VERTICAL SHEAR RESISTANCE IN A SLIM FLOOR COMPOSITE SECTION

Transcription

1 VERTICAL SHEAR RESISTANCE IN A SLIM FLOOR COMPOSITE SECTION Pentti Mäkeläinen 1, Jing Zhang 2 and Simo Peltonen 3 1, 2 Laboratory of Steel Structures, Department of Civil and Environmental Engineering, Helsinki University of Technology P.O.Box 21 FIN 215 TKK, Finland E mail: pentti.makelainen@tkk.fi, jing.zhang@tkk.fi 3 Peikko Finland Oy, PL 14, Vipusenkatu 2, 1511 Lahti, Finland E mail: simo.peltonen@peikko.com Abstract: In this article, a new application of headed studs will be presented. The use of headed studs is to increase the vertical shear resistance of the Finnish composite slim floor beam named as Deltabeam. This type of composite slim floor beam can be analyzed by strut and tie model (CEB FIP Model Code 199). The purpose of using the headed studs is to take advantage of its tensile resistance when embedded in concrete and make it to behave as "tie" in composite beam. The typical strut and tie truss model (CEB FIP Model Code 199) is applied to analyze the total behavior of the composite slim floor beam. In this situation, the headed stud acts as tensile chord in truss model. The two key problems will be discussed: what is the behavior of the headed stud in the composite slim floor beam and how to estimate its vertical tensile resistance. Because of the special cross section properties of this Finnish composite beam, some proper simplifications are needed in the analyzing procedure. The full scale tests were arranged to find out the real behavior and failure load of the single headed stud. The analysis procedure and the results of the experiments will be compared and discussed. As a conclusion, headed studs can be applied into this composite beam to enhance the vertical shear resistance. More research work will be carried and the more reliable and economic solutions are expected. Key words: Headed studs, composite slim floor beam, vertical shear resistance, failure cone, pull out, tests. 1. Introduction Headed studs are widely used in composite building members in which they behave as shear connectors to make sure the composite action between steel and concrete. Even though, there are some applications in which the headed studs are used to increase the vertical shear resistance of concrete I Beams [1]. In these concrete I beams, the vertical shear resistances are increased by utilizing the tensile strength of double heads studs. In this article, a new method will be developed and applied to increase the vertical shear resistance of a slim floor composite beam, which is one typical Finnish slim floor beam named as Deltabeam. The significant feature of this new method is to take advantages of the tensile strength of the concrete when the inside studs are under tension load and pull out, and as a failure mode concrete cone will be break out together with the studs. Deltabeam is a hollow steel concrete composite beam made from welded steel plates with holes in the sides. The box section of the steel beam is concreted at site during construction concreting doubles the stiffness of the beam. After the concrete has hardened, Deltabeam acts as a composite beam working together with hollowcore slabs, composite slabs, or in situ concrete slabs, as a uniform load bearing structure (see Fig 1). The shear connection for Deltabeam is achieved by the dowel action between the steel web and concrete appearing in the openings through the steel section, after the hardening of the concrete [2]. Deltabeam has structural and economical advantages like other composite beams; it has considerable good load bearing capacity and fire resistance. The strut andtie Model [3] can be applied for analysis and design of Deltabeam. This model was developed by Dr. Leskelä [4]. Anyhow, in some situations, when thin bottom plates are used, the vertical shear resistance of the Deltabeam becomes critical in some design cases; the strut force in the concrete content enclosed in the steel sections exceeds the resistance of the bottom plate. (a) The initial steel section of the beam (b) Concrete cast and the slabs fixed

2 (c) The finished ones slim floor composite beam Fig 1. Deltabeam phases in different construction stage [2] The idea of applying the headed studs to enhance the vertical shear resistance comes from that it is possible to safely exploit the tensile capacity of the concrete when design anchors, given that a sufficient conservative factor of safety is used [5]. When the concrete struts trend to push out, the headed studs inside concrete are under the tension load, this internal tensile force can be transferred to the concrete (base material) by means of a bearing interlock between the studs and the base material. In this way, tensile strength of the concrete around the stud can be used. It provides the possibility of using the headed studs in the Deltabeam to reinforce the concrete against the premature failures due to push out. Fig 2. Tension failure modes (Eligehausen et al. 26 [5]) 2. The headed studs 2.1 Literature review The headed studs used in this article are deformed steel bars, short relative to the length of concrete members, and provided with forged head for anchorage at one end. The diameter of the shaft is about 1/3 times of the diameter of the forged head. The diameter of the stud shaft used in this study is 2 mm, with the steel grade of A5HW. The purpose of using headed studs is to take the tensile bearing capacity in the concrete to increase the "vertical chords" capacity of the Deltabeam. Therefore, it is vital to study about the behaviors of headed studs, such as the failure modes, the failure load and the loaddisplacement curves. Anchors typically exhibit four possible failure modes, shown in Fig 2, when loaded in tension. Each of modes is characterized by a unique load displacement behavior. Fig 3 depicts the idealized load displacement curves for various tension failure modes for fasteners suggested by Fuchs et al [6]. Fig 3. Idealized load displacement curves for tensile loaded anchors exhibiting various failure modes [6] Headed stud anchorages, in general exhibit steel failure, concrete cone failure or concrete splitting failure depending on the steel grade, concrete strength, embedment depth, thickness of component and spacing or edge distance. Pull out failure will occur only if the mechanical interlock (bearing surface) is too small. The experiments have shown that an anchor head area equal to 9 or 1 times the cross sectional area of the stem can provide secure mechanical anchorage with negligible slip and develop the full yield force for studs in yielding [7]. The headed studs discussed in this article fulfill this condition; therefore, the pull out failure won't happen. Steel failure is ductile failure and happens by yielding of headed stud before any break out of concrete occurs [6]. The load displacement curve d, in Fig 3, results if the steel is ductile and if sufficient bolt length is provided for the steel elongation to occur. Concrete cone failure is a brittle failure mode characterized by the formation of a cone shaped fracture surface in the concrete (Fig 2, b 1 ). The full tensile capacity of the concrete is utilized. Headed studs with an adequately large bearing surface will generate concrete cone breakout failure if the steel capacity is not exceeded.

3 A load displacement curve characteristic of concrete cone breakout failure is shown in Fig 3, curve b. Splitting failure occurs when dimensions of the concrete component are limited (Fig 2, c 1 ), the stud is installed closed to an edge (Fig 2, c 2 ) or a line of studs is installed in close proximity to each other (Fig 2, c 3 ). As discussed above, the concrete cone break out failure is the most possible failure mode for studs inside the concrete under the tensile load. In engineering practice, headed studs are indeed often used to transfer loads into reinforced concrete members. Provided the steel strength of the stud as well as the load bearing area of the head is large enough, a headed stud subjected to a tensile load normally fails by cone shaped concrete breakout. A typical concrete cone observed in experiments is shown in Fig 4 [8]. The failure is due to the failure of concrete in tension by forming a circumferential crack. the embedment depth h ef surface, therefore, corresponds to ( 3h ef following values can be taken: scr, N = 3. hef ccr, N =1. 5hef, (see Fig 5 (a)). The failure 2 ). In general, the Fig 4. Typical concrete breakout cone obtained in the tests [8] 2.2 Concrete cone resistance A concrete cone failure in a headed stud under tensile load is characterized by the formation of a conical fracture surface initiating and radiating from the top of the anchor head, provided there are sufficient distances from edges and corners. The initiation of crack starts already under very small loads. The crack propagation is small until about 9% of the bearing capacity is reached, and then it increases considerably [9]. The main influence factors of the bearing capacity are the mechanical properties of the concrete, the area of the failure surface and the embedment depth of the anchor. Several models exist to describe the concrete cone resistance of anchors, such as: The Concrete Capacity Design (CCD) Model The Fracture Toughness Model The Sawade Model The Tensile Strength Model The CCD model predicts best the mean concrete cone failure load. It has also the advantage of simplicity and suitability for design purposes. The Concrete Capacity Design model (CCD) was developed by Fuchs et al., 1995 [6], in an attempt to provide a model that is easy to use and that lends itself to analyzing group and edge effects [1]. The fracture cone is idealized as a pyramid, assuming a quadratic base length of three times Fig 5. Idealized concrete cone for individual fastening under tensile loading after CCD method This fracture mechanics theory is adopted in CEB design guide for fastenings in concrete [11], the limitation of the minimum anchorage depth of the studs and the cracking condition of the base material are also taken into account in this design guide. The concrete properties under tension are modeled by means of the tensile strength only, which is calculated from the concrete compressive strength using empirical formulas. The characteristic resistance N Rk,c of a single headed stud without edge and spacing effects, anchored in cracked concrete, is calculated as [11]: N Rk, c 1 ck ef N = k f h [ ] (1).5.5 where 7.5[ N mm ] k = (2) 1 / Different k1 values ( k 1 9. ) may be taken, if proved in the pre qualification tests. The characteristic resistance N Rk, c of a headed stud or a group of headed studs in the case of concrete failure is given by the following equation [11]: N Rk, c N Rk, c ΨA, N Ψs, N Ψec, N Ψre, N Ψucr, N = (3) The design value of resistance is: N Rk, c N Rk, c, d = (3a) n γ Mc n : Number of tensioned anchors in the group γ : The partial safety factor Ψ s,n Mc : The factor to take into account the influence of edges of the concrete member on the distribution of stresses in the concrete.

4 Ψ ec,n : The factor to take into account a group effect when different tension loads are acting on the individual anchors of a group. The above two factors Ψ s, N and Ψ ec, N are not necessary to be taken into account in this study. Ψ : Shell spalling factor to take into account that re,n the strength of anchors with a small anchorage depth. Ψ : Factor to take into account whether an ucr,n anchorage is in cracked or non cracked concrete. In the application case of this study, the anchorage depth is larger enough and the shell spalling factor can be taken as Ψ re, N = 1. ; and the concrete might be assumed as cracked, then Ψ ucr, N = 1.. So, the most important factor in equation (3) is Ψ A, N. It is the factor to take into account the geometric effects of spacing and edge distance either for a single stud or a group anchors. For single anchors, the failure surface might not be a as the base of an idealized quadratic pyramid with length equal to3 h due to the edge effects, which means the ef break out cone may be truncated if the stud located close to an edge. For a group of studs, each anchor in the group develops the failure surface of a single anchor, which may overlap with the failure surface from its neighbor, depending on the spacing between them. The resulting failure surface is equal to the enclosed area of the failure surfaces of all anchors. The factor Ψ is calculated by A, N the following formula [11]: Ac, N Ψ A, N = (4) A A c,n c; N : Area of concrete cone of an individual anchor with a large spacing and edge distance at the concrete surface, idealizing the concrete cone as a pyramid with a height equal to s,. A c, N cr N : Actual area of concrete cone of the anchorage at the concrete surface. It is limited by overlapping concrete cones of adjacent anchors ( < ) as well as by edges of the concrete member ( deduced from the idealized failure cone. s s cr, N c c cr, N 2.3 Assumption about the failure surface < ). It may be In the above review, it is shown that the concrete cone failure load is largely influenced by the actual area of concrete cone of the stud at the concrete surface, the tensile stress of the concrete and the anchor depth h ef. The failure surface of a single stud cast inside the Deltabeam shaped concrete block is an important subject to be studied in this research. The cross section of the Deltabeam is a trapezoidal cross section. As a consequence, the pull out behavior of the single stud should be investigated in such shaped trapezoidal section. Assume the length of the specimen is enough for a single stud to develop the failure along the longitudinal direction of it. Obviously, the edge effects in transverse direction of the beam must be significant, while there are not edge effects along the longitudinal direction, see Fig 6 (b), compared with the idealized failure cone in Fig 6 (a). The assumed failure surface in Fig 6 (b) is hatched by shadows; the area of the shadows can be calculated according to geometrical dimensions of the beam. (a)idealized concrete failure cone and corresponding failure surface (b)assumed concrete failure cone for the Deltabeamshaped concrete block and corresponding failure surface Fig 6. Cooperation of the failure surface 3. Tests In order to inspect and verify the failure mode, the failure surface assumed in previous part, to get the inclined angle of breaking out concrete cone and to obtain the maximum failure load of a single headed stud, a series of commonly used size of Deltabeam shaped concrete blocks were cast with the corresponding studs inside (see Fig 7), the length of the concrete specimens is 1 meter long, the dimensions of the cross section are shown in Fig 8. Fig 7. The shape of specimens for single studs pulled out from Deltabeam shaped concrete block

5 with; the other two displacement measures were arranged at the top surface in the both ends of the specimens. Fig 9. The setup of the tests Fig 8. The shape of specimens for single studs pulled out from Deltabeam shaped concrete block There are three specimens in the tests. The specimens are named with D26 3, D26 4 and D32 3. The main dimensions of the specimens are shown in Table 1. The failure patterns got from the tests were considerable fitting the concrete cone failure mode; see Fig 1 (a), (b), and (c). The corresponding inclinations between the failure surface and the surface of the concrete members were 32.º, 31.º and 33.5º. These results are quite close to the angle 35º assumed in the CCD method and CEB design code mentioned in part 2 of this article. Table 1. The main dimensions of the specimens Width of bottom flange (mm) Height of specimen (mm) Length of stud (mm) D26 3 D26 4 D Diameter of the 2 stud (mm) The concrete grade is C3 (cubic)/ 7 days, the steel grade of the studs is A5HW The setup of the tests are carefully arranged to make sure the accuracy of the results, see Fig 9. The bottom part of the specimens with thickness of 2 mm and the cantilever parts along the specimens are used to fix the specimens along the longitudinal direction and avoid the bending moments in the middle point at the top surface of the specimens. Additionally, the specimens are also fixed at middle points of the cantilever parts from both sides. The steel reinforce bars are added at top level of the bottoms of the specimens, avoiding the shear cracking at the concrete corners. The loading speed in the load history was1 kn / s. One displacement measure was arranged at the top surface of the steel plates, which the studs were welded (a) Specimen D26 3 (b) Specimen D26 4

6 (c) Specimen D32 3 Fig 1. Failure shapes of the specimens The failure loads are listed in Table 2. The failure loads according to the assumptions shown in Fig 6 (b) can be calculated according to equation (1), (2) and (3). The results are listed in Table 3. Table 2. The failure loads in the tests Test No. Name of the beam F max_test (kn) 1 D D D Table 3. The failure loads according to the calculations Calculation No. Name of the beam F max_cal (kn) 1 D D D There are obvious variations between the two groups of loads in Table 2 and Table 3, the variation is about 38% for D26 3, 22% and for D26 4 and 4% for D32 3. The reason for these variations is that real failure surface is not exactly as the one assumed in Fig 6 (b). Theatrically, the summit of the failure cone starts from the stems of the studs, and the cracks around will continuously grow with an angle of 35º to the top surface of the concrete until the cracks reaching the edges. In the failure specimens, the lowest points of the cracks observed from the side surface of the specimens are almost at the same level of the heads of the studs. This phenomenon indicates that the cracking in transverse direction of the specimens did not develop accurately with an angle of 35º to the top surface of the specimens as the CCD model. Another phenomenon can also be noticed from the tests, the cracking lines in the longitudinal direction of the cones can be observed from the side surface of the specimens, these cracks develop first horizontally along the longitudinal direction of the specimens in some certain distance, and after that they start to develop to the top surface of the concrete and form the break out cones. The above two phenomena cause the differences between the actual area of failure surface and the theoretical assumptions. The real areas of cracking surfaces measured from the failure specimens are about 18 35% more than the theoretical ones. It gives good explanations for the variations between the results in Table 2 and Table 3. As a conclusion, the failure mode in the above tests can be cataloged into concrete cone failure, the inclined angles of breaking out concrete cone are quite close to 35º and the areas of failure surfaces assumed based on the theory are smaller than the actual ones, which indicate this assumption is conservative and safe. 4. Vertical shear resistance of Deltabeam The strut and tie model (or truss model), pioneered by Ritter (1899) and Mörsch (199), has been greatly advanced during the past decades. It has widely used to analyze the force transfer mechanisms and design concrete beams, or unusual circumstances. The Deltabeam is one type of hollow slim floor composite beam; the concrete body inside the steel sections provides the possibility of using truss model [3] when analyzing the flow of internal forces. The vertical shear resistance of the Deltabeam can be evaluated by considering a strut and tie system, which will develop in the concrete inside the boxed steel section [12]. The resistance is defined by the component failure. It is assumed that before the onset of shear failure the concrete is cracked diagonally in the region of the maximum shear force, and there are two main reasons, which will lead to the development of the shear failure: (1) Compression failure of the concrete in the diagonal struts, the failure load expressed by D _ ; R S (2) Yielding of the webs between the web holes, the failure load expressed by D _. R W

7 Deltabeam under vertical load should be analyzed and tested. The work will bring other two interesting topics: The principle of arrangement of the studs into Deltabeam The composition action when studs applied into this composite beam. The principle of arrangement of studs into Deltabeam is an optimizing problem, since the analysis of the beam is based on the strut and tie model [3]. This model provides the flexibility to adjust the struts angle to get more reliable and economic solutions. The study of the composite action can get more efficient usage of all the materials included in this composite beam. (a) Geometry for considering the diagonal cracking inside the steel section of the Deltabeam [4] (b) Truss model according to the design assumption of the Deltabeam Fig 11. Truss model analysis for Deltabeam Then the minimum value of the D R _ S and R W D _ in vertical direction provides the limitation of the ultimate shear resistance of the beam. The shear resistance of Deltabeam can be contributed by several parts: The force anchored by the web holes due to the dowel action between the steel web and concrete appearing in the openings through the steel section The force anchored by the bottom flange The force anchored by other possible elements. If the bottom steel flange of the beam is thick enough, the ultimate resistance D ult can be developed unconditionally [4]. However, when the bottom flange is not thick enough or the bottom flange has lost its action (such as fire situation), the contribution of steel bottom flange would be considerable small or neglected. The left anchorage forces could be not sufficient to prevent the concrete strut crushed out or the failure of the steel webs between the holes. The shear resistance of the beam will decrease without doubts. As the tests show in previous part, the steel headed studs can employ the local capacity of the concrete to carry tensile stresses. They can be arranged into Deltabeam. When the beam is under the vertical load, the concrete struts have tendency to crush down, as a consequence, the reaction forces drive the studs in tensile loads. The studs start to contribute the vertical shear resistance to the beam until failures occur. Reference 1. Gayed, R.B., and Ghali, A. Double Head Studs as Shear Reinforcement in Concrete I Beams. ACI: Structural Journal VOL. 11, NO.4. 2.Peltonen, S. and Leskelä, M. V. Connection Behaviour of a Concrete Dowel in a Circular Web Hole of a Steel Beam: Composite Construction in Steel and Concrete V, South Africa, Comité Euro International du Béton, CEB FIP Model Code 199, Thomas Telford, Ltd., London, 1993, 437 p. 4. Leskelä, M.V. General Principle for Evaluating of the Vertical Shear Resistance of the Deltabeam Normal Temperature Design and Fire Design. January Eligehausen, R.; Mallée, R and Silva, J. F. Anchorage in Concrete Construction, 26. p55; P Fuchs, W.; Eligehausen, R. and Breen, J. B. Concrete Capacity Design (CCD) Approach for Fastening to Concrete. ACI: Structural Journal VOL. 92, NO Ghali, A. and Youakim, S. A. Headed Studs in Concrete: State of the Art. ACI: Structural Journal VOL. 12, NO Eligehausen, R. Mallée, R. and Rehm, G. Befestigungstechnik, Ernst and Sohn, Berlin, Germany, Sawade, G. Ein energetisches Materialmodell zur Berechnung des Tragverhaltens von zugbeanspruchtem Beton, Dissertation, University of Stuttgart, Bazant, Z. P. Size effect in blunt fracture: Concrete, Rock, Metal. Journal of Engineering Mechanics, Vol. 11, No. 4, CEB: COMITE EURO INTERNATIONAL DU BETON, Design of Fastenings in Concrete, Leskelä, M.V., Vertical Shear Resistance of Deltabeam Normal Temperature Design. A report paper for Deltatek, Lahti. December 1995, Oulu, Finland. 5. Summary and prospection According to the above research work, it is sure that the headed studs can be applied into Deltabeam to provide the contribution to the vertical shear resistance. More work will be carried out in the following research. The behaviors of the studs together with