Steel-plate concrete (SC) structures are currently constructed using steel plates, stud anchors (headed stud anchors), and filled concrete. This construction method is commonly applied to composite bridges that combine both steel and concrete elements as an economical option. To achieve the expected performance of a composite structure, it is necessary to confirm the bonding capability between the concrete and stud materials, which have heterogeneous properties. In SC structures, studs (also known as shear connectors, stud connectors, or headed stud connectors) are welded to steel plates to combine the concrete and surface steel plates [1].

El-Lobody et al. [2] investigated composite girders using a finite element model with 8-node three-dimensional solid elements. Their models predicted deflection behavior and stress distribution along the length of the beam for both solid slabs and precast hollow core elements. Lam et al. [3] examined the shear and load-slip behavior of shear connectors under shear forces. Lin et al. [4] studied the effects of transverse bending moments on stud connections in steel-concrete composite beams, identifying both concrete cone pull-out failure and stud fractures. These failure modes were influenced by stud length under transverse bending moments. Xiang et al. [5] investigated the spacing of studs between concrete slabs and steel girders under transverse bending moments. This study is only tangentially related to the present research, as it focuses on wide shape beams rather than surface steel plates, but it provides insights into the behavior of stud connections under transverse loads.

Badie et al. [6] studied the limits of stud spacing for clusters of studs used in precast concrete panels with wide-shape beams. They performed push-off tests using full-scale composite beams and found that doubling the number of studs per cluster did not significantly affect fatigue. They concluded that full composite action occurred when the spacing between stud clusters was extended to 1220 mm.

J. Qureshi et al. [7] investigated the effects of sheeting thickness and shear connector position on the strength and ductility of shear connectors in long-span composite bridge girders. The authors studied the influence of sheeting thickness and shear stud position on the strength, ductility, and failure modes of the headed shear connector in steel-concrete composite beams. One of the interested variables was the transverse spacing of the shear connectors. Xu et al. [8] also studied the influence of sheeting thickness and shear connector position in composite bridges. Their research focused on the behavior of group studs under biaxial loading in compression. The authors found group studs may lead to comparatively more severe concrete damage at the ultimate stage.

Wang et al. examined the push-out behavior of large stud connectors in steel composite beams. In their study, an empirical shear load-slip equation was proposed, incorporating the maximum stud diameter (25 mm) [9]. Delhomme et al. [10] conducted pullout tests on long anchor bolts, identifying major failure modes such as rod fracture, rod sliding, and cone-shaped concrete breakout. Ballarini et al. [11] studied tension failure mechanisms in rods, including fracture, sliding, and breakout strengths, using 28 specimens to investigate ultimate loads and the relationship between tensile capacity and compressive strength. The variables of the tests were the embedment depth h, the support reaction distance d, and the age of specimens.

Chen et al. [12] examined anchor bolt failure due to the combined effects of tension and shear. DeVries et al. [13] investigated the anchorage capacity of shallow embedment in concrete. Sartipi et al. [14] studied the tensile response of post-installed anchor connections in both reinforced and plain concrete beams, focusing on key parameters such as embedment depth, section width, and reinforcement effects in post-installed chemical anchors.

Eligehausen et al. [15] researched the behavior and design of adhesive-bonded anchors, identifying potential failure modes such as concrete breakout, mortar-concrete interface failure, and steel-mortar interface failure. Fuchs et al. [16] proposed a behavioral model for concrete breakout failure, which is now incorporated into ACI 318-19 [17]. While concrete breakout failure has been extensively studied, no equations were available to predict the ultimate tensile strength of torque-controlled expansion anchors until Chen et al. [18] proposed a design strength for these anchors.

An experimental investigation on normal concrete to examine the pullout capacity of cast-in-place anchors with embedded circular surrounding studs around rebar under monotonic loading conducted by Turker et al. [19] conducted an experimental investigation into the pullout capacity of cast-in-place anchors with embedded circular studs around rebar under monotonic loading. They carefully studied rebar geometry, steel type, bar spacing, concrete cover, concrete strength, and confinement. Mahrenholtz et al. [20] examined the design standards of post-installed and cast-in-place anchors using both EN 1992-4 and ACI 318. The authors discussed the basic anchor design and underlying production qualification.

Delhomme et al. [21] presented results from pullout tests on large-embedment anchors cast in reinforcement blocks. They studied edge effects and identified failure modes, including concrete cone failure, pullout failure, and combined pullout and concrete cone failure, in both cracked and uncracked sections using headed anchors and ribbed bars.

The paper adopts the concrete cone method in accordance with KCI [22], KDS [23], and ACI 349 [24]. The strength and stress behaviors of adhesive-bonded anchors are discussed, focusing on group and edge effects when studs and tie bars are combined.

According to Table 9 and Table 12, it is observed that only the edges of the tie bar yield from top view, while the elasticity at the middle of the tie bar remains under tension. From these results, this paper presents the failure mechanism as shown in Figure 14.

Figure 14 illustrates that the elastic behavior of the concrete around the studs is lost under maximum tensile loads, leading to the formation of shear lines [16]. Simultaneously, the tie bars placed between the studs elongate beyond their yield limit, causing concrete cone failure within the interference area of the tie bars—similar to what occurs around the studs. Considering this, the concrete failure area of SC structures with studs and tie bars can be calculated using the same method as SC structures with only studs. It is thus assumed that the maximum tensile load is lower than the expected load if the concrete around the tie bars retains its elasticity. The proposed method for estimating the tensile capacity of SC structures with both studs and tie bars is based on the ACI 318 [17] and KEA [25] guidelines for determining anchorage concrete breakout strength under tension. This report defines the effective plastic length of tie bars under tension as the length of the tie bar in a plastic state. In previous research on anchors in general structures, shallow embedment is typically defined as 3–5 times the bar diameter. The main categories of this model are concrete cone failure and the concrete capacity model. The embedment length (effective plastic length) is directly related to anchor failure. In this paper, the effective plastic length of tie bars is calculated by applying the following assumptions:

The mechanism and method for calculating the effective plastic length, ${\delta }_i,$ are presented in Figure 15 and Equation (6).

The effective plastic length, ${\delta }_i$, over the variable length x x, can be summarized through algebraic integration by hand. In Equation (6), it is assumed that the ratio of length is proportional to the ratio of strain, which leads to Equation (7). The strain ratios used in Equation (6) are derived from experimental results. The theoretical lengths, l 1 l 1 and l 2 l 2, vary and change based on the different strain values observed in the tests.

The effective plastic lengths of the tie bars, calculated using Equations (6) and (7), are presented in Table 13 and Table 14. Table 14 provides the effective plastic lengths based on the diameter of the tie bar. In these cases, it is assumed that the tension applied to the tie bar is proportional to the strain ratio of each tie bar. Additionally, the average displacement of the tie bars is considered equal to the displacement of the specimen in which the tie bars are embedded.

From Table 14, the effective plastic lengths of the tie bars in GTST-1s, in which the studs are placed so that the concrete failure areas between the studs do not overlap, are 4.56 times the diameter of the tie bars on average. In GTST-2s, in which the studs are placed so that the concrete failure area overlaps that of other studs, the effective plastic lengths are about 1.94 times the diameter of the tie bars on average. Therefore, it is necessary to think of the ranges between 2D through 5D (conservatively) for practical design purposes.

Figure 16 presents the suggested effective concrete failure areas, indicated with hatching, for the GTST-1 and GTST-2 specimens, accounting for the influence of tie bars. These effective areas exclude the regions affected by the tie bars’ interference. The proposed concrete failure areas for the stud group, along with the effective number of studs based on the effective plastic length of tie bars at 2D, 3D, and 5D, are outlined in Table 15. For calculating the tensile strength of the anchors while considering the effect of tie bars, the projected concrete failure area is denoted as $A_{Nc.t}$ as shown in Equation (8), where the 9($l_{1or2}^2$) was used instead of 9$h_{ef}^2$, and the number of effective studs considering the tie bars’ effect is defined as $n_{eff,s}$ as shown in Equation (9).

Equation (10) presents the suggested method for calculating the tensile load of SC structures with studs and tie bars, while Equation (11) compares this method to the results from performance tests. The performance tests revealed that numerous tie bars were in a plastic state at the maximum tensile load. However, for safety in design, Equations (10) and (11) conservatively apply the average yield load of UTIs (240 kN). The maximum tensile load of a single stud in SC structures $N_{b,test}$, used in Equation (10), corresponds to the average yield load of USTs (161 kN). The area $N_{b,test}$, in Equation (11) is the area calculated by accounting for the influence of tie bars, as shown in Table 16.

Table 16 provides a comparison between the suggested method and the test results by dividing the test values by those derived from the assumptions, similar to Table 10. In Table 15, if one can get modified $N_b$ using Equations (10) and (11), the one can evaluate various failure cases once more by the normalization using 1.0. From the comparison, the case using an effective plastic length of 2D for the tie bars most closely aligns with the performance test results. Meanwhile, using a plastic length of 3D proves to be the most effective for safety considerations in design. The three calculations (2D, 3D, and 5D) based on test data simplify the maximum load-bearing strength for the GTST specimens, allowing for comparison under assumptions such as (a) tensile load of studs and tie bars using nominal tensile stress, (b) average maximum tensile load of UST and yield load of UTI, and (c) maximum tensile load of GST-2 and yield load of UTI, as seen in Table 10, where effective length is represented by diameter instead of $h_{ef}$.