vertical displacement was 21 mm. In this loading stage, the lower flange was in the plastic regime.
For 225 mm of spacing, with the midspan vertical displacement at 15 mm, the results were similar to the previous beam. However, the maximum von Mises stresses in the lower flange, web, and upper flange were 288 MPa, 288 MPa, and 116 MPa, respectively. At the ultimate strength (Figure 21b), with the midspan vertical displacement at 38 mm, the lower flange, half the web depth, and the upper flange were in the plastic regime. With the variation of the transverse reinforcement rate and the in situ concrete strength, it was possible to verify some differences in the shear-slip and moment-deflection relationships (Figures 22 and 23).
On the other hand, considering 175 mm of spacing between the shear studs, for the midspan vertical displacement at 15 mm, only the support region reached the yield strength. The von Mises stresses in the lower flange, web, and upper flange were 316 MPa 288 MPa, and 116 MPa, respectively. At the ultimate strength (Figure 21a), the midspan vertical displacement was 21 mm. In this loading stage, the lower flange was in the plastic regime.  For 225 mm of spacing, with the midspan vertical displacement at 15 mm, the results were similar to the previous beam. However, the maximum von Mises stresses in the lower flange, web, and upper flange were 288 MPa, 288 MPa, and 116 MPa, respectively At the ultimate strength (Figure 21b), with the midspan vertical displacement at 38 mm the lower flange, half the web depth, and the upper flange were in the plastic regime. With the variation of the transverse reinforcement rate and the in situ concrete strength, it was possible to verify some differences in the shear-slip and moment-deflection relationships (Figures 22 and 23).  It was observed that for the models with 175 mm of spacing, there were some differences in the relationships presented in Figure 22

Design
In this section, the results are presented in a summarized way, considering the ductile behavior (Figure 24), the maximum midspan vertical displacement for the service limit state for composite floors (Figure 25), and SCI P401 [19] procedure ( Figure 26); and con- It was observed that for the models with 175 mm of spacing, there were some differences in the relationships presented in Figure 22

Design
In this section, the results are presented in a summarized way, considering the ductile behavior ( Figure 24), the maximum midspan vertical displacement for the service limit state for composite floors (Figure 25), and SCI P401 [19] procedure ( Figure 26); and considering the strength models for shear studs presented in [19,20]. Considering full interaction and that NPA lies in the concrete slab (Equations (4)-(10)), in which A a is the steel-section crosssectional area, C c is the concrete-flange axial strength, f y is the steel-section yield strength, L is the composite-beam length, M pl is the plastic moment of the composite section, Q R is the shear-connector strength, t c is overall depth of the concrete flange (including the concrete topping), T a is the axial strength of the steel section in tension, and L ϕ is the transverse reinforcement length.
0.85 f c bt c ≥ A a f y (5) T a = A a f y (8) For partial interaction, the linear method was used, according to Eurocode 4 (Equation (11)), in which Mpl,a is the plastic moment of the steel section, Mpl,FULL is the plastic moment of the composite section with full shear connection, and η is the ratio of the sum of the strength of the shear studs provided to the sum of the strength of the shear studs needed for full shear connection.
For a presentation of the results, a hypothesis of the minimum spacing was made; i.e., 120 mm providing full interaction. On the other hand, for the other spacings, partial interaction was considered. Therefore, for the spacings of 120 mm, 175 mm, 225 mm, the interaction degrees were 1.0, 0.7, and 0.5, respectively. As shown in Figure 24, only one situation for the W360x51 section presented a ductile behavior (fc = 25 MPa, φ = 10 mm, and 225 mm of spacing). On the other hand, for all W460x74 and W530x72 models, considering 225 mm of spacing, ductile behavior was observed. This means that the greater the area of the steel cross-section and the greater the spacing between the shear studs, the greater the sliding in the steel-concrete interface. Respecting the midspan vertical displacement limit for floors (L/200), according to Eurocode 4, 52 observations were found below the limit value, specifically for all models of full interaction ( Figure 25). Therefore, another observation was that the smaller the interaction degree, the greater the midspan vertical displacement. Finally, considering the calculation procedures mentioned in this For partial interaction, the linear method was used, according to Eurocode 4 (Equation (11)), in which Mpl,a is the plastic moment of the steel section, Mpl,FULL is the plastic moment of the composite section with full shear connection, and η is the ratio of the sum of the strength of the shear studs provided to the sum of the strength of the shear studs needed for full shear connection.
For a presentation of the results, a hypothesis of the minimum spacing was made; i.e., 120 mm providing full interaction. On the other hand, for the other spacings, partial interaction was considered. Therefore, for the spacings of 120 mm, 175 mm, 225 mm, the interaction degrees were 1.0, 0.7, and 0.5, respectively. As shown in Figure 24, only one situation for the W360x51 section presented a ductile behavior (fc = 25 MPa, φ = 10 mm, and 225 mm of spacing). On the other hand, for all W460x74 and W530x72 models, considering 225 mm of spacing, ductile behavior was observed. This means that the greater the area of the steel cross-section and the greater the spacing between the shear studs, the greater the sliding in the steel-concrete interface. Respecting the midspan vertical displacement limit for floors (L/200), according to Eurocode 4, 52 observations were found below the limit value, specifically for all models of full interaction ( Figure 25). Therefore, another observation was that the smaller the interaction degree, the greater the midspan vertical displacement. Finally, considering the calculation procedures mentioned in this section, a total of 60 observations were found in the conservative zone (MFE ≤ MRk). The observations that were shown to be unsafe (MFE > MRk) were verified for models in which full interaction was considered ( Figure 26). For partial interaction, the linear method was used, according to Eurocode 4 (Equation (11)), in which M pl,a is the plastic moment of the steel section, M pl,FULL is the plastic moment of the composite section with full shear connection, and η is the ratio of the sum of the strength of the shear studs provided to the sum of the strength of the shear studs needed for full shear connection.
For a presentation of the results, a hypothesis of the minimum spacing was made; i.e., 120 mm providing full interaction. On the other hand, for the other spacings, partial interaction was considered. Therefore, for the spacings of 120 mm, 175 mm, 225 mm, the interaction degrees were 1.0, 0.7, and 0.5, respectively. As shown in Figure 24, only one situation for the W360 × 51 section presented a ductile behavior (f c = 25 MPa, ϕ = 10 mm, and 225 mm of spacing). On the other hand, for all W460 × 74 and W530 × 72 models, considering 225 mm of spacing, ductile behavior was observed. This means that the greater the area of the steel cross-section and the greater the spacing between the shear studs, the greater the sliding in the steel-concrete interface. Respecting the midspan vertical displacement limit for floors (L/200), according to Eurocode 4, 52 observations were found below the limit value, specifically for all models of full interaction ( Figure 25). Therefore, another observation was that the smaller the interaction degree, the greater the midspan vertical displacement. Finally, considering the calculation procedures mentioned in this section, a total of 60 observations were found in the conservative zone (M FE ≤ M Rk ). The observations that were shown to be unsafe (M FE > M Rk ) were verified for models in which full interaction was considered ( Figure 26).

Comparative Analyses
In this section, a comparison of the models developed in the present work was performed with those presented by Ferreira et al. [25] (Figure 27).

Comparative Analyses
In this section, a comparison of the models developed in the present work was performed with those presented by Ferreira et al. [25] (Figure 27). As noted, in some models, the higher PCHCS provided greater strength. This difference reached a maximum of 30%, considering the ratio of the 150 mm-depth PCHCS models to the 265 mm-depth PCHCS models. These values were measured considering the W360x51 section. With the increase in the steel cross-section (sections W460x74 and W530x72), this difference was not so significant. This demonstrated that for the models studied, it was not advantageous to increase the depth of the PCHCS, since the collapse was determined by the slab. In addition, the greater the depth of the hollow-core slab, the greater the weight of the structural system due to the higher consumption of concrete, and thus the higher the costs. Therefore, from a sustainable and structural-efficiency point of view, the 150 mm depth PCHCS was the best option of the models studied.

Conclusions
Steel-Concrete composite beams with precast hollow-core slabs are a sustainable so- As noted, in some models, the higher PCHCS provided greater strength. This difference reached a maximum of 30%, considering the ratio of the 150 mm-depth PCHCS models to the 265 mm-depth PCHCS models. These values were measured considering the W360 × 51 section. With the increase in the steel cross-section (sections W460 × 74 and W530 × 72), this difference was not so significant. This demonstrated that for the models studied, it was not advantageous to increase the depth of the PCHCS, since the collapse was determined by the slab. In addition, the greater the depth of the hollow-core slab, the greater the weight of the structural system due to the higher consumption of concrete, and thus the higher the costs. Therefore, from a sustainable and structural-efficiency point of view, the 150 mm depth PCHCS was the best option of the models studied.

Conclusions
Steel-Concrete composite beams with precast hollow-core slabs are a sustainable solution, and a better understanding of their parameters will yield more efficient designs. The present study developed a reliable finite element model to investigate some limitations imposed in the design recommendations of Steel-Concrete composite beams with precast hollow-core slabs, such as hollow-core-slab depth, transverse reinforcement rate, and shear-stud spacing. A parametric study was carried out, considering a 265 mm hollow-core unit with a concrete topping, since the SCI P401 recommendation is only applicable for 150-250 mm-deep hollow-core units. The parameters investigated were the in situ concrete strength, the transverse reinforcement rate, the interaction degree, and the steel crosssection. In total, 81 models were analyzed. The numerical results were compared with models of Steel-Concrete composite beams models, considering a 150 mm hollow-core unit with a concrete topping. In general, for the models that were considered under the partialinteraction hypothesis, there was a better efficiency of the structural system, providing greater deformations. Therefore, when designing Steel-Concrete composite beams with hollow-core slabs, considering partial interaction is a viable option, since it reduces the cost of the project, due to the smaller number of shear studs to be used, as well as the labor. Specifically, considering the parameters analyzed, it was concluded that: 1.
In all models, the ultimate strength was reached by excessive cracking of the precast hollow-core slab. This occurred because the neutral plastic axis lay within the -core slab, a factor that generated tensile stresses. Thus, dimensioning Steel-Concrete composite beams with deeper hollow-core slabs is not advantageous. This is because the resistance is governed by the concrete slab, a factor that does not take advantage of the steel section. Therefore, in these analyzed models, there was a waste of material.

2.
The greater the area of the steel cross-section, the greater the use of the steel section. When there is a larger steel cross-section, there is an increase in the plastic axial strength of the steel profile. This increase causes the neutral plastic axis to descend toward the steel profile, causing only compression stresses in the hollow-core slab. 3.
The greater the spacing of the shear studs, the greater the use of the steel section. When considering the hypothesis of partial interaction, as presented for the models with 175 mm and 225 mm of spacing, the structural system can achieve ductile behavior, a factor that favors the ability of the structural elements to deform without reaching the ultimate strength. The use of a smaller number of shear connectors (175 mm and 225 mm models) provided resistance equivalent to the 120 mm models. Therefore, using a lower amount of material for the design of a structural system, as was the case with modeled Steel-Concrete composite beams, from the point of view of sustainability, there is a reduction in the embodied energy, since a smaller number of installed connectors will require a smaller amount of electricity consumption.

4.
The transverse reinforcement rate had little influence on the ultimate strength of the models analyzed. This was because in most models, the fragile behavior was verified.

5.
With the variation of the in situ concrete strength, there were no significant differences in the ultimate strength. Therefore, the use of lower in situ concrete strength can be advantageous; that is, the lower the concrete resistance, the greater the possibility that the plastic neutral axis will lie within the steel section. However, it is worth mentioning that the strength of concrete is also related to durability, a factor that certainly influences the life cycle of the structural element. The greater the durability of the structural system, the less the need for excessive maintenance, thus contributing to the reduction of waste and embodied energy. 6.
Ductile behavior was observed for models with 225 mm of spacing, considering the W460 × 74 and W530 × 72 sections. It also was verified that the lower the interaction degree, the greater the midspan vertical displacement, which may exceed the limit of L/200.

7.
Regarding the verification of strength with the calculation procedure, some models that considered full interaction proved to be unsafe (M FE ≤ M Rk ). On the other hand, all observations considering partial interaction proved to be safe (M FE > M Rk ). 8.
The numerical models with a 265 mm hollow-core unit presented greater resistance than the models with a150 mm hollow-core unit, considering the W360 × 51 section. However, for the W460 × 74 and W530 × 72 sections, there were no significant differences. The basic difference between the models compared was 115 mm of precast concrete. Therefore, for the numerical models evaluated, using a smaller amount of precast concrete provided a better efficiency of the structural system. The use of a lower volume of concrete in a structural project provides a reduction in the structure's own weight, and in terms of sustainability, a lower amount of CO 2 emissions.