Longitudinal shear in the tension flanges of composite concrete beams made continuous

In continuous concrete T‐beams, tension flange plays a remarkable role for the hogging moment capacity at the support area. When precast beams are connected as a continuous structure, longitudinal reinforcement is spread in the flange overhangs at the negative moment area of the continuity connection, which causes longitudinal shear in the tension flange's web‐flange junction. The level of reinforcement spreading influences the magnitude of in‐plane forces at the junction, which can cause the flanges to crack and eventually separate from the web. This separation must be prevented by providing transversal reinforcement in the flanges. Longitudinal shear between web and flange and the required transversal reinforcement are experimentally and computationally studied in cantilever composite T‐beams with the flange in tension. A comparison of the experimental and computational results revealed that longitudinal shear distribution in accordance with conventional beam theory does not always yield safe side results. Analyses made with a particularly drawn truss model and the modified compression field theory are in better agreement with the experimental results.


| INTRODUCTION
Underground parking has gained in popularity, with space in high-density and valuable land areas being freed up for more active uses. Deck structures at ground level are usually heavily loaded, laborious to design, and expensive to construct. The capacity of normal simplespan prestressed concrete girders is often insufficient for carrying these heavy deck loads combined with the required span lengths. In order for precast prestressed beams in these deck structures to be utilized, the application of the structure needs to be improved.
A common way in bridge construction for increasing the capacity of single span precast prestressed beams is to connect them to a continuous structure. Continuity is achieved with an in situ cast deck slab and diaphragm over intermediate support. In this method, the girders Discussion on this paper must be submitted within two months of the print publication. The discussion will then be published in print, along with the authors' closure, if any, approximately nine months after the print publication. behave as simple spans for dead loads before the continuity is achieved. After that, the composite section of the prestressed beam and cast-in-place deck slab bear the superimposed dead and live loads as a continuous girder. Throughout this article, the term composite beam will refer to a hybrid structure which is a combination of a prestressed precast concrete girders and an in situ cast concrete slab.
In a continuous girder, mid-span flexural moments and maximum deflections are reduced and moment redistribution is possible. This paper is part of a dissertation which purpose is to explore the potentials single span, prestressed concrete beams made continuous in heavily loaded parking deck structures. A recently published paper 1 is a part of the same dissertation and studies negative moment capacity of the structure.
A general procedure to create continuity between precast beams is to embed reinforcing bars across supporting piers in a situ-cast deck slab to provide the negative moment continuity. [2][3][4] When the amount of longitudinal reinforcement providing negative moment capacity is high, the tensile reinforcement is commonly distributed in the flange overhangs of the composite T-section. It has been suggested that reinforcement of the tension flange should be spread to a wider breadth than the web to control the crack widths of the flange. If the reinforcement is concentrated over the web, the amount of cracks can remain small but crack widths increase considerably. 5,6 When the flange of a T-beam participates with the web in resisting flexural forces, the integrity of the junctions of the flanges with the web must be preserved. This means that adequate transversal reinforcement must be provided regardless of whether the flange is in tension or in compression. If the beams have no transverse reinforcement in their flanges, the separation of the flanges from the web will cause a premature failure of the beam once cracking occurs at the web-flange junction. Clearly, it cannot be accepted that a flange falls off. Minimum nominal transverse reinforcement should be sufficient to avoid this, but it will not necessarily ensure that the flange continues to work properly as part of the cross section after cracking. 7 Eurocodes suggest procedures for considering longitudinal shear between web and flanges of T-section and provide guidance in determining transverse reinforcement to the flanges. 8,9 European guidance allows longitudinal shear in the flanges to be checked using a truss model (TM; see Figure 1) or from elastic cross-sectional analysis using beam theory. 11 Previous research has established that these methods lead in general to a safe design of the transverse F I G U R E 1 Membrane forces at the flange-web junctions in the tension flange of the T-beam (modified from Razaqpur and Ghali 10 ) reinforcement of compression flanges, but they may also yield unsafe results for tension flanges, even if there is no transverse bending. 12 The function of continuity connection between precast prestressed beams made continuous has been extensively studied. However, less attention has been paid to the decks' transversal reinforcement. According to the AASHTO design specifications, section "Bridges Composed of Simple Span Precast Girders Made Continuous," all longitudinal reinforcement of the deck slab may be used for the negative moment connection. Required transversal reinforcement has not received any attention at the specifications. 13 In precast prestressed bridges, the beams are placed close together and the flange width is limited. In the bridges, the self-weight of the girders is the major part of the loading and the negative moment over supports is often minor; as a result, the amount of longitudinal reinforcement at the top plate is insignificant. The situation is different in parking deck structures, where the beam-to-beam distance might be several meters and the load after continuity connection pays a considerable role. When the amount of tensile top reinforcement increases, the need to spread it wider to the overhangs becomes necessary. Subsequently, the need for transversal reinforcement becomes more critical.
The objective of this research is to provide experimental results and study the longitudinal shear between the flange and the web at intermediate support in composite precast beams made continuous. Hogging moment area of the continuous structure is isolated as a cantilever beam and studied. This paper provides an overview from simple to more precise available methods for analyzing longitudinal shear at the web-flange junction of the tension flange. Theoretical results are compared to experimental values and discussed. It is hoped that this research will contribute to a deeper understanding of the required transverse reinforcement of the studied structure.

| DESIGN OF TRANSVERSE REINFORCEMENT IN TENSION FLANGES OF T-BEAMS
When the loads are applied over the web of the T-shaped cross section as shown in Figure 1, the flanges near their junctions with the web are subjected to membrane forces N x , N y , and N xy , where x and y are the horizontal axes parallel and perpendicular to the beam axis. These forces can cause cracking in the flanges along the web-flange junction. If sufficient reinforcement is not provided, the cracks will lead to separation of the flanges from the web. The definition of tensile forces N x and N x + dNx is quite straightforward, according to the conventional beam theory (CBT), while the assessment of N xy and N y is rather controversial. Note that in this paper, N x , N y , and N xy are assumed to be force per unit length, and σ x , σ y , and τ xy are assumed to be stresses. The next section concerns the generally used methods to evaluate longitudinal shear and transversal stresses and forces in design. The central thesis of this paper is to study longitudinal shear in the tension flanges. Although transverse bending moment and vertical shear has also influence on transverse reinforcement of the studied structure they are not included in this study. For the sake of clarity, this paper concentrates on only one isolated component of the phenomenon.

| Web-flange longitudinal shear stress τ xy distribution
Longitudinal shear stress τ xy , at the junction between one side of a flange and the web of the tension flange, can be determined according to elastic cross-sectional analysis using the CBT. Shear stress at the cracked stage can be approximated by Equation (1) or (2). In the structure studied in this paper, both approaches yield the same results.
where ΔN fx is the change in the normal force in one side of the flange over the length Δx and Δx is the length under consideration. The maximum value that may be assumed for Δx is half the distance between the cross section where the moment is 0 and the section where the moment is maximum. Where point loads are applied, the length Δx should not exceed the distance between point loads. [9][10][11] where V is the shear force of the cross section, z is the inner lever arm, corresponding to the bending in the cross section, A sF is part of A s , placed in one flange overhang, A s is the total amount of the flexural reinforcement area, and h f is the thickness of the flange at the junction.

| Transversal stress σ y
Two most common methods available to define the variation of transversal stress σ y are based on the τ xy distribution and truss analogy. One option is to draw out detailed TM for the structure (see Figure 1). This strut and tie model covers the crushing resistance of the concrete struts and the tensile strength of the transverse reinforcement. Another less labor-consuming practical design approach is to avoid the need to draw TMs and determine longitudinal shear from elastic cross-sectional analysis using beam theory. According to CBT, 9,11,14 σ y can be determined with Equation (3) where θ f is the angle of transversal compressive struts in the flange (Figure 1).
F I G U R E 2 Shear envelope of cantilever beam according to elastic design and considering the "shift rule" Various values for the angle of the tension flange transversal compression strut of the truss can be found in the literature. According to References 9,15, and 16, the recommended values for the angle spread are 38.6 ≤ θ f ≤45 , 26.7 ≤ θ f ≤35 , and 35 ≤ θ f ≤50 , respectively. On a result of these recommendations, tanθ f varies between 0.5 and 1.2.
The method of calculating flange shear stress from the vertical shear force envelope of the beam gives only approximate information on where to place transverse reinforcement along the beam. It is advised to "shift" the shear force envelope to improve compatibility with the location of transverse reinforcement. The shear force envelope may be shifted with distance a l determined in Equation (4). 9,11 The length of the shift depends on the angle of compression strut θ w of the web truss. The lower angle value is, the larger the shift is. The effect of the shift rule on the cantilever beam shear envelope is presented in Figure 2. It shall be distinguished that same kind of shift, which amount depends on the angle of transversal compressive struts, occurs also in the flange. This shift cannot however happen without transverse reinforcement of the flange and because of that this shift cannot be considered in full when defining where to place transverse reinforcement.
where θ w is the vertical compressive struts in the web ( Figure 1). A more detailed TM can be used to determine nonconstant σ y distributions along the web-flange junction. 5,11,14,17 In the tension flange TM, special attention must be given to the end region of the truss. In approaches presented by Bachmann et al., concentration of transverse steel at the cantilever beam end is especially needed when the tension flange does not have a considerable overhang (see Figure 3) beyond the cross section of zero moment. 5,11,14,17 A fitted TM proposed for the test beams of this research is presented in Section 5.6.

| EXPERIMENTAL STUDY
The objective of the experimental program was to study longitudinal shear at the web-flange junction in the tension flange of four prestressed beams made continuous. The continuity connections hogging moment capacity and ductility were also studied for the same test beams. The results of the negative bending capacity tests are presented by Kytölä et al. 1

| Specimens and loading setup
Each test specimen consists of two 3-m-long prefabricated prestressed concrete rectangular (BxH = 280 Â 480 mm 2 ) beams, which were connected in the laboratory by a transversal diaphragm and longitudinally reinforced deck slab (bxh = 1500 Â 120 mm 2 ). The composite action between precast beams and the in situ cast deck slab was secured with U-shaped stirrups (H1, #10, c/c = 50 mm) and a rough contact surface. Top surface of the precast beams had at least 3 mm roughness at about 40 mm spacing, achieved by raking. Prestressed beams were embedded to the diaphragm by 200 mm. The completed test beams were 6.25-m-long cantilever T-beams, and their aim was to be an isolated model of a half-scale, heavily loaded parking deck structure's intermediate support area.
The nominal dimensions and reinforcement of the test beams are shown in Figure 3. All the deck slabs of the tested beams had identical longitudinal and transversal (#16 c/c 100 mm) reinforcement. The longitudinal reinforcement ratio was high (ρ = 5.9%) and the established transverse reinforcement ratio was selected so that the theoretical load, predicted with Equation (3), of the beam causing web-flange longitudinal shear failure is greater than the load that causes bending failure, regardless which θ f value was selected from the recommended range. Prestress force and reinforcement of the precast beams varied but it did not considerably influence longitudinal shear of the web-flange junction. Precast beam parts of one of the test beams did not have any prestress force. Remaining three test beams had four to twelve bottom strands and two top strands. All strands were straight throughout the girder length. Prestress at launching was 1350 MPa. Additional information (not vital for this study) about the test beams is presented by Kytölä et al. 1 Four test girders were tested in negative bending over a central support. The loading points were over the web at both ends of the cantilever beam. The support was directly under the diaphragm column, simulating the action of hogging moment in a continuous composite beam. Load was applied with a hydraulic jack over the web until failure occurred at the compression side of the beam near the support. The system was load controlled and the used loading rate was 50 kN/min. In every load step, visible cracks of the flange slab were highlighted with a marker pen.

| Material properties
The mean cylinder strength of the precast girder's concrete was 72 MPa, and for the deck and diaphragm 55-57 MPa. Maximum aggregate size for both slab and beam concrete was 16 mm. Compaction of the concrete was conducted by vibration. The cast-in-place deck was covered with plastic film for about 30 h after casting. The increase of the strength of the deck concrete was followed with 14 field cured cylinders (d = 150 mm, h = 300 mm), and the strength was tested at the time of each loading. The measured concrete cylinder strengths and loading ages of the decks are presented in Table 1. The material properties of reinforcements are given in Table 2.

| Instrumentation
The flanges of the test beams were divided into three critical cross sections called A (x = 0), B (x = 1235 mm), and C (x = 2200 mm), which were measured. Nine strain gauges (SGB-A1, A2, A3, B1, B2, B3, C1, C2, C3), three per each critical cross section, were attached to the longitudinal reinforcement on one side of the flange to measure strain distribution along the flange. In addition, two strain gauges (SGB-B4, C4) were arranged on the transverse reinforcement located on the flanges at the webflange junction of cross sections B and C. Figure 4 presents the concrete casting moment of the flange parts of the test beams. The positions of the instrumented cross sections A, B, and C are highlighted.
The in-plane load-deformation response of the reinforced concrete flange at cross-sections B and C was measured with measurement frames ( Figure 5). The frames consisted of six diverging displacement sensors (DG-B1-B6, C1-C6), with the aim being to measure average in-plane strains in cracked flanges at the point of cross sections B and C (measured area 700 Â 700 mm 2 ). The measured area was wide enough to include a few cracks, so that the measured data could be compared to the calculated average values presented in Section 5.8. Not all the results of the measurement frames could be utilized, and the reasons for that are explained in Section 5.2. The location and nomination of instrumentation of the test beams is presented in Figure 6. Reinforcement: Stresses at cracks: Crack widths, w: Allowable shear stress on crack The design of reinforced concrete elements subjected to significant shear is a complex engineering problem. Generally used design approaches presented in Section 2 predict the shear strength of the flange based on the TM and CBT. When it comes to the longitudinal shear capacity of the web-flange junction, the literature has highlighted the poor accuracy of these approaches in some situations compared to experimental results. 10,17 More sophistication can be applied in evaluating longitudinal shear by applying a nonlinear analysis of the compression field theory. 18 An expressive but relatively complex nonlinear analysis method called the modified compression field theory (MCFT) was developed in the 1980s. It is able to predict more accurately the full load deformation relationships and shear strength for membrane elements subjected to in-plane shear and normal stresses. In the model, cracked concrete is treated as a new material with its own stressstrain relations. Equilibrium, compatibility, and stressstrain relationships are formulated in terms of average stresses and average strains. The model takes into account tensile stresses in the concrete between the cracks. 19 Table 3 summarizes the MCFT for the twodimensional case studied in this paper.
Membrane-2000, a structural software program developed by Bentz, conducts the nonlinear sectional analysis for reinforced concrete shells that are subjected to inplane forces N x , N y , and N xy and models its full loaddeformation relationship based on MCFT, as presented in  In this study, the computational MCFT examinations have been conducted with Membrane-2000. 22 5 | RESULTS AND DISCUSSION

| Observations from loading tests
Few thin cracks were observed at the slab part of the test specimens prior to the loading, most likely caused by differential shrinkage between the deck and the precast beam. Until the load level reached $25% of the failure load more transverse cracks appeared in the slab at the support area. Inclined cracks caused by longitudinal shear were shown at the load level of 25-55% of the failure load. The pattern of cracking of the flange plate was fixed at a load level of 55% of failure load and did not change with increasing load. Cracks at the support area were perpendicular to the beam's longitudinal axis, almost parallel to this axis at the end of the cantilever beam and between them with correspondingly changing inclination. The crack patterns of the test beams showed clear signs of longitudinal shear effects. Tension flange crack patterns of test beam number 7 are presented in Figure 7. The figure presents crack formation at different load levels and the final crack pattern. The pattern of test 7 is similar to that found in tests 5, 6, and 8.
The selected combination of longitudinal and transverse reinforcement in the test beams was sufficient to control the longitudinal cracking in the web flange junction and ensure the integrity of the section. According to visual observations, none of the tested beams reached longitudinal shear failure in the web-flange junction. It was also found in all the tests that the horizontal plane of the junction remained undamaged.
The observed failure mode of the test beams was flexural failure. Failure of all test beams was clearly controlled by tension, and extensive yielding of the longitudinal deck reinforcement was evident over the support before the crushing of the composite beam's soffit concrete. The vertical deflections of the cantilever beam ends were considerable prior to the failure (L/32-L/17). 23 According to strain gauge bar measurements (SGB-A1,  Table 4 summarizes the loading capacities of the test beams. It shows the maximum cantilever load P max and the maximum experimental bending moment M max over the support (x = 225 mm) of all tested beams. Table 4 also shows the relative tested negative bending moment at the onset of first yielding of top reinforcement over the intermediate support. Self-weight of the test beam and the weight of loading equipment are included in the values presented in Table 4.

| Transverse bending due to longitudinal curvature
Measurement frames (DG-B1-6 and DG-C1-6) 30-100 mm above slab top surface (presented in Section 3.3) were intended to measure in-plane deformations of cross sections B and C caused by shear and axial stresses. The measurement frames yielded measuring data for four directions at six locations, which would have been sufficient for defining the average main strains and angle of compression spread of the elements. From the crack pattern, it was concluded that the diagonal rods of the measurement frames were approximately in the direction of the main strains. One diagonal rod measured roughly the main compression strain and the other the main tension strain. However, according to the measuring data both diagonal rods were in tension.
A feasible explanation for these results is the transversal bending of the flange overhang due to the beam curvature (flange-curl phenomenon) combined with high eccentricity of the displacement sensors in measuring frames. The flange-curl phenomenon has been discovered in several earlier experimental studies. Previous research has established that, even if no loads are applied at the web-flange outstands, transverse moments are produced at the web-flange junctions when a beam develops longitudinal curvature (see Figure 8). Though this flange-curl phenomenon is not a major effect, appreciable vertical deflections of unloaded flange outstands have been recorded in many tests. 5,17,24,25 The tested cantilever beams exhibited high longitudinal curvature values which are presented by Kytölä et al. 1 Experimental results of the measurement frames indicate that some transverse deflections were also observed in these tests. Because of transverse deflections, only the shear strain of the measured cross sections B and C could be reliably determined according to the measurement frames DG-B5-6 and DG-C5-6. Other data gained from the frames were not utilized in this study. The shear strain data of these measurements are used in the results presented in Section 5.8. For simplification, flange-curl phenomenon is disregarded at computational analysis made in following sections.

| Flange longitudinal strains
Flange longitudinal reinforcement strains were measured at cross sections A, B, and C. In every cross-sectional longitudinal strain was measured from three points (1: over the web, 2: y = 360 mm, and 3: y = 720 mm). This information was useful when verifying if the whole flange width was effective during loading. Figure 9 represents the flange longitudinal reinforcement strain and stress profile for different load levels across flanges at three different cross-sections. The F I G U R E 8 Bending of a flange due longitudinal curvature of a beam (modified from Jonasson 24 ) presented case reflects the general behavior of all tested beams.
Cross section A: Nonuniform bending stresses and strains across the flange width were observed. Strains over the web were higher than those of the reinforcement remote from the web. As the load level increases to near failure, reinforcement reaches the yield limit and the stress profile turns into uniform. The strain profile, F I G U R E 9 Longitudinal strain and stress distribution in the reinforcing bars of test beam 7 across the flange at locations SGB-A1-3, -B1-3, and -C1-3 and different values of load F I G U R E 1 0 Flange transversal strain diagrams according to strain gauge measurements from transverse reinforcement SGB-B4 and SGB-C4 however, is unevenly distributed during the whole loading test. At the maximum load level, strains over the web increased considerably.
Cross section B: Both the stress and strain profiles were uniformly distributed. The whole flange width was effective from start to finish. Reinforcement reaches the yield limit at the end of the loading test.
Cross section C: Both the stress and strain profiles were uniformly distributed. The whole flange width was effective from start to finish. Maximum stress level reached at failure was approximately 60% of the yield strength.
Some national design specifications and data from experimental studies suggest that shear lag of composite Tbeams could be neglected at ULS on the basis of concrete cracking and reinforcement yielding, allowing stresses to redistribute across the flange. 11,26,27 Conflicting experimental results have also been published, according to which a reduction in effective width value was observed as the load level increased. 18,28 Effective width at intermediate support increases as the loading proceeds if observed from stress distribution, on the other hand strain distribution indicates effective width reduces. EN 1992-1-1 uses the same effective width for both SLS and ULS. 9,11

| Flange transverse strains
Flange transverse strains were measured with strain gauges in the transverse reinforcement at cross sections B and C (SGB-B4, SGB-C4 at Figure 6). Figure 10 represents the transverse strain values at different tests and load steps. Transversal strains of the reinforcement are insignificant up to a load level of approximately P = 200 kN, apart from the strain result of Test 5 cross section B. According to the crack patterns presented in Figure 7, longitudinal shear cracking took place also at the same load level. After that, transversal strains begin to increase. The leaps seen in the strain-load relation are due to the load increase were stopped in order to observe deck cracking at every load step. Strains at location C were greater compared to cross section B and the distribution increased toward the cantilever end, except in Test 8 where the strains at cross section C were minor. Transverse reinforcement did not yield, but the strains were high, reaching 62-93% of the yield strain.
Due to lack of space, used transverse reinforcement were straight bars without any hooks at the ends. From the design specification viewpoint, the anchorage conditions of these bars were not complete. Despite of this test, results indicate that transversal reinforcement worked properly, and the anchorage was adequate.

| Web-flange longitudinal shear stress τ xy distribution
An analytical approach is used to evaluate longitudinal shear stress distribution at the web-flange junction from the intermediate support to the tip of the cantilever beam. According to Equation (1) and Figure 1, shear stress can be determined from the change of the normal force in the flange. Reinforcement strains of the tested tension flange are measured at cross sections A, B, and C. The bending moment at the tip of the cantilever is null and the normal force of the flange is assumed to be null at the end of the deck's longitudinal tension reinforcement. For the estimation of axial normal force N fx along the beam in the flange, results of strain gauge bar measurements (SGB-A1-3, -B1-3, and -C1-3, see Figure 6) were used. From these measuring points, three ΔN fx values (the change in longitudinal force in the flange) could be determined (at regions A-B, B-C, and C-Tip of the cantilever). The reinforcement stress-strain relation presented in Table 3 was used to convert the strain gauging to stress distribution. Tension resultant force N fx could be determined by integrating tension stress into the flange. This methodology has uncertainties because it takes into account only reinforcement stresses and does not consider concretes contribution to the tensile force. Due to limitations of experimental data, the influence of residual tensile stresses in the cracked concrete and aggregate interlock cannot be included to the presented experimental results. Closely spaced crack patterns presented in Figure 7 and minor variation between experimental results shown in Figure 11 might be related to that these possible sources of error are not significant near the final load level of the specimen. Table 5 shows normal forces of the flange overhang at cross sections A, B, and C of test beam 8 at different load levels. It can be seen from the table that the change in the normal force between cross sections A and B is insignificant. On the other hand, normal force at cross section C is considerable, taking into account that the section is only at a 600 mm distance from the loading point.
Measured longitudinal shear stress distributions at the junction between one side of the flange and the web of all tested cantilever beams are presented in Figure 11. The results of test 6 are not presented because one relevant gauge bar was damaged and hence its shear distribution could not be evaluated. Elastic and shifted calculated shear stress distributions based on CBT presented in Section 2.1 are also implemented to the figure. What stands out from the tested shear distribution is

Shear stress at between cross sections A and B (=AB)
is negligible during loading and zero at the maximum load where the reinforcement is yielding in both sections. 2. The shape of the shear stress distribution changes during loading. These changes may partly be explained by the fact that methodology used to determine experimental shear stress does not take concrete tensile stresses into consideration. 3. At the maximum load, shear stress concentrates more under the loading point and the shape of the distribution is triangular rather than a square  Figure 12 presents redistribution of the shear stress between different cross sections during loading. The test setup is an isolated part of a complete continuous structure. It is important to bear in mind the possible bias between these two structures. Direct conclusions of shear stress distribution of a continuous girder cannot be drawn from the results of this study.

| Transversal force N y at web-flange junction
CBT avoids the need to construct a TM, and the required transverse reinforcement per unit length can be determined in accordance with Equation (3). The equation is based on the smeared TM, where the struts and ties are not discrete. Figure 13 presents the test beam's TM, which deals with the shear flow for a complete beam on the basis of pure truss actions. Compared to the beam theory described above, it has the advantage of taking into account the distribution of shear along the web-flange junction. Overhang beyond the section of zero moment is dealt with the adjusted truss angle in the end zone (increased θ f ) to adapt the truss to the length available for the dispersion of forces across the flange. The procedure was proposed by Bacchetta and Bachmann. 15,17 Figure 13 treats the longitudinal reinforcement outside the web as two units, one in each flange outstand. Full effective flange breadth is also presumed. The longitudinal reinforcement ratio of the test beams was also kept the same for the full length of flange. When the whole flange breadth is not required for flexural resistance, the method presented in Figure 13 may lead to unnecessary demands for transverse flange reinforcement. A more detailed model about flange truss is presented in Figure 14, where reinforcement outside the web is divided into four units. The force in the tension units along beam length is tailored with measured strain distributions presented in Figures 9 and 10. Adapted TM at Figure 14 takes also into consideration measured compression angle values of the flange presented at incoming Section 5.7. Flange corners at the end of the cantilever tips without concrete cracking were presumed to be not effective. Also, this model is clearly a simplification, but it does however lead to more evenly distributed transversal reinforcement and does make it clear that the decrease of longitudinal steel forces with decreasing bending moment is far slower than implied by the simplification (m/z). 25 To illustrate how the force in the transverse reinforcement required by the presented methods (CBT and TM) compares with the corresponding measured values in cross sections B and C in the loading test, Figure 15 shows the variation of this force along the flange-web connection of the test beam. The shifting of the N y diagram, determined according to CBT, is explained in Section 2.2. The strength of the provided constant transverse steel (Ø = 16 mm, c/c = 100 mm) in the flange is also presented.
The tested N y is obtained by multiplying the area of the transverse steel per unit length of the connection by its maximum stress. Obviously, tested N y cannot exceed the strength of the provided reinforcement. However, if the yield limit of the provided transversal reinforcement is reached, it indicates the need for more reinforcement to improve serviceability. 10 The provided reinforcement exceeds the reinforcement area of CBT. None of the tested transversal F I G U R E 1 6 Method to define angle ϴ f according to test results. The results are presented in Figure 17 F I G U R E 1 7 Calculated and measured angle ϴ f between the concrete compression strut and the web's longitudinal axis reinforcement yielded, but the force in them was greater than CBT predicted with low ϴ f values. According to the TMs provided, transverse reinforcement at flange overhang beyond zero bending moment was inadequate.
Shear stress distribution presented in Figure 11 also indicates that concentrated transversal reinforcement would have been needed at the end region of the test beam. Unfortunately, transversal strain measurement was not made at the end of the cantilever tip.

| ϴ f in the test beam's tension flange
In order to determine angle ϴ f between the concrete compression strut and the web's longitudinal axis, a $1-m-long part of the tested deck slab on the other side of the web between cross sections B and C was studied separately. Shear, longitudinal and transversal strains were measured at cross sections B and C. With the help of measured data and the TM, the relation of the mean angle ϴ f and shear stress between cross sections B and C could be evaluated at a cracked state. The method used is presented in Equation (5) and Figure 16.
The studied element is subjected to axial resultant forces N Bx and N Cx in x direction and longitudinal shear N xy at the junction of the flange and the web. As a result, transversal reinforcement becomes active. The relation between shear stress and the angle of the compression strut at the junction of the web and the flange was analyzed with Membrane-2000 (presented in Section 4). The 200 Â 200 mm 2 membrane element which is subjected to in-plane forces N xM and N xyM between cross sections B and C at the junction of the web and flange was cut out and studied. The ratio between two loads acting on the element's edge planes of the studied membrane element could be determined at a cracked state with the help of measured σ xBC and τ xyBC (Figure 16). The value of N xM used in the analysis was determined according to six reinforcement bars that were nearest to the web-flange junction. The relation of the loads, determined with the method described above, reached a constant value after cracking stress was exceeded in all tests at the load level of 35% of maximum load which means that at section BC while shear stress is lower than $2.5 MPa concretes contribution to the shear capacity is considerable. After the shear stress reached the value 35% of the maximum load (=2.5 MPa) for the studied element BC, the relation of Both calculated and tested angle relation to shear stress are presented in Figure 17. At the beginning of the loading, the measured angle value is zero, whereas calculated ϴ f starts from value 72 . The difference of the curves at the beginning of the loading is the consequence of the method to evaluate the tested angle. The procedure is based on the strut-and-tie model which does not take the contribution of concrete into consideration. The defined angle value determined this way is not relevant until the concrete has cracked. The curves can be divided into three separate development stages: 1. τ xy = 0-1 MPa: According to the calculated result, the angle is large and feasible cracks are nearly perpendicular to the beam axis. Concrete reaches its peak tension stress at the sharp inclination change of the curve and the first cracks appear. Tested angle value is zero which is not a valid result. The reason for this inconsistent result is that at this stage force at transversal reinforcement is for the most part nonexistent, which means that shear force is transmitted through concrete. 2. τ xy = 1-2.5 MPa: Both concrete and transversal reinforcement are active, and the angle value changes. Calculated and measured angle values approach each other. Values are still away from each other because the shear stress has not reached 35% of the maximum after which experimental results are valid. 3. τ xy = 2.5-6 MPa: Shear stress and force at transversal reinforcement increase at the same rate, which means that the capacity of concrete is exceeded. In addition to tested and calculated transversal compression angle values, Figure 17 provides an overview of recommended ϴ f range from different references. Both calculated and tested angle values are at the upper bound of the range and are in good agreement.
Previous studies have reached similar ϴ f -τ xy relations for experimentally studied tension flanges. 24 5.8 | Shear stress τ xy -shear strain γ xy relation In addition to longitudinal and transversal strains, shear strain was also measured from the tested cross sections B and C (DG-B5-6 and DG-C5-6, Figures 5 and 6). Combining the results from shear strain measurements and the τ xy definition presented in cross section 5.5, the τ xy -γ xy relation could be drawn for cross sections B, BC, and C (see Figure 18). Shear strain at cross section BC was assumed to be the average of values measured from cross sections B and C. For the computational study, small membrane elements were separated from the junction of the web, and the flange at cross sections B, BC, and C alike was done in the previous paragraph for cross section BC. Relations of τ xy -γ xy were then calculated with Membrane-2000. The ratios between in-plane forces N xyM and N xM subjected to membrane elements were defined in cross sections B and C with the same methods described for cross section BC previously. Loading ratios are presented in Table 6. Information of the development of the cracking of the flange has been added to computational curves.
At cross section B, normal force is dominant compared to shear and the tested and calculated τ xy -γ xy relations are in good agreement. The tested relation seems to reach the maximum shear stress a bit earlier than the calculated curve. When the ratio of shear force increases closer to the cantilever tip, the disparity between calculated and measured relation increases. This inconsistency may be partly due to measurement frames measuring an average shear strain for the whole flange outstanding while the computational results are from the web flange junction. Taking into consideration the variation that the test results have between each other, the calculated estimation made with Membrane-2000 compared to the test results is good. According to the analysis made with Membrane-2000, the further away from the central support the section is the higher the maximum τ xy capacity it has.

| CONCLUSIONS
The purpose of the current study was to examine longitudinal shear stress of the web and flange junction at the hogging moment area of a continuous composite T-beam made from separate precast concrete girders and cast-inplace deck slab. Longitudinal shear-stress distribution and transversal strains of the flange were experimentally tested from four half-scale cantilever specimens, and the results were compared to methods found from literature. The conclusions of this study can be listed as follows: 1. One of the more significant findings to emerge from this study is that longitudinal shear distribution between the web and the flange according to CBT is not always at a safe side. A notable difference between analytical and tested longitudinal shear distribution was observed. The magnitude of tested longitudinal shear stress at failure at the end of the cantilever tip was almost double compared to the value based on CBT, smeared truss and maximum recommended compression angle value. 2. Both experimental and analytical findings suggest that the cantilever beam requires concentration of transverse steel at the beam end. The computational examples made with discrete TM showed that simplified methods may, however, lead also to unnecessary demands for transverse flange steel. Required transversal reinforcement at the end part of the tested cantilever beam according discrete TM examples was two to three times greater than provided reinforcement. This requirement seems overconservative taking into consideration that the tested flange did not reach shear failure. 3. The experimentally and analytically determined compression angle value ϴ f at studied cross section BC was about 50 , which is at the upper bound of recommended angle values presented in Model Code 2010. This is much more than the recommended design values (ϴ f = 27-31 ) of the highly cited paper by Bacchetta and Bachmann. 15 4. Between the first yielding of longitudinal reinforcement at the hogging moment area and final failure, the test beams developed a long plastic hinge near the continuity connection. At that stage, shear stresses disappeared along the length of the plastic hinge and concentrated at the cantilever end. Without adequate transversal reinforcement, this redistribution could not been happened, and the failure load and mode of the studied structure might have been different. 5. Flange shear cracking started at a relatively early phase of loading. Conventionally longitudinal shear is considered a ULS phenomenon. Parking deck structures are located at aggressive environmental conditions and have strict cracking width limits. Further investigation and experimentation into cracking caused by longitudinal shear at SLS is recommended. 6. Clear shear lag phenomenon was detected at flange longitudinal reinforcement strains over the support of the tested beams tension flanges. By contrast, at the cross-sectional remote from support, strains were evenly distributed. 7. The MCFT is a convenient method in analyzing the in-plane shear deformation response of the flange of the T-shaped cross section. 8. Experimental study on complete continuous Tshaped composite beams is needed to gain information on web flange junctions longitudinal shear distribution. 9. More research concerning the combined effects of longitudinal shear, transverse bending, and vertical shear on transversal reinforcement of T-beams flange is needed.

ACKNOWLEDGMENTS
The authors gratefully acknowledge the financial support provided by the Finnish concrete industry. The authors would also like to thank Mr Jani Kujala for his assistance in the laboratory phase of this study.
NOTATION a l Reference 9 (9.2) A s total amount of flexural reinforcement area A sf part of A s , placed in one side of the flange overhang E c0 concrete tangent modulus at stress σ c = 0 MPa F c concrete compressive force at Flange h f deck thickness L distance between loading point and intermediate support ( Figure 3) σ x , σ y , τ xy stress at specified section and direction (MPa) N x , N y , N xy force per unit at specified section and direction (kN/m) N f resultant force at specified section and direction (kN) P load at cantilever tip during load test r radius of curvature V shear force of the cross-section y f width of one side of the flange outstand ( Figure 3) z inner lever arm, corresponding to the bending in the cross section γ xy shear strain Ɛ x , Ɛ y strains at directions x and y Ɛ 1 , Ɛ 2 principal strains ϴ f angle between the concrete compression strut and the web's longitudinal axis at flange ϴ w angle between the concrete compression strut and the beam's axis at web ρ geometric reinforcement ratio A s /bd v ci shear stress on the crack at MCFT analysis ρ x , ρ y reinforcement ratio for x and y directions DATA AVAILABILITY STATEMENT Data available on request from the authors.