FlexuralDesign andAnalysis of Composite Beamswith Inverted-T Steel Girder with Ultrahigh Performance Concrete Slab

-is study intends to improve the efficiency of the composite beam combining a slab made of steel fiber-reinforced ultrahigh performance concrete (UHPC) and a steel girder without top flange. To that goal, the experiment is conducted on 24 composite beams fabricated with varying compressive strength of UHPC, steel fiber content, stud spacing, and slab thickness to evaluate the behavior of the studs and the flexural behavior of the composite beam combining the UHPC slab and the inverted-T steel girder. -e experimental results show the test members developed sufficient ductile behavior with respect to the slip limit of 6mm stipulated in Eurocode-4 and regardless of the considered test variables. -e experimental ultimate horizontal shear force is seen to be clearly larger than the static strengths of the stud predicted by Eurocode-4 and AASHTO-LRFD. Improved design formulae for the composite beam shall be derived to reflect the UHPC slab thickness.


Introduction
In order to overcome the low tensile and flexural strengths of conventional concrete, study is being actively conducted worldwide on steel fiber-reinforced ultrahigh performance concrete (UHPC) developing compressive strength higher than 120 MPa through the admixing of steel fiber in high performance concrete [1][2][3].While, the flexural behavior of fiber-reinforced concrete can be influenced by specimen size, concrete casting method, and support devices [4].Such steel fiber reinforced UHPC is known to present improved deflection, flexural strength, and postcracking ductile behavior compared to conventional concrete.
Composite structures are probably the most appropriate application enabling to take full advantage of the outstanding properties of UHPC, and various solutions combining a UHPC slab and a steel girder were successfully developed [5,6].In addition, numerical expression for flexure of UHPC beam has been successfully derived by the strain compatibility relation [7].
Yoo and Yoon [8] carried an extensive review for the behavior of various UHPFRC structures under different loading conditions, such as flexure, shear, torsion, and highrate loads (impacts and blasts), with practical applications of UHPFRC in architectural and civil structures.
Among the latest achievements and to increase the economy in the material, Europe through the European Commission EUR 25321 developed the preco-beam, a composite beam combining a UHPC deck and an inverted-T steel girder of which the top is worked to have puzzle, fin or clothoidal dowel shape [9]. is dowel shape is obtained by oxycut of the web that may affect the fatigue behavior of steel [10].Following the same idea and in order to ease the fabrication of the composite beam and to prevent this fatigue problem, the composite beam combining a slab made of steel fiber-reinforced UHPC and a steel girder without the top flange shown in Figure 1 was proposed [11,12]. is composite beam was conceived considering the fact that the top flange of the steel girder might be superfluous when the composite beam is formed by composing a UHPC slab with the steel girder considering the high stiffness developed by the UHPC slab and that the shear connector can fulfill the role of the top flange of the steel girder.However, in the configuration shown in Figure 1, the studs needed for the composition of the steel girder with the UHPC slab must be disposed in the web of the girder because of the absence of the upper flange.
In a previous paper [12], the authors presented an experimental and analytical study on the flexural behavior of the proposed composite beam using the inverted-T steel girder and slabs made of UHPC with compressive strength higher than 180 MPa and considering the stud spacing and slab thickness as variables.
e experimental results obtained from 8 composite beam specimens made it possible to recommend stud spacing ranging between 100 mm and 2 to 3 times the thickness of the slab.Considering that there is still no clear agreement on the limit compressive strength defining UHPC and that this compressive strength will affect significantly the behavior of the proposed composite beam, the present paper examines experimentally the behavioral characteristics of the shear connection and the flexural behavior of the composite beam based upon the results of a series of tests on 24 composite beam specimens with a inverted-T steel girder and steel fiberreinforced UHPC slab considering the compressive strength of UHPC, the mix ratio of steel fiber, the stud spacing, and slab thickness.

Material and Test Setup.
ree compressive strengths of 120, 150, and 180 MPa are adopted as design strength of UHPC.UHPC samples were extracted during the fabrication of the flexural test members to perform compressive and tensile material tests for the establishment of the material models.
e steel fibers have length of 19.5 and 16.3 mm and are admixed with respective volume fractions of 1.0% and 0.5% according to the considered mix.Table 1 arranges the physical properties of the steel fibers for each of the UHPCs considered in this study.

Test Variables and Shape of Specimens.
A total of 24 specimens were fabricated considering the compressive strength of UHPC (120, 150, and 180 MPa), the UHPC slab thickness (50 and 100 mm), and the stud spacing (50, 100, 200, and 400 mm) as test variables.Table 2 lists the test members with their designation and corresponding characteristics.Figure 2 describes the sectional dimensions and details of the test members.e slab thickness is selected as a test variable to examine the effect of the embedment depth of the shear connector welded to the girder web on the composite behavior.e stud spacing is changed to derive the appropriate spacing enabling to secure the performance of the composite beam with the inverted-T steel girder.Finally, the compressive strength of UHPC and the mix ratio of steel fiber are chosen as test variables to examine the flexural behavior of the composite beam according to the compressive and tensile strength of UHPC [13,14].For the 120 MPa and 150 MPa test members, Figure 2 presents the original cross section (Figure 2(b)) and the modified cross section (Figure 2(c)).
e modified cross section corresponds to some fabrication error in the dimension of the bottom flange of the steel girder, which was fabricated with a width shorter by 3 mm. is small fabrication error resulted in nonnegligible    Advances in Civil Engineering di erence in the moment of inertia and on the experimental results.erefore, this so-called modi ed cross section was considered as a new case, and the corresponding change in the behavior of the composite beam was additionally observed.Figure 3 shows, respectively, the inverted-T steel girders installed with the forms for placing the UHPC slab and the completed test members.Figure 4 presents the setup for the loading test together with the layout of the sensors.Moreover, the literature reported that placing of UHPC from end of the member allowed better structural performance than placing UHPC at midspan of the member due to uidity of UHPC mixture [15].It a ects orientation of the steel bers in a longitudinal direction parallel to the exural tensile stresses at midspan of the beam.erefore, the UHPC mixture in this study was placed from end of the member to center.e bers in the UHPC mix were added into the mixer with small amounts by hands to prevent lumps in the mixture.

Shear Connector and Steel
Girder.Two types of studs are adopted (Figure 2(e)).Both types have identical height of 50 mm with respective shank diameter and head diameter of 13 and 22 mm (Detail B) and 18.5 and 34 mm (Detail A).
e choice to use two types of studs was done to t with the di erent performances developed by the 180 MPa UHPC mix and the 120 MPa and 150 MPa UHPC mixes.From the direct tensile test, the yield strength and the ultimate strength of the shear connector are found to be 371 MPa and 472 MPa, respectively.Besides, the steel girder is made of structural steel SM490.Referring to the data provided by the manufacturer, the yield strength and ultimate strength of the steel girder are 397 MPa and 550 MPa, respectively.3, C stands for compression failure and cracking, and T for crack on tensile area.inner slab thickness and larger stud spacing eased the occurrence of axial cracks on the top face of the slab.ese cracks can be attributed to the tensile stresses developed through the redistribution of the force concentrated in a small area around the stud to the neighboring concrete [16].Concretely, the 120 MPa and 150 MPa members with stud spacing larger than 200 mm experienced axial cracking on the top face of the slab regardless of the slab thickness.Except member 180f-50-100, axial cracking occurred only for the 180 MPa members with slab thickness of 50 mm and stud spacing larger than 200 mm. is observation may indicate that stable composite behavior without occurrence of axial cracking on the top face of the slab would be achieved with stud spacing shorter than 200 mm and high compressive strength of UHPC or thick UHPC slab.

Test Results and Discussion
e 120 MPa members failed through compression of concrete immediately after yielding of steel.e 150 MPa members showed postyielding ductile behavior before failure through compression of concrete.However, spalling of the connection of the stud occurred in the members with stud spacing larger than 200 mm and regardless of the compressive strength.Moreover, signi cant degradation of the ultimate load is observed for stud spacing of 400 mm.On the other hand, for the 180 MPa members with slab   is situation rendered it impossible to evaluate the e ect of the di erence in the amount of steel ber on the tensile strength of concrete.Eurocode-4 [17,18] de nes the characteristic relative slip, δ uk as 0.9δ u , where δ u is the relative slip measured at load P RK corresponding to the ultimate load reduced by 10%.Eurocode-4 assesses ductile behavior when this characteristic relative slip is larger than 6 mm and states that stable behavior is achieved by the composite member in such case.For comparison with the stipulations of Eurocode-4 [17], Table 4 arranges the yield load at the bottom ange of the steel girder, the ultimate load, the failure load, the relative slip at 90% of the failure load, and the characteristic relative slip measured in the tests.
In view of Table 4, the test members, except member 120f-50-400, are seen to develop characteristic relative slip ranging between 7.32 and 15.16 mm. is indicates that all the specimens develop su cient ductile behavior since these values exceed signi cantly the ductile behavior limit of 6 mm recommended in Eurocode-4.
Member 120f-50-400 with thin slab, the largest stud spacing and the lowest compressive strength of UHPC among the considered mixes presents the most unfavorable conditions in term of structural resistance.Despite such weakness, this member experiences a characteristic relative slip of 5.36 mm that is slightly inferior to the 6 mm ductile behavior limit of Eurocode-4.
is limit can be satis ed easily through slight modi cation of the inverted-T steel girder.7 and 8 plot the load-concrete strain curves at the top and bottom of the slab.e ultimate compressive strain of the UHPC slab is approximately 0.004, which is in good agreement with the results of previous studies on the material behavior of UHPC [12,19,20].It can also be observed that the structural performance degrades with larger stud spacing because of the debonding of concrete around the stud before the development of the UHPC material capacity.

Load-Strain Curves of UHPC Slab. Figures
For the test members with slab thickness of 50 mm, compressive strain is developed at the bottom of the slab at early loading due to the position of the neutral axis in the web of the steel girder.With the increase of the load, debonding of the shear connection at midspan occurred, and the members started to show noncomposite behavior resulting in the development of tensile strain at the bottom of the slab.

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Besides, the test members with slab thickness of 100 mm developed tensile strain at the bottom of the concrete slab from early loading to failure due to the position of the neutral axis at the level of the concrete slab.

Load-Strain Curves of Inverted-T Steel Girder.
Figure 9 plots the load-strain curves at the ange of the inverted-T steel girder.e yield strain of the steel girder remains below 0.002, which is in good agreement with the tensile test results of the material [12,19,20].Here also, it can be observed that the structural performance degrades with larger stud spacing because of the debonding of concrete around stud before the development of the UHPC material capacity.
Unlike the other test members, member 180f-100-50 underwent failure without yielding.is peculiar behavior seems to be due to the large thickness and excessively   Advances in Civil Engineering dense arrangement of the studs, which made the compressive failure of the concrete slab occur prior to the debonding of concrete around stud or yielding of steel girder [12].
Similar behavior can be observed for members 180f-100-400, 120f-50-200, 120f-50-400, 150f-50-400, and 150f-100-400.For these members, the reason can be attributed to large thickness and excessively scattered arrangement of the studs, 12 Advances in Civil Engineering which made the concrete slab fail through noncomposite and compression-flexure prior to the debonding of concrete around the stud.

Evaluation of Shear Connector by Horizontal Shear Force.
Eurocode-4 [16,17] recommends the smallest value between (1) and (2) be the design shear resistance of the headed shear connector.
where c v � partial factor (1.25), d � stud shank diameter, f u � specified ultimate tensile strength of the material of the stud, f ck � compressive strength of concrete, and E cm � elastic modulus of concrete, and where h sc � overall nominal height of the stud.Equation ( 5) expresses the nominal shear resistance of one stud shear connector embedded in the concrete deck recommended in AASHTO-LRFD [21].
where ϕ sc � resistance factor, A sc � cross-sectional area of stud, E c � modulus of elasticity of concrete, and F u � minimum specified tensile strength of one stud.e horizontal shear force working on the slab calculated indirectly using the concrete strains measured at the top and bottom of the slab and the static strength of the stud calculated by means of (1)-( 5) of Eurocode-4 [18] and AASHTO-LRFD [21] are compared in Table 5.Here, the static strength of the stud obtained by (1)-( 5) represents the physical resistance of the stud itself owing to the outstanding performance of UHPC [12].
Figure 10 plots the load-horizontal shear force curves of the specimens.As a matter of fact, the horizontal shear force becomes larger with thicker slab and denser arrangement of the studs [12].e comparison of the ultimate shear force of the test members and the static strengths of the stud given by the design formulae in (1)-( 5) reveals that the average ratio is 1.92 for Eurocode-4 and 1.31 for AASHTO-LRFD.
e members with large stud spacing of 200 and 400 mm exhibited larger values than those provided by the design formulae.After the noncomposite behavior, the UHPC slab and the stud developed higher ultimate strength than the expected resistance.e members with stud spacing shorter than 100 mm experienced sudden failure through flexure before the stud could develop its proper capacity.
In Table 5, the comparison of the experimental and predicted shear resistances with respect to the stud spacing shows that the ratio of the experimental shear force to the design shear strength increases with thicker slab and larger stud spacing. is can be explained by the reduction of the horizontal shear force caused by the noncomposite behavior  14 Advances in Civil Engineering resulting from larger stud spacing.e reason for the larger experimental results obtained for thicker slabs can be found in the fact that the current design formulae assume the static strength of the stud to be the resistance of the stud itself in the case where UHPC develops outstanding performance.is implies that the current design formulae cannot re ect the thickness of the slab for high performance concretes like UHPC.In the future, improved design formulae should be derived based upon experimental data for high performance concretes like UHPC.Note that, future studies should be additionally conducted on full-scale specimens since the speci cations of Eurocode-4 [17,18] and AASHTO-LRFD [21] used for the comparison in this study cannot consider the scale e ect produced by cyclic loading and scaled specimens.

Conclusions
e following conclusions can be drawn based on the experimental results: (1) Larger stud spacing with thin slab eased the occurrence of axial cracks along the steel girder at the top face of the slab.e occurrence of these axial cracks could be attributed to the tensile stress generated by the redistribution of the load concentrated in a small area around the stud to the wider neighboring concrete.(2) e composite beam specimens developed su cient ductile behavior since the characteristic relative slip ranging between 7.32 and 15.16 mm exceeded signi cantly the ductile behavior limit of 6 mm stipulated in Eurocode-4.(3) e horizontal shear force increased with thicker slab and denser arrangement of the studs.e comparison of the ultimate horizontal shear force of the test members and the static strengths of the stud given by design codes revealed that the experimental results were larger by 1.92 and 1.31 times than the predictions of Eurocode-4 and AASHTO-LRFD, respectively.e members with large stud spacing exhibited larger values than those predicted by the design formulae.After the noncomposite behavior, the UHPC slab and the stud developed higher ultimate strength than the expected resistance.e members with short stud spacing experienced sudden failure through exure before the stud could develop its proper capacity.(4) e thickness of the slab could not be re ected by the current design formulae of Eurocode-4 and AASHTO-LRFD in the case of high performance concretes like UHPC.Improved design formulae should be derived in the future based upon experimental data for high performance concretes like UHPC.

3. 1 .Figure 2 :
Figure 2: Sectional dimensions and details of test members (unit: mm).(a) Overall dimensions of composite beam members; (b) original 120 MPa and 150 MPa test members; (c) modi ed 120 MPa and 150 MPa test members; (d) 180 MPa test members; (e) details of studs for 120 MPa and 150 MPa members (left) and for 180 MPa members (right).

Table 1 :
Physical properties of steel fiber per UHPC mix.

Table 2 :
Designation and characteristics of composite beam members.

Table 3 :
Crack and failure patterns of test members.

Table 4 :
Yield, ultimate and failure load, and characteristic slip measured in the loading test.

Table 5 :
Comparison of experimental ultimate horizontal shear force and predicted shear strength without safety factor.