2.1 Vertical load tests

The MA and MC models tested with vertical load parallel to axis 2-2 of the beam to generate bending stresses around axis 3 and shear stresses in axis 2, (axes shown in (Figure 6d)). There were three specimens for each case. The objective was to observe the bending and shearing performance of the beam, the failure mechanism and the way the load is transmitted. The load was applied to the steel beam in the direction of gravity, as they work in service, and shown in (Figure 6), to represent the way the steel deck slabs transmit most of the weight to the concrete beam. Displacements were measured with three Linear Variable Differential Transformers, (LVDTs) outlined in (Figure 6c), and monotonic loads until the element was led to failure.

Figure 6 Application of the load in the vertical direction on MC and MD models 

(Figure 7) shows that the slope of the load-deformation curve is the same for tensile and compressed steels until the concrete reaches its maximum strength, which occurs in the order of deformations of = 0.0001 (^{Mander et al. 1988}). From that point on, the load curve starts to slope differently from the deformation curve. (Figure 7c) and (Figure 7d) are Abaqus models and illustrate the deformations and stresses in the 1-1 directions of the beam, showing the formation of compression struts in the area under the mixed connection.

Figure 7 Model MC2, a) tested model; b) Deformation of tensile and compressed steel; c) Deformation in direction 1-1; d) Stresses in direction 1-1 

(Figure 8) shows the load-deformation behavior of the 4 strain gauges and the load-displacement curve of 3 LVDT sensors placed in the node section. The THEORETICAL MODEL column in (Table 1) shows the theoretical failure load of 100.65 kN without reduction coefficients ϕ=0.9 and 0.85 of calculated with the ACI formulas for bending beams, recognizing at this point that the node is D region and it is not appropriate to apply those formulas. This value is lower than the average load obtained from the experiment that originates the yielding in the 103 kN tensile steel, under the FAILURE LOAD column in (Table 1) and represented in (Figure 8). Before the theoretical failure, obvious cracking begins, with the first cracks visible for a load of approximately 78 kN in all models.

Table 1 Loading values and yield moment of the tensile steel 

(Figure 8) shows that compressed steel has a higher elastic behavior, tensile steel a first elastic stage until the concrete deforms ε_c=0,0001 at a load of 35.86 kN (3656) kg, then the steel goes into yielding at typical deformations greater than 0.002 and the beam fails at a load greater than the theoretical load. It was concluded that the node does not decrease the bending strength of the beam.

Figure 8 Model MC2 curve; a) load-deformation curve; b) load-displacement curve 

2.2 Horizontal load tests

Three specimens were tested with a horizontal load named MA in order to observe the penetration hardness of the steel beam through the node. The load is applied in the longitudinal direction to the steel beam I, parallel to the axis 3 of the beam. See the diagram in (Figure 9). It was equipped with two LVTD sensors and 4 strain gauges as shown in (Figure 3a). The steel beam had two handle-shaped steels to prevent slippage.

Figure 9 MA models tested in the longitudinal direction of the node 

Figure 10 MA models tested in the longitudinal direction of the node 

The evolution of the damage observed in the experiments, such as the damage shown in (Figure 10) and the graphs in (Figure 11), demonstrate that the collapse is due to the shear failure of the steel beam and that the longitudinal tensile or compressive reinforcement of the concrete beam does not reach yielding.

In (^{Castañeda and Mieles 2017}) computer models of buildings with hybrid nodes with three independent variables and two levels were made (experiment 2³): height of the building, rectangularity in floor plan and type of node; in all cases, it was found that the type of node influences the structural response of the dependent variables moment, shear and floor drift. In these same computer models, the maximum axial force of the hybrid node steel beams was sought. The results, which were less than 1 kN, compared with the axial force results of the experimental test in the structure laboratory, indicate that a good behavior of the node without anchors can be expected under axial load, also the continuity of the secondary steel beam must be added. The laboratory test record shown in (Figure 11) for load-deformation indicates that the first tensile yield of the concrete is stronger than the maximum possible stress of the models of computer experiment 2³ for the horizontal load.

Figure 11 MA models tested in the longitudinal direction of the node 

This is due to the fact that the design of the concrete beam and the node are dominated by moments acting around axis 3 see (Figure 9). The moments of axis 2 do not dominate the design, as the lateral load is mostly taken up by the concrete nodes and frames. The hybrid node takes little axial load since the steel beam has little stiffness compared to parallel concrete beams. If the accepted deformation for simple tensile concrete is compared with the deformations of the strain gauges placed on the horizontal experimental test beams in (Figure 11), it can be seen that the service axial forces of a building with hybrid nodes do not govern the behavior of the node. However, it is advisable to use some kind of anchorage in the hybrid node according to the axial load as shown in (Figure 12).

Figure 12 Options to attach a secondary beam to a main beam or to a column 

2.3 Comparison with previous node failure experiences

On April 16, 2016, a 7.8 (Mw) earthquake occurred in Ecuador which had its epicenter in the coastal province of Manabí. Many buildings collapsed and others were damaged. The authors of this study inspected the behavior of buildings with hybrid nodes and steel deck slabs after the earthquake. The damages described were presented in (^{Castañeda and Mieles 2017}); (^{Castañeda and Mieles 2016}). Comparing the damages of the natural laboratory of the earthquake with the tested nodes it is observed that the cracking form coincides, as it is observed in the pictures of this article and pictures of the aforementioned works.

3.1 Strut and Tie Model

The geometry of the struts and ties has been located by the observation of the damage progress during the test (Figure 14a) and (Figure 15b), it is verified by the deformations and stresses in the direction 1-1 of the models in finite elements in Abaqus of (Figure 7c) and (Figure 7d).

Figure 14 Strut and tie model, a) Damage observed in the test, b) Geometry of struts, c) Suspension proposal 

In the STM in (Figure 14) and (Figure 15), the strut angles P₃ and P₄ are greater than 25 degrees and comply with 23.2.7 of ACI 318-14. The length of D region, (Figure 14b), according to the Saint Venant principle will have the same length as twice the effective height "d", resulting in the geometry and balance of struts and ties shown in (Figure 15), then, transmitting these stresses to region B.

The forces F_us or F_ut on the STM reinforcement for any hybrid node beam can be generalized by naming the span on each side of the node as l₁=n₁d and l₂=n₂d, respectively see (Figure 15) and the total span as l=nd. Once the reinforcement is solved, the forces on the struts and ties in the node area are summarized in (Table 2) and (Table 3).

Figure 15 Identification of struts and ties for the STM of the hybrid node 

The width of the b_f flange of the steel beam serves as a support plate against the action of P load and when passing through the hybrid node it needs to develop a concrete strength in the node zone 2 greater than or equal to the compressive force of P load and to comply with F_nn≥F_us, where F_nn is the strength in the face of the hydrostatic node zone 2, also guaranteeing the strength of that node zone CCC since all the concurrent forces are less than or equal to P. It can be shown that F_us=P, then P ≤ ϕ F_nn⋅area of beam I, where ϕ =0,75 and β_n=1. The width of the flange that acts as a support plate for the steel beam must be greater than or equal to b_f obtained from (Equation 1), where b is the width of the concrete beam:

(1)

To exemplify (Equation 1), it is replaced with the average P of 103 kN obtained in the experiments (Table 1) and the data of the hybrid direction through node explained in (Figure 3) is obtained that the minimum width is 3.1 cm < 5 cm, satisfies the real width of the drop-in girder I and conditions the width of the converging P₃ and P₄ struts.

(2)

In the ties, the following must be complied with: ϕF_nt≥ F_ut, where ϕ=0,75, F_nt is the nominal strength of the tie, and F_ut, is the factored tractive effort of the tie a relationship that gives rise to (Equation 2). The tensile steel area of the T₃ tie is obtained with (Equation 2), making F_ut equals to from (Table 2) to generalize to any beam. In order to compare with the As of tensile strength resulting from the ACI 318 bending formulas, the factored bending load is used and the moment is calculated with M_u=ϕA_sf_y (d-a⁄2), and data from (Figure 3). The axial failure load is P=(4 M_u)⁄l= 90 kN. The 90 kN in (Equation 2) results in A_st3=3,57 cm², 16% higher than 3.08 cm² calculated according to the bending theory. The axis of the T₃ tie is conditioned by the continuity of the steel in the B region and its width w_t can be taken as the diameter of the bars plus twice the cover measured with respect to the surface of the bars according to R23.8 of ACI 318-14.

The steel required for ties T₁ and T₂ can be calculated with (Equation 2), replacing F_ut for T₁ and T₂ from (Table 2). The steel thus obtained must be distributed in the form of stirrups in the D region. The summary of the ties is shown in (Table 2) calculated for the average experimental failure load from (Table 1).

Table 2 Summary of forces and steel areas of ties with the average test load 

Struts must comply with ϕF_ns≥ F_us, where ϕ=0,75, F_ns is the nominal strength of a strut as defined in 23.4 of ACI 318-14, and F_us is the factored compression force of the strut. From these relationships, the width of a strut w_s results from (Equation 3). The strength of the STM struts for the hybrid node, by the action of the P load, is shown in (Table 3), where F_us is replaced by the formulas for P₁, P₂ and P₃, as applicable, β_s=0,6 for P₁ y P₂ and β_s=0,4 for P₃ according to (Table 3) of ACI 318-14.

(3)

Table 3 Summary of forces and widths of struts with the average test load 

Nodes must comply with ϕF_nn≥ F_us, where ϕ=0,75, F_nn is the nominal strength of one face of the node, and F_us is the factored compressive force of the strut. If the width of the flange of the beam I b_f in (Figure 16a), which serves as the support plate at the node, is greater than or equal to that obtained by (Equation 1), the design strength of the faces of node 2 ϕ F_nn2 will be greater than the forces applied by the struts F_us P₁, P₂, P₃ y P₄ since the width b_f in (Equation 1) will be greater than the widths required by (Equation 3). In node zone 4, which is symmetrical with 5 in (Figure 16b), the transfer of stresses to the B region of the tie T₃ is guaranteed by the continuity of the tensile steel along the beam. The tie T₁, which must be placed in the form of stirrups, provides the strength by the strut P₃. For node 1 in (Figure 14b), the strength of the node zone is ensured by the compression block of the strut P₁. An application summary of the experimental test carried out with the average failure loads is shown in (Table 4).

Figure 16 STM nodes. a) Node 2 type CCC according to ACI 318-14; b) Node 4 type CTT according to ACI 318-14 

Table 4 STM node verification applied to the tested beams 

The incorporation of suspensions is proposed for future experimental tests. The total support force must be transferred to the top of the member (beam) using a hanging reinforcement (suspensions) distributed over the width of the web of the support beam, such as those shown in (Figure 14c) (^{FIP 1999}). The transmission of forces from the steel beam to the concrete beam makes it indirect support (^{ACI-445 2002}). In order to satisfy the balance at the node for the upward forces of the tie rods, suspensions are required. These suspensions or stirrups should be located within the intersection of the web of the main concrete beam and the load-transferring beam (^{Novak 2010}). An appropriate detail for a node in a beam - concrete beam, requires the use of suspension stirrups well anchored to the main beam (^{Nilson et al. 2010}). Indirect supports have been dealt with in some codes with detailed rules indicating the need to have suspensions, but they have not yet been incorporated in ACI 318-14.