Capacity of Shear Key Joints of Reinforced Concrete Open-Web Sandwich Plates

(e shear key in the reinforced concrete open-web sandwich plate (RCOSP) is a block joint that connects with the top chord and the bottom chord. In order to understand the failure mode of the shear key and verify the accuracy of the current algorithm, a total of 9 test pieces are prepared and classified 3 groups were assigned longitudinal reinforcement (LR) ratios of 0.49%, 0.82%, and 1.24%, respectively.(e horizontal concentrated static loading under simple support condition is carried out.(e test results show that the shear key is horizontally cut and the concrete is pulled apart or crushed along the direction of chord width at the shear keychords area; the strain level of the concrete and stirrup of the shear key is lower averagely; the development of the horizontal displacement and the strain of the longitudinal bars of the test pieces goes through elastic, elastoplastic, and plastic stages; the ultimate load of the test pieces has almost no relationship with the reinforcement ratio of shear key but is controlled by the degree of crack development in the area where shear key connects with the chords. To avoid the current algorithm overestimating the shear capacity of shear key, the restricted condition of shear section is proposed. (e finite element analysis (FEA) further verifies that the restricted condition of shear section proposed in this paper is reasonable and necessary.


Introduction
e open-web sandwich plate floor is a kind of novel floor developed on the basis of open-web grid, its appearance is similar to that of the reinforced concrete open-web grid in Figure 1(a), and the height of the open-web grid is 1/16 to 1/ 18 in short span direction [1]. e open-web part is composed of top chord, bottom chord, and the shear key that connects with top and bottom chords; the surface course is cast-in-situ or precast reinforced concrete slab; see Figure 1(b) for its composition. is floor overcomes the disadvantage that the shear stiffness of the open-web grid is bad and has the following advantages: (1) It is mostly used in large-span (commonly used span is 18 to 30 m) multistory building and the floor height is small (1/24 to 1/30 in short span direction), improving the land utilization (2) e space between top chord and bottom chord can be used as channel for various kinds of pipelines; no suspended ceiling is required, playing a part in beautifying appearance and saving story height e study shows that, under the action of vertical load, the bending deflection with the top chord and bottom chord of the RCOSP is obvious, but the shear key mainly shows the shear deformation [2], the deformation of the open-web sandwich plate mainly is bending, which accounts for about 85% of total deformation, and the shear deformation accounts for about 15% [3] of total deformation. e flexural behavior [4] and seismic behavior of the steel open-web sandwich plate are discussed by numerical analysis methods [5].
As the shear key is connecting the top and bottom chords of the open-web sandwich plate, it directly affects the integral mechanical properties of the open-web sandwich plate; understanding the mechanical properties and failure mode of the shear key in various kinds of open-web sandwich plates becomes the focus of the study at present. e experimental study on reciprocating loading of shear key joints of steel open-web sandwich plates (SOSP) with/ without stiffening chord provided is carried out, the results show that two types of joints have better seismic behavior and can meet the project design requirements, and the photo of the structure is shown in Figure 2(a) [6]. e experimental study on the shear key of SOSP shows that the joint has better shear bearing capacity and ductility [9,10]. A static loading test on shear key joints of SOSP is performed and the formula of the intersection beam analogy method is obtained [11]. e shear connectors also appear in the composite beam and beam column joints. By experimental study an empirical equation to predict the load capacity of the V-shaped shear connector is obtained [12]. e shear strength, shear stiffness, failure mode, and relative slip characteristics of perforated panel connection joint in corrugated steel web composite beam are studied by means of tests [13]; the mechanical property of stud connectors in a fire and its influence on connection performance of the composite beam are studied [14]. Combined with experiments and finite element analysis, the failure mode and shear bearing capacity computational formula of high strength bolt connected in composite beam are obtained [7,15], and the photo of the structure in [14] is shown in Figure 2(b). e test results show that the stud or bolt connection in light steel composite beam can ensure better shear bonding strength [16]; the H-shaped steel composite wooden beam can adopt inclined bolt steel-wood composite joint for shear connection [17]. e shear connection performance of woodconcrete composite beam is studied by using experimental method [8,18], and the photo of the structure in [18] is shown in Figure 2(c). e experimental study on external stiffening chord joint between square hollow section column and H-shaped steel beam and steel-concrete column-steel beam composite joint is carried out, and the computational method of shear strength is proposed [19,20]. e study shows that if the web in the beam column joint area is reinforced by using asymmetric chamfer, the shear bearing capacity of the joint area can be improved [21]. e gene expression program can be used to predict the computational model of shear bearing capacity of reinforced concrete beam column joint [22]. e studies in [23,24] give the computational model and computational formula that are suitable for shear strength of reinforced concrete beam column joint under the action of earthquake. e above studies mainly focus on different types of shear key joints in the steel open-web sandwich plate and other types of shear connection, while the experimental study of shear key joint in RCOSP has not been performed. e current algorithm considers that the stress of shear key joint is similar to that of the reinforced concrete corbel; the shear bearing capacity is mainly controlled by the single side LR of shear key joint [1]. To verify the accuracy of the current algorithm for shear bearing capacity of the shear key of RCOSP and understand the failure mode of shear key of the   Advances in Materials Science and Engineering RCOSP, a total of 9 test pieces in 3 groups with different LR ratios of shear key are designed. e centralized static loading is carried out to obtain the crack development and failure mode of test pieces, understand the relationship of shear bearing capacity with LR ratios of shear key joint, and obtain the load-displacement curves of test pieces.

Design of the Components.
e experiment in this paper is completed in Key Laboratory of Structural Engineering of Guizhou Province, China. e mechanical simplified model of test pieces is shown in Figure 3; the sizes of test pieces are indicated in Figure 4(a). ree groups of test pieces with LR ratios of shear key of 0.49%, 0.82%, and 1.24%, respectively, are designed, three test pieces are prepared for each group, and the reinforcement arrangement of each group of test pieces is given in Table 1. e test pieces are prepared in horizontal position, as it is shown in Figure 5.

Mechanical Properties of Materials.
ree groups of specimens were poured with ready-mixed concrete. Test results of the concrete cube compressive strength of each specimen group are shown in Table 2. e tensile strength and elastic modulus were calculated from the compressive strength [25]. Mechanical performance parameters of steel bar are shown in Table 3.

Loading Device and System.
For the simple support of shear key joint, the single point horizontal centralized loading is adopted, a 100T Jack is selected for loading, and a 50T load transducer is used to control the load values; the design of test loading device is shown in Figure 6, and the physical diagram of the loading device is shown in Figure 7. e loading rate is approximately 7 kN/min, a load of 15 kN is applied to each test piece at the first stage, a load of 30 kN is applied at each stage from the second stage, each stage of load is stabilized for a time duration of 10 min, and the crack development condition during the load stabilizing is observed and a corresponding note is made.

Arrangement of Measuring Points.
To measure the horizontal displacement of the test pieces, a displacement meter shown in Figure 8 is arranged. e reinforcement strain gauges are arranged on the chord LR, shear key LR, and shear key stirrup, 32 reinforcement strain gauges are arranged on each test piece, and the positions and numbers of the arrangement are shown in Figure 9. e concrete strain gauges are arranged on the shear key and chord  Figure 2: e structures in reference. (a) e steel structure in [6]. (b) e steel-concrete composite structure in [7]. (c) e wood-concrete composite structure in [8].   surface, the positions and numbers of the arrangement are shown in Figure 10, and 26 concrete strain gauges are arranged on an individual test piece. In the experiment, the synchronous collection of data from displacement meter, load transducer, and strain measuring are enabled by the test system.

Description of Experimental
Phenomena. e experimental phenomena and the failure load values of 3 groups of test pieces are roughly the same; the crack development process and law are described by taking test piece 3-A as an example. It is stipulated in the following description that the shear key is taken as the center, the left side refers to the end that is close to the horizontal loading, and the right side refers to the end that is close to the fixed hinged bearing. As the occurrence of cracks on the front and back of the shear key-chord connected area is almost similar, only the cracks on the front of the shear key-chord connected area are described:     Figure 11, the contour lines of specimen are shown.   Advances in Materials Science and Engineering In Figure 12, the development of concrete cracking is shown, and in Figure 13, the failure forms of specimens are shown.

Failure Characteristics
(1) No matter how the LR ratio of shear key is, the areas where the test pieces are seriously damaged are located at the places where the shear key connects with the chords, which shows that the shear key is cut under the action of horizontal force. Continuously loading to the test piece after the shear key was horizontally cut, the chords neighboring to the shear key show numbers of inclined cracks ( Figure 13 e failure bearing capacity of all specimens does not increase with the LR ratio of shear key, and the failure pattern does not change with the increase of the ratio. e reason is likely to be as follows: e vertical height of shear key is requested to be less than or equal to its cross section size; namely, shear key is a block joint, the influence of the bending deformation is small, and hence, the LR ratio of shear key playing an important role under the action of bending moment cannot change the failure pattern. e y-1 y-2 y-3 Advances in Materials Science and Engineering 7 Figure 12: Cracking diagram of fracture development process. Crack distribution under (a) loading at 35%, (b) loading at 55%, (c) loading at 75%, and (d) under loading at the failure load.

Experimental Results and Analysis
In this paper, the time when the LR strain of shear key reaches the yield strain value or significant turning point occurs on the load-displacement curve is taken as the yield condition of the test pieces, and the time when no more load increase is possible is taken as the failure moment of the test pieces.  Figure 14 shows the load-strain curve of the LR on the left side of the shear key, where 1-C, 1-B, 2-B, and 2-C are the data at measuring point 4; 1-A and 2-A are the data at measuring point 12. Figure 15 shows the loadstrain curve of the LR on the right side of the shear key, where 1-A is the data at measuring point 13; 2-A and 2-C are the data at measuring point 17; 1-B, 1-C, and 2-B are the data at measuring point 21. Figure 16-18 show the load-strain curves of concrete, respectively, at measuring points 34, 37, and 47. In Figures 14 and 15, at the initial stage of loading, the strain of LR of shear key grows very slowly and the values are very small. When the load reaches 140 kN, the strain growth rate becomes faster. Meanwhile, the strain values of some specimens increase sharply after the load reaches 140 kN, probably for the concrete cracking near the longitudinal bar, and the force has been passed to longitudinal bar. When the load reaches about 75% of the failure load, the load growth rate becomes slow; the strain of LRs increases sharply, showing significant yielding characteristics. In case of loading continuously, after the ultimate load is reached, the load-strain curves of the LRs begin to fall, showing the failure of the test pieces. e strain value of LRs on the right side of shear key of most test pieces is 80% to 95% of that on the right side, showing that the transmission force of the test device is reliable.

Strain of LR, Concrete, and
In Figures 16 to 18, at the initial stage of loading, the load-strain curves of concrete of the shear key grow approximately linearly, indicating that the test piece is at the stage of elastic stress. When the load reaches about 75% of the failure load, the load growth rate becomes slow. Continuing to load, after the ultimate load is reached, the loadstrain curves of the concrete begin to fall, showing the failure of the test pieces. e concrete strain values of test pieces 1-B and 3-C are significantly smaller than that of other test pieces; this may be possibly caused by sliding of a bearing position of this test piece. Probably for the fabrication error of 2-A, the strain value of No. 47 measuring point is obviously larger than that of other specimens, and the ultimate load is obviously smaller than that of other specimens.
e strain values of measuring points 34 and 47 near the shear key-chords connection area are obviously bigger than the values of measuring point 37 in the middle of shear key; this is mainly because the shear key-chords connection area is affected by shear force, bending moment, and axial force, while the middle of shear key is mainly affected by shear force.
Ignoring the influence of bending moment, the diagonal lines of 45°and 135°are the principal stress directions of shear keys. Referring to the concrete strain values of the shear key (shown in Figure 19), the strain values of measuring point 34 along the diagonal direction of the shear key are the largest, followed by the values of measuring point 33 along the horizontal direction, and the values of measuring point 35 along the vertical direction are the smallest, indicating that the direction along the diagonal of shear key can be approximately the direction of the principal compressive stress of the shear key.

Strain of Stirrup.
e strain values and change tendency of shear key stirrups for various test pieces are similar. Figures 20 to 22 show the load-strain curves at measuring points 29 to 32 of test pieces 1-A, 2-A, and 3-A.
In Figures 20 to 22, the absolute values of stirrup strain increase with the load, but the values are small when the test pieces fail, showing that the stirrups of shear key are not subjected to big force; it mainly acts to fix the LRs, and the stirrups can be arranged according to constructional reinforcement. e strain values of measuring points 29 and 32 of test piece 1-A and measuring point 32 of test piece 3-A are bigger than those at other measuring points; the main reason is that the measuring points 29 and 32 are in the area where the shear key connects with chords, and the area is under the composite stress state. e strain of the measuring points can be divided into tension and pressure; this may be possibly caused by the strain gauges that are affected by the surrounding concrete particles.

Load-Displacement Curve.
e absolute values of y-2 and y-3 displacements of the displacement meters are roughly equal; the horizontal displacement of test pieces can be obtained by subtracting the y-2 value from the y-1 value of the displacement meter. e load-displacement curves in horizontal direction of 3 groups are given below as shown in Figure 23.
In Figure 23, prior to cracking, the displacement of various test pieces develops slowly; the relationship between displacement and load is approximately linear; this indicates that the test pieces are at elastic working state; after cracking and before yielding, the slopes of curves of various test pieces reduce gradually; this is because the cracking with the chord weakens the overall lateral stiffness of the test pieces and makes the curve gradually slow down; after the test pieces yield, the displacement increases quickly with the Advances in Materials Science and Engineering application of the load; the curves of the test pieces have smooth sections; this indicates that the test pieces have better deformation capacity; after the ultimate load is reached, the increase of loading becomes impossible; the displacement further increases and indicates that the test pieces failed. In fact, curve variation rule of Figure 23 is similar to that of other types of reinforced concrete members [26][27][28].   Figure 23. In this paper, the corresponding load at the yield of the test pieces is taken as the yield load V y ; the corresponding displacement is yield displacement Δ y ; maximum load value during loading is called ultimate load V u , the corresponding displacement is called ultimate displacement Δ u , and the corresponding values are given in Table 4. V y increases with the LR ratio of shear key; the ultimate load V u does not increase with the LR ratio of shear key; it can be judged by combining with the abovementioned experimental phenomena that the final failure of the test pieces is controlled by the degree of crack development of shear key-chords connection area and has no relationship with the LR ratio of shear key.

Computation of Shear Bearing Capacity
In the computation as follows, the measured values in Tables 2 and 3 are converted to design strength [29]: where α c1 is the ratio of prism strength to cube strength, C50 and less take 0.76, C80 takes 0.82, and the intermediate is linear interpolation; α c2 is the brittleness reduction coefficient of concrete, C40 and less take 1.0, C80 takes 0.87, and the intermediate takes linear interpolation; δ is variation coefficient of compressive strength of concrete cube block.

Computational Method of Shear Bearing Capacity and
Discussion. At present, it is considered that the stress pattern of the shear key is similar to the reinforced concrete corbel. e concrete of shear key is mainly compressed, that is, similar to the corbel belly concrete, and the LRs of shear key are mainly tensile, that is, similar to the corbel LRs. e corresponding calculation formula and the calculation diagram (see Figure 24) are put forward [30]. e calculation formula controlled by the cracks of shear key is as follows: e diagram and formula for calculating the shear bearing capacity of current algorithm are given as follows: In diagram, V(V k ) is the bigger one among the axial force between top chords and bottom chords, a is the distance from the bottom chord centroid axis to the bottom surface of the top chord, b is the width of the shear key cross section, h is the height of shear key cross section, h 0 is the effective height of shear key cross section, a s is the distance from the position where the resultant force of LR for shear key acts to the edge of the concrete, l n is the height of shear key in vertical direction, h 1 is the height of bottom chord, and h 2 is the height of top chord. A s is the area of single side LR of the shear key, and the ratio of single side is requested to be equal to or larger than the values of 0.2% and 0.45 f t /f y , the minimum LR ratio of the shear key cross section is 0.6%, f y is the yield strength of LR of shear key, and f tk is concrete axial tensile strength standard value.
According to test phenomena, the load of test specimens when oblique cracks appear at the area where the shear key connects the chords is about 140 to165 kN, and the shear bearing capacity of specimens calculated by formula (6) is 149 kN, and the relative error is 6% to 11%, so formula (6) can accurately predict the corresponding load when oblique cracks appear at the connection of shear key-chord.
In Figures 14 and 15, the strain values of the LRs are very small before the concrete cracking at the shear key-chords connection area. However, after cracks appear in this area, the LRs strain of shear key increases sharply. In Figures 15 to  18, the shear key concrete is mainly under compression, and the strain values along the diagonal direction are the largest, so the following can be concluded: (1) Before concrete cracking at shear key-chords connection area, the load mainly acts on the concrete. When the load reaches the value calculated by formula (6), the LRs of shear key begin to resist the external force and are mainly subjected to tensile force. (2) Ignoring the tensile strength of shear key concrete, it can be approximately considered that the shear key along a diagonal direction is the direction of the principal compressive stress. (3) In combination with (1) and (2), it can be known that the stress pattern of shear key under horizontal load is similar to that of reinforced concrete corbel, so the current theory is reliable.  Table 4 with the values calculated by formula (7), the shear bearing capacity of group 1 (ratio is 0.49%) and group 2 (ratio is 0.82%) computed by formula (7) is obviously smaller than Advances in Materials Science and Engineering the corresponding values of V y , and the value of 3-C (ratio is 1.24%) is bigger than the corresponding value V y , while the values of 3-A and 3-B are less than the corresponding V y .
In engineering application, the yield bearing capacity is taken as the design value of bearing capacity. It can be obtained from the comparison results between formula (7) and the test: when the LR ratio of shear key is 0.49% and 0.82%, the results calculated by formula (7) are conservative and safe for engineering application, while when the ratio is 1.24%, the results calculated by formula (7) are probably bigger than the yield values and not safe for engineering application. It can be speculated that, for test specimens, if the LR ratio of shear key is greater than 1.24%, the results calculated by formula (7) may be larger than the ultimate shear capacity, which is obviously unsafe. is is because the shear capacity calculated by formula (7) will increase with the LR ratio of shear key, neglecting the fact that the final failure is controlled by the degree of concrete crack development at shear key-chords connection area and almost has no relationship with the LR ratio of shear key. So, to avoid formula (7) overestimating the shear capacity of shear key, a calculation formula based on the joint size to limit the maximum shear bearing capacity of shear key should be proposed.

e Restricted Condition of Shear Section.
Based on the failure pattern, the shear key is cut along its cross section, the ultimate shear capacity has almost no relationship with the LR ratio of shear key, and the relative errors are large between the results of formula (7) and the test. It can be concluded that the ultimate shear bearing capacity of shear key is determined by the size of chords and shear key and the strength of concrete. e ratio of the vertical height l n of shear key to the cross section height h is generally required to be less than or equal to 1 [1]; the shear key is a deep flexural member that is placed vertically.
In Chinese code, the single span reinforced concrete deep flexural member is shown in Figure 25, and the l/h is requested to be less than 5. e restricted condition of shear section of the reinforced concrete deep flexural member is shown as In formula (8), the h 0 /b is required to be less than or equal to 4, where V is the shear bearing capacity design value; l is the calculation span and is required to be not less than 2h; h is the height of cross section; h 0 is the effective height of cross section; b is the width of cross section; β c is the concrete strength influence coefficient, C50 and less take 1.0, C80 takes 0.8, and between C50 and C80 is linear interpolation; f c is concrete axial compressive strength design value, to test pieces; it can be computed according to formula (2); e shear key joint is integrated with the top and bottom chords; the shape is different from the reinforced concrete deep flexural member shown in Figure 25. According to the test, after the shear key is cut along the cross section, the load can continue to increase, and the concrete cracks of top and bottom chords near shear key develop quickly. It can be concluded that the cross section size of chords has effect on  shearing bearing capacity. In engineering applications, the cross section widths of chords and shear key are equal. erefore, the effect of chords on shearing bearing capacity can be approximately considered as the effect of cross section height of chords, and taking the value of l/l n to consider the effect of chords, the restricted condition of shear section of shear key is given as follows: k is the introduced shear bearing capacity correction factor, taking k as 0.53 for matching the load that the concrete is crushing at the shear key-chords; b, h, l, and l n have the same meanings as 5.1. l/l n represents the influence of the bottom and top chord dimensions on the formula; β c , f c have the same meanings as formula (8).
e shear bearing capacity calculated by formula (9) is defined as V 2 , and V u , V y , V 1 , and V 2 of various groups of test pieces and their ratios are given in Table 5.
e loading coefficient is defined as c u , and c u � V 2 /V u . e experimental phenomena reveal that the cut of shear key is almost simultaneous with the concrete crushing of shear key-chords connection area. So taking the concrete crushing of shear key-chords connection area as the mark of ultimate limited states, the corresponding c u in Chinese code is 1.30 [31]. As shown in Table 5, c u is 1.32 to 1.41, indicating that the calculated results by formula (9) are safe. e relative error between V y and V 2 is 2%-24%; this indicates that the calculated result of formula (9) is close to the yield values of the test. e values of V u /V 1 decrease with the increasing of the LR ratio of shear key. If the LR ratio of shear key is larger than the value in group 3, the values of V u /V 1 are likely smaller than 1 for the ultimate shearing bearing capacity controlled by the degree of concrete cracking development in connection area.

Finite Element Analysis (FEA)
6.1. Introduction of FEA. In finite element analysis, the solid unit element is applied to simulate the concrete and the link 8 element is adopted to simulate the steel bar [32,33]. e solid unit element can achieve both cracking and crushing of the concrete material. e failure criterion of the concrete is employed by the William and Warnke five-parameter criterion [34] and the shear transfer coefficients for an open and closed crack are 0.2 and 0.2, respectively [35]. e Bilinear Isotropic Hardening is used to simulate the nonlinear behavior of the reinforcement [36]. Poisson's ratio of concrete and steel is 0.2 and 0.3, respectively [29]. e displacement is taken as the criterion of convergence. e mechanical property parameters of concrete and reinforcement are calculated by converting them into design values based on the results of Tables 2 and 3. e constraint and loading mode of FEA is the same as the test specimens. By considering that the shear key-chords connection area is at combined stress state, the failure of the test pieces can be determined according to the strength theory. In the test, the concrete along the width of shear key-chords connection area is crushed or pulled apart when loading to about 75% of the ultimate load, taking the third principal stress of concrete at the shear key-chords connection area σ 3 � f c as the criterion to judge the failure of test pieces, named as failure mark 1. Meanwhile, to compare the yielding loads of FEA and test when the stress values of LR of shear key reach f y , the stress of LR of shear key reaches f y as the second mark of failure, named as failure mark 2. e results of failure marks 1 and 2 should be calculated separately.

Results of FEA.
e finite element (FE) models are distinguished using the prefix "FE" followed by the group numbers 1, 2, and 3, respectively. e pictures of model are displayed in Figure 26.
e results of FEA and its ratio to the values in Tables 4  and 5 are shown in Table 6:

Results under Failure Mark 1.
e shear bearing capacity of FE1, FE2, and FE3 is almost equal; namely, the shear bearing capacity has no relation with the reinforcement ratio of shear key. e values of V/Vu are 0.71-0.76. In the experiment, when concrete in the connection area is crushed (compressive stress attained f c ), the corresponding load is only approximately 75% of the ultimate load. So, the shearing bearing capacity of FEA and test matches well. e stress distribution of steel bars of FE models is shown in Figure 27. In Figure 27(a), the maximum tensile stress of LRs of shear key is close to the yield strength, while the values of FE2 and FE3 in Figures 28(b) and 28(c) are smaller than the corresponding yield strength, and the results are also consistent with the load-strain curves in Figure 14.
For FE1-FE3, the relative errors of V and V y are within 20%, indicating that the shear bearing capacity calculated by FEA is in good agreement with the yield shearing bearing capacity of test. When the FE models failed, the distribution of concrete cracks and crushing and the compressive stress of FE1-FE3 are similar. Figures 28 and 29 show the distribution of concrete cracks and crushing and the third principal compressive stress of FE3 at failure, respectively.
In Figure 28, the cracks and crushing mainly distribute in the shear key-chords connection area, which are consistent with the distribution of test in Figures 12 and 13. In Figure 29, the maximum compressive stress of concrete appears at the shear key-chords connection area, which is consistent with the failure mode shown in Figure 13(f ); the direction along the diagonal of shear key is the direction of the primary compressive stress of concrete, which is consistent with the experimental results in Figure 19. Combined with the above analysis, the FE models under failure mark 1 are reliable and the results of FEA have reference value.    e distribution of concrete cracks and crushing and the concrete compressive stress under failure mark 2 is similar to those in failure mark 1. Figure 30 shows the steel bar stress distribution of FE1-FE3 under failure mark 2.
In Figure 30, the tensile stress of the LR of shear key is larger than those in Figure 27, indicating that the yield of the LR of shear key is later than the crushing of concrete at the shear key-chords connection area, which is consistent with the test. In FE3, the LR of shear key cannot reach the yield strength for the little increasing of shear bearing capacity after the yielding of LR of chords, which is consistent with the results that the average strain values of LR of shear key in 3-A and 3-B do not yield. e shear bearing capacity V of FE1 and FE2 is smaller than the Vu obtained from the test and the relative errors of V and V y are 3% and 16%, respectively. e shear bearing capacity V of FE3 is larger than the V y and V u of test. So, the FEA is reliable under the small ratio of LR in shear key. Under large ratio of LR in shear key, the joint loses bearing capacity for the concrete crack development at shear key-chords connection area before the yielding of LR of shear key. erefore, the shear bearing capacity of failure mark 2 under large ratio of shear key is larger than the ultimate shear capacity of joint. e deformation shapes of FE1-FE3 are similar. e horizontal displacement of failure mark 1 is smaller than that of failure mark 2 for the concrete crushing at shear keychords connection is earlier than the yielding of LR in shear key. e deformation diagram of FE3 of failure marks 1 and 2 is shown in Figure 30, and the test deformation diagram is shown in Figure 31, and the deformations in Figures 30 and  31 match well. e horizontal displacement value obtained by FEA is smaller than test displacement value; the main reasons are as follows: (1) there is an error with the test device, and (2) the failure of FEA is earlier than that of test specimens.
In conclusion, no matter how the ratio is, failure mark 1 can accurately predict the shear capacity corresponding to the crushing of concrete at shear key-chords connection area. Under small LR ratio of shear key, failure mark 2 can accurately predict the shear bearing capacity corresponding to the yielding of LR of shear key, but when the LR ratio of shear key is large, the result of failure mark 2 may be larger than the ultimate bearing capacity of specimen.
To further clarify the relationship between the shear bearing capacity of 2 failure marks and the LR ratio of shear key and the values of formulas (7) and (9), the models FE4 and 5 are added. In Figure 32, the shear bearing capacity of FE1-FE5 is compared with the formula results. e shear bearing capacity of formula (9) is equivalent to the result of failure mark 1, which does not increase with the LR ratio of shear key but is basically unchanged, indicating that formula (9) can accurately predict the crushing of concrete at shear key-chords connection area. e shear capacity calculated by formula (7) and failure mark 2 increases with the LR ratio of shear key. For formula (7), when the LR ratio of shear key is less than 1%, the shear bearing capacity of formula (7) is smaller than that of formula (9) and failure mark 1; when the LR ratio of shear key is larger than 1%, the shear bearing capacity of formula (7) is larger than that of formula (9) and failure mark 1. For failure mark 2, when the LR ratio of shear key is less than 0.5%, the shear bearing capacity of failure mark 2 is smaller than that of formula (9) and failure mark 1; when the LR ratio of shear CRACKS AND CRUSHING STEP=1 SUB=25 TIME=1 key is larger than 0.5%, the shear bearing capacity of failure mark 2 is larger than that of formula (9) and failure mark 1. e test shows that the shear capacity of the joint can be increased by about 25% after concrete crushing at shear keychords connection area. For formula (7) and failure mark 2, when the LR ratio of shear key is larger than 1% and 0.5%,

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Advances in Materials Science and Engineering respectively, the shear capacity of for formula (7) and failure mark 2 may be larger than the ultimate shear capacity of the joint.
For the safety and convenience of engineering application, the shear bearing capacity of joint can be calculated by formula (7), and to avoid formula (7) overestimating the shear bearing capacity of joint, the value of formula (7) needs to be smaller than the value of formula (9).

Parameter Analysis.
To further verify the accuracy of formula (9), the parameterized analysis was carried out by taking the concrete strength, LR ratio of shear key, and the size of joint as parameter, taking the failure mark 2 as the failure of FE models.
In FEA, for the stirrup reinforcement ratio of chords and shear keys, the LR ratio of chords is the same as the test specimen, and the integral reinforcement model was adopted for the steel. e mechanical property parameters of concrete are taken as the design values specified in [29], the yield strength of the reinforcement is 360 MPa, and the elastic modulus is 2 × 10 5 MPa. e relevant parameters of the FE models are shown in Table 7.
e shear bearing capacity calculated by formula (9) and FEA are shown in Figures 33-35.

Conclusion
(1) e failure of shear key is controlled by the degree of crack development in shear key-chords connection area, the shear key is horizontally cut, and the concrete of connection area is crushed or pull apart. e failure mode and ultimate shear bearing capacity have almost no relationship with the LR ratio of shear key.
(2) e load stress-strain curves of longitudinal bars and load-displacement curves of shear key have obvious yield characteristics and underwent elastic, elastoplastic. and plastic stages. e stirrup of shear key can be arranged according to the constructional reinforcement. (3) e stress pattern of shear keys is similar to the reinforced concrete corbel, and formula (6) can accurately estimate the corresponding load value when the shear key-chord connection area cracks. (4) According to the failure pattern and the restricted condition of reinforced concrete deep flexural member in Chinese code, formula (9) to calculate the shear bearing capacity of shear key is put forward. In engineering application, the shear bearing capacity of shear key can be calculated by formula (7), but the value cannot be larger than the value calculated by formula (9); namely, the shear bearing capacity should meet the restricted condition of shear section. (5) e FEA results of the test specimens are consistent with those of test results, and the parametric analysis further verifies the reason of the restricted condition of shear section proposed in this paper.
Data Availability e bearing capacity data used to support the findings of this study are included within the article.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper.

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