Static Performance of Pre-Fabricated and Cast-in-Place Joints Formed by Inserting Steel Secondary Beam into Concrete Girder

Abstract

Joints formed by inserting steel secondary beam (SSB) into concrete girders have been increasingly used in engineering practice (e.g., electric power). To demonstrate the static performance of these joints, two key variables including the construction method (prefabricated, cast-in-place) and the insertion form of SSB (unilateral, bilateral) were considered. The test results indicated that the failure mode of each joint was concrete punching by the inserted SSB. Compared with the joint specimens with unilateral insertion of SSB, the failure mode of the joint with bilateral insertion was changed from multiple to single cracking, exhibiting more obvious brittleness. When high-performance cement-based grouting materials were incorporated into the joint, the assembly and ductility of the joint were effectively improved. Compared with the cast-in-place counterparts, the displacement ductility coefficients of joints with prefabricated unilaterally and bilaterally inserted beams were enhanced by 22.9% and 41.3%, respectively. Moreover, a theoretical model was developed to evaluate the punching shear resistance of such joints with favorable accuracy.

1. Introduction

Compared with conventional reinforced concrete structures, steel-concrete composite structures have been increasingly used because of their favorable structural performance, such as high strength and good deformation capacity [1,2,3]. In composite beams incorporating steel and concrete, the concrete girder is generally taken as the end beam of the steel secondary beam (SSB). There are three common types of joints consisting of an SSB and a concrete girder: (1) Lug joint. SSB is directly placed on the side lug of the concrete girder [4], as shown in Figure 1a; (2) Embedded joint. The shear connectors are embedded inside the concrete girder and connected with the web of SSB using high-strength bolts [5], as shown in Figure 1b; and (3) Inserted joint. SSB is directly inserted into the concrete girder after some structural treatments. With multiple advantages, such as high stiffness, low cost, and convenient construction, inserted joints are widely used in the structural applications at large-capacity thermal power plants [6].

The failure modes of the inserted joints are usually characterized by shear failure of concrete girder, bending failure of SSB, and pull-out failure of SSB [6]. To avoid pull-out failure at the inserted end of the SSB, it is generally necessary to ensure that the insertion depth of the SSB is not shorter than one-third of the width of the concrete girder [7]. Structural treatments, such as setting welded anchor bars [8] or anchoring end plates [9] at the inserted end of the SSB, could not only strengthen the anchorage ability but also optimize the mechanical properties of the joints. The height difference between the bottoms of the girder and the secondary beam is the key factor affecting the failure mode of such joints. A critical value of the height difference exists, which dominates the transition of the failure mode. Specifically, when the difference exceeds the critical value, the failure mode may be changed from concrete girder shear failure to SSB bending failure [10]. In addition, partially or completely cutting the flange of the inserted SSB can effectively prevent the development of a weak area in the concrete girder, thus reducing the adverse impact induced by SSB on the concrete girder [6,11].

Compared with the extensive studies on reinforced concrete beam-column joints [12,13] and steel beam-column joints [14,15], the research on joints formed by inserting SSB into concrete girders is not sufficient. The study conducted by Sun et al. [5] revealed that setting the floor slab and increasing the rigidity of SSB could improve the bearing capacity of such joint. Recently, Li [16] investigated the static performance of joints formed by inserting SSB into concrete girders. The test results indicated that the ultimate failure of the specimen was initiated by the yielding of the bottom flange of the SSB, with good anchorage in the joint region. Based on relevant studies, the shear resistance mechanism of the reinforced concrete beam-column joint was dominated by the combined action of the concrete diagonal compression struts and the truss mechanism [17], as illustrated in Figure 2. Moreover, the modified compression field theory was widely adopted to estimate its bearing resistance [18]. Nevertheless, the failure mechanism of the joints formed by inserting SSB into concrete girders remains unclear. It necessitates a better understanding of such joints.

With the establishment of goals for peak carbon emissions and carbon neutrality in China, the development of prefabricated structures has become a promising solution in engineering practice. Nevertheless, in prefabricated structures, the performance of the connections of individual structural components is particularly critical. High-performance cement-based materials have the advantages of good flexibility and favorable crack resistance. Various types of high-performance cement-based materials were added to joints under different loading conditions [19,20,21]. At present, although some studies have focused on the performance of the inserted SSB-concrete girder joint, the main construction method adopted in previous research is limited to the cast-in-place strategy. To realize the assembly of this type of joint, it is desired to develop a type of pre-fabricated joint formed by directly inserting SSB into a concrete girder. Moreover, most of the available studies focused on unilaterally inserted SSB. In actual construction projects at power stations; however, SSBs are usually inserted into both sides of the concrete girder. Therefore, it is urgent to clarify the failure mechanism and behavior of joints where SSBs are bilaterally inserted in concrete girders.

To this end, this study aimed to investigate the static performance of cast-in-place and prefabricated joints formed by inserting SSB in concrete girders under monotonic loading. For each type of joint, the SSBs were unilaterally and bilaterally inserted into the concrete girders. The mechanical behavior of the joints was comprehensively analyzed by a comparative study of different configurations. Finally, based on a further understanding of the failure mechanism, a theoretical model was developed to evaluate the punching shear resistance of such joints. This may contribute to a more reliable design of pre-fabricated joints formed by inserting SSB into concrete girders in engineering practice.

2. Experimental Program

2.1. Design of Specimens

Two construction methods of the concrete girder, including prefabrication and cast-in-place strategy, were included in this study. Moreover, regarding the insertion of SSBs, two types of configurations were considered, including unilateral and bilateral insertions. Thus, a total of four series of joint specimens were designed, namely, cast-in-place and unilateral insertion (denoted as SJ-1), prefabricated and unilateral insertion (denoted as AJ-1), cast-in-place and bilateral insertion (denoted as SJ-2), and prefabricated and bilateral insertion (denoted as AJ-2). The details of various joints are shown in Figure 3.

The span of the girder was 2000 mm. The cross-sectional size of the concrete girder was 200 mm × 300 mm, 20 mm in concrete cover thickness. The top flange and the upper part of the web (50 mm in height) in the inserted steel beam were cut for ease of insertion. The inserted depth of SSB into the concrete girder was 70 mm. The top surface of the concrete girder was on the same horizontal plane as that of the inserted steel beam (Figure 3) so that the slab could be laid later. The diameter of spirals in unilateral and bilateral inserted joints was 6 and 8 mm, respectively. The stirrup spacing was 100 mm in all specimens. To simulate the constraint effect of columns on the concrete girders in actual structures, concrete piers with sufficient stiffness were cast at both ends of the concrete girders. The ends of longitudinal reinforcement embedded in concrete girders were inserted into the concrete piers. In addition, the concrete piers were fixed to the ground with embedded U-bolts. For prefabricated joint specimens, as shown in Figure 3a,c, grooves were pre-set in the concrete girder’s mid-span, with a size of 200 mm × 220 mm. The unilateral groove depth was 85 mm, and the bilateral groove depth was the same width as that of the girder. Transverse stiffeners with the same thickness as the flange and the same width as the secondary beam were added on both sides of SSB to reduce the possible overall instability of the secondary beam in the loading process. The strengthening range was 200 mm around the mid-span of the SSB. The joint details are shown in Figure 4.

The specimen preparation was briefly described as follows. The SSB was prepared according to the requirements (Figure 5a). The mold for cast-in-place and prefabricated joints are given in Figure 5b,c, respectively. An extruded board with specific dimensions was placed in the notch area before the insertion of SSB. After compaction using a vibrator, the upper surface of each specimen was carefully smoothed and then checked using a spirit level. The specimens after concrete casting are illustrated in Figure 5d. After 14 days of curing with the molds, the molds were removed from the specimens. Regarding the prefabricated joints, the cement-based grout materials were carefully poured into the notch. After grouting was completed, the specimens were carefully cured for 28 days.

2.2. Material Properties

The same batch of commercial concrete with a target grade of C50 was used to cast the concrete girder. According to the compression test results of three standard concrete cubes (150 mm inside length), the 28 day cubic compressive strength (f_cu) was 62.6 MPa. The HRB400 steel bars were used in the concrete girder, while the Q345B steel plate was used to prepare the SSB. The properties of reinforcement and steel plate were summarized in

Table 1. Mechanical properties of steel.

Steel Bar/Plate	Yield Strength/MPa	Tensile Strength/MPa
Stirrup with diameter of 6 mm	417	597
Stirrup with diameter of 8 mm	435	613
Longitudinal bar with diameter of 12 mm	439	614
Longitudinal bar with diameter of 16 mm	424	603
Web plate with thickness of 6 mm	363	542
Flange plate with thickness of 9 mm	403	556

as per GB/T 228.1-2010 [22]. Based on GB/T 50448-2015 [23], the basic properties of cement-based grout materials used in this study were determined (

Table 2. Basic properties of cement-based grout materials.

Initial Fluidity/mm	Fluidity after 30 min/mm	Difference of Vertical Expansion Rate between 3 h and 24 h/%	28 d Flexural Strength/MPa	28 d Compressive Strength/MPa
322.5	314	0.4	15.3	72.0

).

2.3. Test Procedure

The monotonic static loading was applied to the mid-span of the SSB through a hydraulic jack. The loading device of the specimen is shown in Figure 6. A load-controlled loading scheme (5 kN/min) was adopted. Each loading step was 15 kN before cracking, then 10 kN after cracking, and 5 kN around the ultimate state. The duration of each loading step was 10 min. Each end of the SSB was inserted into a concrete girder, which may be considered as a beam with fixed ends under concentrated load at the mid-span. After the ultimate state, the applied load was manually stopped when the load dropped to 85% of the peak value. Notably, regarding the loading test on the bilaterally inserted specimens, the weight of the distribution beam was also considered in this study. Thus, the total load on such specimens was a summation of the applied load and the weight of the distribution beam.

Figure 6a,b show the layout of displacement transducers and strain gauges in unilateral insertion and bilateral insertion joints, respectively. The mid-span displacement of the concrete girder and the SSB could be measured by the displacement transducers. Strain gauges were attached to typical locations of steel bars (including longitudinal reinforcement and stirrups) in the concrete girders, as presented in Figure 6c. The applied load was monitored by the force transducer.

3. Analysis of Test Results

3.1. Failure Process

Figure 7 and Figure 8 show the typical failure modes of unilaterally inserted and bilaterally inserted joint specimens. Each type of joint underwent punching failure of concrete by the inserted SSB. No obvious local buckling was observed near the loading point of the SSB. In addition, for the prefabricated joints, the cement-based grout material was well bonded to the original concrete, and no debonding occurred between the grout materials and the concrete substrate. Overall, the failure modes of the four types of joints were similar to each other.

For unilaterally inserted specimens, in the initial stage, the mid-span displacements of the SSB increased approximately linearly with load (P). The concrete girder at the joint was affected by the shear force and torque transmitted by the SSB, which was subjected to the combined effect of flexure, shear, and torsion. As P was increased, the bending moment of the concrete girder played a dominant role. When P was increased to approximately 0.7 P_max (where P_max is the peak load), a flexural crack with approximately 220 mm in height was initiated in the outer side of the concrete girder mid-span, and then the length and width of flexural cracks developed slowly. With a further increase in P, the shear action had an increasingly significant effect on the concrete girder. When P was increased to approximately 0.8~0.9 P_max, two diagonal cracks occurred successively near the lower flange of SSB. The punching angles were approximately 30~45° relative to the concrete girder’s bottom. The diagonal crack finally passed through to the bottom of the girder.

For bilaterally inserted specimens, the concrete girder at the joint was affected by the shear force transmitted by the SSB, which caused the concrete girder in a state of combined flexural shear stress. Theoretically, the torques transmitted by two bilaterally inserted SSBs would balance, although unbalanced torque inevitably occurred in the loading process due to possible eccentricity and other factors. However, the unbalanced torque in the bilaterally inserted specimen was much smaller than that in the unilaterally inserted specimen. This influence could thus be ignored. With the increasing P, the bending moment in the concrete girder had a dominant role. When P was increased to approximately 0.5 P_max, many small flexural cracks were found under the lower flange of the SSB, and the lengths of the cracks were approximately 18 mm. As P continued to increase, the shear force in the concrete girder played a major role. When the load was increased to approximately 0.6~0.8 P_max, inclined cracks were developed near the lower flange of the SSB. The punching angle was gradually decreased from 45° to 35°, and the crack width in the concrete girder was increased to 6~8 mm, as presented in Figure 8.

In summary, the cone-shaped failure surface was observed in all specimens. No obvious spiral cracks or twisted failure inclines were found. Therefore, the failure mode was punching failure of the concrete girder by the inserted SSB. Based on force analysis, the bilaterally inserted joint was subjected to much greater shear force than the unilaterally inserted joint, which resulted in the increased brittleness of bilaterally inserted specimens at failure. Moreover, multiple diagonal cracks were merged to form a single diagonal crack. More severe damage tended to result in a steeper punching angle.

3.2. Load–Displacement Curves of SSB

The load (P) vs. mid-span displacement (Δ) curves of SSB are presented in Figure 9. At a given configuration, the bearing capacities of specimens within the same figure were similar, regardless of cast-in-place or prefabrication. As shown in Figure 9, in the early loading stage, Δ of the SSB was small, and the curves exhibited a relatively good linear relationship. When the beam was loaded to the cracking load, Δ began to experience a rapid increase, and the growth rate of the load slowed down. When the punching crack appeared, the load increment experienced a significant decline until the ultimate load was reached. Subsequently, the curve entered into the descending branch. The cast-in-place specimen had a steeper descending part than the prefabricated counterpart. This indicated that prefabricated joints had better post-ultimate ductility in this case.

3.3. Load–Strain Relationship

Based on the strain gauges installed on the spirals, the longitudinal bars, and the mid-span bottom of the SSB (Figure 6), the development of strains could be monitored. The load–strain relationship curves of three steel components are presented in Figure 10. These full-range load–strain responses might be divided into four stages (elastic stage, cracking stage, yield stage, and ultimate stage) according to three dividing points. The load corresponding to concrete cracking (P_cr) is the dividing point between the elastic and cracking stages. The load corresponding to the yielding of stirrups (P_y) is the dividing point between the cracking and yield stages. The peak load (P_max) is the dividing point between yield and ultimate stages. The values of load corresponding to each characteristic stage are summarized in

Table 3. Load corresponding to characteristic point.

Specimen	Pcr /kN	Py /kN	Pmax /kN
SJ-1	80.1	133.2	146.6
AJ-1	75.2	128.1	145.4
SJ-2	124.9	230.2	256.4
AJ-2	125.3	224.8	259.4

.

(1)

Stage I: Elastic stage

At a low level of applied load, the three steel components are within the range of elastic deformation. Within this stage, no obvious cracks were found. The load was approximately linearly increased with the strain.

(2)

Stage II: Cracking stage

Flexural cracking dominated stage: Minor vertical cracks were found at the concrete girder mid-span. With the development of bending cracks, bending moment is increasingly resisted by the longitudinal bars in the concrete girder. The slope of the SSB curve began to decrease. The strain of longitudinal reinforcement experienced a sudden increase, leading to a transition point at the corresponding curves.

Punching shear cracking dominated stage: Minor diagonal cracks occurred near the lower flange of the SSB. The shear force transmitted from the SSB was resisted by the spirals in the joint core area. A more rapid development of inclined shear cracks was observed. The slope of the SSB curve continued to decrease. The strain of steel spirals experienced a sudden increase, leading to a transition point at the curve.

(3)

Stage III: Yield stage

With the continued increase in the load, the diagonal cracks directly penetrate the concrete girder’s bottom. The crack width continued to increase. The strains of steel spirals and longitudinal bars were significantly increased, consistently reaching the corresponding yield strains of the two types of steel bars.

(4)

Stage IV: Ultimate stage

After the steel yield stage, the joint specimens entered the ultimate stage. Multiple major diagonal cracks occurred successively in concrete girders. The bottom part of concrete girders inserted by the SSB experienced punching shear failure characterized by a cone-shaped failure surface.

3.4. Displacement Ductility Coefficient

The displacement ductility coefficient (μ) is an important parameter characterizing the elastic–plastic deformation capacity of structural members [24], which is expressed as

$$\mu ={\displaystyle \frac{{\Delta }_u}{{\Delta }_y}}$$

(1)

where Δ_y is yield displacement, which is determined according to the P-Δ curve through the energy equivalence method [25]; Δ_u is ultimate displacement, which is herein taken as the mid-span deflection of the SSB corresponding to post-peak load dropped to 0.85 P_max. The values of μ for all specimens are summarized in

Table 4. Displacement ductility coefficient.

Specimen	∆y /mm	∆u /mm	μ
SJ-1	6.83	11.7	1.71
AJ-1	6.10	12.8	2.10
SJ-2	8.60	11.9	1.38
AJ-2	7.33	14.3	1.95

.

As shown in Table 4, the μ values of SJ-2 and AJ-2 decreased by 19.3% and 7.1%, respectively, compared with those of SJ-1 and AJ-1. For joint specimens with the same type of construction method (cast-in-place or prefabrication), bilaterally inserted specimens showed more obvious brittleness than unilaterally inserted counterparts. The displacement ductility coefficient of AJ-1 increased by 22.9% compared to that of SJ-1, and the μ value of AJ-2 increased by 41.3% compared with that of SJ-2. For both the unilaterally and bilaterally inserted specimens, the prefabricated joints had better ductility than corresponding cast-in-place specimens. This is because the cement-based grouting materials used in prefabricated specimens had high fluidity and underwent microscopic expansion, which thus could effectively fill the tiny gap at the interface between the old and new concrete. In addition, the grouting groove was deeply roughened when the specimen was made. Therefore, the interlocking between the cement-based grouting materials and the original concrete was improved, leading to effective bonding in the joint area. Moreover, the cement-based grout materials used in this study had a low ratio of compression to tension and good flexibility, which indicated favorable deformability in prefabricated joints [26]. It should be noted that the failure of AJ-2 seems to be more severe and brittle than SJ-2, as shown in Figure 8. This could be partially attributable to the fact the AJ-2 had experienced a much larger mid-span displacement than the SJ-2 at the ultimate state (Figure 9).

4. Prediction of Punching Shear Resistance

The concrete girder was pushed out in the form of a punched cone by the inserted SSB at final failure. It was assumed that the reinforcements were elastic-perfectly plastic material, and the yield stress was reached at failure. The effects of aggregate interlocking on the cracked surface and reinforcement dowel action in the concrete girder were ignored.

According to GB 50010-2010 [27], the punching resistance (V) of a joint consists of three parts:

$$V=V_c+V_{sv}+V_{sb}$$

(2)

where V_c is the punching capacity of the concrete; V_sv is the shear capacity of stirrups; and V_sb is the shear capacity of bend-up reinforcement.

V_c could be expressed as

$$V_c={\alpha }_c{S}_c{f}_t$$

(3)

where α_c is the coefficient of the resistance of concrete to punching, which is 0.5 according to the code requirements; f_t is the uniaxial tensile strength of concrete, $f_t={0.395f}_{cu}^{0.55}$; and S_c is the effective area of the concrete girder punched by the insertion end of the SSB.

The shear-bearing capacity of stirrups could be expressed as:

$$V_{sv}={\alpha }_{sv}{f}_{yv}{A}_{svu}$$

(4)

where α_sv is shear bearing capacity coefficient of stirrups, which is 0.8 according to the specification requirements; f_yv is the tensile strength of stirrups, and A_svu is a sectional area of all stirrups intersecting within the propagation range of the diagonal crack induced by punching.

The punching capacity of the bend-up reinforcement can be expressed as:

$$V_{sb}={\alpha }_{sb}{f}_y{A}_{sbu}\sin \theta$$

(5)

where α_sb is the coefficient of punching capacity of bend-up steel bars, which is 0.8 according to the specification requirements; f_y is the tensile strength of bend-up bars; A_sbu is the sectional area of all bend-up bars intersecting within the propagation range of punching diagonal crack; and θ is the angle between bend-up bars and concrete girder bottom.

Figure 11 shows the calculation model of the unilateral insertion joint. According to the punching failure mechanism, only the contribution of the concrete area formed by the insertion end of the SSB was conservatively considered. B, h₀, a₀, and B₀ represent the width of the SSB, an effective height difference of the girder and SSB, the effective insertion depth of the SSB, and the effective width of the concrete girders, respectively. The angle of the inclined section of the punching cone was taken as 30° based on statistical analysis of test results. Under the condition that the tops of the primary and secondary beams were kept at the same height, the height difference between the concrete girder and the SSB also increased with the increasing height of the concrete girder, which resulted in a change in the effective punching area. The following two cases were considered, as illustrated in Figure 11.

In the first case, when h₀ ≤ B₀ − a₀, the effective punching area can be expressed as

$$S_c=\left({\displaystyle \frac{2a_0}{\tan 30°}}+b\right)h_0+{\displaystyle \frac{2h_0^2}{\tan 30°}}$$

(6)

In the second case, when h₀ > B₀ − a₀, the effective punching area can be expressed as

$$S_c=b\left(B_0-a_0\right)+{\displaystyle \frac{2B_0{h}_0}{\tan 30°}}$$

(7)

Therefore, the punching resistance of the joint by a unilateral inserted SSB can be expressed as

$$V=0.5f_t\left[\left({\displaystyle \frac{2a_0}{\tan 30°}}+b\right)h_0+{\displaystyle \frac{2h_0^2}{\tan 30°}}\right]+0.8f_{yv}{A}_{svu}+0.8f_y{A}_{sbu}\sin \theta \hspace{1em}\hspace{1em}(h_0\le B_0-a_0)$$

(8)

$$V=0.5f_t\left[b\left(B_0-a_0\right)+{\displaystyle \frac{2B_0{h}_0}{\tan 30°}}\right]+0.8f_{yv}{A}_{svu}+0.8f_y{A}_{sbu}\sin \theta \hspace{1em}\hspace{1em}\left(h_0\ge B_0-a_0\right)$$

(9)

To illustrate the effect of key parameters on the shear capacity, a parametric study was conducted based on one of the developed models (Equation (8)), as shown in Figure 12. The benchmark of the parametric study was described as follows: concrete cube strength f_cu = 40 MPa, effective insertion depth of the SSB a₀ = 70 mm, effective height difference of the girder and SSB h₀ = 110 mm, width of the SSB b = 150 mm, yield stress of stirrups f_yv = 400 MPa. No bend-up reinforcement was herein considered for simplification. According to the parametric study, the shear capacity was significantly increased with the concrete strength and the effective height difference. By contrast, the yield stress of stirrups and the width of SSB had a less significant effect on the shear capacity compared with the aforementioned two aspects.

A simplified calculation model for bilateral insertion joints is presented in Figure 13. The angle of the inclined section of the punching cone was 35° according to the actual test observations, and the following two cases were considered.

In the first case, where h₀ ≤ B₀ − a₀, according to geometric relations, the area affected by the punching cone can be expressed as

$$S_c=2h_0\left({\displaystyle \frac{2a_0}{\tan 35°}}+b\right)+{\displaystyle \frac{4h_0^2}{\tan 35°}}$$

(10)

In the second case, where h₀ > B₀ − a₀, the area affected by the punching cone is determined as

$$S_c=2b\left(B_0-a_0\right)+{\displaystyle \frac{4B_0{h}_0}{\tan 35°}}$$

(11)

Therefore, the punching resistance of joints formed by bilaterally inserting SSB into concrete girders can be calculated as

$$V=0.5f_t\left[2h_0\left({\displaystyle \frac{2a_0}{\tan 35°}}+b\right)+{\displaystyle \frac{4h_0^2}{\tan 35°}}\right]+0.8f_{yv}{A}_{svu}+0.8f_y{A}_{sbu}\sin \theta \left(h_0\le B_0-a_0\right)$$

(12)

$$V=0.5f_t\left[2b\left(B_0-a_0\right)+{\displaystyle \frac{4B_0{h}_0}{\tan 35°}}\right]+0.8f_{yv}{A}_{svu}+0.8f_y{A}_{sbu}\sin \theta \left(h_0\ge B_0-a_0\right)$$

(13)

Regarding the joint shear capacity,

Table 5. Evaluation of punching shear resistance.

Specimen	Calculated Value /kN	Experimental Value /kN	Relative Error /%
SJ-1	71.1	73.3	3.0
AJ-1	71.3	72.7	1.9
SJ-2	123.9	128.2	3.4
AJ-2	124.1	129.7	4.3

shows the comparison between theoretically predicted and experimental results. Relative errors between theoretical predictions and experimental results were generally between 2% and 5%, and the predicted results of shear capacities were smaller than corresponding test results, which provided a certain safety reserve and a reference for practical engineering applications. Notably, for cast-in-place insertion specimens, f_t in the design formula of the joint bearing capacity is concrete tensile strength. For prefabricated insertion specimens, f_t is the weighted average value of tensile strengths of concrete and grouting material according to the actual volume proportion of the punching cone. The proportion of grouting materials in the punching cone was much smaller than that of concrete. Therefore, there was little difference in the predictions of the punching capacity of cast-in-place and prefabricated joints, which was consistent with the experimental results.

In design practice, it should be ensured that the punching shear resistance of the joint, calculated using Equations (8), (9), (12), and (13), should be larger than the applied shear force. If not, the cross-sectional area of the concrete section or the amount of steel reinforcement should be further adjusted. The contribution of the concrete is properly quantified based on the punching shear mechanism under different cases, leading to more reliable prediction results. The developed model holds the potential to improve the current design standards.

5. Conclusions

In this study, joints were formed by inserting a steel secondary beam (SSB) into concrete girders. Their mechanical behavior was studied experimentally under monotonic static loading. Two forms of insertions were considered, and two construction methods were designed. The failure modes of the four types of joints, variations in applied load, and development of strains in SSB and internal reinforcement were analyzed and compared. The following main conclusions may be drawn:

(1)

Punching failure at the bottom of the concrete girder by the inserted SSB occurred in all joint specimens. Diagonal cracks with inclination angles of 30–35° appeared between the lower flange of the SSB and the concrete girder bottom. A punching cone formed in the damaged area, and the stirrup reached its yield strain within the punching cone range.

(2)

The joint specimens with bilaterally inserted beams showed more obvious brittleness than those with unilateral inserted beams, and the failure mode was changed from multi-crack to single-crack. The cracks formed by punching were steeper for the case of a bilaterally inserted joint.

(3)

There was the limited difference in the punching capacities of prefabricated and cast-in-place joints, but the displacement ductility coefficient of the AJ-1 joint increased by 22.9% compared with the SJ-1 counterpart, and the displacement ductility coefficient of AJ-2 increased by 41.3% compared with the case of SJ-2. This indicated that the application of high-performance cement-based grout materials in the prefabricated inserted joints resulted in better deformation ability.

(4)

According to the punching failure mechanism of the joints formed by inserting SSB into concrete girders, design equations for the punching capacity were proposed with favorable accuracy. The equations provided a useful reference for designing this type of joint in engineering practice.

It may be worth noting that there are some limitations in this study. The number of specimens is currently very limited. More investigations covering a wider range of geometry and concrete strength are still desired to demonstrate the effect of key variables. Furthermore, finite element (FE) modeling may be employed to clarify the stress distribution and interaction mechanism. This would be the subject of future research, thus enabling a better understanding of the behavioral characteristics of such joints.