Behavior and strength of welded stud shear connectors in composite beam. Comportamiento y resistencia de conectores tipo perno en vigas compuestas

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1 Rev. Fac. Ing. Univ. Antioquia N. 63 pp Junio, 2012 Behavior an strength of wele stu shear connectors in composite beam Comportamiento y resistencia e conectores tipo perno en vigas compuestas Jorge Douglas Bonilla Rocha 1*, Enrique Mirambell Arrizabalaga 2, Rafael Larrúa Queveo 3, Carlos A. Recarey Morfa 4 1 Department of Mathematics. Universia e Ciego e Ávila. Cuba. 2 Department of Construction Engineering. Universitat Politecnica e Catalunya. Spain. 3 Department of Civil Engineering. Universia e Camagüey. Cuba. 4 Department of Civil Engineering. Universia Central e Las Villas. Cuba. (Recibio el 23 e mayo e Aceptao el 23 e mayo e 2012) Abstract In this paper the behaviour of stu shear connectors in composite structures is analyse. The composite section is forme by steel profiles connecte to soli concrete slabs. Some effective numerical moels using the finite element metho to simulate the push-out test are propose. The results obtaine from the numerical analysis were verifie against experimental results. The material nonlinearities were consiere in the moels. A bilinear moel for steel was consiere, an a moel of plastic amage (Concrete Damage Plasticity) in concrete was also aopte. The shear connection capacity obtaine from the finite element analysis is compare with the connection strength calculate using the American Specification an the European Coe for heae stu shear connector in soli slab composite section. Moifications to existing expressions in these coes are propose. New factors that improve the preiction of the shear connection capacity are consiere Keywors: Composite beams, connectors, heae stu shear, push-out test, finite element metho, steel structures Resumen En este trabajo se analiza el comportamiento e conectores tipo perno e estructuras compuestas. La sección compuesta está formaa por un perfil e acero conectao a una losa maciza e hormigón. Se proponen varios * Autor e corresponencia: teléfono: , fax: , correo electrónico: jorgebr@informatica.unica.cu (J. Bonilla) 93

2 Rev. Fac. Ing. Univ. Antioquia N. 63. Junio 2012 moelos numéricos e la simulación el ensayo push-out, utilizano el métoo e elementos finitos. Los resultaos obtenios el análisis numérico son valiaos contra resultaos experimentales. Se consiera la no linealia e los materiales, empleano un moelo bilineal para el acero y un moelo e año plástico para el hormigón. La capacia e la conexión obtenia a partir el análisis por elementos finitos se compara con la calculaa usano la Normativa Americana y el Cóigo Europeo para conectores tipo perno en sección compuesta e losa maciza. Se proponen varias moificaciones a las expresiones existentes en ichos cóigos, one se consieran nuevos factores que mejoran la preicción e la capacia resistente última e la conexión Palabras clave: Vigas compuestas, conectores, perno, ensayo push-out, métoo e los elementos finitos, estructuras e acero Introuction This paper escribes the structural performance of shear connection in soli slab composite beams. The behaviour of heae stus in composite beams epens on many factors, incluing strength an imensions of heae stu shear connectors, compressive strength of concrete, spacing of the stu shear connectors an heightiameter ratio of the stus. Push-out tests are commonly use to etermine the capacity of shear connection. Finite element moelling of shear connection can provie an efficient alternative to costly an time consuming full-scale push-out tests. Lam an Elloboy [1], Elloboy an Young [2] evelope an accurate nonlinear finite element moel to stuy the behaviour of heae stu shear connectors in composite sections. In this paper an accurate nonlinear three-imensional finite element moel to stuy the behaviour of heae stu shear connectors in composite beams using the program ABAQUS/CAE Ver is presente. The material nonlinearities are consiere in the moels. A moel of plastic amage (Concrete Damage Plasticity) in concrete has been aopte, an a elastic-perfectly plastic moel for steel has been consiere. The results obtaine from the finite element analysis were verifie against the experimental results obtaine by Lam an Elloboy [1]. In this work, the results of the finite element analysis were compare with the American Specification AISC (2005) [3] an the European Coe EC-4 (2004) [4] for steel-concrete composite structures. It was observe that the AISC [3] overestimates the stu strength, while the EC-4 [4] in some cases overestimate the stu strength, but in another cases unerestimates it. This paper proposes a new equation that improves the preiction of the stu strength capacity, where a reuction factor is introuce in orer to consier the effect of the longituinal spacing of the stus on the shear connection capacity. Besies, a new reuction factor is propose to take into account the effect of the height to iameter ratio of the stus. Finally, the results obtaine from the new equation are compare with AISC [3], EC-4 [4] an the numerical analysis. A sc E c E cm E s Nomenclature Cross-section area of heae stu shear connector Diameter of heae stu shear connector Initial Young s moulus of concrete Mean value of the secant moulus of concrete tabulate in EC-4 Initial Young s moulus of heae stu shear connector 94

3 Behavior an strength of wele stu shear connectors in composite beam Compressive cyliner strength of concrete f ck f y f u h c Compressive cyliner strength of concrete Yiel stress of heae stu shear connector Specifie minimum ultimate tensile strength of the heae stu shear connector Ultimate tensile strength of the heae stu material Height of heae stu shear connector Q sc-aisc Nominal unfactore esign strength calculate using AISC Q sc-ec-4 Nominal unfactore esign strength calculate using EC-4 Q sc-ne Q sc-test R g R p α γ Capacity of shear connection per stu obtaine from finite element analysis Capacity of shear connection per stu obtaine from the new expression (Eq. 6) Capacity of shear connection per stu obtaine from push-out tests Reuction factor Reuction factor Reuction factor Reuction factor Ultimate strength of heae shear stu connectors The esign stanars for shear stus in composite beam are covere by AISC [3] an EC-4 [4]. In AISC, the nominal shear of a stu shear connector is governe by the general equation: (1) This equation (1) aopts the following form (Eq. 2) for shear stus in solis concrete slabs: (2) EC-4 [4] gives a similar approach for etermining the ultimate resistance of stu connectors (Q sc ) by presenting the formulas below, where Q sc is taken as: where α is etermine by: (3) Description of push-out test specimen This stuy is base on the virtual simulation of the push-out test. For the calibration an valiation of the numerical moel, the virtual simulation of four push-out tests is mae, where only the concrete strength varies (see table 1). The experimental results have been taken from [1]. Table 1 Results of ultimate loa of the experimental push-out tests (Lam an Elloboy [1]) Specimen Dimensions of the stu Concrete compressive strength Ultimate loa in push out test SP-1 19 x SP-2 19 x SP-3 19 x SP-4 19 x

4 Rev. Fac. Ing. Univ. Antioquia N. 63. Junio 2012 The test specimen is compose by a segment of W10x49 profile an two rectangular slabs of concrete of 619 x 469 x 150 mm (length x with x thickness) imension, locate at each sie of the profile in contact with the flange. The connection between the slab an the profile is obtaine by means of a stu connector with f y = an E s = (see figure 1) Loa Connector Figure 1 Diagram of the test specimen A B Finite element moel General Generally, for a successful numerical moelling of the connection moelling, all the components associate with it must be properly represente. ABAQUS, which is a general purpose finite element moelling package, was utilize for this finality. With this system, it is possible to consier the three-imensional geometry, material nonlinearity, an to inclue element interface an constraint conitions. Bounary conitions a) Stu: There are two surfaces of interaction: one that guarantees the stu-profile union, an the stu-concrete interface. The stuconcrete interface is treate as a rigi surface, although it is known that there is not a full continuity between both materials. Lam an Elloboy [1] use a rigi contact in the stu-concrete interface by isconnecting those noes which have been verifie that o not participate in the contact (see figure 2). Stu concrete contact Loa Area without contact Stu concrete contact Stu W profile contact Figure 2 Stu-concrete contact surfaces b) Concrete slab: The friction force that is generate in the slab-profile union is not consiere, as usually one in push-out proceures. A normal contact between both materials was only generate. The support of the slab is obtaine in the lower part (surface 1 in figure 3); all noes of the concrete slab in the opposite irection of loaing (surface 1) are restricte from moving in the Z irection to resist the compression loa. Distribute loa Point 1 Surface 1 Surface 1 Figure 3 Isometric view of the virtual specimen geometry Finite element type an mesh ensity The results obtaine in [5] show that the use of C3D6 elements to moel the stu connector an the concrete slab aroun the stu an C3D4 elements to moel other parts of the slab is the aequate configuration, which prouces better results, accoring to real test. For this configuration, the moel for four ifferent mesh ensities has been stuie. This was one by placing a mesh of variable ensity in the slab, increasing the mesh 96

Behavior an strength of wele stu shear connectors in composite beam towars the slab-stu contact area. The mesh has a uniform size in the connectors (see figure 4).

5 Behavior an strength of wele stu shear connectors in composite beam towars the slab-stu contact area. The mesh has a uniform size in the connectors (see figure 4). Figure 4 Mesh iagram a) Stu, b) Slab, c) Profile Application of loa The loa was applie incrementally on the steel web, as show in figure 3, to small intervals, where the size of such intervals was selecte automatically by ABAQUS, base on the conition of numerical convergence. In this case, the loa was applie using the moifie RIKS algorithm. The basis of this algorithm is Newton s metho. The isplacements of the profile for each loa intervals are controlle in point 1 (see figure 3). Material moeling of concrete The concrete material was moelle consiering a moel of plastic amage evelope by Lubliner et al. [6], an available in ABAQUS. This moel consiers the most important phenomena of concrete base on the theoretical principles of the Mohr-Coulomb s moifie moel. Moelling of the steel Base on Lam an Elloboy [1], Elloboy an Young [2] an Nie an Cai [7], for the moeling of concrete-steel composite structures a bilinear behaviour was aopte for the case of steel, base on Von Mises criterion. Verification of finite element moel The shear connection capacity per stu obtaine from the tests (Q sc-test ) an the finite element analysis ( ), as well as the loa-slip behaviour of the heae shear stu, was examine. Table 2 shows a comparison of the capacities of shear connection obtaine experimentally an numerically. Goo agreement between numerical an experimental result is observe. A maximum ifference of 4.7 % was observe between experimental an numerical results for push-out test specimen SP-3. Table 2 Numerical an experimental results of loa capacity for the four specimens Spec. Q sc-test Q sc-test / SP SP SP SP Mean Note: The table shows the loa capacity per stu. Effect of concrete strength on stu strength An analysis about the effect of concrete strength on stu strength by means of numerical simulation was mae in [5]. It showe that the capacity of shear connection increase when concrete strength increase. That fact is also consistent with [8]. Effect of cross-section area of the stu shank an steel strength on stu strength By using numerical simulation, a stuy about the effect of the cross-section area of the stu shanks an the steel strength on the stu strength was carrie out in [5]. As the cross-section area is increase, there is an increase in the connections bearing capacity, escribe by a linear tenency. On the other han the variation of the ultimate tensile strength of the stu have little influence upon the connection bearing capacity. Therefore, this is not a very significant parameter. 97

6 Rev. Fac. Ing. Univ. Antioquia N. 63. Junio 2012 Effect of the height to iameter ratio of the stu on the stu strength A new factor (α) to reuce stu strength with h c / ratio variation is estimate in [9] by the authors of this paper, which consiers the influence of concrete strength an stu iameter variation. The reuction factor (α) is etermine for each stu iameter from 9.52 to mm, accoring to concrete strength an h c / ratio. In table 3 the (α) reuction factor is explicitly represente. Table 3 Reuction factor (α) a h c / EC If the (α) value obtaine from the expression of EC-4 that appears in the last row of table 3 is compare with the value obtaine in [9] an presente in table 3, a substantial ifference is observe, which in some cases amounts to 25%. 98

7 Behavior an strength of wele stu shear connectors in composite beam Effect of the longituinal spacing of the stus on stu strength When the stu connectors are too close to each other, the stress inuce by the stus overlap an the connection bearing capacity ecreases. The stu connectors calculation methos suggeste in the international coes o not take into account this effect. A reuction factor (γ) of the capacity of shear connection was etermine in [9] for cases when the connectors were close to each other. In table 4 the reuction factor from 9.52 to mm stus iameter is observe, accoring to concrete strength an longituinal spacing. Table 4 Reuction factor (γ) Gamma Longituinal spacing

8 Rev. Fac. Ing. Univ. Antioquia N. 63. Junio 2012 Correction of the ultimate strength calculation for 22 an 25 mm iameter stus A parametric stuy was conucte using finite element moels for 12.7 x 65, x, x, x 130 an 25.4 x 130 mm heae shear stus with various concrete strength values of 20, 25, 30, 35 an 40. The ultimate tensile strength of the stus use was The results were compare with the calculate values obtaine from the equations given by AISC [3] an EC-4 [4]. Figure 5 shows graphically the results of this comparison. It is interesting to note that the result from AISC inicate a much higher shear capacity than the those results obtaine using both EC-4 [4] an the finite element solution analyze in this paper. The equations given by AISC [3] overestimates the stu strength in all analyze stu an concrete strength values. For example, there are ifferences ranging from 30 % to % for mm an 25.4 mm stus in all the analyze concrete strength values. On the other han, the expression given in EC-4 [4] gave a goo correlation with the FE solutions for 12.7, an mm stus; however, the expression overestimates the stu strength for an 25.4 mm iameter stus. These consierations are in accorance with the work of Lam an Elloboy [1] (12.70 mm), ( = 65 ksi) (a) (15.88 mm), ( = 65 ksi) (b) (19.05 mm), ( = 65 ksi) (c) EC-4 (2004) AISC (2005) FE f' c (22.22 mm), ( = 65 ksi) () EC-4 (2004) AISC (2005) FE f' c (25.4 mm), ( = 65 ksi) (e) EC-4 (2004) AISC (2005) FE f' c EC-4 (2004) AISC (2005) FE f' c EC-4 (2004) LRFD (2005) FE f' c Figure 5 Coes comparison of shear capacity for heae shear stus: (a) x 65 mm, (b) x mm, (c) x mm, () x 130 mm, (e) x 130 mm In orer to improve the preiction of the shear connection capacity in an 25.4 mm stus, an experimental esign [3 x 3 x 3 (3 3 )] was carrie out to etermine which variable combinations ha greater influence on the connection bearing capacity as well as to assess how these variables affect this property. The factors consiere were: ultimate tensile strength of steel ( ), stu iameter () an concrete strength ( ). Three levels were consiere for each factor: two

9 Behavior an strength of wele stu shear connectors in composite beam extreme levels an an intermeiate level. In the case of the iameter, a fictitious intermeiate level (fl) was consiere even though this iameter is not commercially available. In orer to establish the range of variation of the levels of the ultimate tensile strength of steel, the experimental stuies of Rambo-Roenberry [10] have been taken as a reference (see table 5). Table 5 Variables an levels of experimental esign Factorial esign (3 3 ) Factor Levels Ultimate tensile strength of steel ( ) (65), 499., 551.() (ksi) Stu iameter () 22.22(7/8), 23. [fl], 25.40(1) mm (in) Concrete strength ( ) 20(2900), 30, 40(50) (psi) With a configuration similar to the specimen presente by [1], a simulation, with a previous calibration, was performe in orer to etermine the connection strength for each one of the combinations in the experimental esign. In table 6 several combinations as well as outputs of the numerical simulation are shown. Several regression analyses were carrie out with these combinations an outputs, using the statistical software SPSS v A total of 15 statistical moels were analyze. The moels that better preicte the connection bearing capacity were selecte after analyzing the R 2 coefficient. Finally, the selecte moel was the following (Eq. 4): (4) For esign purposes an in accorance with current coes of practice, the previous expression is simplifie an the following equation is obtaine (Eq. 5): (5) Table 6 Results of each combination in the experimental esign Specimen Specimen Q sc- FE P-LM-1 22, ,18 95,69 P-LM-15 25, , 151,12 P-LM-2 22, ,18 125,19 P-LM-16 25, ,18 141,37 P-LM-3 22, , 145,36 P-LM-17 22, ,18 113,86 P-LM-4 22, , 101,77 P-LM-18 22, , 131,28 P-LM-5 25, ,18 110,55 P-LM-19 22, , 135,39 P-LM-6 25, ,,26 P-LM-20 22, , 99,14 P-LM-7 25, , 1,50 P-LM-21 25, , 147,14 P-LM-8 25, ,18 162,83 P-LM-22 23, , 152,02 P-LM-9 23, , 161,49 P-LM-23 22, , 119,24 P-LM-10 23, ,18 139,94 P-LM-24 23, , 105,30 P-LM-11 23, ,18 102,44 P-LM-25 23, , 142,08 101

10 Rev. Fac. Ing. Univ. Antioquia N. 63. Junio 2012 Specimen Specimen Q sc- FE P-LM-12 23, , 107,57 P-LM-26 23, ,18 127,10 P-LM-13 25, , 174,48 P-LM-27 23, , 132,24 P-LM-14 25, , 115,50 Note: E c is estimate accoring to ACI-318 (2005) Figure 6 shows the results of the preictions using the stuie coes, Eq. 5 an the FE solution. It is possible to see how Eq. (5) offers stu strength values which are more conservative than those of the American Specification an the European Coe conservative unconservative Figure 6 Preiction by the stuie coes an the Eq. (5) against FE solution New expression for calculating the shear connection capacity By introucing the α an γ reuction factors in Eq. 5, as well as a new β factor for mm an 25.4 mm stus, the following expression is obtaine: (6) where α is in function of the (h c /) ratio (see tab. 3), β is 0.37 for mm, an 0.32 for mm, γ is in function of the longituinal spacing (see tab. 4); A sc is expresse in m 2 ;, E c an are expresse in. Table 7 shows a comparison of the capacities of shear connection obtaine from the finite element solution, the EC-4 [4] an the new expression (Eq. 6). The effect of the h c / ratio on the preiction of the stu strength is taken into account. It is possible to see that the new expression offers the better preictions with a /Q sc-ne ratio mean value of an the corresponing coefficient of variation of In this analysis the effect of the longituinal spacing between connectors on stu strength is not consiere, therefore γ = 1. Table 7 Effect of the hc/ ratio on the stu strength 102 h c / Q sc-ec-4 Q sc-ne / / Q sc-ec-4 Q sc-ne

11 Behavior an strength of wele stu shear connectors in composite beam h c / Q sc-ec-4 Q sc-ne / / Q sc-ec-4 Q sc-ne Mean COV It is worth pointing out that in the new expression a new reuction factor was introuce so as to take into account the effect of the longituinal spacing on the connection bearing capacity, which causes the calculation proceure to be iterative. In the first iteration, the longituinal spacing is not known, an γ=1 shoul be consiere. The iterative process is stoppe when in the last iteration there is not observable ifference between the longituinal spacing obtaine in the previous iteration an the current iteration. Accoringly, the amount of connectors calculate in each iteration shoul be istribute in the composite beam. Table 8 shows a comparison of the connection bearing capacity obtaine from the finite element solution, the AISC [3], the EC-4 [4] an the new expression (Eq. 6). In this case the effect of the longituinal spacing on the stu strength preiction is taken into account. In this analysis, the new expression also offers better preictions with a /Q sc-ne ratio mean value of an the corresponing coefficient of variation of Table 8 Effect of the longituinal spacing on the stu strength x h c Sp. / / / Q sc-ec-4 Q sc-aisc Q sc-ne x x x x x x x x Mean COV

12 Rev. Fac. Ing. Univ. Antioquia N. 63. Junio 2012 Conclusions Accurate nonlinear finite element moels have been evelope to investigate the behaviour of shear connection in soli slab composite beams. The moels take into account the nonlinear material properties of concrete, steel beams an heae stu shear connectors. The shear connection capacity an the loa-slip behaviour of heae stu were preicte from the finite element analysis, an the results were compare with experimental results. The parametric stuy showe that the expression given in EC-4 [4] prouce better results when compare with FE results, while it woul appear that the AISC [3] might have overestimate the shear connection capacity. Furthermore, all the coes seem to overestimate the shear capacity of the an 25.4 mm iameter heae stus. A moification of the expression given in EC-4 is propose in this work. The constant 0.37 of the equation was change to 0.32 for an 25.4 mm iameter heae stus. A new reuction factor (γ) was introuce in orer to consier the effect of the proximity of the stu connectors, an the reuction factor propose by the EC-4 to consier the h c / ratio was also moifie. The comparison of the shear connection capacity obtaine from the finite element analysis, the new expression an the esign rules specifie by the American Specification an the European Coe have shown that the new expression (Eq. 6) prouce better results with a goo correlation with the finite element analysis. References 1. D. Lam, E. Elloboy. Behavior of Heae Stu Shear Connectors in Composite Beam. Journal of Structural Engineering, ASCE. Vol pp E. Elloboy, B. Young. Performance of shear connection in composite beams with profile steel sheeting. Journal of Constructional Steel Research. Vol pp AISC. Loa an resistance factor esign specification for structural steel builing. American Institute of Steel Construction. Chicago (USA) pp Eurocoe 4 (EN ). Desing of Composite Steel an Concrete Structures. European Committee for Stanarization. Part 1.1(2004). Brussels, Belgium pp J. Bonilla. Estuio el comportamiento e conectaores tipo perno e estructuras compuestas e hormigón y acero meiante moelación numérica. Tesis e Doctorao. Universia Central e Las Villas. Sta Clara, Cuba pp J. Lubliner, J. Oliver, S. Oller, E. Oñate. A Plastic- Damage Moel for Concrete. International Journal of Solis an Structures. Vol pp J. Nie, C. Cai. Steel-Make specific Composite Beams Consiering Shear Slip Effects. Journal of Structural Engineering. Vol pp J. Ollgaar, R. Slutter, J. Fisher. Shear Strength of Stu Connectors in Lightweight an Normal-Weight Concrete. Engineering Journal, AISC. Vol pp J. Bonilla, R. Larrúa, C. Recarey, E. Mirambell. Corrección el cálculo e la capacia resistente última e conectaores tipo perno e estructuras mixtas en la tipología e viga-losa maciza. Revista Ingeniería Civil, CEDEX. No pp M. Rambo. Behavior an Strength of Wele Stu Shear Connectors. Ph. D. Thesis. University of Blacksburg. Virginia, EE.UU pp

OF CHS. associated. indicate. the need. Rio de Janeiro, Brazil. a) Footbridge Rio. d) Maria Lenk. CHS K joints

OF CHS. associated. indicate. the need. Rio de Janeiro, Brazil. a) Footbridge Rio. d) Maria Lenk. CHS K joints EUROSTEEL 2, August 3 September 2, 2, Buapest, Hungary A NUMERICAL EVALUATION OF CHS T JOINTS UNDER AXIAL LOADS Raphael S. a Silva a, Luciano R. O. e Lima b, Pero C. G. a S. Vellasco b, José G. S. a Silva