Behavior of composite beams with external prestressing in sagging moment regions

Civil, Vitória, ES, Brasil Abstract: Prestressed composite steel-concrete structures are scarcely used due to a lack of clear standardized design guidelines and formulations on the subject. The present research aims to present design methodologies for steel-concrete composite beams with external pretension applied via straight tendons. A computer program to perform structural analysis of such beams was developed based on two different methodologies: the first one is presented in ABNT NBR 8800:2008, in which the guidelines for the design of composite beams with compact webs are adjusted to include the effects of the pretension force. The second methodology is extracted from international literature and presents a structural design process based on stress distribution on the beam. Ninety prestressed and thirty non-prestressed beams were analyzed and designed with the aforementioned computer program to evaluate the influence of beam length, degree of symmetry of the steel profile and eccentricity of the pretension force on the mechanical resistance of the beams. It was observed that, although the prestressing force considerably improved resistance to bending, it introduced high compression stresses on the steel profile; hence, the pre-stressing of composite beams is proved efficient only for steel profile; monosymmetry degree of the steel profile and eccentricity of the prestressing force. The latter was restricted to two different locations for prestressing tendons, above and below the bottom flange of the steel profile. Results indicate that the composite beams of steel and concrete without prestressing (VM) and prestressed (VMP) with an L d ⁄


INTRODUCTION
External prestressing applied to steel-concrete composite beams results in elements of great structural efficiency, able to cover large spans and resist high loads with reduced structural weight. This technique is of interest for structural recovery and / or reinforcement of existing structures presenting severe pathologies caused by deterioration due to environmental agents or increases in service loads such as, for example, a bridge that experiences an increase in traffic or other loads throughout its lifespan.
Advantages of using external prestressing systems include: the absence of sheaths, which facilitates the building process, making construction more agile; possibility of reducing cross-sections, resulting in lighter and more efficient structural elements; reduction of prestressing losses due to friction, which may even be neglected when using unbonded tendons; external tendons with simpler lines and easier verification after installation; since tendons are external, they are easily inspected and can be re-prestressed or even replaced without interrupting the use of the structure. Figure 1 shows different cross-section types for composite beams with external prestressing tendons. Studies indicate that the application of prestressing to composite steel-concrete structures is recent. Ayyub et al. [2] and Troitsky [1] state that in 1959, Szilard [3] suggested methods for the analysis and design of prestressed composite steel-concrete beams considering the effects of concrete shrinkage and creep. Hoadley [4], in 1963, investigated the behavior of simply supported steel and steel-concrete composite beams, prestressed with high resistance tendons and constant eccentricity along the beam. Strass [5], in the following year, developed an experimental study of composite steel-concrete beams subjected to positive bending moment. In 1966, Regan [6] analyzed the effects of variations in slab thickness, prestressing forces and load types on the behavior of simply supported composite steel-concrete beams.
Saadatmanesh et al. [7] to [8] published a series of analytical and experimental studies on prestressed composite beams in the regions of sagging and hogging bending moments. The authors reported some of the advantages of using prestressing in composite beams such as: reductions in the weight of structural steel; increases in the range of the linear elastic regime of the structure; increased strength; and improvements in fatigue and fracture behavior.
Saadatmanesh et al. [9] tested two composite beams, one subjected to positive bending moment and the other to negative bending moment. The steel beams were prestressed before concrete casting to prevent cracking of the slab. Force versus displacement graphs of the beams were plotted, as well as graphs of force versus strain of the concrete, steel beam and prestressing bars. The values measured experimentally correlated well with values predicted by Saadatmanesh et al. [7], who used internal force equilibrium equations and strain compatibility.
Chen and Gu [10] experimentally determined the strength of sagging moment regions in prestressed composite steel-concrete beams. In the first stage, the beams were tested without prestressing until the bottom flange of the steel beam began yielding, at which point the beams were unloaded. In the second stage, prestressing was applied to the composite beams before loading. The methodology adopted made it possible to analyze the behavior of the composite beams without prestressing. Additionally, based on the deformation compatibility of the tendons and the beam in the anchoring section and by balancing internal forces, the equation of the neutral axis is derived. A simplified expression to determine increases of stress on the tendons is developed, according to the method used to evaluate the capacity of the prestressed composite beam.
In Brazil, among studies on the use of external prestressing in composite beams, one can mention Nelsen [11] and Linhares [12]. Nelsen [11] presented a systematic approach for the analytical design procedure of simply supported and externally prestressed composite steel-concrete I-beams based on requirements from ABNT NBR 8800: 2008 [13], with emphasis on ultimate limit states (ULS). The author studied the influence of prestress force levels, eccentricity of the tendons and constructive methodology (pre-tensioning or post-tensioning) on the strength of structural elements, using spreadsheets developed with the software MathCAD.
Linhares [12] carried out a case study of an externally prestressed composite box-girder bridge featuring two continuous spans, proceeding to an analytical verification following design criteria from AASHTO-LRFD. An initial model consisting of spatial frame bars was developed with the software STRAP for the structural analysis of the system, followed by the creation of a more refined finite element model featuring shell elements with the aid of the computer program SAP2000, to confront and validate the results of the initial model, especially in terms of stresses and displacements. The author concluded that prestressing the composite beam resulted in a small increase in flexural strength in the region subjected to positive bending moment, proving to be of little advantage, according to the AASHTO design criteria. The calculation of prestress force losses due to friction resulted in a small value, since the span only presented two inflection points.
Recently, Lou et al. [14] developed a FE model to analyze composite steel and concrete beams with external prestressing under short and long-term loads, aiming to compare results with composite steel and concrete beams without prestressing. The effect of geometric non-linearity was added by considering the flexural and axial interaction in the finite element formulation, updating the eccentricities of the tendons in the numerical procedure. Results confirmed that prestressing composite beams considerably improved their behavior under short loads. However, there was no noticeable difference on the response to time-dependent effects.
Liban and Tayşi [15], on the other hand, performed a numerical analysis of a simply supported pre-tensioned composite beam with overhangs, in order to observe the behavior of regions subjected to positive and negative bending moments, and also assess the influence of tendon position on the behavior of the structure. Results show that it is more beneficial for the structure to place the straight tendon near the top flange of the profile, thus obtaining an ultimate load approximately 22% larger than if the straight tendon was positioned near the bottom flange of the profile.
On this research, a computer program was developed using Microsoft Office Excel [16] with an interface in Visual Basic language, in the Microsoft Visual Basic Express environment [17]. The program performs the analysis and design of simply supported composite steel and concrete beams with external prestressing and straight tendons (pre-tension), checking safety conditions for ultimate limit states and the serviceability limit state (SLS) of excessive deflection.

Theoretical formulation
The Brazilian standard NBR 8800: 2008 [13] addresses the design of composite steel and concrete beams without prestressing. Thus, for this research, the design equations were adjusted to include the effects of prestressing forces. This force is estimated according to Nunziata [18], considering that the maximum compressive stress in the central section of the steel profile at the time of prestressing cannot exceed the design yield strength of steel, according to Equation 1. _ a n p p g n p yd a a a It is worth mentioning that at first, since the element is subjected to pre-tensioning with prestressing occurring before the application of the construction loads, the steel beam must resist all the stresses introduced by prestressing. As such, the formulation of Equation 1 uses the properties of the steel profile. Isolation of the prestressing force P results in Where: P is the prestressing force, yd f is the design yield strength of the steel of the profile, g M is the maximum bending moment caused by the weight of the profile, a W is the elastic section modulus of the steel profile, _ p a e is the eccentricity of the prestressing tendon in relation to the center of gravity of the steel cross-section, a A is the cross-sectional area of the steel profile, p γ is a safety factor applied to the prestressing force and n β is the amplification factor of the prestressing force, introduced to compensate for losses in prestress force, taken as 1.1. Equation 2 was adjusted to fit the flexo-compression interaction curve of NBR 8800: 2008 [13]. Assuming that the design axial force is greater than 20% of the design resistance to axial force, Equation 3, the prestressing force value is obtained according to Equation 5. Furthermore, the term related to the bending moment due to the weight of the steel beam cannot be considered when the tendon layout is straight, since the effects favoring structural safety do not occur at the supported cross-sections in this case.

Sd Sd
Rd Rd With the application of the gravitational loads of construction, an increase in the value of the initial prestressing force is assumed, which varies according to the configuration of the prestressing tendon and the distribution of the load. This increase in the value of the initial prestressing force, called force increment, can be calculated in several ways, such as: with the application of the principle of virtual work (Troitsky [1]); deformation increment method or finite element method. If a straight tendon is considered, the expressions to determine the increase in prestressing force ∆P are Equation 6 for uniformly distributed load q and Equation 7 for two symmetrically placed concentrated loads F of same magnitude, at a distance a from supports.
where a E is the modulus of elasticity of the steel profile, p E is the modulus of elasticity of the prestressing tendon, L is the length of said tendon, equal to the length of the beam, tr I is the moment of inertia of the composite section, p A is the area of active reinforcing steel, tr A is the area of the transformed composite section, _ p tr e is the eccentricity of the prestressing tendon in relation to the centroid of the composite section and q is the uniformly distributed load. Remaining variables are defined according to Equation 5.

Simplifying assumptions
The present study was limited to the verification of simply supported composite steel and concrete beams with external prestressing (pre-tension) in regions of positive moment. The steel section and the prestressed composite section were designed with procedures defined in the standards: ABNT NBR 8800: 2008 [13], ABNT NBR 6118: 2014 [19], ABNT NBR 7482: 2008 [20] and ABNT NBR 7483: 2008 [21]. Some premises that simplify the analysis and limit the scope of the study were adopted, namely: • Compact steel section, that is, local flange or web buckling is not expected, meaning that a Q = s Q = Q = 1; • Complete interaction between steel and concrete materials, guaranteed by the proper design of stud bold shear connectors; • Unshored construction; • Solid reinforced-concrete slab; • Tensile strength of concrete is neglected; • Straight line tendon; • Verification is limited to the mid-span section, where the largest bending moment is expected; • Shear force is resisted only by the steel profile.

PRESENTATION OF THE PROGRAM
The program verifies the ultimate resistance to bending of the prestressed composite beam according to the methodology adopted by ABNT NBR 8800: 2008 [13] but with the modifications proposed in item 1.1 of this paper. Doubly and monosymmetric steel profiles are accepted by the program. There is also the option of using the procedure proposed by Nunziata [18], which checks the stresses on steel and concrete.
Design routines were developed in the form of flowcharts to systematize the entire script and assist in the elaboration of the program. The routines illustrate the procedures performed, clarifying the sequence of calculations, indicating the design equations used and the basic commands needed such as decision and data selection. In total, 11 routines were developed. Routine 1 calculates the position of the elastic neutral axis, ENA, and the moment of inertia of the homogenized composite section. Routines 2 and 3 calculate the design resistance to compression and the design resistance to bending moment of the steel profile, respectively. Routines 4 and 5 are intended, respectively, for calculating the prestressing force and its increase. Routine 6 verifies the combined bending and axial stresses of the steel profile.
Routine 7 calculates the position of the plastic neutral axis, PNA, measured from the top of the slab, symbolized by the letter a when it passes through the slab and by yLNP when it crosses the steel profile. This routine also provides an expression for the ultimate bending moment of the composite section.
Routine 8 calculates the ultimate shear force, routine 9 determines the midspan deflection of the prestressed composite section and in routine 10, the calculation of stresses on steel and concrete is presented. Finally, routine 11 includes the calculation of the number of shear connectors needed for full interaction. The complete flowcharts for routines 1 to 11 are presented in Ribeiro [22].
The logic used in the program, enumerated below, performs the design in three stages of the lifespan of the structure: phase 1, during construction, when the steel profile resists the construction loads and the prestressing force; phase 2, when composite behavior is developed and the composite beam supports immediate loads such as live loads attributed to occupation and finally phase 3, when long-term effects are considered. Table 1 shows the loads considered in the structural analysis and Table 2 shows the load factors according to ABNT NBR 8800: 2008 [13] for construction load combination (before curing) and for normal load combination (after curing). Applied loads are calculated using construction combinations in phase 1 and normal combinations in phases 2 and 3.
• Call routine 3 -Calculation of the resistance to bending of the steel profile, • Call routine 8 -Calculation of the design resistance to shear force ( Rd V ) of the steel profile; • Verification • Calculation of the design bending moment ( • Call routine 7 -Calculation of PNA and design resistance to bending moment ( For simplification, it is assumed that only the steel profile resists axial forces. • Calculation of the design shear force ( _ • Verifies if • Calculation of forces due to concrete shrinkage (P9): , cs ∞ ε is the strain caused by shrinkage.
• Calculation of the design axial force ( • Flexo-compression verification: For simplification, it is assumed that only the steel profile resists axial forces. Also, the design resistance to bending of phase 3 is the same as in phase 2. 3) Call routine 9 -Calculation of deflection. 4) Design according to Nunziata [18]: • Calls design routine 10 by verification of stresses.

EXPERIMENTAL VALIDATION
To validate the changes proposed to the formulations of ABNT NBR 8800: 2008 [13], two experiments on pretensioned prestressed composite beams were used, one tested by Ayyub et al. [2] and the other tested by Chen and Gu [10].

Experiment performed by Ayyub et al. [2]
The prestressed composite beam tested by Ayyub et al. [2], named Specimen A, Figure   Since prestressing was carried out before concreting the slab, increments in prestressing force were determined using the weight of fresh concrete and the experimental load, totaling an increase of 74.92 kN at the end of the test. Thus, the prestressing force at the moment of collapse is equal to 270.92 kN.
The ultimate limit state observed for the beam studied was the crushing of the concrete slab, which occurred for a bending moment of 586.51 kN.m. Calculating the characteristic resistance to bending moment according to the methodology proposed herein resulted in a value of 515.7 kN.m, 12.07% less than the ultimate load observed experimentally, showing that the proposed methodology favors structural safety.

Experiment performed by Chen and Gu [10]
The prestressed composite beam tested by Chen and Gu [10], named BS2, Figure 3  In this test, prestressing was carried out after concreting the slab, therefore only the test load was considered in the calculation of the prestressing force, totaling an increase of 72.1 kN at the end of the test, thus obtaining a prestressing force at collapse of 297.3 kN.
The ultimate limit state of the beam studied was the crushing of the concrete slab, which occurred for a bending moment of 373.2 kN.m. The characteristic resistance to bending moment, according to the methodology proposed herein, was 351.67 kN.m, therefore 5.77% less than the ultimate load verified experimentally, showing that the proposed methodology once again favors structural safety.

Parametrization models
In the parametrized models, the composite beams analyzed feature double or monosymmetric steel profiles with smaller top flanges. The profiles are made of structural steel ASTM A572 gr. 50 ( y f equal to 345 MPa and u f equal to 450 MPa). According to ABNT NBR 8800:2008 [13], monosymmetric cross-sections must meet the criteria given in Equations 20 and 21.
where: yc I is the moment of inertia of the compressed flange in relation to the axis that crosses the web at mid-thickness; yt I is the moment of inertia of the tensioned flange in relation to the axis that crosses the web at mid-thickness; fs A is the area of the upper flange, w A is the area of the web and fi A is the area of the bottom flange of the steel profile. In this study, the inverse of the coefficient y α is called degree of monosymmetry, m α , which may vary from 1 (for doubly symmetric sections) to a maximum value of 9.
To assess the influence of the degree of monosymmetry, profiles with the same cross-section area, equal to 178.00 cm 2 , were selected. The weight of the steel I-beams is chosen as the same for all models on purpose, to allow an analysis of which geometric configuration provides the most resistant prestressed composite beam with the same cost. The height of the profiles was fixed at 550 mm, the thickness of the web at 12.50 mm and the width of the lower flange at 300 mm. The other parameters of the profiles were chosen to meet the specified steel area and provide variations in the degree of monosymetry ( )  In total, one hundred and twenty composite steel and concrete beams were designed by the program, 90 of which are prestressed composite beams with eccentricity values of 630, 730 or 780mm. The remaining 30 models do not feature prestressing tendons. The models were named according to the presence or absence of prestressing using the acronyms VMP and VM, respectively. The prefixes VMP and VM are followed by the eccentricity values of prestressing tendons in relation to the top of the concrete slab, in turn followed by span length and the model number. Thus, the VMP 730x9x1 model indicates a prestressed composite beam with tendons located at 730mm from the top of the concrete slab, beam span equal to 9m and model number 1.

Methodology
Ultimate limit state verifications related to bending moment and shear force were performed along with checks of the serviceability limit state of excessive deformation. The verification of the interaction between axial and flexural forces was also performed. Tables 3 and 4 present the necessary checks for each of the aforementioned phases, considering the pre-tension method, that is, tendons are prestressed before casting the concrete slab. Table 3. Design verifications of prestressed steel-concrete composite beam -ULS.  To proceed with the analysis of the results, the values of applied and resistant bending moment are presented for the cross section at the middle of the beams, for phase 2. This is because these forces refer to the methodology from ABNT NBR 8800: 2008 [13] which does not address the effects of creep and shrinkage in ULS analyses, only in the calculation of deflection. The design stresses acting on the elements are presented for phase 3 because calculations are based on Nunziata [18], which considers the effects of shrinkage and creep in ULS verifications.

Influence of the ratio between span length and profile height
Regarding the flexural strength of composite beams without prestressing (VM), the analysis of the graph in Figure  5 allows us to observe that, when the L d ⁄ ratio goes from 16 to 31, there is an increase in the resistance to bending moment of 10.9% for doubly symmetric section and approximately 10.1% for the section with a degree of symmetry of 2.07 and approximately 9.0% for sections with a degree of symmetry of 2.83, 3.88 and 5.22. This increase in strength is a result of the increase in the effective width of the beam, in turn due to a larger span length.
In Figure 6, the composite steel and concrete beams without prestressing (VM) and the prestressed (VMP) with L d ⁄ ratio equal to approximately 31 did not meet the design criteria for flexural and axial interaction, since the utilization index ( ) a2 i was greater than 1. For L d ⁄ ratios of 16 to 25, the beams met the design criteria with clearance. As such, for the studied load type, it is noted that an L d ⁄ ratio equal to 27 would be the most advantageous in economic terms, since the utilization index ( ) a2 i was the closest to 1.
Regarding the flexural strength of prestressed beams (VMP), it is observed that the ultimate bending moment increases practically linearly as the L d ⁄ ratio increases from 16 to 27 for all degrees of monosymetry. It is also observed that the beams with monosymmetric sections present the highest resistance to bending moment, reaching an increase of 35.6% when the L d ⁄ ratio grows from 16 to 27 for the sections with a monosymmetry index of 2.83, 3.88 and 5.22; 38.12% for the section with a degree of monosymmetry equal to 2.07 and 38.75% for the doubly symmetrical section. For values of L d ⁄ ratio equal to 27 and larger, the increase in resistance to bending moment is small for both monosymmetric sections (about 1%) and for the doubly symmetric section (about 3%). The ratio between the resistance to bending moment of the prestressed composite beams and that of the unstressed composite beams, shows that the ultimate bending moment of the prestressed composite beams is much higher than that of the composite beams without prestressing tendons; 21% and 55% greater for L d ⁄ ratios of 16 and 31, respectively in the case of doubly symmetrical section; and 21% and 49% higher for the L d ⁄ ratio equal to 16 and 31, respectively, in the case of the section with the highest monosymmetry degree. Larger spans have a higher ratio because as the span increases, in addition to the increase in the effective width, the value of the prestressing force also increases, which contributes to a significant portion of the ultimate bending moment.
From Figure 5 it should be noted, as expected, that the bending moment acting on the prestressed composite beams is much lower than that of the conventional beams, being 35% and 34% lower for L d ⁄ ratios equal to 16 and 31 respectively for doubly symmetrical sections; and 34% and 29% higher for the L d ⁄ ratio equal to 16 and 31 respectively for the section with the highest monosymmetry degree. The bending moment resulting from the application of the prestressing force reduces the bending moment acting on the prestressed composite beams. The ratio between the bending moment of the composite beams with prestressing and that of the composite beams without prestressing was almost constant, around 38%, which shows that prestressing considerably reduces bending effects regardless of span length.
Although prestressing presented considerable benefits, reducing the magnitude of bending moments and increasing flexural strength, improvements in beam utilization index ( ) a2 i is less evident, as seen in Figure 6, because the compression force on the profile due to the prestressing force introduces compression stresses that add to the stresses arising from bending. Significant improvements in the utilization index only occur for the doubly symmetrical section, for all L d ⁄ ratios. For sections with a lower degree of monosymmetry (2.07 and 2.83), the benefits of prestressing are only observed in smaller spans. In cross-sections with a higher degree of monosymmetry (3.88 and 5.22), prestressing was not advantageous, resulting in a lower utilization rate. If NBR 8800: 2008 [13] included the effects of shrinkage and creep in the calculation of design loads, there would be an average increase of approximately 4.1% to 10.7% for L d ⁄ ratios of 31 to 16, respectively. The ultimate bending moment of phase 3 is the same as that of phase 2.

Influence of the degree of monosymmetry
According to Figure 7, the composite beams without prestressing show an increase in the ultimate bending moment  There is a small increase of 2.2%, 2.7%, 0.37%, 0.40%, 2.3% and 9.3% in design bending moment for L d ⁄ ratios equal to 16,19,22,25,27 and 31, respectively, when the monosymetry index increases from 1.0 to 2.83. This is a result of the prestressing force taking the properties of the cross section and the span length into account. For monosymmetry index values greater than 2.83, (from 2.83 to 5.22) variations in design load are small. Figure 8, the use of monosymmetric profiles is only interesting from an economic point of view for composite beams without prestressing, in which a reduction in utilization rate is observed when the monosymetry degree increases from 1.0 to 2.83.    The design bending moment is slightly influenced by eccentricity. For the smallest value of eccentricity, ( p e = 630mm), the design bending moment increases an average of 1.64% when eccentricity increases 100 mm ( p e =730 mm) and 2.41% when eccentricity increases 150 mm ( p e = 780 mm). Figures 10,11 and 12 show that the L d ⁄ ratios equal to 19, 22 and 25 present a behavior similar to that of the models with L d ⁄ ratios of 16, regarding variations in flexural strength as a function of eccentricity. For the lowest eccentricity value ( p e = 630mm), the ultimate bending moment decreases by an average of 9.09% (Figure 10), 7.66% ( Figure 11) and 6.72% (Figure 12) when the eccentricity increases 100 mm ( p e = 730 mm) and decreases on average 10.92% (Figure 10), 9.91% ( Figure 11) and 9.39% (Figure 12) when the eccentricity increases 150 mm ( p e = 780 mm). Once again, the internal moment suffers little influence from the eccentricity. In relation to the lower eccentricity value ( p e = 630mm), the design bending moment increases on average 2.37% ( Figure 10) and 1.6% ( Figure 11) and decreases on average 2.0% ( Figure 12) when the eccentricity increases by 100 mm ( p e = 730 mm). When the eccentricity increases by 150 mm ( p e = 780 mm), the design bending moment increases on average 3.1% (Figure 10), 2.28% ( Figure 11) and decreases on average 1.39% (Figure 12).

Influence of eccentricity
In short, for L d ⁄ ratios equal to 16,19,22 and 25, the eccentricity of 630 mm provides the greatest flexural strength for all degrees of monosymmetry and, also, the lowest bending moment in most cases, thus this eccentricity would be ideal for designs featuring the aforementioned L d ⁄ ratios.    For the L d ⁄ ratio equal to 31, Figure 14, in relation to the lowest eccentricity value ( p e = 630mm), the design resistance to bending moment increases on average 0.27% when the eccentricity increases 100 mm ( p e = 730 mm) and increases by an average of 2.94% when the eccentricity increases by 150 mm ( p e = 780 mm). The design bending moment decreases on average 9.30% when the eccentricity increases by 100 mm ( p e = 730 mm) and decreases on average 5.81% when the eccentricity increases by 150 mm ( p e = 780 mm). In summary, it is concluded that a more comprehensive analysis is necessary to determine the ideal value of design eccentricity for prestressed composite beams, since the flexural behavior, in terms of resistant and applied bending moment, differs in relation to eccentricity changes according to the selected / L d ratio. It is important to note that, in the methodology used herein, the variation in the eccentricity of the tendon implies a variation in the value of the initial prestressing force, according to the flexo-compression interaction equation (Equation 5). Therefore, an increase in eccentricity does not always cause an increase in bending resistance, since the initial prestressing force is reduced to meet the conditions given in Equation 5.

Analysis of stresses
The stresses were determined considering the interaction of axial forces and bending moment for phase 3, according to the methodology of Nunziata [18]. Figure 15 shows that the design stresses on the upper flange of the steel profile are smaller than the design yield stress of steel ( yd f = 31.4 kN / cm 2 ) in all models studied, except for the composite beams without prestressing with an / L d ratio equal to 31 and prestressed composite beams with an L d ⁄ ratio equal to 31 and eccentricity of 630 mm. The composite beams without prestressing present compressive stresses on the upper flange that are considerably larger than the values observed for prestressed composite beams. It is also observed that the variation in the eccentricity ( )  From the graph in Figure 16, regarding the stresses on the bottom flange of the steel profile, it is noted that the models of composite beams without prestressing do not meet criteria for the design yield stress of steel, except for the models with an L d ⁄ ratio equal to 16 and in some models with an L d ⁄ ratio of 19. Thus, many of the beams without prestressing that do not pass the Nunziata methodology [18] meet the criteria of ABNT NBR 8800: 2008 [13]. This is due to the former being more conservative since it considers the beginning of yield at a point on the cross-section as the failure criteria, while the criteria of ABNT NBR 8800: 2008 [13] considers the plastic hinge formation as the ULS.
Still concerning stresses on the lower flange of the steel profile, most of the prestressed composite beams meet the criterion for yield stress limits, except for models with an L d ⁄ ratio equal to 31. According to the graph presented in ABNT NBR 8800: 2008 [13], the models with eccentricity of 680 mm and monosymmetry indexes equal to 2.83; 3.88 and 5.22 present the smallest stresses.  Figure 17 shows the normal design stress on the top surface of the concrete slab as a function of the L d ⁄ ratio. It is observed that the design stress on the concrete portion of the models without prestressing is less than that of prestressed composite beams. No case exceeded the ultimate stress of . cd 0 85 f , equal to 1.51 kN / cm 2 . Input data used to calculate each model is given in Table 3.

Analysis of displacements
The maximum deflection of the prestressed composite beams and of composite beams without prestressing was determined by homogenizing the composite section according to the computer routine from which the displacements at midspan are obtained. Figure 18 shows the maximum deflection value of the beams for different / L d ratios. It is noted that prestressing has a significant influence on the Serviceability Limit State of excessive deformation when analyzing the reduction of the midspan deflection of the prestressed composite beam in relation to the nonprestressed composite beams, percentage-wise [(d VM -d VMP) )/d VM , (%)]. According to Figure 18, for an L d ⁄ ratio of 31 and eccentricity of 630 mm, the midspan deflection of the prestressed composite beam (d VMP = 78.92 mm) is less than half the value found for the composite beam without prestressing (d VM = 178.42 mm), with a reduction of 56%. The midspan deflection reduction reaches 72% for an L d ⁄ ratio of 19 and eccentricity of 630 mm, where the deflection is reduced from 27.16 mm to 7.69 mm.
It is also noted that for L d ⁄ ratios smaller than 25, there is no significant change in the midspan deflection of prestressed beams when the eccentricity value is changed. For / L d ratios equal to 27 and 31, however, higher values of eccentricity of the prestressing force presented smaller displacements. A deflection reduction percentage of 34% is achieved between eccentricity values of 730mm and 630mm and 25% between the eccentricities of 730mm and 780 mm.
In summary, the analysis of results allowed an assessment of the benefits of applying external prestressing in composite beams for controlling both ULS and SLS, since there was an increase in strength and stiffness of the beams.

CONCLUSION
The main objective of this research was to study the behavior of composite steel and concrete beams with external prestressing using the pre-tensioning technique with straight tendons. A computer program was developed to calculate design forces and design cross-sections as regions of positive bending moment of the beams following two design methodologies: one based on ABNT NBR 8800: 2008 [13] and the other according to Nunziata [18]. In both methodologies, the prestressing strength is estimated according to Nunziata [18]. The program checks safety conditions for Ultimate Limit States and the Serviceability Limit State of excessive deformation.
A parametric study, using the computer program developed, was implemented in 120 composite steel and concrete beams of different characteristics, 90 of them with external prestressing and 30 of them without prestressing. The influence of the following parameters was evaluated: ratio between the length of the beam and the height of the steel profile; monosymmetry degree of the steel profile and eccentricity of the prestressing force. The latter was restricted to two different locations for prestressing tendons, above and below the bottom flange of the steel profile.
Results indicate that the composite beams of steel and concrete without prestressing (VM) and prestressed (VMP) with an L d ⁄ ratio of approximately 31 do not meet the combined bending-compression design criteria for the load applied, 5 kN/m 2 of live load, since the utilization rate was larger than 1. For L d ⁄ ratios ranging from 16 to 25, the beams meet the design criteria with clearance. It should be noted that the L d ⁄ ratio equal to 27 would be the most advantageous in economic terms since the utilization rate was the closest to 1.
Although prestressing has generated a considerable improvement in the behavior of the composite beams under bending, reducing the design bending moment and increasing the ultimate bending moment, its improvement in the rate of utilization of the beam was less noticeable, because the compression force on the steel profile due to the prestressing force introduces compressive stresses that are added to stresses arising from bending. Significant improvements in the utilization index only occur for the doubly symmetrical section. For sections with a lower monosymmetry (2.07 and 2.83), the beneficial effects of prestressing are only observed in smaller spans. In cross-sections with a higher monosymmetry degree (3.88 and 5.22), prestressing is not advantageous, resulting in smaller utilization rates when compared to beams without prestressing.
It was also concluded that the use of monosymmetric profiles in composite beams is only interesting from an economic point of view for beams without prestressing a with monosymmetry index smaller than 2.83.
For the three cases of tendon eccentricity (630, 730 and 780 mm) studied, it was observed, for L d ⁄ ratios equal to 16,19,22 and 25, that the 630 mm eccentricity provides the greatest flexural strength and the smallest design bending moment, so this eccentricity would be ideal for the design. For L d ⁄ ratios equal to 27 and 31, it was not possible to establish the ideal design eccentricity, since the eccentricity that provides the largest bending resistance also provides the highest value of design bending moment.
Finally, it is observed that prestressing has a significant influence on the control of the SLS of excessive displacement when analyzing reductions in deflection at the midspan of prestressed composite beams in relation to unstressed composite beams. The result analysis allowed the observation of the benefits of applying external prestressing in composite beams for controlling ULS and SLS, since there was an increase in both strength and stiffness of the beams.
Although underutilized in Brazil due to little knowledge of the system and its design methods, it is clear that prestressed composite steel and concrete beams have great relevance for maintenance projects, recovery of existing structures and design of large new structures. International scientific literature presents theoretical and experimental studies aimed at understanding the structural behavior of this type of beam, and this research contributed to a greater understanding of design methodologies for these structural elements.