sustainability

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

Felipe Piana Vendramell Ferreira 1 , Konstantinos Daniel Tsavdaridis 2,* , Carlos Humberto Martins 3 and Silvana De Nardin 1

1 Department of Civil Engineering, Federal University of São Carlos, 13565-905 São Carlos, São Paulo, Brazil; [email protected] (F.P.V.F.); [email protected] (S.D.N.) 2 School of Civil Engineering, Faculty of Engineering and Physical Sciences, University of Leeds, Leeds LS2 9JT, UK 3 Department of Civil Engineering, State University of Maringá, 87020-900 Maringá, Paraná, Brazil; [email protected] * Correspondence: [email protected]; Tel.: +44(0)-113-343-2299

Abstract: 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 Citation: Ferreira, F.P.V.; Tsavdaridis, loads. The publication SCI P401, in accordance with Eurocode 4, is however limited to hollow-core K.D.; Martins, C.H.; De Nardin, S. slabs with depths from 150 to 250 mm, with or without a concrete topping. This paper aims to Steel-Concrete Composite Beams investigate hollow-core slabs with a concrete topping to understand their effect on the flexural with Precast Hollow-Core Slabs: A Sustainable Solution. Sustainability behavior of Steel-Concrete composite beams, considering the hollow-core-slab depth is greater than 2021, 13, 4230. https://doi.org/ the SCI P401 recommendation. Consequently, 150 mm and 265 mm hollow-core units with a concrete 10.3390/su13084230 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 Academic Editor: Jorge de Brito 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, Received: 17 March 2021 meaning that the same strength can be obtained for a smaller number of shear studs, i.e., less energy Accepted: 7 April 2021 consumption, thus a reduction in the embodied energy. The calculation procedure, according to Published: 10 April 2021 Eurocode 4 was in favor of safety for the partial-interaction hypothesis.

Publisher’s Note: MDPI stays neutral Keywords: composite beams; hollow-core slabs; sustainable; finite element analyses with regard to jurisdictional claims in published maps and institutional affil- iations. 1. 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 Copyright: © 2021 by the authors. materials of buildings [1]. In Whitworth and Tsavdaridis [2,3], optimization studies were Licensee MDPI, Basel, Switzerland. This article is an open access article presented in Steel-Concrete composite beams with the objective of presenting sustainable distributed under the terms and structural designs by minimizing the embodied energy. The study showed that it is conditions of the Creative Commons possible to reduce the embodied energy of these structural systems, considering the design Attribution (CC BY) license (https:// recommendations of Eurocode 4 [4]. creativecommons.org/licenses/by/ Conventional Steel-Concrete composite beams have a concrete slab that is placed at 4.0/). the upper flange of the downstand steel profile. In this context, three types of slabs can be

Sustainability 2021, 13, 4230. https://doi.org/10.3390/su13084230 https://www.mdpi.com/journal/sustainability Sustainability 2021, 13, 4230 2 of 25

used: solid, composite or precast hollow-core slabs (PCHCSs). In composite beams with PCHCSs, a cast in situ concrete topping is usually made to provide a smooth and uniform finish [5]. The concrete topping can increase the strength and stiffness of the structural system [6,7]. Other factors influence the strength of PCHCSs, such as the intensity of the actual prestress, the prestress transmission length, the depth of the slab, and filled cores [8]. PCHCSs are widely used in countries with cold climates in the construction of residential or industrial buildings due to their fast installation. In Albero et al. [9], the estimate of the number of PCHCS floors installed in Europe was estimated to be close to 1 billion square meters. The use of PCHCSs offers advantages; e.g., large spans, speed of construction, and reduced construction costs [5,10–14]. In the European Union, according to Ahmed and Tsavdaridis [15], construction and building are responsible for about 40% of environmental impact. In Dong et al. [16], the precast and cast in situ construction methods were compared using a case study. The authors concluded that the precast construction could lead to a 10% carbon reduction for one cubic meter of concrete. The PCHCS is an industrialized structural element that consumes less energy when constructed in-house in comparison to in situ, and with a minimum waste of concrete, and thus with an overall lower carbon footprint. In terms of sustainability, the PCHCS is a structural element that contributes not only to the speed of construction, but also to the significant reduction of CO2 emissions due to the lower consumption of concrete. The present study aims to examine the flexural behavior of Steel-Concrete composite beams with PCHCSs and a concrete topping, considering a hollow core unit (HCU) depth greater than the SCI P401 recommendation. The finite element (geometrical nonlinear analysis) model was developed based on tests [17,18]. The results were compared with the SCI P401 procedure [19], and thus analytical models of shear-stud resistance capacity were employed [19,20].

2. Background Lam [17] and Lam et al. [21] presented flexural tests on Steel-Concrete composite beams with PCHCSs. A four-point bending was considered. In these studies, the concrete topping was not considered. The experimental results showed a sudden failure due to the shear studs rupturing and the concrete cracking, resulting in a loss of stiffness. Lam et al. [22] complemented the previous studies and carried out a parametric study in which they observed that with an increase in the depth of PCHCSs (150 mm to 200–250 mm), there was an increase in the ultimate strength. However, the slab could fail due to excessive cracking. Ellobody and Lam [23] investigated the shear studs and the gap while considering the flexural behavior. The authors concluded that the shear-stud resistance increased with the increase of the gap, and the in situ infill concrete strength influenced the strength of the shear studs. In 2003, SCI P287 [24] was published; it is a design criteria for composite beams with PCHCSs [17]. This publication was subsequently updated to SCI P401 [19]. The document gathers recommendations of minimum dimensions, such as arrangement of the shear studs and transverse reinforcement. However, some limitations were observed, such as application only for 150–250 mm HCU depths; 12 mm or 16 mm transverse reinforcement diameters are recommended for composite construction. For partial shear connection, 16 mm diameter bars should be provided; for HCUs up to 260 mm, 16 mm diameter bars should be considered, spaced at 200–350 mm. For full interaction, if the plastic neutral axis (PNA) lies within the slab, the interaction degree must be reduced, or the size of the steel profile increased. A technical report (COPPETEC, PEC-18541/2016), which was presented by Batista and Landesmann [18], described tests on composite beams with PCHCSs and concrete topping. According to the authors, at the ultimate strength, the loss of stiffness was due to excessive cracking. In Ferreira et al. [25], a parametric study was presented, considering PCHCSs with 150 mm of depth and 50 mm of concrete topping. In this study, the presence of the concrete topping increased the strength of the composite beams by at least 7%. As observed, few studies have investigated the behavior of Steel-Concrete composite beams with PCHCSs [26]. Tawadrous and Morcous [4] and Sustainability 2021, 13, x 3 of 24

strength of the composite beams by at least 7%. As observed, few studies have investigated the behavior of Steel-Concrete composite beams with PCHCSs [26]. Tawadrous and Morcous [4] and El-Sayed et al. [5] showed that, due to the successful use Sustainability 2021, 13, 4230 of PCHCSs, deeper HCUs were developed to resist higher loads and3 ofto 25 support longer spans. In this scenario, some researchers carried out tests to investigate the behavior of deeper PCHCSs [12,13,27–32]. However, these investigations did not consider composite behavior,El-Sayed et i.e., al. [5 Steel-Concrete] showed that, due composite to the successful beams. use of PCHCSs, deeper HCUs were developed to resist higher loads and to support longer spans. In this scenario, some researchers carried out tests to investigate the behavior of deeper PCHCSs [12,13,27–32]. 3.However, Numerical these Model: investigations Validation did not considerStudy composite behavior, i.e., Steel-Concrete compositeIn this beams. section, the methodology of the validation study is described. The ABAQUS software3. Numerical [33] Model: was Validationused. Three Study types of Steel-Concrete composite beams were modeled, consideringIn this section, symmetry: the methodology of the validation study is described. The ABAQUS 1.software 150 [mm33] was of used.HCU Threedepth types with of a Steel-Concrete chamfered end composite (Figure beams 1a); were modeled, 2.considering 150 mm symmetry: of HCU depth and 50 mm of concrete topping with a squared end (Figure 1. 1501b); mm of HCU depth with a chamfered end (Figure1a); 2. 150 mm of HCU depth and 50 mm of concrete topping with a squared end (Figure1b);

3.3. 265 mm mm of HCUof HCU depth depth and 50 and mm of50 concrete mm of topping concrete with topping a squared with end (Figure a squared1c) . end (Figure 1c).

(a)

(b)

Figure 1. Cont. SustainabilitySustainability 20212021, 13,, 13x , 4230 4 of 25 4 of 24

(c)

FigureFigure 1. 1.Parts Parts of of Steel-Concrete Steel-Concrete composite composite beams withbeams a hollow with corea hollow slab: ( acore) 150 slab: mm of (a hollow-) 150 mm of hollow- core-slabcore-slab depth depth with with a chamfered a chamfered end; (b end;) 150 mm(b) of150 hollow-core-slab mm of hollow-core-slab depth and 50 mm depth of concrete and 50 mm of con- cretetopping topping with a squaredwith a end;squared (c) 265 end; mm of(c) hollow-core-slab 265 mm of hollow-core-slab depth and 50 mm depth of concrete and topping 50 mm of concrete toppingwith a squared with end.a squared end. Geometrical nonlinear analyses were processed using the Static Riks method. This methodGeometrical was previously nonlinear used in [25 analyses,34–40] and were is based processed on the arc-length using method.the Static Residual Riks method. This methodstresses were was notpreviously considered. used These in stresses[25,34–40] do not and influence is based the on ultimate the arc-length strength of method. Resid- ualcomposite stresses beams were subjected not considered. to only positive These moments. stresses The do residual not influence stresses increase the ultimate the strength of compositeeffects of the beams negative subjected moment [41 to,42 only]. positive moments. The residual stresses increase the effects3.1. Tests of the negative moment [41,42]. The numerical models were calibrated considering tests on Steel-Concrete composite 3.1.beams Tests with PCHCSs, at 150 mm and 265 mm of depth, and with or without a concrete topping. Figure2 and Table1 show the details of the tests [ 18,43], in which d is the steel- The numerical models were calibrated considering tests on Steel-Concrete composite beam depth, bf is the steel-flange width, tf is the steel-flange thickness, tw is the steel-web beamsthickness, withb is PCHCSs, the effective at slab 150 width, mm gandis the 265 gap, mmhc isof the depth, depth and of the with HCU, orc iswithout the a concrete topping.concrete-topping Figure thickness, 2 and TableLe is the 1 distanceshow the between details the of end the of thetests beam [18,43], and the in support, which d is the steel- beamLp is the depth, distance bf between is the steel-flange the load application width, point tf is and the the steel-flange support, Lb is thickness, the unrestrained tw is the steel-web length, ϕ is the diameter of the transverse reinforcement, fy,f is the yield strength of the thickness, b is the effective slab width, g is the gap, hc is the depth of the HCU, c is the flange, fy,w is the yield strength of the web, fy,s is the transverse reinforcement yield strength, concrete-topping thickness, Le is the distance between the end of the beam and the sup- fc,HCU is the HCU compressive strength, and fc,in is the in situ infill compressive strength. port, Lp is the distance between the load application point and the support, Lb is the unre- strainedTable length, 1. Details φ is of the specimens diameter (in mm of and the MPa). transverse reinforcement, fy,f is the yield strength

Model d bf tf tofw theb flange, g fy,w h cis thec yield Le strengthLp ofLb the ϕweb,f y,ffy,s is fthey,w transversefy,s fc,HCU reinforcementfc,in yield CB1 355 171.5 11.5 7.4strength, 1665 fc,HCU 65 is 150 the HCU - 150compressive 1500 5700 strength, 16 310 and 355fc,in is 585the in 50 situa 32infilla compressive CB2 355 171.5 11.5 7.4 1665 65 150 - 150 1500 5700 8 310 355 473 50 a 26 a CB3 299 306 11 11strength. 1756 156 150 50 185 1915 5830 12.5 345 345 500 45 b 30 b CB4 299 306 11 11 1756 106 265 50 185 1915 5830 12.5 345 345 500 45 b 30 b a Cubic resistance; b cylindric resistance.

(a) (b) Figure 2. Geometric details of tests (in mm): (a) lateral view; (b) section. Sustainability 2021, 13, x 4 of 24

(c) Figure 1. Parts of Steel-Concrete composite beams with a hollow core slab: (a) 150 mm of hollow- core-slab depth with a chamfered end; (b) 150 mm of hollow-core-slab depth and 50 mm of con- crete topping with a squared end; (c) 265 mm of hollow-core-slab depth and 50 mm of concrete topping with a squared end.

Geometrical nonlinear analyses were processed using the Static Riks method. This method was previously used in [25,34–40] and is based on the arc-length method. Resid- ual 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].

3.1. 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 steel- beam depth, bf is the steel-flange width, tf is the steel-flange thickness, tw is the steel-web 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 sup- port, Lp is the distance between the load application point and the support, Lb is the unre- strained length, φ is the diameter of the transverse reinforcement, fy,f is the yield strength Sustainability 2021, 13, 4230 of the flange, fy,w is the yield strength of the web, fy,s is the transverse reinforcement 5yield of 25 strength, fc,HCU is the HCU compressive strength, and fc,in is the in situ infill compressive strength.

(a) (b)

FigureFigure 2.2. Geometric details of tests (in(in mm):mm): (a)) laterallateral view;view; ((b)) section.section.

The shear-stud dimensions were 19 × 125 mm2 (CB1 and CB2) and 19 × 135 mm2 (CB3 and CB4). The shear-stud spacing of the CB1 and CB2 models was 150 mm. For models CB3 and CB4, the spacing between the shear studs was 200 mm.

3.2. Materials The concrete-damage plasticity (CDP) [44–46] 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 Table2, in which ψ is the dilation angle, ξ is the eccentricity, σb0 is the initial equibiaxial compressive yield stress, σc0 is the initial uniaxial compressive yield stress, Kc is the ratio of the second stress invariant on the tensile meridian to that on the compressive meridian, and µ is the viscosity parameter.

Table 2. Concrete Damage Plasticity input parameters [25,38,40].

Parameter Value Ref. Ψ (◦) (In situ concrete) 40 [47,49] Ψ (◦) (HCU concrete) 28 [28] ξ 0.1 (default) [28,33,47,49] σb0/σc0 1.16 (default) [28,33,47,49] Kc 2/3 (default) [28,33,47,49] µ (s−1) 0.001 -

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.

σ β (ε/ε ) = c c (1) βc fc βc − 1 + (ε/εc)

σ β (ε/ε ) = c t (2) βc ft βc − 1 + (ε/εt)  f 3 β = c + 1.55(MPa) (3) c 32.4 Sustainability 2021, 13, x 6 of 24

Sustainability 2021, 13, 4230 6 of 25 concrete tensile strength, and βc is the stress–strain relationship form factor of concrete in compression. where εc is the strain corresponding to concrete compressive strength, εt is the strain f f 3.3. Interaction corresponding to concrete tensile strength, c is the compressive concrete strength, t is the concrete tensile strength, and βc is the stress–strain relationship form factor of concrete Figure 3 showsin compression. the pairs of interactions. The tie constraint technique allowed us to simulate the perfect3.3. bond Interaction between the contact surfaces. The contacts between the concrete and the transverse reinforcementsFigure3 shows the were pairs made of interactions. through The the tie embedded constraint technique region allowed [33]. The us to nor- mal/tangential behaviorsimulate thewas perfect considered bond between between the contact the surfaces. steel Thebeam contacts and between PCHCS, the concretethe steel beam and gap, theand actuator the transverse and concrete reinforcements topping, were made and throughthe shear the embeddedstud and region gap. [The33]. Theshear normal/tangential behavior was considered between the steel beam and PCHCS, the steel studs were locatedbeam in andthe gap,gap, the using actuator the and same concrete technique topping, and presented the shear stud in and[52]. gap. The The friction shear coefficient was basedstuds on were the located Coulomb in the gap, friction using themodel. same techniqueThe literature presented reports in [52]. some The friction values of the friction coefficientcoefficient [53–55]. was based Friction on the Coulomb coefficients friction model. of 0.2 The and literature 0.3 were reports adopted some values for of the the friction coefficient [53–55]. Friction coefficients of 0.2 and 0.3 were adopted for the gap gap and headed studand headedand the stud steel and thebeam steel an beamd slab and slabinterfaces, interfaces, respectively respectively [55 ].[55].

Figure 3. Surface-to-surface interactions.Figure 3. Surface-to-surface interactions.

3.4. Boundary Conditions 3.4. Boundary ConditionsThe boundary conditions (Figure4) were applied considering the symmetry at midspan The boundary(U zconditions= URx = URy (Figure= 0) [25,37 4)–40 were]. The verticalapplied displacement considering was restrainedthe symmetry at the supports at mid- (Uy = 0) and the lateral displacement at the ends of the slab (Ux = 0). Displacement control span (Uz = URx = URwasy used.= 0) [25,37–40]. The difficulties The with vertical softening displacement materials can be avoidedwas restrained by applying at a simplethe sup- ports (Uy = 0) andform the oflateral displacement displaceme control [56nt,57 at]. Thethe disadvantagesends of the in slab displacement (Ux = 0). control Displacement are related control was used. toThe the selectiondifficulties of the with appropriate soften displacementing materials variable can [58 be]. Thus,avoided the variable by applying selected a simple form of displacementfor the stopping control criterion was[56,57]. the midspan The disadvantages vertical displacement. in displacement control are related to the selection of the appropriate displacement variable [58]. Thus, the varia- ble selected for the stopping criterion was the midspan vertical displacement. Sustainability 2021, 13, 4230 7 of 25 SustainabilitySustainability 2021 2021, ,13 13, ,x x 77 ofof 2424

FigureFigureFigure 4. 4. 4.Boundary Boundary Boundary conditionsconditions conditions of of of the the the CB3 CB3 CB3 model. model. model.

3.5.3.5.3.5. DiscretizationDiscretization Discretization TheTheThe discretizationdiscretization discretization of of thethe elements elements is is shown shown in in in Figure Figure Figure 5. 55. .The The The dimension dimension dimension values values values of of ofthe the theelementselements elements were were were adopted adopted adopted according according according to to the the to literat theliterat literatureureure [28,53,54], [28,53,54], [28,53, 54and and], andwith with with respect respect respect to to the the to mas- mas- the masterterter and and and slave slave slave surfaces. surfaces. surfaces. The The TheS4R S4R S4Relement element element was was wasa a quadrilateral quadrilateral a quadrilateral element element element with with with four four fournodes. nodes. nodes. This This Thiselementelement element had had reduced hadreduced reduced integration. integration. integration. According According According to to the the ABAQUS, ABAQUS, to the ABAQUS, Dassault Dassault Dassault Systèmes, Systèmes, Syst software softwareèmes, software[33],[33], the the [C3D8R 33C3D8R], the element C3D8Relement elementhad had eight eight had nodes, nodes, eight redu redu nodes,cedced reducedintegration, integration, integration, supported supported supported plastic plastic analysis plasticanalysis analysiswithwith large large with deformations, deformations, large deformations, and and allowed allowed and the allowedthe visualization visualization the visualization of of the the crack crack of in thein the the crack CDP CDP in model. model. the CDP The The model.T3D2T3D2 element element The T3D2 had had element 2-node 2-node hadlinear linear 2-node displacement. displacement. linear displacement.

FigureFigureFigure 5. 5. 5.Discretization. Discretization. Discretization.

3.6.3.6.3.6. ResultsResults Results

TheTheThe results resultsresults are areare presented presentedpresented in in Figurein FigureFigure6 and 66 andand Table TableTable3, in which3,3, inin whichwhichMFE MisMFE theFE isis bending thethe bendingbending moment mo-mo- ofmentment finite of of elementfinite finite element element model, model, model,MTest M MisTestTest the is is bendingthe the bending bending moment moment moment of experimentalof of experimental experimental tests, tests, tests,δFE δ δFEFEis is is the the the midspanmidspanmidspan verticalvertical vertical displacement displacement of of the the the finite finite finite element element element models, models, models, and and and δ δTestTestδ is Testis the theis mid-pan mid-pan the mid-pan verti- verti- verticalcalcal displacementdisplacement displacement ofof thethe of tests. thetests. tests. ItIt waswas It possible waspossible possible toto observeobserve to observe thethe yieldingyielding the yielding atat thethe atlowerlower the flange,lowerflange, flange,andand inin and thethe in CB1CB1 the and CB1and andCB2CB2 CB2 models,models, models, thethe the crackingcracking cracking waswas was observedobserved observed inin in thethe the lower lower partpart of ofof the thethe PCHCSs,PCHCSs,PCHCSs, according according according to to to Lam Lam Lam [17 [17]. [17].]. The The The behaviors behaviors behaviors of of theof the the CB3 CB3 CB3 and and and CB4 CB4 CB4 models models models were were were similar similar similar to thosetoto thosethose presented presentedpresented in Batista inin BatistaBatista and Landesmann andand LandesmannLandesmann [18]; that [18];[18]; is, thatthat there is,is, was therethere a propagation waswas aa propagationpropagation of cracks ofof thatcrackscracks started that that instarted started the central in in the the partcentral central of thepart part PCHCS of of the the PCHCS andPCHCS extended and and extended extended over the over over entire the the width. entire entire width. width. Sustainability 2021, 13, 4230 8 of 25 Sustainability 2021, 13, x 8 of 24

600 600 500 500 400 400 300 300 M (kN.m) M (kN.m) 200 200 Test Test 100 FE 100 FE 0 0 0 10203040 0 1020304050 Mid-span vertical displacement (mm) Mid-span vertical displacement (mm)

(a) (b) 1000 1200

800 1000 800 600 600 400

M (kN.m) M (kN.m) 400 Test Test 200 FE 200 FE 0 0 0 20406080 0 204060 Mid-span vertical displacement (mm) Mid-span vertical displacement (mm)

(c) (d)

Figure 6. Validation results: (a) CB1 model;model; ((b)) CB2CB2 model;model; ((cc)) CB3CB3 model;model; andand ((dd)) CB4CB4 model.model.

Table 3. Comparison of finite element analyses and tests results. Table 3. Comparison of finite element analyses and tests results.

MTest δTest MFE δFE Model M δ M δ MFE/Mtest δFE/δtest Model Test Test FE FE M /M δ /δ (kN.m)(kN.m) (mm)(mm) (kN.m)(kN.m) (mm)(mm) FE test FE test CB1 497 32 496 33 1.00 1.03 CB1 497 32 496 33 1.00 1.03 CB2CB2 474 35 35 485 485 34 34 0.95 0.95 0.97 CB3CB3 846 70 70 895 895 71 71 0.95 0.95 1.00 CB4CB4 985 37 37 1015 1015 35 35 1.03 1.03 0.95

4. Numerical Model: Parametric Study The following were the general considerations for thethe parametricparametric study:study: 1. TheThe thickness thickness of of the the concrete concrete topping topping was was 50 50 mm; 2. TheThe total total transverse transverse reinforcement reinforcement length length was was 1000 + gg,, in in mm; mm; 3. AA welded welded steel steel mesh mesh with with 4.2 4.2 mm mm ×× 100100 mm mm was was considered considered [20,25]; [20,25]; 4. LP26LP26 units units (Figure (Figure 77),), withwith ffcc == 40 40 MPa MPa and and gg == 70 70 mm, mm, were were considered; considered; 5. ForFor the the steel beam, the ASTM A572 Gr.50Gr.50 steelsteel waswas adoptedadopted (f(yfy == 345345 MPa).MPa). TheThe Young’sYoung’s module and the Poisson’s ratio were 200 GPa and 0.3, respectively; 6. TheThe composite composite beams beams were were simply simply supported supported,, and and subjected subjected to to four-point bending. TheThe loads loads were were spaced in L/4 from from each each support. support. Stiffeners Stiffeners were were placed at the support andand points points of of loads; loads; 7. TheThe midspan midspan vertical vertical displacement of a maximum valuevalue equalequal toto LL/100/100 was adopted asas a a stopping stopping criterion criterion [25]. [25]. The studied parameters are shown in Table 4. Sustainability 2021, 13, x 9 of 24 Sustainability 2021, 13, 4230 9 of 25

Sustainability 2021, 13, x 9 of 24

Figure 7. LP26 units (in mm). FigureFigure 7. LP26 7. units LP26 (in mm). units (in mm). The studied parameters are shown in Table4. Table 4. Parametric study. Table 4. Parametric study. Table 4. Parametric study.Parameters Variation Section W360x51, W460x74, and W530x72 ParametersParameters Variation Variation In situ concreteSection strength (MPa) W360x51, W460x74, 25, 30, andand W530x72 40 TransverseIn situ concrete reinforcement strength (MPa) diameter (mm) 25, 10, 30, 12.5, and 40and 16 TransverseShear-stud reinforcement spacing diameter (mm) (mm)Section 10, 125, 12.5, 175, and and 16 275 W360x51, W460x74, and W530x72 Shear-studIn spacingsitu (mm)concrete strength 125,(MPa) 175, and 275 25, 30, and 40 5. Results and Discussion 5. ResultsIn Transversethis and section, Discussion the results reinforcement are discussed, according diam to eterthe steel (mm) cross-sections that 10, 12.5, and 16 wereIn analyzed. this section, At thethe resultsend of arethis discussed, section, th accordinge results are to the compared steel cross-sections with the resistant that were cal- analyzed.culation procedures At the end offorShear-stud this Steel-Concrete section, the results compositspacing aree compared beams, (mm) as with well the as resistantwith the calculationresults pre- 125, 175, and 275 proceduressented in Ferreira for Steel-Concrete et al. [25], compositeconsidering beams, a 150 asmm well depth as with of the the PCHCS results presentedwith concrete in Ferreiratopping. et al. [25], considering a 150 mm depth of the PCHCS with concrete topping. 5. Results and Discussion 5.1.5.1. W360x51 W360x51 Section Section ConsideringConsideringIn this aa spacingspacing section, between the shear shear resultsstuds studs of of 120 120 aremm, mm, for discussed, for the the midspan midspan vertical verticalaccording dis- to the steel cross-sections that displacementplacement at at 15 15 mm, mm, only only the the region region where where the beam waswas supportedsupported reachedreached the the yield yield strength.strength.were TheTheanalyzed. maximum maximum vonvon At Mises Mises the stresses stresses end in in of the the lowerthis lower flange, section,flange, web, web, and andth upper eupper results flange flange are compared with the resistant cal- werewere approximately approximately 290 290 MPa, MPa, 260 260 MPa, MPa, and and 115 115 MPa, MPa, respectively. respectively. When When the the composite composite beamculation reached the procedures ultimate strength, forfor the Steel-Concrete midspan vertical displacement composit at 26 mm,e the beams, as well as with the results pre- beam reached the ultimate strength, for the midspan vertical displacement at 26 mm, the lower flange and approximately 1/4 of the web depth were in the plastic regime. The yield lower flange and approximately 1/4 of the web depth were in the plastic regime. The yield strengthsented was reachedin Ferreira in none of theet regions al. [25], where theconsidering shear studs were located. a 150 The mm von depth of the PCHCS with concrete strength was reached in none of the regions where the shear studs were located. The von Mises stresses in the upper flange were approximately 200 MPa. The ultimate strength was Misestopping. stresses in the upper flange were approximately 200 MPa. The ultimate strength governed by excessive cracking of the PCHCS (Figure8). was governed by excessive cracking of the PCHCS (Figure 8). 5.1. W360x51 Section Considering a spacing between shear studs of 120 mm, for the midspan vertical dis- placement at 15 mm, only the region where the beam was supported reached the yield strength. The maximum von Mises stresses in the lower flange, web, and upper flange were approximately 290 MPa, 260 MPa, and 115 MPa, respectively. When the composite beam reached the ultimate strength, for the midspan vertical displacement at 26 mm, the lower flange and approximately 1/4 of the web depth were in the plastic regime. The yield

Figurestrength 8. Final configuration was reached for W360x51, in fc = 25none MPa, φ =of 10 mm,the and regions 120 mm of spacing. where the shear studs were located. The von Figure 8. Final configuration for W360x51, fc = 25 MPa, ϕ = 10 mm, and 120 mm of spacing. MisesWith thestresses variation of inthe transversethe upper reinforcement flange rate andwere in situ apprconcreteoximately strength, 200 MPa. The ultimate strength therewas were governed no differences by in the excessive shear-slip and crac moment-deflectionking of the relationships PCHCS (Figure (Figure 8). 9).

Figure 8. Final configuration for W360x51, fc = 25 MPa, φ = 10 mm, and 120 mm of spacing.

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). Sustainability 2021, 13, 4230 10 of 25

Sustainability 2021, 13, x 10 of 24 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 (Figure9).

800 1000

800 600 600 400 400 V (kN) φ=10 mm φ=10 mm 200 φ=12.5 mm M (kN.m) φ=12.5 mm 200 φ=16 mm φ=16 mm 0 0 01234 0 102030 Slip (mm) Mid-span vertical displacement (mm) (a) (b) 800 1000

800 600 600 400 400 V (kN) φ=10 mm φ=10 mm 200 φ=12.5 mm M (kN.m) φ=12.5 mm 200 φ=16 mm φ=16 mm 0 0 01234 0 102030 Slip (mm) Mid-span vertical displacement (mm) (c) (d)

FigureFigure 9. Influence 9. Influence of transverse of transverse reinforcement reinforcement for for the the W360x51 section section with with 120 120 mm mm of spacing:of spacing: (a) Shear-slip(a) Shear-slip relationship relationship for fc for= 25fc =MPa; 25 MPa; (b) (moment-deflectionb) moment-deflection relationship relationship for for ffcc = 2525 MPa;MPa; ( c()c shear-slip) shear-slip relationship relationship for fforc = 40fc = MPa; 40 MPa; and (dand) (d) moment-deflectionmoment-deflection relationship relationship for for fc f=c =40 40 MPa. MPa.

ThisThis can can be be explained explained as as a a function function ofof thethe depthdepth and and area area of of the the steel steel cross-section cross-section in relationin relation to the to depth the depth and andeffective effective area area of the of the PCHCS PCHCS and and concrete concrete topping. topping. Upon Upon reach- reaching the ultimate strength, as shown in Figure8, the neutral plastic axis (NPA) was ing the ultimate strength, as shown in Figure 8, the neutral plastic axis (NPA) was in the in the concrete topping, a factor that generates excessive tensile stresses in the PCHCS. concreteThis can topping, be concluded a factor since that in thegenerates final configuration, excessive tensile the upper stresses part of in the the PCHCS, PCHCS. which This can bewas concluded in the region since of in pure the bending,final configuration, was damaged. the Another upper importantpart of the observation PCHCS, which was the was in thefragile region behavior of pure of bending, the composite was damaged. beams, since Another the slip valuesimportant at the observation steel-concrete was interface the fragile behaviorwere less of than the 6composite mm, a parameter beams, that since Eurocode the slip 4 values [4] considers at the to steel-concrete characterize the interface ductile were lessbehavior than 6 (Figuremm, a 9parameter). Due to this that fragile Eurocode behavior, 4 [4] with considers the variation to characterize of parameters, the suchductile be- havioras transverse (Figure reinforcement9). Due to this rate fragile and inbehavior situ concrete, with strength, the variation there were of parameters, no significant such as transversedifferences reinforcement in terms of stresses, rate and both in in thesitu shear conc studsrete strength, and in the there transversal were reinforcement,no significant dif- considering the ultimate strength. Some examples are illustrated in Figure 10. For the ferences in terms of stresses, both in the shear studs and in the transversal reinforcement, models with fc = 25 MPa, it was observed that the smaller the transverse reinforcement considering the ultimate strength. Some examples are illustrated in Figure 10. For the diameter, the lower the von Mises stresses in the shear stud. For fc = 25 MPa, the von modelsMises with stresses fc = in 25 the MPa, shear it studs was showed observed a variation that the of onlysmaller 6 MPa. the Ontransverse the other hand,reinforcement for diameter,fc = 40 MPa the, lower there were the novon variations Mises stresses between in the the von shear Mises stud. stresses For infc = the 25 shear MPa, studs the von with Mises stressesthe variation in the shear of the studs transverse showed reinforcement a variation diameter. of only The6 MPa. observations On the other for f chand,= 30 MPa for fc = 40 MPa,were there similar. were no variations between the von Mises stresses in the shear studs with the variation of the transverse reinforcement diameter. The observations for fc = 30 MPa were similar. Sustainability 2021, 13, 4230 11 of 25 Sustainability 2021, 13, x 11 of 24

Sustainability 2021, 13, x 11 of 24

(a) (b)

Figure 10. The von Mises stresses in headed studs for the W360x51 section and spacing of 120 mm: (a) fc = 25 MPa and φ = Figure 10. The von Mises stresses(a) in headed studs for the W360x51 section and spacing(b) of 120 mm: (a) fc = 25 MPa and 10 mm; (b) fc = 40 MPa and φ = 16 mm. ϕ = 10 mm; (b) fc = 40 MPa and ϕ = 16 mm. Figure 10. The von Mises stresses in headed studs for the W360x51 section and spacing of 120 mm: (a) fc = 25 MPa and φ = 10 mm; (b) fc = 40 MPa and φ = 16 mm.On the other hand, for the shear-stud spacing at 175 mm and 225 mm, for the mid- On the other hand, for the shear-stud spacing at 175 mm and 225 mm, for the midspan span vertical displacement at 15 mm, the behavior was similar to the models with 120 mm vertical displacement at 15 mm, the behavior was similar to the models with 120 mm ofOn spacing. the other However, hand, for at the shear-studultimate streng spacingth, theat 175midspan mm and vertical 225 mm, displacements for the mid- were spanof spacing.greater vertical than displacement However, in the previous at at the 15 ultimatemm,situation, the be strength,withhavior the was maximum the similar midspan tovalue the vertical modelsequal to withdisplacements 36 mm, 120 mmconsid- were ofgreater spacing.ering than φ =However, 16 in mm, the previousfc =at 40 the MPa, ultimate situation, and 175 streng mm withth, of the spacing.the maximum midspan For the vertical value situation equaldisplacements in which to 36 mm, the were spacing considering greaterϕ =was 16 than mm,225 mm,infc the= the 40 previous midspan MPa, andsituation, vertical 175 mm withdispla of thecement spacing. maximum reached For value the42 mm, situationequal considering to 36 in mm, which consid-φ = 10 the mm spacing c eringwasand 225φ =f c16 mm,= mm,25 MPa. the f =midspan 40 Regarding MPa, and vertical the 175 ultimate mm displacement of spacing. strength, For reachedthe the composite situation 42 mm, in beams which considering with the spacing shear-studϕ = 10 mm was 225 mm, the midspan vertical displacement reached 42 mm, considering φ = 10 mm andspacingfc = 25 of MPa 175 .mm Regarding and 225 mm the made ultimate better strength, use of the the steel composite section; that beams is, approximately with shear-stud andspacinghalf fc = the25 of MPa. 175web mmdepthRegarding and reached 225 the mm ultimateplas madetification strength, better (Figure use the of 11).composite the Then, steel thebeams section; greater with that the shear-stud is, spacing approximately be- spacinghalftween the of web the175 shear depthmm and studs, reached 225 the mm plastificationbetter made the better use useof (Figure the of steelthe 11 steel ).section. Then, section; the that greater is, approximately the spacing between half the web depth reached plastification (Figure 11). Then, the greater the spacing be- the shear studs, the better the use of the steel section. tween the shear studs, the better the use of the steel section.

(a)

(a)

(b)

(b)

Figure 11. Final configuration for the W360x51 section: (a) 175 mm of spacing, fc = 40 MPa, and ϕ = 16 mm; and (b) 225 mm of spacing, fc = 25 MPa, and ϕ = 10 mm. SustainabilitySustainability 2021 2021, 13, 13x , x 12 12of 24of 24

Sustainability 2021, 13, 4230 FigureFigure 11. 11.Final Final configuration configuration for forthe the W360x51 W360x51 section: section: (a) (175a) 175 mm mm of spacing,of spacing, fc = f4012c = ofMPa,40 25 MPa, and and φ = φ = 16 mm;16 mm; and and (b) (225b) 225 mm mm of spacing,of spacing, fc = f25c = MPa,25 MPa, and and φ = φ 10 = mm.10 mm.

TheThe Thevariation variation variation in inbothin both both the the the transverse transverse transverse reinforcement reinforcement reinforcement rate rate (Figures rate (Figures (Figures 12 and 12 13 12and) and and 13) the 13) and and the the in in situsitu concretein concrete situ concrete strength strength strength showed showed showed significant significant significant differences differencesdifferences in in thein the the shear-slip shear-slip and and moment-and moment-deflec- moment-deflec- tiontion relationships.deflection relationships. relationships.

800800 10001000

600600 800800 600600 400400

V (kN) 400 V (kN) φ=10φ=10 mm mm 400 φ=10φ=10 mm mm M (kN.m) 200200 φ=12.5φ=12.5 mm mm M (kN.m) φ=12.5φ=12.5 mm mm 200200 φ=16φ=16 mm mm φ=16φ=16 mm mm 0 0 0 0 0246024600 10203040 10203040 SlipSlip (mm) (mm) Mid-spanMid-span vertical vertical displacement displacement (mm) (mm) (a) (a) (b)( b)

FigureFigure 12. Figure 12.Influence Influence 12. Influence of transverseof transverse of transverse reinforcement reinforcement reinforcement for for forthe the the W360x51 W360x51 W360x51 section, section, section,fc = f 40c = fMPa40c = MPa40 and175 MPa and175 mmand175 of mm spacing: mm of spacing:of (a) spacing: shear-slip (a) (shear-slipa) shear-slip relationship;relationship;relationship; and and (b) ( andmoment-deflectionb) moment-deflection (b) moment-deflection relationship. relationship.

800800 10001000 800800 600600 600600 400400 400

V (kN) 400 V (kN) φ=10φ=10 mm mm φ=10φ=10 mm mm M (kN.m) 200200 φ=12.5φ=12.5 mm mm M (kN.m) φ=12.5φ=12.5 mm mm 200200 φ=16φ=16 mm mm φ=16φ=16 mm mm 0 0 0 0 02460246 0204002040 SlipSlip (mm) (mm) Mid-spanMid-span vertical vertical displacement displacement (mm) (mm) (a) (a) (b)( b)

FigureFigure 13. Figure 13.Influence Influence 13. Influence of transverseof transverse of transverse reinforcement reinforcement reinforcement for for for thethe W360x51the W360x51 W360x51 section, section, section,fc = 40 fcMPa = f c40 = and 40MPa 225MPa and mm and of225 spacing: 225 mm mm of (a) spacing: shear-slipof spacing: (a) (shear-a) shear- slipslip relationship; relationship;relationship; and and and (b) ( (bmoment-deflectionb)) moment-deflection moment-deflection relationship. relationship. relationship.

As shown in the illustrations, even with the variation of the transverse reinforcement Asrate Asshown and shown in situin thein concrete the illustrations, illustrations, strength, even the even initial with with stiffnesses the the variation variation of the of composite theof the transverse transverse beams reinforcement modeled reinforcement rate rate andand inwere situin situ similar, concrete concrete showing strength, strength, that the the differencesinitial initial stiffnesses stiffnesses of these of relations theof the composite werecomposite significant beams beams inmodeled the modeled non- were were sim- sim- ilar,ilar, showinglinear showing branch. that that Althoughthe the differences differences the ultimate of theseof moment these rela rela hadtionstions an were approximate were significant significant value in for thein the the nonlinear models nonlinear branch. branch. AlthoughAlthoughillustrated the the ultimate (ϕ ultimate= 10 mm, moment momentϕ = 12.5 had mm, had an and anappr ϕappr=oximate 16oximate mm), value the value models for for the with the modelsϕ models= 10 mmillustrated illustrated and (φ (=φ 10 = 10 ϕ = 12.5 mm showed similar behavior in the shear-slip and moment-deflection relation- mm,mm, φ =φ 12.5 = 12.5 mm, mm, and and φ =φ 16 = 16mm), mm), the the models models with with φ =φ 10 = 10mm mm and and φ =φ 12.5 = 12.5 mm mm showed showed ships, and were different from the model with ϕ = 16 mm (Figures 12 and 13). According to similarsimilarLam behavior et behavior al. [22 ],in with inthe thethe shear-slip increase shear-slip in and the and transversemoment-deflection moment-deflection reinforcement relationships, rate, relationships, the flexural and strength and were were different different fromfrom capacitythe the model model increases, with with butφ =φ reduces 16 = 16mm mm the (Figures ductility, (Figures 12 leading 12and and 13). to fragile13). According According rupture. to Lamto Lam et al.et al.[22], [22], with with the the increaseincrease inAnother thein the transverse importanttransverse reinforcement observation reinforcement was rate, that rate, the in the noflexural modelflexural strength presented strength capacity for capacity the W360x51 increases, increases, but but re- re- ducesducessection the the ductility, did ductility, the composite leading leading to beams fragileto fragile show rupture. ductile rupture. behavior. Thus, it was possible to conclude that in all models analyzed for W360x51 section, the ultimate strength was characterized Anotheras fragile.Another important In mostimportant observations observation observation for both was 175was that mm that in and noin 225 nomodel mmmodel ofpresented spacing, presented the for von for the Misesthe W360x51 W360x51 sec- sec- tiontion didstresses did the the in composite the composite shear studs beams werebeams lessshow show than ductile the ductile models behavior. behavior. with 120 Thus, mm Thus, of spacing.it wasit was possible For possible example, to toconclude conclude thatthat infor allinfc = allmodels 25 models MPa, analyzed considering analyzed for the for W360x51 175 W360x51 mm and sect 225section, mmion, the models, the ultimate ultimate the von strength strength Mises stresseswas was characterized in characterized as asfragile. thefragile. shear In studsInmost most wereobservations observations lower than for the for modelboth both 175 with 175 mm 120 mm mmand and of 225 spacing. 225 mm mm Aof similarofspacing, spacing, situation the the von von Mises Mises occurred for f = 30 MPa. On the other hand, for f = 40 MPa, there were models in which stressesstresses in thein the shearc shear studs studs were were less less than than the the modelsc models with with 120 120 mm mm of spacing.of spacing. For For example, example, the von Mises stresses in the shear studs, considering 175 mm and 225 mm of spacings, forfor fc = f c25 = 25MPa, MPa, considering considering the the 175 175 mm mm and and 225 225 mm mm models, models, the the von von Mises Mises stresses stresses in thein the shearshear studs studs were were lower lower than than the the model model with with 120 120 mm mm of ofspacing. spacing. A similarA similar situation situation oc- oc- curredcurred for for fc = f c30 = 30MPa. MPa. On On the the other other hand, hand, for for fc = f c40 = 40MPa, MPa, there there were were models models in whichin which the the vonvon Mises Mises stresses stresses in thein the shear shear studs, studs, considering considering 175 175 mm mm and and 225 225 mm mm of spacings,of spacings, were were greatergreater than than the the model model with with 120 120 mm mm of spacing.of spacing. This This was was observed observed specifically specifically for for trans- trans- versal-reinforcementversal-reinforcement diameters diameters equal equal to 10to 10mm mm and and 12.5 12.5 mm. mm. Sustainability 2021, 13, x 13 of 24

Sustainability 2021, 13, 4230 5.2. W460x74 Section 13 of 25 Considering 120 mm of spacing between the shear studs, for the midspan vertical were greater than the model with 120 mm of spacing. This was observed specifically for transversal-reinforcementdisplacement diameters at 15 equal mm, to 10 only mm and 12.5the mm. region in which the beam was supported reached the 5.2.yield W460x74 strength. Section The von Mises stresses in the lower flange, web, and upper flange were Considering 120 mm of spacing between the shear studs, for the midspan vertical displacement290 MPa, at 15 mm,290 only MPa, the region and in which 120 the MPa, beam was respectively. supported reached the When the composite beam reached its ul- yieldtimate strength. Thestrength, von Mises stresses the inupper the lower flange,flange web, and and upper approx flange wereimately 1/4 of the web depth were in the 290 MPa, 290 MPa, and 120 MPa, respectively. When the composite beam reached its ultimateplastic strength, regime. the upper flange The and von approximately Mises 1/4 stresses of the web depth in were the in theupper flange were 230 MPa. The ultimate plastic regime. The von Mises stresses in the upper flange were 230 MPa. The ultimate strengthstrength was governed was by excessivegoverned cracking by of the excessive PCHCS (Figure 14cr). acking of the PCHCS (Figure 14).

FigureFigure 14. Final 14. configuration Final configuration for the W460x74 section, forfc the= 25 MPa,W460x74ϕ = 10 mm, section, and 120 mm fc = 25 MPa, φ = 10 mm, and 120 mm of spacing. of spacing.

With the transverse reinforcement rate variation and in situ concrete strength, there were no differencesWith in the the shear-slip transverse and moment-deflection reinforcement relationships (Figurerate 15variation). and in situ concrete strength, there As noted, there were no significant differences in the behavior of these analyzed compositewere beams, no becausedifferences the ultimate strengthin the was shear-slip achieved by excessive and cracking moment-deflection of the relationships (Figure 15). 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. 1000 Due to this fragile behavior, with the variation of the parameters1400 such as transverse rein- forcement rate and in situ concrete strength, there were small differences in the magnitude of the von Mises stresses, specifically in the shear studs. Some examples1200 are illustrated in 800 Figure 16. 1000 600 800 400 600 V (kN) φ=10 mm φ=10 mm φ=12.5 mm M (kN.m) 400 φ=12.5 mm 200 φ=16 mm 200 φ=16 mm 0 0 0246 0 10203040 Slip (mm) Mid-span vertical displacement (mm) (a) (b) 1000 1400 1200 800 1000 600 800 400 600 V (kN) φ=10 mm φ=10 mm φ=12.5 mm M (kN.m) 400 φ=12.5 mm 200 φ=16 mm 200 φ=16 mm 0 0 0246 0 10203040 Slip (mm) Mid-span vertical displacement (mm) (c) (d) Figure 15. Influence of transverse reinforcement for the W460x74 section and 120 mm of spacing: (a) shear-slip relationship for fc = 25 MPa; (b) moment-deflection relationship for fc = 25 MPa; (c) shear-slip relationship for fc = 40 MPa; and (d) moment-deflection relationship for fc = 40 MPa.

As noted, there were no significant differences in the behavior of these analyzed com- posite beams, because the ultimate strength was achieved by excessive cracking of the PCHCS, a situation analogous to the W360x51 section. Another important observation Sustainability 2021, 13, x 13 of 24

5.2. W460x74 Section Considering 120 mm of spacing between the shear studs, for the midspan vertical displacement at 15 mm, only the region in which the beam was supported reached the yield strength. The von Mises stresses in the lower flange, web, and upper flange were 290 MPa, 290 MPa, and 120 MPa, respectively. When the composite beam reached its ul- timate strength, the upper flange and approximately 1/4 of the web depth were in the plastic regime. The von Mises stresses in the upper flange were 230 MPa. The ultimate strength was governed by excessive cracking of the PCHCS (Figure 14).

Figure 14. Final configuration for the W460x74 section, fc = 25 MPa, φ = 10 mm, and 120 mm of spacing. Sustainability 2021, 13, 4230 14 of 25 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).

1000 1400 1200 800 1000 600 800 400 600 V (kN) φ=10 mm φ=10 mm φ=12.5 mm M (kN.m) 400 φ=12.5 mm 200 φ=16 mm 200 φ=16 mm 0 0 0246 0 10203040 Slip (mm) Mid-span vertical displacement (mm) (a) (b) 1000 1400 1200 800 1000 600 800 400 600 V (kN) φ=10 mm φ=10 mm φ=12.5 mm M (kN.m) 400 φ=12.5 mm 200 φ=16 mm 200 φ=16 mm Sustainability 2021, 13, 0x 0 14 of 24

0246 0 10203040 Slip (mm) Mid-span vertical displacement (mm) (c) (d) was the fragile behavior of the composite beams, a situation similar to the W360x51 sec- Figure 15. InfluenceInfluence of transverse tion. Due reinforcement to this fragile forfor thethe behavior, W460x74 sectionsectionwith the andand va 120120riation mm of of spacing: the parameters ( a) shear-slip shear-slip such relationship as transverse for fc = 25 MPa; (b) moment-deflection relationship for fc = 25 MPa; (c) shear-slip relationship for fc = 40 MPa; and (d) for fc = 25 MPa; (b) moment-deflectionreinforcement relationship rate and forin situfc = 25concrete MPa; ( cstre) shear-slipngth, there relationship were small for fdifferencesc = 40 MPa; andin the (d )mag- moment-deflection relationship for fc = 40 MPa. moment-deflection relationshipnitude for fofc = the 40 MPa.von Mises stresses, specifically in the shear studs. Some examples are illus- trated in Figure 16. As noted, there were no significant differences in the behavior of these analyzed com- posite beams, because the ultimate strength was achieved by excessive cracking of the PCHCS, a situation analogous to the W360x51 section. Another important observation

(a) (b)

Figure 16. The von von Mises Mises stresses stresses in in headed headed studs studs for for the the W460x74 W460x74 section section and and 120 120 mm mm of ofspacing: spacing: (a) (fac )=f c25= MPa 25 MPa andand φ = 10 mm; and (b) fc = 40 MPa and φ = 16 mm. ϕ = 10 mm; and (b) fc = 40 MPa and ϕ = 16 mm.

For the fc = 25 MPa models, the smaller the transverse reinforcement diameter, the lower the von Mises stresses in the shear studs.studs. There was no variation in the stresses in the shear studs for ffcc = 25 MPa. A similar situation occurred forfor ffcc = 30 MPa models.models. For the fc == 40 40 MPa MPa models, models, the the von von Mises Mises stresses stresses in in the the shear studs varied with the variation of the transverse reinforcement diameter. Unlike the ffcc = 25 MPa models, the smaller the transverse reinforcement reinforcement diameter, diameter, the the greater greater the the von Mises stresses stresses in in the the shear studs. studs. This variation reached approximately 20 MPaMPa betweenbetween ϕφ == 10 mm and φϕ = 16 mm. Considering the the models models with with 175 175 mm mm and and 225 225 mm mm of ofspacing, spacing, it was it was possible possible to ob- to serveobserve two two different different situations. situations. In relation In relation to the to the175 175mm mmof spacing, of spacing, for the for midspan the midspan ver- tical 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.

(a) Sustainability 2021, 13, x 14 of 24

was the fragile behavior of the composite beams, a situation similar to the W360x51 sec- tion. 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 mag- nitude of the von Mises stresses, specifically in the shear studs. Some examples are illus- trated in Figure 16.

(a) (b)

Figure 16. The von Mises stresses in headed studs for the W460x74 section and 120 mm of spacing: (a) fc = 25 MPa and φ = 10 mm; and (b) fc = 40 MPa and φ = 16 mm.

For the fc = 25 MPa models, the smaller the transverse reinforcement diameter, the lower the von Mises stresses in the shear studs. There was no variation in the stresses in the shear studs for fc = 25 MPa. A similar situation occurred for fc = 30 MPa models. For 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. Sustainability 2021, 13, 4230 This variation reached approximately 20 MPa between φ = 10 mm and φ = 1615 ofmm. 25 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 steel vertical displacement at 15 mm, the yield strength was not reached in any region of the steelprofile. profile. The Themaximum maximum von von Mises Mises stresses stresses in in the the lower lower flange,flange, web, web, and and upper upper flange flange were were290 MPa, 290 MPa, 290 290MPa, MPa, and and 120 120 MPa, MPa, respectively. respectively. WhenWhen the the composite composite beams beams reached reached the theultimate ultimate strength, strength, only only part part of of the the lower lower flangeflange was was in in the the plastic plastic regime regime (Figure (Figure 17a). 17a). For For225 225mm mm of spacing of spacing between between shear shear studs, studs, thethe ultimateultimate strength strength was was characterized characterized with with the thelower lower flange, flange, half half the the web web depth,depth, and and part part of theof the upper upper flange, flange, which which were in were the region in the region of thethe loadingloading application application point, point, in the in plasticthe plastic regime regime (Figure (Figure 17b). This 17b). was This the was model the in model in which the the composite composite action action took took advantage advantage of the of strength the strength of the steelof the profile. steel profile.

Sustainability 2021, 13, x 15 of 24

(a)

(b)

FigureFigure 17. 17. FinalFinal configuration configuration forfor the the W460x74 W460x74 section: section: (a )(a 175) 175 mm mm of spacing,of spacing,fc = f 40c = MPa,40 MPa, and and φ = 10ϕ mm;= 10 mm;and and(b) 225 (b) 225mm mm of ofspacing, spacing, fc f=c =40 40 MPa, MPa, and and φϕ = 16 mm.

TheThe variation inin bothboth the the transverse transverse reinforcement reinforcement rate rate and theand in the situ in concrete situ concrete strengthstrength (Figures (Figures 18 18 and and 19 19)) showed showed significant significa differencesnt differences in the in shear-slip the shear-slip and moment- and moment- deflection relationships. deflection relationships. 1000 1400 1200 800 1000 600 800 400 600 V (kN) fc=25 MPa fc=25 MPa fc=30 MPa M (kN.m) 400 fc=30 MPa 200 fc=40 MPa 200 fc=40 MPa 0 0 0246 0 10203040 Slip (mm) Mid-span vertical displacement (mm) (a) (b) Figure 18. Influence of in situ concrete strength for the W460x74 section, φ = 12.5 mm and 175 mm of spacing: (a) shear- slip relationship; and (b) moment-deflection relationship.

1000 1400 1200 800 1000 600 800 400 600 V (kN) fc=25 MPa fc=25 MPa fc=30 MPa M (kN.m) 400 fc=30 MPa 200 fc=40 MPa 200 fc=40 MPa 0 0 02468 0 1020304050 Mid-span vertical displacement (mm) Slip (mm) (a) (b) Figure 19. Influence of in situ concrete strength for the W460x74 section, φ = 16 mm and 225 mm of spacing: (a) shear-slip relationship; and (b) moment-deflection relationship.

These differences were observed for the concrete with the highest strength and trans- versal-reinforcement diameters equal to 12.5 mm and 16 mm. Figure 18 shows that the Sustainability 2021, 13, x 15 of 24 Sustainability 2021, 13, x 15 of 24

(b) (b) Figure 17. Final configuration for the W460x74 section: (a) 175 mm of spacing, fc = 40 MPa, and φ = Figure 17. Final configuration for the W460x74 section: (a) 175 mm of spacing, fc = 40 MPa, and φ = 10 mm; and (b) 225 mm of spacing, fc = 40 MPa, and φ = 16 mm. 10 mm; and (b) 225 mm of spacing, fc = 40 MPa, and φ = 16 mm. Sustainability 2021, 13, 4230 16 of 25 The variation in both the transverse reinforcement rate and the in situ concrete 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 moment- strength (Figures 18 and 19) showed significant differences in the shear-slip and moment- deflection relationships. deflection relationships. 1000 1400 1000 1400 1200 800 1200 800 1000 1000 600 800 600 800 400 600 V (kN) 400 fc=25 MPa 600 fc=25 MPa M (kN.m) V (kN) fc=30fc=25 MPa MPa 400 fc=30fc=25 MPa MPa 200 fc=30 MPa M (kN.m) 400 fc=30 MPa 200 fc=40 MPa 200 fc=40 MPa fc=40 MPa 200 fc=40 MPa 0 0 00246 00 10203040 0246Slip (mm) Mid-span0 10203040vertical displacement (mm) Slip (mm) Mid-span vertical displacement (mm) (a) (b) (a) (b) FigureFigure 18.18. InfluenceInfluence ofof in in situ situ concrete concrete strength strength for for the the W460x74 W460x74 section, section,ϕ =φ12.5 = 12.5 mm mm and and 175 175 mm mm of spacing:of spacing: (a) shear-slip(a) shear- slipFigure relationship; 18. Influence and ( bof) inmoment-deflection situ concrete strength relationship. for the W460x74 section, φ = 12.5 mm and 175 mm of spacing: (a) shear- relationship;slip relationship; and (b and) moment-deflection (b) moment-deflection relationship. relationship. 1000 1400 1000 1400 1200 800 1200 800 1000 1000 600 800 600 800 400 600 V (kN) fc=25 MPa 600 fc=25 MPa

400 M (kN.m) V (kN) fc=30fc=25 MPa MPa 400 fc=30fc=25 MPa MPa 200 fc=30 MPa M (kN.m) 400 fc=30 MPa 200 fc=40 MPa 200 fc=40 MPa fc=40 MPa 200 fc=40 MPa 0 0 0 002468 0 1020304050 02468Slip (mm) Mid-span0 1020304050 vertical displacement (mm) Slip (mm) Mid-span vertical displacement (mm) (a) (b) (a) (b) Figure 19. Influence of in situ concrete strength for the W460x74 section, φ = 16 mm and 225 mm of spacing: (a) shear-slip Figurerelationship;Figure 19. 19.Influence Influence and (b) of moment-deflection of in in situ situ concrete concrete strength strengthrelationship. for for the the W460x74 W460x74 section, section,ϕ =φ 16= 16 mm mm and and 225 225 mm mm of of spacing: spacing: (a )(a shear-slip) shear-slip relationship;relationship; and and (b )(b moment-deflection) moment-deflection relationship. relationship. These differences were observed for the concrete with the highest strength and trans- These differences were observed for the concrete with the highest strength and trans- versal-reinforcementThese differences diameters were observed equal to for 12.5 the mm concrete and 16 with mm.the Figure highest 18 shows strength that and the transversal-reinforcementversal-reinforcement diameters diameters equal equal to 12 to.5 12.5mm mmand 16 and mm. 16 mm.Figure Figure 18 shows 18 showsthat the 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 fc = 30 MPa showed a different behavior in the shear-slip and moment-deflection relation- ships. 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, consid- ering 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 fc = 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 fc = 30 MPa models. For fc = 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. Sustainability 2021, 13, x 16 of 24

greater the concrete strength, the greater the initial stiffness of the composite beam, alt- hough 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 fc = 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, consid- ering 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 fc = 25 MPa models, the von Mises stresses in the shear studs, consid- ering 175 mm and 225 mm of spacing, were greater than the models with 120 mm of spac- ing. A similar behavior occurred for fc = 30 MPa models. For fc = 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.

Sustainability 2021, 13, 4230 17 of 25 5.3. W530x72 Section Considering 120 mm of spacing, for the midspan vertical displacement at 15 mm, the 5.3.region W530x72 where Section the composite beam was supported and the lower flange reached the yield resistance.Considering The 120 mm maximum of spacing, for von the midspanMises verticalstresses displacement in the lower at 15 mm, flange, the web, and upper flange region where the composite beam was supported and the lower flange reached the yield resistance.were 345 The MPa, maximum 316 von MPa, Mises stressesand 230 in the MPa, lower resp flange,ectively. web, and upperWhen flange the composite beam reached werethe 345 ultimate MPa, 316 MPa, strength and 230 MPa,(Figure respectively. 20), for When the the compositemidspan beam vertical reached thedisplacement at 22 mm, the ultimate strength (Figure 20), for the midspan vertical displacement at 22 mm, the lower flangelower and flange approximately and 1/4approximately of the web depth 1/4 were of in thethe plastic web regime. depth were in the plastic regime.

FigureFigure 20. 20.Final Final configuration configuration for the W530x72 for the section, W530x72fc = 40 section, MPa, ϕ = fc 16= 40 mm, MPa, and 120 φ = mm 16 mm, and 120 mm of spacing. of spacing.

TheThe ultimate ultimate strength wasstrength governed was by excessive governed cracking by of excess the slab.ive It is cracking important of the slab. It is important toto note note that inthat these in models, these there models, were a betterthere use were of the a steel be section,tter use in comparisonof the steel section, in comparison with the previous cross-sections. This was due to the fact that the steel section had a depth andwith area the greater previous than the other cross-sections. steel sections studied. This So,was the due NPA tendedto the to fact move that in the the steel section had a depth directionand area of the greater steel section, than a factor the thatother favored steel the sections resistance studied. of the hollow-core So, the slab, NPA tended to move in the thusdirection reducing tensionof the stresses. steel Withsection, the variation a factor of the that transverse favored reinforcement the resistance rate and of the hollow-core slab, in situ concrete strength, there were no differences in the shear-slip and moment-deflection relationshipsthus reducing (similar totension previous stresses. situations). RegardingWith the the variat von Misesion stresses of the in transverse the shear reinforcement rate and studs,in situ there concrete were no significant strength, differences, there reaching were valuesno di betweenfferences 556 and in 570the MPa. shear-slip and moment-deflec- On the other hand, considering 175 mm of spacing between the shear studs, for the midspantion relationships vertical displacement (similar at 15 mm, to only previous the support situat regionions). reached Regarding the yield strength. the von Mises stresses in the Theshear von Mises studs, stresses there in the were lower flange,no significant web, and upper diff flangeerences, were 316 reaching MPa, 288 MPa, values between 556 and 570 and 116 MPa, respectively. At the ultimate strength (Figure 21a), the midspan vertical displacementMPa. 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). Sustainability 2021, 13, x 17 of 24

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,

Sustainability 2021, 13, 4230 288 MPa, and 116 MPa, respectively. At the ultimate strength (Figure 21a),18 the of 25 midspan vertical displacement was 21 mm. In this loading stage, the lower flange was in the plastic regime.

(a)

(b)

Sustainability 2021, 13, x Figure 21.21.Final Final configuration configuration for for the the W530x72 W530x72 section: section: (a) 175 (a mm) 175 of mm spacing, of spacing,fc = 40 MPa, fc = 40 and MPa,ϕ 18= andof 24 φ =

16 mm;mm; and and (b ()b 225) 225 mm mm of spacing,of spacing,fc = f 40c = MPa,40 MPa, and andϕ = 16 φ mm.= 16 mm.

For 225 mm of spacing, with the midspan vertical displacement at 15 mm, the results 1000 were similar to the previous beam.1400 However, the maximum von Mises stresses in the 1200 800 lower flange, web, and upper flange were 288 MPa, 288 MPa, and 116 MPa, respectively. At the ultimate strength (Figure1000 21b), with the midspan vertical displacement at 38 mm, 600 the lower flange, half the web depth,800 and the upper flange were in the plastic regime. With 400 the variation of the transverse reinforcement600 rate and the in situ concrete strength, it was V (kN) φ=10 mm

M M (kN.m) φ=10 mm possible to verifyφ=12.5 somemm differences400 in the shear-slip and moment-deflection relationships 200 φ=12.5 mm φ=16 mm (Figures 22 and 23). 200 φ=16 mm 0 0 0246 0 10203040 Slip (mm) Mid-span vertical displacement (mm) (a) (b)

FigureFigure 22. Influence 22. Influence of transverse of transverse reinforcement reinforcement forfor the the W530x72 W530x72 section, section,fc = 25fc = MPa 25 MPa and 175 and mm 175 of mm spacing: of spacing: (a) shear-slip (a) shear- slip relationship;relationship; andand ( b(b)) moment-deflection moment-deflection relationship. relationship.

1000 1400 1200 800 1000 600 800 400 600 V (kN) φ=10 mm φ=10 mm φ=12.5 mm M (kN.m) 400 φ=12.5 mm 200 φ=16 mm 200 φ=16 mm 0 0 0246810 0 1020304050 Slip (mm) Mid-span vertical displacement (mm) (a) (b) 1000 1400 1200 800 1000 600 800 400 600 V (kN) φ=10 mm φ=10 mm φ=12.5 mm M (kN.m) 400 φ=12.5 mm 200 φ=16 mm 200 φ=16 mm 0 0 0246810 0 1020304050 Slip (mm) Mid-span vertical displacement (mm) (c) (d) Figure 23. Influence of transverse reinforcement for the W530x72 section and 225 mm of spacing: (a) shear-slip relationship for fc = 25 MPa; (b) moment-deflection relationship for fc = 25 MPa; (c) shear-slip relationship for fc = 30 MPa; and (d) moment-deflection relationship for fc = 30 MPa.

It was observed that for the models with 175 mm of spacing, there were some differ- ences in the relationships presented in Figure 22, considering a transverse reinforcement diameter of 12.5 mm and fc = 25–30 MPa. On the other hand, for the models with 225 mm of spacing, these differences were observed (Figure 23) for a transverse reinforcement di- ameter of 16 mm and similar strength values for concrete. It is important to note that the behaviors shown in Figures 22 and 23 were similar to those presented in Figures 12 and 13.

5.4. 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- Sustainability 2021, 13, x 18 of 24

1000 1400 1200 800 1000 600 800 400 600 V (kN) φ=10 mm

M M (kN.m) φ=10 mm φ=12.5 mm 400 200 φ=12.5 mm φ=16 mm 200 φ=16 mm 0 0 0246 0 10203040 Slip (mm) Mid-span vertical displacement (mm) (a) (b) Sustainability 2021, 13, 4230 19 of 25 Figure 22. Influence of transverse reinforcement for the W530x72 section, fc = 25 MPa and 175 mm of spacing: (a) shear- slip relationship; and (b) moment-deflection relationship.

1000 1400 1200 800 1000 600 800 400 600 V (kN) φ=10 mm φ=10 mm φ=12.5 mm M (kN.m) 400 φ=12.5 mm 200 φ=16 mm 200 φ=16 mm 0 0 0246810 0 1020304050 Slip (mm) Mid-span vertical displacement (mm) (a) (b) 1000 1400 1200 800 1000 600 800 400 600 V (kN) φ=10 mm φ=10 mm φ=12.5 mm M (kN.m) 400 φ=12.5 mm 200 φ=16 mm 200 φ=16 mm 0 0 0246810 0 1020304050 Slip (mm) Mid-span vertical displacement (mm) (c) (d)

FigureFigure 23. 23.Influence Influence of transverseof transverse reinforcement reinforcement for fo ther the W530x72 W530x72 section section and and 225 225 mm mm of spacing:of spacing: (a) ( shear-slipa) shear-slip relationship relationship for fc = 25 MPa; (b) moment-deflection relationship for fc = 25 MPa; (c) shear-slip relationship for fc = 30 MPa; and (d) for fc = 25 MPa; (b) moment-deflection relationship for fc = 25 MPa; (c) shear-slip relationship for fc = 30 MPa; and (d) moment-deflection relationship for fc = 30 MPa. moment-deflection relationship for fc = 30 MPa.

It wasIt was observed observed that that for for the the models models with with 175 175 mm mm of of spacing, spacing, there there were were some some differ- differ- encesences in thein the relationships relationships presented presented in Figurein Figure 22 ,22, considering considering a transverse a transverse reinforcement reinforcement diameterdiameter of 12.5of 12.5 mm mm and andfc = fc25–30 = 25–30 MPa. MPa. On On the the other other hand, hand, for for the the models models with with 225 225 mm mm ofof spacing, spacing, these these differences differences were were observed observed (Figure (Figure 23 23)) forfor a transverse reinforcement reinforcement di- diameterameter of of 16 16 mm mm and and similar similar strength strength values values for for concrete. concrete. It isIt is important important to to note note that that the the behaviorsbehaviors shown shown in Figuresin Figures 22 and 22 and 23 were 23 were similar similar to those to those presented presented in Figures in Figures 12 and 12 13 and. 13. 5.4. Design 5.4.In Design this section, the results are presented in a summarized way, considering the ductile behaviorIn (Figure this section, 24), the the maximum results are midspan presented vertical in a summarized displacement way, for the considering service limit the stateductile forbehavior composite (Figure floors 24), (Figure the 25maximum), and SCI midspan P401 [19 ]vertical procedure displacement (Figure 26 );for and the considering service limit thestate strength for composite models for floors shear (Figure studs presented 25), and SCI in [ 19P401,20 ].[19] Considering procedure full (Figure interaction 26); and and con- that NPA lies in the concrete slab (Equations (4)–(10)), in which Aa is the steel-section cross- sectional area, Cc is the concrete-flange axial strength, fy is the steel-section yield strength, L is the composite-beam length, Mpl is the plastic moment of the composite section, QR is the shear-connector strength, tc is overall depth of the concrete flange (including the concrete topping), Ta is the axial strength of the steel section in tension, and Lϕ is the transverse reinforcement length. ∑ QR ≥ Aa fy (4)

0.85 fcbtc ≥ Aa fy (5)

Cc = 0.85 fcba (6)  L/4 b ≤ (7) 2Lφ + g

Ta = Aa fy (8) Sustainability 2021, 13, x 19 of 24

sidering the strength models for shear studs presented in [19,20]. Considering full inter- action and that NPA lies in the concrete slab (Equations (4)–(10)), in which Aa is the steel- section cross-sectional area, Cc is the concrete-flange axial strength, fy is the steel-section yield strength, L is the composite-beam length, Mpl is the plastic moment of the composite section, QR is the shear-connector strength, tc is overall depth of the concrete flange (in- cluding the concrete topping), Ta is the axial strength of the steel section in tension, and Lφ is the transverse reinforcement length. ≥ QAfR ay (4) ≥ 0.85 fccbt A ayf (5) = Ccc0.85 f ba (6) L /4 b ≤ (7) Sustainability 2021, 13, x  20 of 24 2Lgφ + 

Sustainability 2021, 13, 4230 TA= f 20 of(8) 25 50 aay

40 T =≤a atc (9) 30 0.85Ta fbc a = ≤ tc (9) 0.85 fcb 20  da MT=+−d ta 10 M =plT a+ t − c (10)(10) pl a 222c 2

0 W360x51:25-10-1.0 W360x51:25-12.5-1.0 W360x51:25-16-1.0 W360x51:30-10-1.0 W360x51:30-12.5-1.0 W360x51:30-16-1.0 W360x51:40-10-1.0 W360x51:40-12.5-1.0 W360x51:40-16-1.0 W360x51:25-10-0.7 W360x51:25-12.5-0.7 W360x51:25-16-0.7 W360x51:30-10-0.7 W360x51:30-12.5-0.7 W360x51:30-16-0.7 W360x51:40-10-0.7 W360x51:40-12.5-0.7 W360x51:40-16-0.7 W360x51:25-10-0.5 W360x51:25-12.5-0.5 W360x51:25-16-0.5 W360x51:30-10-0.5 W360x51:30-12.5-0.5 W360x51:30-16-0.5 W360x51:40-10-0.5 W360x51:40-12.5-0.5 W360x51:40-16-0.5 W460x74:25-10-1.0 W460x74:25-12.5-1.0 W460x74:25-16-1.0 W460x74:30-10-1.0 W460x74:30-12.5-1.0 W460x74:30-16-1.0 W460x74:40-10-1.0 W460x74:40-12.5-1.0 W460x74:40-16-1.0 W460x74:25-10-0.7 W460x74:25-12.5-0.7 W460x74:25-16-0.7 W460x74:30-10-0.7 W460x74:30-12.5-0.7 W460x74:30-16-0.7 W460x74:40-10-0.7 W460x74:40-12.5-0.7 W460x74:40-16-0.7 W460x74:25-10-0.5 W460x74:25-12.5-0.5 W460x74:25-16-0.5 W460x74:30-10-0.5 W460x74:30-12.5-0.5 W460x74:30-16-0.5 W460x74:40-10-0.5 W460x74:40-12.5-0.5 W460x74:40-16-0.5 W530x72:25-10-1.0 W530x72:25-12.5-1.0 W530x72:25-16-1.0 W530x72:30-10-1.0 W530x72:30-12.5-1.0 W530x72:30-16-1.0 W530x72:40-10-1.0 W530x72:40-12.5-1.0 W530x72:40-16-1.0 W530x72:25-10-0.7 W530x72:25-12.5-0.7 W530x72:25-16-0.7 W530x72:30-10-0.7 W530x72:30-12.5-0.7 W530x72:30-16-0.7 W530x72:40-10-0.7 W530x72:40-12.5-0.7 W530x72:40-16-0.7 W530x72:25-10-0.5 W530x72:25-12.5-0.5 W530x72:25-16-0.5 W530x72:30-10-0.5 W530x72:30-12.5-0.5 W530x72:30-16-0.5 W530x72:40-10-0.5 W530x72:40-12.5-0.5 W530x72:40-16-0.5

10

Mid-spanverticaldisplacement (mm) 8

6 "Section":"In situ concrete strength"-"Diameter"-"Interaction degree"

4 Slip(mm) Figure 25. Maximum midspan vertical displacement at ultimate behavior. 2 For partial interaction, the linear method was used, according to Eurocode 4 (Equa-

0 W360x51:25-10-1.0 W360x51:25-12.5-1.0 W360x51:25-16-1.0 W360x51:30-10-1.0 W360x51:30-12.5-1.0 W360x51:30-16-1.0 W360x51:40-10-1.0 W360x51:40-12.5-1.0 W360x51:40-16-1.0 W360x51:25-10-0.7 W360x51:25-12.5-0.7 W360x51:25-16-0.7 W360x51:30-10-0.7 W360x51:30-12.5-0.7 W360x51:30-16-0.7 W360x51:40-10-0.7 W360x51:40-12.5-0.7 W360x51:40-16-0.7 W360x51:25-10-0.5 W360x51:25-12.5-0.5 W360x51:25-16-0.5 W360x51:30-10-0.5 W360x51:30-12.5-0.5 W360x51:30-16-0.5 W360x51:40-10-0.5 W360x51:40-12.5-0.5 W360x51:40-16-0.5 W460x74:25-10-1.0 W460x74:25-12.5-1.0 W460x74:25-16-1.0 W460x74:30-10-1.0 W460x74:30-12.5-1.0 W460x74:30-16-1.0 W460x74:40-10-1.0 W460x74:40-12.5-1.0 W460x74:40-16-1.0 W460x74:25-10-0.7 W460x74:25-12.5-0.7 W460x74:25-16-0.7 W460x74:30-10-0.7 W460x74:30-12.5-0.7 W460x74:30-16-0.7 W460x74:40-10-0.7 W460x74:40-12.5-0.7 W460x74:40-16-0.7 W460x74:25-10-0.5 W460x74:25-12.5-0.5 W460x74:25-16-0.5 W460x74:30-10-0.5 W460x74:30-12.5-0.5 W460x74:30-16-0.5 W460x74:40-10-0.5 W460x74:40-12.5-0.5 W460x74:40-16-0.5 W530x72:25-10-1.0 W530x72:25-12.5-1.0 W530x72:25-16-1.0 W530x72:30-10-1.0 W530x72:30-12.5-1.0 W530x72:30-16-1.0 W530x72:40-10-1.0 W530x72:40-12.5-1.0 W530x72:40-16-1.0 W530x72:25-10-0.7 W530x72:25-12.5-0.7 W530x72:25-16-0.7 W530x72:30-10-0.7 W530x72:30-12.5-0.7 W530x72:30-16-0.7 W530x72:40-10-0.7 W530x72:40-12.5-0.7 W530x72:40-16-0.7 W530x72:25-10-0.5 W530x72:25-12.5-0.5 W530x72:25-16-0.5 W530x72:30-10-0.5 W530x72:30-12.5-0.5 W530x72:30-16-0.5 W530x72:40-10-0.5 W530x72:40-12.5-0.5 W530x72:40-16-0.5 tion (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. "Section":"In situ concrete strength"-"Diameter"-"Interaction degree" Sustainability 2021, 13, x MM=+() M − Mη 20 of(11) 24 Figure 24. Maximum steel–concrete interfacepl plslips,, a at ultimate pl FULL behavior. pl , a Figure 24. Maximum steel–concrete interface slips at ultimate behavior. For a presentation of the results, a hypothesis of the minimum spacing was made; 50 i.e., 120 mm providing full interaction. On the other hand, for the other spacings, partial

40 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 30 situation for the W360x51 section presented a ductile behavior (fc = 25 MPa, φ = 10 mm,

20 and 225 mm of spacing). On the other hand, for all W460x74 and W530x72 models, con- sidering 225 mm of spacing, ductile behavior was observed. This means that the greater 10 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 dis-

0 W360x51:25-10-1.0 W360x51:25-12.5-1.0 W360x51:25-16-1.0 W360x51:30-10-1.0 W360x51:30-12.5-1.0 W360x51:30-16-1.0 W360x51:40-10-1.0 W360x51:40-12.5-1.0 W360x51:40-16-1.0 W360x51:25-10-0.7 W360x51:25-12.5-0.7 W360x51:25-16-0.7 W360x51:30-10-0.7 W360x51:30-12.5-0.7 W360x51:30-16-0.7 W360x51:40-10-0.7 W360x51:40-12.5-0.7 W360x51:40-16-0.7 W360x51:25-10-0.5 W360x51:25-12.5-0.5 W360x51:25-16-0.5 W360x51:30-10-0.5 W360x51:30-12.5-0.5 W360x51:30-16-0.5 W360x51:40-10-0.5 W360x51:40-12.5-0.5 W360x51:40-16-0.5 W460x74:25-10-1.0 W460x74:25-12.5-1.0 W460x74:25-16-1.0 W460x74:30-10-1.0 W460x74:30-12.5-1.0 W460x74:30-16-1.0 W460x74:40-10-1.0 W460x74:40-12.5-1.0 W460x74:40-16-1.0 W460x74:25-10-0.7 W460x74:25-12.5-0.7 W460x74:25-16-0.7 W460x74:30-10-0.7 W460x74:30-12.5-0.7 W460x74:30-16-0.7 W460x74:40-10-0.7 W460x74:40-12.5-0.7 W460x74:40-16-0.7 W460x74:25-10-0.5 W460x74:25-12.5-0.5 W460x74:25-16-0.5 W460x74:30-10-0.5 W460x74:30-12.5-0.5 W460x74:30-16-0.5 W460x74:40-10-0.5 W460x74:40-12.5-0.5 W460x74:40-16-0.5 W530x72:25-10-1.0 W530x72:25-12.5-1.0 W530x72:25-16-1.0 W530x72:30-10-1.0 W530x72:30-12.5-1.0 W530x72:30-16-1.0 W530x72:40-10-1.0 W530x72:40-12.5-1.0 W530x72:40-16-1.0 W530x72:25-10-0.7 W530x72:25-12.5-0.7 W530x72:25-16-0.7 W530x72:30-10-0.7 W530x72:30-12.5-0.7 W530x72:30-16-0.7 W530x72:40-10-0.7 W530x72:40-12.5-0.7 W530x72:40-16-0.7 W530x72:25-10-0.5 W530x72:25-12.5-0.5 W530x72:25-16-0.5 W530x72:30-10-0.5 W530x72:30-12.5-0.5 W530x72:30-16-0.5 W530x72:40-10-0.5 W530x72:40-12.5-0.5 W530x72:40-16-0.5 placement 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,

Mid-spanverticaldisplacement (mm) another observation was that the smaller the interaction degree, the greater the midspan vertical displacement. Finally, considering the calculation procedures mentioned in this "Section":"In situ concrete strength"-"Diameter"-"Interaction degree" 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 Figure 25. Maximum midspan vertical displacement at ultimate behavior. Figurefull 25. interaction Maximum wasmidspan considered vertical displacement(Figure 26). at ultimate behavior.

1500 FE For partial interaction, the linear method was used, according to Eurocode 4 (Equa- SCI P401 tion (11)), in which Mpl,a is the plastic moment of the steel section, Mpl,FULL is the plastic 1200 Araújo et al. moment of the composite section with full shear connection, and η is the ratio of the sum 900 of the strength of the shear studs provided to the sum of the strength of the shear studs needed for full shear connection. 600 M (kN.m) =+ − η 300 MMpl pl,, a() M pl FULL M pl , a (11)

0 W360x51:25-10-1.0 W360x51:25-12.5-1.0 W360x51:25-16-1.0 W360x51:30-10-1.0 W360x51:30-12.5-1.0 W360x51:30-16-1.0 W360x51:40-10-1.0 W360x51:40-12.5-1.0 W360x51:40-16-1.0 W360x51:25-10-0.7 W360x51:25-12.5-0.7 W360x51:25-16-0.7 W360x51:30-10-0.7 W360x51:30-12.5-0.7 W360x51:30-16-0.7 W360x51:40-10-0.7 W360x51:40-12.5-0.7 W360x51:40-16-0.7 ForW360x51:25-10-0.5 W360x51:25-12.5-0.5 W360x51:25-16-0.5 W360x51:30-10-0.5 aW360x51:30-12.5-0.5 presentationW360x51:30-16-0.5 W360x51:40-10-0.5 W360x51:40-12.5-0.5 W360x51:40-16-0.5 W460x74:25-10-1.0 W460x74:25-12.5-1.0 W460x74:25-16-1.0 W460x74:30-10-1.0 W460x74:30-12.5-1.0 W460x74:30-16-1.0 W460x74:40-10-1.0 ofW460x74:40-12.5-1.0 W460x74:40-16-1.0 W460x74:25-10-0.7 theW460x74:25-12.5-0.7 W460x74:25-16-0.7 W460x74:30-10-0.7 results,W460x74:30-12.5-0.7 W460x74:30-16-0.7 W460x74:40-10-0.7 W460x74:40-12.5-0.7 W460x74:40-16-0.7 W460x74:25-10-0.5 W460x74:25-12.5-0.5 aW460x74:25-16-0.5 hypoW460x74:30-10-0.5 W460x74:30-12.5-0.5 W460x74:30-16-0.5 W460x74:40-10-0.5 W460x74:40-12.5-0.5 thesisW460x74:40-16-0.5 W530x72:25-10-1.0 W530x72:25-12.5-1.0 W530x72:25-16-1.0 W530x72:30-10-1.0 ofW530x72:30-12.5-1.0 W530x72:30-16-1.0 theW530x72:40-10-1.0 W530x72:40-12.5-1.0 W530x72:40-16-1.0 W530x72:25-10-0.7 minimumW530x72:25-12.5-0.7 W530x72:25-16-0.7 W530x72:30-10-0.7 W530x72:30-12.5-0.7 W530x72:30-16-0.7 W530x72:40-10-0.7 W530x72:40-12.5-0.7 W530x72:40-16-0.7 W530x72:25-10-0.5 spacingW530x72:25-12.5-0.5 W530x72:25-16-0.5 W530x72:30-10-0.5 W530x72:30-12.5-0.5 W530x72:30-16-0.5 W530x72:40-10-0.5 W530x72:40-12.5-0.5 wasW530x72:40-16-0.5 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 "Section":"Insituation for situ the concrete W360x51 strength"-"Diameter"-"Interaction section presented a ductile behavior degree" (fc = 25 MPa, φ = 10 mm, and 225 mm of spacing). On the other hand, for all W460x74 and W530x72 models, con- Figure 26. sideringComparison 225 mm ofof finitespacing, element ductile models behavior vs. analytical was observed. procedures. 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 dis- placement 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).

1500 FE SCI P401 1200 Araújo et al.

900

600 M (kN.m)

300

0 W360x51:25-10-1.0 W360x51:25-12.5-1.0 W360x51:25-16-1.0 W360x51:30-10-1.0 W360x51:30-12.5-1.0 W360x51:30-16-1.0 W360x51:40-10-1.0 W360x51:40-12.5-1.0 W360x51:40-16-1.0 W360x51:25-10-0.7 W360x51:25-12.5-0.7 W360x51:25-16-0.7 W360x51:30-10-0.7 W360x51:30-12.5-0.7 W360x51:30-16-0.7 W360x51:40-10-0.7 W360x51:40-12.5-0.7 W360x51:40-16-0.7 W360x51:25-10-0.5 W360x51:25-12.5-0.5 W360x51:25-16-0.5 W360x51:30-10-0.5 W360x51:30-12.5-0.5 W360x51:30-16-0.5 W360x51:40-10-0.5 W360x51:40-12.5-0.5 W360x51:40-16-0.5 W460x74:25-10-1.0 W460x74:25-12.5-1.0 W460x74:25-16-1.0 W460x74:30-10-1.0 W460x74:30-12.5-1.0 W460x74:30-16-1.0 W460x74:40-10-1.0 W460x74:40-12.5-1.0 W460x74:40-16-1.0 W460x74:25-10-0.7 W460x74:25-12.5-0.7 W460x74:25-16-0.7 W460x74:30-10-0.7 W460x74:30-12.5-0.7 W460x74:30-16-0.7 W460x74:40-10-0.7 W460x74:40-12.5-0.7 W460x74:40-16-0.7 W460x74:25-10-0.5 W460x74:25-12.5-0.5 W460x74:25-16-0.5 W460x74:30-10-0.5 W460x74:30-12.5-0.5 W460x74:30-16-0.5 W460x74:40-10-0.5 W460x74:40-12.5-0.5 W460x74:40-16-0.5 W530x72:25-10-1.0 W530x72:25-12.5-1.0 W530x72:25-16-1.0 W530x72:30-10-1.0 W530x72:30-12.5-1.0 W530x72:30-16-1.0 W530x72:40-10-1.0 W530x72:40-12.5-1.0 W530x72:40-16-1.0 W530x72:25-10-0.7 W530x72:25-12.5-0.7 W530x72:25-16-0.7 W530x72:30-10-0.7 W530x72:30-12.5-0.7 W530x72:30-16-0.7 W530x72:40-10-0.7 W530x72:40-12.5-0.7 W530x72:40-16-0.7 W530x72:25-10-0.5 W530x72:25-12.5-0.5 W530x72:25-16-0.5 W530x72:30-10-0.5 W530x72:30-12.5-0.5 W530x72:30-16-0.5 W530x72:40-10-0.5 W530x72:40-12.5-0.5 W530x72:40-16-0.5

"Section":"In situ concrete strength"-"Diameter"-"Interaction degree"

Sustainability 2021, 13, 4230 21 of 25

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.   Mpl = Mpl,a + Mpl,FULL − Mpl,a η (11)

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 (fc = 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 Sustainability 2021, 13, x vertical displacement. Finally, considering the calculation procedures mentioned21 in of this 24

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). Figure 26. Comparison of finite element models vs. analytical procedures. 5.5. Comparative Analyses 5.5. Comparative Analyses In this section, a comparison of the models developed in the present work was performedIn this withsection, those a comparison presented by of Ferreira the models et al. developed [25] (Figure in 27 the). present work was per- formed with those presented by Ferreira et al. [25] (Figure 27).

1500 150 mm 265 mm 1200

900 (kN.m) 600 M

300

0 W360x51:25-10-1.0 W360x51:25-12.5-1.0 W360x51:25-16-1.0 W360x51:30-10-1.0 W360x51:30-12.5-1.0 W360x51:30-16-1.0 W360x51:40-10-1.0 W360x51:40-12.5-1.0 W360x51:40-16-1.0 W360x51:25-10-0.7 W360x51:25-12.5-0.7 W360x51:25-16-0.7 W360x51:30-10-0.7 W360x51:30-12.5-0.7 W360x51:30-16-0.7 W360x51:40-10-0.7 W360x51:40-12.5-0.7 W360x51:40-16-0.7 W360x51:25-10-0.5 W360x51:25-12.5-0.5 W360x51:25-16-0.5 W360x51:30-10-0.5 W360x51:30-12.5-0.5 W360x51:30-16-0.5 W360x51:40-10-0.5 W360x51:40-12.5-0.5 W360x51:40-16-0.5 W460x74:25-10-1.0 W460x74:25-12.5-1.0 W460x74:25-16-1.0 W460x74:30-10-1.0 W460x74:30-12.5-1.0 W460x74:30-16-1.0 W460x74:40-10-1.0 W460x74:40-12.5-1.0 W460x74:40-16-1.0 W460x74:25-10-0.7 W460x74:25-12.5-0.7 W460x74:25-16-0.7 W460x74:30-10-0.7 W460x74:30-12.5-0.7 W460x74:30-16-0.7 W460x74:40-10-0.7 W460x74:40-12.5-0.7 W460x74:40-16-0.7 W460x74:25-10-0.5 W460x74:25-12.5-0.5 W460x74:25-16-0.5 W460x74:30-10-0.5 W460x74:30-12.5-0.5 W460x74:30-16-0.5 W460x74:40-10-0.5 W460x74:40-12.5-0.5 W460x74:40-16-0.5 W530x72:25-10-1.0 W530x72:25-12.5-1.0 W530x72:25-16-1.0 W530x72:30-10-1.0 W530x72:30-12.5-1.0 W530x72:30-16-1.0 W530x72:40-10-1.0 W530x72:40-12.5-1.0 W530x72:40-16-1.0 W530x72:25-10-0.7 W530x72:25-12.5-0.7 W530x72:25-16-0.7 W530x72:30-10-0.7 W530x72:30-12.5-0.7 W530x72:30-16-0.7 W530x72:40-10-0.7 W530x72:40-12.5-0.7 W530x72:40-16-0.7 W530x72:25-10-0.5 W530x72:25-12.5-0.5 W530x72:25-16-0.5 W530x72:30-10-0.5 W530x72:30-12.5-0.5 W530x72:30-16-0.5 W530x72:40-10-0.5 W530x72:40-12.5-0.5 W530x72:40-16-0.5

"Section":"in situ concrete strength"-"Diameter"-"Interaction degree"

FigureFigure 27. 27. ComparativeComparative analyses analyses between between 150 150 mm mm and and 265 mm PCHCS depth with concrete topping.

AsAs noted, noted, in in some some models, models, the the higher higher PCHCS PCHCS provided provided greater greater strength. strength. This This differ- dif- enceference reached reached a maximum a maximum of 30%, of 30%, considering considering the ratio the ratioof the of 150 the mm-depth 150 mm-depth PCHCS PCHCS mod- elsmodels to the to 265 the 265mm-depth mm-depth PCHC PCHCSS models. models. These These values values were were measured measured considering considering the W360x51W360 × 51section. section. With With the the increase increase in in thethe steelsteel cross-sectioncross-section (sections(sections W460 W460x74× 74 and W530x72),W530 × 72), this this difference difference was was not not so so significan significant.t. This This demonstrated demonstrated that that for for the the models studied,studied, it it was was not not advantageous advantageous to to increase increase the the depth of the PCHCS, since the collapse waswas determined determined by the slab. In In addition, addition, the the greater greater the the depth depth of of the the hollow-core hollow-core slab, the greatergreater the the weight weight of of the the structural structural system system du duee to to the the higher higher consumption consumption of of concrete, 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.

6. Conclusions Steel-Concrete composite beams with precast hollow-core slabs are a sustainable so- lution, and a better understanding of their parameters will yield more efficient designs. The present study developed a reliable finite element model to investigate some limita- tions 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 hol- low-core unit with a concrete topping, since the SCI P401 recommendation is only appli- cable 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 cross-section. In total, 81 models were analyzed. The numerical results were com- pared with models of Steel-Concrete composite beams models, considering a 150 mm hol- low-core unit with a concrete topping. In general, for the models that were considered under the partial-interaction hypothesis, there was a better efficiency of the structural sys- tem, providing greater deformations. Therefore, when designing Steel-Concrete compo- site 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 Sustainability 2021, 13, 4230 22 of 25

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.

6. 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 cross- section. 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 partial- interaction 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 Sustainability 2021, 13, 4230 23 of 25

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 (MFE ≤ MRk). On the other hand, all observations considering partial interaction proved to be safe (MFE > MRk). 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 CO2 emissions.

Author Contributions: Conceptualization, F.P.V.F. and K.D.T.; methodology, F.P.V.F., K.D.T. and S.D.N.; software, F.P.V.F.; validation, F.P.V.F.; investigation, F.P.V.F.; writing—original draft prepa- ration, F.P.V.F., K.D.T., C.H.M. and S.D.N.; writing—review and editing, F.P.V.F., K.D.T., C.H.M. and S.D.N.; visualization, K.D.T., C.H.M. and S.D.N.; supervision, S.D.N.; project administration, S.D.N.; funding acquisition, F.P.V.F. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the São Paulo Research Foundation (FAPESP) (grant number #2018/22803-1). Acknowledgments: The authors would like to thank Construção Metálica—Gerdau Aços Brasil for making available the data related to COPPETEC, PEC-18541. Conflicts of Interest: The authors declare no conflict of interest.

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