A method for evaluating the flexural bearing capacity and failure mode of three-dimensional fiber mesh reinforced concrete slabs

Abstract

A method for evaluating the flexural capacity and failure mode of a three-dimensional fiber mesh reinforced concrete slab. This invention relates to methods for evaluating the flexural capacity and failure mode of concrete slabs. The purpose of this invention is to solve the problems of high cost, difficulty in implementation, and limited reference value of evaluation results in evaluating the flexural capacity and failure mode of three-dimensional fiber mesh reinforced concrete slabs. The method involves measuring the geometric parameters of the three-dimensional fiber mesh reinforced concrete slab; measuring and calculating the material parameters of the three-dimensional fiber mesh reinforced concrete slab; calculating the flexural capacity of the normal section of the three-dimensional fiber mesh reinforced concrete slab; calculating the shear capacity of the oblique section of the three-dimensional fiber mesh reinforced concrete slab; and applying the obtained ultimate flexural capacity limit value M of the normal section. u and the ultimate shear capacity of the inclined section V u According to P m and P v The failure modes of three-dimensional fiber mesh reinforced concrete slabs were obtained. This invention belongs to the field of concrete bearing capacity and failure mode evaluation.

Description

Technical Field

[0001] This invention relates to a method for evaluating the flexural bearing capacity and failure mode of concrete slabs, specifically a method for evaluating the flexural bearing capacity and failure mode of three-dimensional fiber mesh reinforced concrete slabs. This invention belongs to the field of concrete bearing capacity and failure mode evaluation. Background Technology

[0002] Three-dimensional fiber mesh reinforced concrete slabs are a new type of slab material manufactured through processes such as casting and spraying, using single or multiple layers of three-dimensional fiber mesh as reinforcement and concrete or other cement-based materials as the matrix. The bearing capacity and failure mode of three-dimensional fiber mesh reinforced concrete slabs under bending loads are crucial indicators that must be considered in the design and application of concrete slabs. Therefore, establishing a systematic and reliable method for evaluating the bending bearing capacity and failure mode of three-dimensional fiber mesh reinforced concrete slabs is essential. Currently, for the bearing capacity testing schemes of traditional reinforced concrete beams, slabs, and other bending members, a complete system combining experimental, theoretical, and numerical simulation methods has been established. However, as a high-performance new type of building slab, research on three-dimensional fiber mesh reinforced concrete slabs is insufficient, and the evaluation schemes for their bending load bearing capacity and failure mode are mostly conducted through pure experiments. For three-dimensional fiber mesh reinforced concrete slabs, the bearing capacity refers to the magnitude of the external force it can withstand, while the failure mode can be divided into two categories: bending failure of the normal section and shear failure of the oblique section. Depending on the size of the test specimen, the test can be divided into full-scale tests and scaled-down tests. For building slabs, the length and width dimensions often reach several meters. Full-scale testing involves preparing a three-dimensional fiber-reinforced concrete slab with dimensions identical or similar to those used in actual engineering projects and conducting bending tests. Scaled-down testing, on the other hand, involves preparing a smaller-sized concrete slab according to relevant specifications and conducting bending tests. After the tests, designers analyze the results to evaluate the load-bearing capacity and failure mode of the three-dimensional fiber-reinforced concrete slab.

[0003] Full-scale tests of the flexural performance of 3D fiber-reinforced concrete slabs involve large specimens, high preparation costs, and high load levels, placing significant demands on testing equipment and personnel. This makes it difficult for manufacturers and testing institutions to meet these requirements. For scaled-down tests, on the one hand, relevant standards are incomplete, providing insufficient guidance; on the other hand, the size effect limits the evaluation of load-bearing capacity. Furthermore, the application conditions of 3D fiber-reinforced concrete slabs are highly complex. Both full-scale and scaled-down tests can only assess load-bearing capacity under simple conditions and cannot fully reflect the condition of 3D fiber-reinforced concrete slabs under complex conditions. In conclusion, evaluating the flexural load-bearing capacity and failure modes of 3D fiber-reinforced concrete slabs through pure experiments is not only costly and difficult to implement, but also yields limited reference value for the evaluation results. Summary of the Invention

[0004] The purpose of this invention is to solve the problems of high cost, difficulty in implementation, and limited reference value of the evaluation of flexural bearing capacity and failure mode of three-dimensional fiber mesh reinforced concrete slabs, and to provide a method for evaluating the flexural bearing capacity and failure mode of three-dimensional fiber mesh reinforced concrete slabs.

[0005] The technical solution of this invention is:

[0006] A method for evaluating the flexural bearing capacity and failure mode of a three-dimensional fiber mesh reinforced concrete slab, the method being implemented according to the following steps:

[0007] Step 1: Measure the geometric parameters of the 3D fiber mesh reinforced concrete slab:

[0008] Step 2: Measure and calculate the material parameters of the three-dimensional fiber mesh reinforced concrete panel;

[0009] Step 3: Calculate the flexural capacity of the cross section of the 3D fiber mesh reinforced concrete slab;

[0010] Step 4: Calculate the shear capacity of the inclined section of the 3D fiber mesh reinforced concrete slab;

[0011] Step 5: Based on the ultimate bending capacity value M of the cross section obtained in Steps 3 and 4 u and the ultimate shear capacity of the inclined section V u The ultimate external load values ​​can be obtained separately: ultimate bending load P. m and shear load limit P v According to P m and P v The size relationship can be used to determine the failure mode of the three-dimensional fiber mesh reinforced concrete slab.

[0012] Furthermore, the parameters measured in step one for the three-dimensional fiber mesh reinforced concrete slab include the cross-sectional width b, cross-sectional height H0, and distance H from each surface layer to the upper surface of the concrete slab. i The total area of ​​each row of longitudinal fiber bundles on the cross section A f Total area of ​​each row of core columns The height h of each layer of three-dimensional fiber mesh i And the distance C between two adjacent weft yarns.

[0013] Furthermore, in step two, the material parameters of the three-dimensional fiber mesh reinforced concrete slab, including the compressive strength f of the concrete prism, are measured and calculated. c uniaxial tensile strength f of concrete t The compressive stress of the concrete just reached f c Concrete compressive strain ε0, concrete ultimate compressive strain ε cuThe ultimate tensile stress of the fiber bundle in a three-dimensional fiber mesh is f. fu .

[0014] Furthermore, the ε0 and ε obtained in step two are... cu Substituting into equations (1) and (2), we obtain the simplified stress coefficients α and β:

[0015] (1)

[0016] (2)

[0017] The distance H from each surface layer to the upper surface of the concrete slab i The relationship between the distance from the neutral axis to the upper surface of the concrete slab and the height x0 of the compression zone satisfies H i >x0, then solve for the ultimate bending moment bearing capacity M of the normal section of the three-dimensional fiber mesh reinforced concrete slab according to equations (3)-(5). u ;

[0018] (3)

[0019] (4)

[0020] (5)

[0021] In the formula, m is the expression that satisfies H i > The number of x0 facets.

[0022] Furthermore, since the number of three-dimensional fiber mesh layers located in the compression zone cannot be determined before calculating the bearing capacity in step three, it is first assumed that all fiber bundles are located on the tension side, and then the calculation is performed using the formula...

[0023] (6)

[0024] (7)

[0025] (8)

[0026] (9)

[0027] Pick: (10)

[0028] (11)

[0029] Obtain x0; determine whether each surface layer satisfies H. i If the value is greater than x0, remove the layers that do not meet the requirements, and continue to obtain x0 according to the above formula until all the remaining layers satisfy H. i >x0.

[0030] Furthermore, substituting the relevant data from steps one and two into equation (12) yields the result under bending load.

[0031] (12)

[0032] V u Ultimate limit of shear capacity of inclined section of three-dimensional fiber mesh reinforced concrete slab.

[0033] Furthermore, in step five, P m and P v Determining the failure mode of 3D fiber mesh reinforced concrete slabs by size:

[0034] If P m >P v This indicates that the bending capacity of the plate's normal section is greater than the shear capacity of its inclined section, and the failure mode is controlled by the weaker inclined section, resulting in shear failure of the inclined section.

[0035] If P m <P v This indicates that the bending capacity of the plate's normal section is less than the shear capacity of its inclined section, and the failure mode is controlled by the weaker normal section, resulting in bending failure of the normal section.

[0036] If P m ≈P v This indicates that the bending capacity of the plate's cross section is similar to the shear capacity of its inclined section, and both failure modes may occur.

[0037] Compared with the prior art, the present invention has the following advantages:

[0038] 1. This application uses a three-dimensional fiber mesh as a reinforcing material for a concrete matrix. The warp and weft yarns of the three-dimensional fiber mesh are interwoven to form upper and lower surface layers, while the core column connects the two surface layers to form a whole.

[0039] 2. This application establishes a theoretical calculation method for the bearing capacity of three-dimensional fiber mesh reinforced concrete slabs, forming a systematic evaluation method for bearing capacity and failure modes. Since the bearing capacity calculation method relies on reasonable assumptions and the actual stress state to establish equations for solution, it can be completed quickly using software, yielding reliable results that fully reflect the bearing capacity of the slab, reducing evaluation costs and improving evaluation efficiency. Furthermore, the theoretical calculation method can evaluate the bearing capacity and failure modes of slabs under complex working conditions, overcoming the limitations of experimental evaluation for complex conditions.

[0040] 3. This application overcomes the implementation difficulties caused by the complexity of the test by using a simple and easy-to-use calculation formula, which can effectively improve the efficiency of the load-bearing capacity and failure mode evaluation scheme of three-dimensional fiber mesh reinforced concrete slabs.

[0041] 4. The calculation formula in this application is based on the stress characteristics of three-dimensional fiber mesh reinforced concrete slabs, and the results obtained are reliable and can accurately reflect the load-bearing capacity of three-dimensional fiber mesh reinforced concrete slabs.

[0042] 5. Based on the calculation formula, this application can obtain the bending capacity of the plate section and the shear capacity of the inclined section. By comparing the magnitude of the two parts, the failure mode of the concrete plate can be effectively predicted.

[0043] 6. The calculation scheme and test in this application complement each other to form a systematic evaluation scheme for three-dimensional fiber mesh reinforced concrete panels, which is conducive to the promotion and application of this type of panel in the construction field. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of a multi-layered, three-dimensional fiber mesh reinforced concrete slab. Figure 1 (a) is a front view of a three-dimensional fiber mesh reinforced concrete slab. Figure 1 (b) Cross-sectional view of a three-dimensional fiber mesh reinforced concrete slab;

[0045] Figure 2 This is a schematic diagram of the test scheme for concrete prisms;

[0046] Figure 3 This is a schematic diagram of the concrete splitting tensile strength test scheme;

[0047] Figure 4 This is a schematic diagram of a single fiber bundle tensile strength test scheme.

[0048] Figure 5 These are stress and strain diagrams of a rectangular section of a three-dimensional fiber mesh reinforced concrete slab in pure bending. Figure 5 (a) is a cross-sectional view of the specimen. Figure 5 (b) is the strain diagram. Figure 5 (c) is a stress diagram. Figure 5 (d) is the equivalent stress diagram;

[0049] Figure 6 This is a diagram illustrating the calculation process of the flexural bearing capacity of a three-dimensional fiber mesh reinforced concrete slab under normal cross-section.

[0050] Figure 7 This is a schematic diagram of the four-point bending test in the embodiment;

[0051] Figure 8 This is a failure mode diagram of the bending failure S1 of the normal section in the embodiment;

[0052] Figure 9 This is a failure mode diagram of the inclined section under shear failure S2 in the embodiment. Detailed Implementation

[0053] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0054] Step 1: Measure the geometric parameters of the 3D fiber mesh reinforced concrete slab:

[0055] like Figure 1 As shown, the parameters measured in step one for the three-dimensional fiber mesh reinforced concrete slab include the cross-sectional width b, cross-sectional height H0, and the distance H from each surface layer to the upper surface of the concrete slab. i The total area of ​​each row of longitudinal fiber bundles on the cross section A f Total area of ​​each row of core columns The height h of each layer of three-dimensional fiber mesh i and the distance C between two adjacent weft yarns;

[0056] Step 2: Measure and calculate the material parameters of the three-dimensional fiber mesh reinforced concrete panel;

[0057] Measure and calculate the material parameters of the three-dimensional fiber mesh reinforced concrete slab, including the compressive strength f of the concrete prism. c uniaxial tensile strength f of concrete t The compressive stress of the concrete just reached f c Concrete compressive strain ε0, concrete ultimate compressive strain ε cu The ultimate tensile stress of the fiber bundle in a three-dimensional fiber mesh is f. fu .

[0058] f c and f t The determination was conducted according to GB-T 50081-2019 "Standard for Test Methods of Physical and Mechanical Properties of Concrete". Simultaneously with the preparation of the three-dimensional fiber-reinforced concrete slab, three 150mm×150mm×300mm concrete prism specimens and three 150mm×150mm×300mm concrete cube specimens were prepared and cured under the same conditions and for the same period as the concrete slab. Figure 7 As shown, after curing, a compressive strength test is conducted using a compressive strength testing machine. c The calculation formula is:

[0059] (1)

[0060] F1 is the failure load of the prism compression test; A1 is the bearing area of ​​the specimen.

[0061] pass Figure 8 The scheme shown yields f t The calculation formula is:

[0062] (2)

[0063] F2 is the failure load of the splitting test; A2 is the area of ​​the splitting surface of the specimen.

[0064] ε0, ε cu According to GB / T 50010-2015 (2024 edition) "Code for Design of Concrete Structures", the following formula is used for calculation:

[0065] (3)

[0066] (4)

[0067] (5)

[0068] The determination of relevant parameters of the three-dimensional fiber mesh fiber bundle was carried out in accordance with the standards GB / T 1446-2005 "General Rules for Test Methods of Fiber Reinforced Plastics", GB / T 3354-2014 "Test Method for Tensile Properties of Directed Fiber Reinforced Polymer Matrix Composites", and GB20310-2006 "Preparation and Determination of Tensile Strength of Glass Fiber Untwisted Rovings". The specific scheme is as follows:

[0069] like Figure 9 As shown, a fiber bundle is first cut from the three-dimensional fiber mesh, and then the two ends of the fiber bundle are tightened with the clamps of the testing machine before a tensile test is performed. fu The calculation formula is:

[0070] (6)

[0071] F3 is the failure load of the fiber bundle tensile test; A3 is the cross-sectional area of ​​a single fiber bundle.

[0072] Step 3: Calculate the flexural capacity of the cross section of the 3D fiber mesh reinforced concrete slab;

[0073] like Figure 5 As shown in (a), the cross-section of the three-dimensional fiber mesh reinforced concrete slab is divided into two parts by the neutral axis (the dotted line in the figure indicates the neutral axis). The area above the neutral axis is the compression zone, and the area below the neutral axis is the tension zone.

[0074] Three-dimensional fiber meshes can withstand significant tensile stress but not compressive stress, while concrete can only withstand compressive stress and is difficult to withstand tensile stress. Therefore, as Figure 5As shown in (c), the stress in the compression zone above the neutral axis is borne by the concrete, while the stress in the tension zone is borne by the three-dimensional fiber mesh. The distance from the neutral axis to the upper surface of the concrete slab is the height of the compression zone, x0. Therefore, for the three-dimensional fiber mesh, when H... i When H ≤ x0, it is located in the compression zone and has no effect; when H i >x0, located in the tension zone, bears tensile stress.

[0075] like Figure 5 As shown in (c), the stress state of concrete under compression is quite complex. To simplify the calculation, it is equivalent to... Figure 5 The state shown in (d) is considered. The complex stress state in the concrete compression zone is equivalent to a simple uniformly distributed load; the maximum compressive stress before this equivalent load is f. c After the equivalent compression, the compressive stress across the entire cross section of the compression zone is αf. c The height of the compression zone before equivalence is x0, and the height of the compression zone after equivalence is βx0. Therefore, α and β are simplified stress diagram coefficients. The equivalence process must satisfy that the magnitude and position of the resultant force remain unchanged before and after equivalence. Based on this, ε0 and ε2 obtained in step two are... cu Substituting into equations (7) and (8), we obtain α and β:

[0076] (7)

[0077] (8)

[0078] like Figure 6 As shown, since the number of three-dimensional fiber mesh layers located in the compression zone cannot be determined before calculating the bearing capacity, it is first assumed that all fiber bundles are located on the tension side. Substituting equations (11) and (12) into equation (9) yields a quadratic equation (13) with x0 as the unknown. This equation has two solutions, one as shown in equation (14); the other must be greater than H1 and is discarded. Determine whether each layer satisfies H i >x0, after removing the surface layers that do not meet the requirements, continue to solve equations (9), (11) and (12) to obtain x0, until all the surface layers that have not been removed satisfy H. i >x0, and count the number of surface layers that meet the requirements, m. Then, solve for the ultimate bending moment bearing capacity M of the normal section of the three-dimensional fiber mesh reinforced concrete slab according to equations (10)-(12). u .

[0079] (9)

[0080] (10)

[0081] (11)

[0082] (12)

[0083] (13)

[0084] Pick: (14)

[0085] (15)

[0086] Step 4: Calculate the shear capacity of the inclined section of the 3D fiber mesh reinforced concrete slab;

[0087] Substituting the relevant data obtained in steps one and two into equation (16) yields the ultimate shear capacity V of the inclined section of the three-dimensional fiber mesh reinforced concrete slab under bending load. u .

[0088] (16)

[0089] Step 5: Destruction Mode Assessment

[0090] Based on the load application scheme and the ultimate bending capacity value M of the normal section obtained in steps three and four. u and the ultimate shear capacity of the inclined section V u The ultimate limit values ​​of external loads can be obtained separately: ultimate bending load P m and shear load limit P v Ultimate bending load P m It is based on the ultimate limit value of the bending capacity of the cross section M. u The maximum external load that the concrete slab can withstand, calculated based on the actual stress state; shear load limit P. v Based on the shear bearing limit value V of the inclined section u The maximum external load that the concrete slab can withstand, calculated based on the actual stress state. P m and P v It can be either a concentrated load or a distributed load. Based on P... m and P v The size relationship yields the failure mode of the three-dimensional fiber mesh reinforced concrete slab: P m >P v This indicates that the flexural bearing capacity of the plate's normal section is greater than its shear bearing capacity, and the failure mode is controlled by the weaker shear section, resulting in shear failure of the shear section; P m <P v This indicates that the flexural bearing capacity of the plate's cross-section is less than its shear bearing capacity, and the failure mode is controlled by the weaker cross-section, resulting in flexural failure. m ≈P v This indicates that the bending capacity of the plate's cross section is similar to the shear capacity of its inclined section, and both failure modes may occur.

[0091] An example is a three-dimensional fiber mesh reinforced concrete slab with a two-layer fiber mesh structure.

[0092] Step 1: Measure the cross-sectional width b and cross-sectional height H0 of the 3D fiber mesh reinforced concrete slab, and the distance H from each surface layer to the upper surface of the concrete slab. i The total area A of each row of longitudinal fiber bundles on the cross section f and the total area of ​​each row of core columns .

[0093]

[0094] Step 2: Measure the compressive strength f of the concrete prism c uniaxial tensile strength f of concrete t The compressive stress of the concrete just reached f c Concrete compressive strain ε0, concrete ultimate compressive strain ε cu The ultimate tensile stress of the fiber bundle in a three-dimensional fiber mesh is f. fu The height h of each layer of three-dimensional fiber mesh i And the distance C between two adjacent weft yarns.

[0095]

[0096] Step 3: Calculate the flexural bearing capacity of the cross section of the 3D fiber mesh reinforced concrete slab.

[0097]

[0098] Step 4: Calculate the shear capacity of the inclined section of the 3D fiber mesh reinforced concrete slab.

[0099]

[0100] Step 5: Destruction Mode Assessment

[0101] (13)

[0102] (14)

[0103] Where: L is the span of the specimen, i.e. the distance between supports.

[0104] M obtained from steps two and three u and V u We can obtain:

[0105]

[0106] From the table, we know that group S1 satisfies P m,t <P v,t Therefore, bending failure occurs at the normal section; group S2 satisfies P.m,t >P v,t Therefore, shear failure occurs at the inclined section.

[0107] Step 7: Comparison and analysis of theoretical and experimental results. The table below shows the comparison between theoretical and experimental values ​​of bearing capacity.

[0108]

[0109] As shown in the table, the calculated results are close to the experimental results and the failure modes are consistent. The failure modes of the two embodiments are shown in the table below. Figure 8 , Figure 9 The method for evaluating the flexural bearing capacity and failure mode of three-dimensional fiber mesh reinforced concrete slabs proposed in this invention is highly accurate and practical.

[0110] Note that the above description is merely a preferred embodiment of the present invention and the technical principles employed. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and various obvious changes, readjustments, and substitutions can be made without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments, and may include many other equivalent embodiments without departing from the concept of the present invention, the scope of which is determined by the scope of the appended claims.

Claims

1. A method for evaluating the flexural bearing capacity and failure mode of a three-dimensional fiber mesh reinforced concrete slab, characterized in that: The method is implemented according to the following steps: Step 1: Measure the geometric parameters of the 3D fiber mesh reinforced concrete slab, including the cross-sectional width b, cross-sectional height H0, and distance H from each surface layer to the upper surface of the concrete slab. i The total area of ​​each row of longitudinal fiber bundles on the cross section A f Total area of ​​each row of core columns The height h of each layer of three-dimensional fiber mesh i and the distance C between two adjacent weft yarns; Step 2: Measure and calculate the material parameters of the three-dimensional fiber mesh reinforced concrete slab, including the compressive strength f of the concrete prism. c uniaxial tensile strength f of concrete t The compressive stress of the concrete just reached f c Concrete compressive strain ε0, concrete ultimate compressive strain ε cu The ultimate tensile stress of the fiber bundle in a three-dimensional fiber mesh is f. fu The ε0 and ε obtained in step two cu Substituting into equations (1) and (2), we obtain the simplified stress coefficients α and β: (1) (2) The distance H from each surface layer to the upper surface of the concrete slab i The relationship between the distance from the neutral axis to the upper surface of the concrete slab and the height x0 of the compression zone satisfies H i >x0, then solve for the ultimate bending moment bearing capacity M of the normal section of the three-dimensional fiber mesh reinforced concrete slab according to equations (3)-(5). u ; (3) (4) (5) In the formula, m is the expression that satisfies H i The number of x0 facets, Substituting the relevant data from steps one and two into equation (12) yields the result under bending load. (12) V u Ultimate shear capacity of inclined section of three-dimensional fiber mesh reinforced concrete slab; Step 3: Calculate the flexural capacity of the cross section of the 3D fiber mesh reinforced concrete slab; Step 4: Calculate the shear capacity of the inclined section of the 3D fiber mesh reinforced concrete slab; Step 5: Based on the ultimate bending capacity value M of the cross section obtained in Steps 3 and 4 u and the ultimate shear capacity of the inclined section V u The ultimate external load values ​​can be obtained separately: ultimate bending load P. m and shear load limit P v Ultimate bending load P m It is based on the ultimate limit value of the bending capacity of the cross section M. u The maximum external load that the concrete slab can withstand, calculated based on the actual stress state; shear load limit P. v Based on the shear bearing limit value V of the inclined section u The maximum external load that the concrete slab can withstand, calculated based on the actual stress state, is determined according to P. m and P v The size relationship can be used to determine the failure mode of the three-dimensional fiber mesh reinforced concrete slab.

2. The method for evaluating the flexural bearing capacity and failure mode of a three-dimensional fiber mesh reinforced concrete slab according to claim 1, characterized in that: In step three, before calculating the bearing capacity, the number of three-dimensional fiber mesh layers located in the compression zone cannot be determined. Therefore, it is first assumed that all fiber bundles are located on the tension side, and then the calculation is performed using the formula... (7) (8) (9) (10) Pick: (11) Obtain x0; determine whether each surface layer satisfies H. i If the value is greater than x0, remove the layers that do not meet the requirements, and continue to obtain x0 according to the above formula until all the remaining layers satisfy H. i >x0.

3. The method for evaluating the flexural bearing capacity and failure mode of a three-dimensional fiber mesh reinforced concrete slab according to claim 1, characterized in that: In step five, P m and P v Determining the failure mode of 3D fiber mesh reinforced concrete slabs by size: If P m >P v This indicates that the bending capacity of the plate's normal section is greater than the shear capacity of its inclined section, and the failure mode is controlled by the weaker inclined section, resulting in shear failure of the inclined section. If P m <P v This indicates that the bending capacity of the plate's normal section is less than the shear capacity of its inclined section, and the failure mode is controlled by the weaker normal section, resulting in bending failure of the normal section. If P m ≈P v This indicates that the bending capacity of the plate's cross section is similar to the shear capacity of its inclined section, and both failure modes may occur.

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