A vertical shear capacity design method, system and storage medium for externally reinforced UHPC-T beams

Abstract

The present invention provides a method, system and storage medium for designing the vertical shear capacity of an externally reinforced UHPC-T-beam. The method comprises: under the proposed structural dimensions of the composite structural beam, calculating the vertical shear force component and the characteristic value of the vertical shear bearing capacity borne by the UHPC rib plate, and the vertical shear force component and the characteristic value of the vertical shear bearing capacity borne by the steel web plate, respectively judging whether the vertical shear force component and the characteristic value of the vertical shear bearing capacity of the two satisfy the set conditions, if both satisfy, proceed to the next step of calculation, if any one does not satisfy, adjust the structural dimensions and recalculate; obtain the characteristic value of the vertical shear bearing capacity controlled by the horizontal shear capacity, and judge whether the characteristic value of the vertical shear bearing capacity satisfies the set conditions with the effect design value of the vertical shear force, if so, end the design, if not, adjust the structural dimensions and recalculate. The vertical shear capacity design method of the composite structural beam in the present invention helps engineering and technical personnel to judge the key mechanical properties of the structure.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge engineering, and in particular to a vertical shear capacity design method, system and storage medium for an externally reinforced UHPC-T beam. Background Art

[0002] With the popularity of ultra-high performance concrete (UHPC), existing bridge technologies in recent years have attempted to use UHPC to replace ordinary concrete (NC) as the main building material to achieve the requirements of reducing deadweight and improving performance, such as steel beam-UHPC bridge deck composite beams, but there are also defects such as the material performance cannot be fully utilized, the amount of steel used and the welding workload are large. In order to make full use of the excellent performance of steel and UHPC materials and further improve the economy and applicability of steel-UHPC composite beams, some new composite beam structures have been proposed. Among the currently disclosed technologies, Chinese patent applications with publication numbers CN112391932A and CN112342889A both propose a UHPC-T-beam using steel as external reinforcement. The idea is to use UHPC to bear the high pressure stress of the upper flange and the low tensile stress of the composite web, and use steel to bear the high tensile stress of the lower part, making full use of the material properties.

[0003] Different from the traditional steel-concrete composite beam, the vertical shear bearing mechanism of the externally reinforced UHPC-T beam is significantly different:

[0004] First, the traditional composite beam is composed of a steel beam with a lower flange, a steel web, an upper flange, and a concrete bridge deck. Since the concrete bridge deck accounts for a small proportion of the beam height, its vertical shear bearing capacity generally does not consider the contribution of the concrete bridge deck, that is, the vertical shear bearing capacity is provided by the steel web. However, since the web of the externally reinforced UHPC-T-shaped beam is composed of UHPC webs and externally reinforced steel webs in a considerable proportion, if the contribution of the UHPC webs to shear resistance is ignored, on the one hand, the size of the externally reinforced steel webs has to be increased to meet the needs, which becomes uneconomical; on the other hand, the UHPC webs that bear part of the shear force have not been checked, and the structure may become unsafe. In order to obtain the vertical shear resistance of the UHPC-T-shaped beam, the UHPC webs and externally reinforced steel webs are considered at the same time, and the two are simply added together. Although there is some improvement, there is a risk of overestimating the vertical shear resistance due to the asynchronous shear force distribution ratio and load history.

[0005] Secondly, the shear connector of the traditional composite beam is located at the interface between the upper flange of the steel beam and the concrete bridge deck, far away from the neutral axis, where the horizontal shear force is small, while the shear connector of the externally reinforced UHPC-T beam is closer to the neutral axis, and the shear connector bears a larger horizontal shear force. The premise for the UHPC-T beam to withstand bending moment and vertical shear force as a whole is that the shear connector is reliable, so its vertical shear capacity may be limited by the horizontal shear capacity of the shear connector. If this is not taken into account, the structure may face a greater safety risk.

[0006] Finally, when the externally reinforced UHPC-T-beam is used as a bridge component, it often bears the combined effects of bending moment and shear force at the same time. Under the positive bending moment, the UHPC web may crack, enter the softening section of the material or quit working, causing the neutral axis of the overall interface to move upward, and the static moment of the steel structure to increase, which leads to an increase in the shear stress of the steel web, and thus causes an increase in the shear force borne by the steel web, that is, the shear force is transferred from the UHPC web to the steel web. For situations where positive bending moment and shear force may be borne at the same time, if the redistribution of shear force between the UHPC web and the steel web is not considered, the design of the steel web will be unsafe.

[0007] In summary, there is an urgent need for a vertical shear capacity design method, system and storage medium for externally reinforced UHPC-T beams to solve the problems existing in the prior art. Summary of the invention

[0008] The purpose of the present invention is to provide a method for designing the vertical shear capacity of an externally reinforced UHPC-T-beam, aiming to solve the problem that there is no corresponding method in the prior art to guide the vertical shear design of a composite structural beam of steel and UHPC to ensure the safety and economy of the bridge. The specific technical scheme is as follows:

[0009] A vertical shear capacity design method for an externally reinforced UHPC-T beam, comprising:

[0010] S1. Obtain the design value of the vertical shear effect of the composite structural beam under the proposed structural size and the design value of the effect of the bending moment ;

[0011] S2. Design value based on the geometric parameters of the cross section of the composite structure beam and the effect of vertical shear force Design values ​​of the effects of bending moment , calculate the vertical shear force component borne by the UHPC rib plate and the vertical shear force component borne by the steel web ;

[0012] S3. Calculation of the characteristic value of vertical shear bearing capacity of UHPC ribbed slabs and the characteristic value of the vertical shear bearing capacity of the steel web ; if exists or , then adjust the structural dimensions of the composite structural beam and return to step S1, otherwise go to step S4; wherein, is the importance coefficient of the composite structural beam, is the material partial factor;

[0013] S4. Calculate the horizontal shear capacity per unit length of the steel tenons and mortises alternately arranged along the longitudinal direction of the bridge on the steel web. , according to the cross-sectional shear stress distribution height z and horizontal shear capacity per unit length Obtain the characteristic value of vertical shear bearing capacity controlled by horizontal shear capacity ;

[0014] S5. If Then adjust the structural dimensions of the composite structural beam and return to step S1, otherwise the design is terminated.

[0015] Preferably, in the above technical solution, step S2 is specifically:

[0016] S2.1. Convert the cross section of the composite structural beam into a cross section of a single material;

[0017] S2.2, divide the cross section into several unit layers in the height direction;

[0018] S2.3. Design value based on the effect of bending moment The distance from the neutral axis NA to the top of the section is obtained iteratively using the section layering method. , and calculate the moment of inertia of the cross section about the neutral axis NA ;

[0019] S2.4, according to the moment of inertia and the design value of the effect of vertical shear Calculate the shear stress of each unit layer, and further calculate the shear force of each unit layer;

[0020] S2.5. Obtain the vertical shear force component borne by the UHPC ribs and the vertical shear force component borne by the steel web .

[0021] Preferably, in the above technical solution, in step S2.1, the cross section of the composite structural beam is converted into a cross section of a single material, specifically:

[0022] Multiply the thickness of the UHPC rib plate in the cross section of the composite structure beam and the width of the UHPC bridge deck by , and obtain the cross section of a single material; among them, the elastic modulus ratio , is the elastic modulus of the steel web, is the elastic modulus of UHPC concrete.

[0023] In the above technical solution, preferably, in step S2.4, the first Shear stress per unit layer for:

[0024] (1),

[0025] Section Shear force per unit layer for:

[0026] (2),

[0027] in, For the The width of the unit layer, Indicates The static moment of the location of the unit layer, For the The area of ​​the unit layer, For the The height of the unit layer.

[0028] In the above technical solution, the vertical shear force component borne by the UHPC rib plate in step S2.5 is preferably for:

[0029] (3),

[0030] Vertical shear force component borne by the steel web for:

[0031] (4),

[0032] in, It is the first UHPC rib plate The shear force of each unit layer, For the steel web Shear force of each unit layer.

[0033] In the above technical solution, preferably, in step S4, the horizontal shear capacity per unit length of the steel tenons and mortise alternately arranged along the longitudinal bridge direction on the steel web is calculated. , specifically:

[0034] Calculate the horizontal shear bearing capacity characteristic value corresponding to the shear failure of the steel tenon :

[0035] (7),

[0036] Calculate the characteristic value of horizontal shear bearing capacity corresponding to the shear failure of the mortise :

[0037] (8),

[0038] Calculation of the characteristic value of the horizontal shear capacity between layers of composite structural beams :

[0039] (9),

[0040] Calculate the horizontal shear capacity per unit length :

[0041] (10),

[0042] in, The longitudinal arrangement spacing of the steel tenons; is the thickness of the steel web; is the yield strength of the steel web; is the shape coefficient of the mortise; is the standard value of cube compressive strength of UHPC concrete; It is the horizontal reinforcement strengthening coefficient in the mortise.

[0043] The preferred vertical shear bearing capacity characteristic value controlled by the horizontal shear capacity in the above technical solution is for:

[0044] (11).

[0045] In the above technical solution, the vertical shear bearing capacity characteristic value of the UHPC rib plate in step S3 is preferably for:

[0046] (5),

[0047] Characteristic value of vertical shear capacity of steel web for:

[0048] (6),

[0049] in, is the yield strength of the steel web; is the thickness of the steel web; is the height of the steel web; is the thickness of the UHPC rib; is the height of the UHPC rib; is the tensile elastic ultimate strength of UHPC concrete; is the ultimate tensile strength of UHPC concrete; It is the sum of the cross-sectional areas of all vertical segments of a single stirrup in the UHPC rib plate; is the spacing of stirrups in the UHPC rib plate; is the yield strength of stirrups in UHPC ribs.

[0050] The present invention also provides a vertical shear capacity design system for an externally reinforced UHPC-T-beam, the system comprising a memory and a processor, and when the processor runs the computer instructions stored in the memory, the vertical shear capacity design method for an externally reinforced UHPC-T-beam is executed.

[0051] The present invention also provides a storage medium, in which computer instructions are stored, and the computer instructions are configured to execute the vertical shear capacity design method of the externally reinforced UHPC-T beam when running.

[0052] The application of the technical solution of the present invention has the following beneficial effects:

[0053] The vertical shear capacity design method of the composite structural beam in the present invention helps engineering technicians to judge the key mechanical properties of the structure. The calculation method is scientific and efficient, which helps to promote the engineering application of the innovative structure (referring to the composite structural beam) and create social and economic value.

[0054] The method of the present invention avoids the deficiency of shear resistance of simply superimposing UHPC ribs and steel webs, takes into account the difference in shear force distribution ratio and load-bearing history of the two materials, and prevents over-design caused by ignoring the contribution of UHPC ribs, and avoids the risk of overestimation caused by simple superposition.

[0055] The method of the present invention clearly identifies the particularity of the position of the tenon and mortise (i.e., the shear connector in the background technology) being close to the neutral axis, and uses the horizontal shear resistance of the tenon and mortise as a limiting condition for the vertical shear resistance. By considering the bearing capacity of the tenon and mortise, the reliability of the structural design is improved.

[0056] The method of the present invention can take into account the influence of the change in the stress mechanism after the UHPC rib plate cracks. Specifically, if the effect design value of the bending moment is The tensile part of UHPC is in the elastic section. The position of the neutral axis NA will not change with the increase of is a fixed value; as If the UHPC ribs are further increased, after the UHPC ribs are softened or cracked under tension, according to the section axial force and bending moment equilibrium conditions, the neutral axis NA will move upward, that is, The static moment and inertia moment of the upper and lower parts of the neutral axis NA change continuously, which causes the bending moment to affect the shear force distribution. It is the design value based on the effect of bending moment The cross-sectional layering method is used to iteratively confirm the The method of the present invention can take into account the effect design value of the bending moment under different stress conditions. The impact of the changes was taken into account, and the redistribution of shear force between the UHPC ribs and the steel webs was considered. By considering the redistribution of force, the safety of the vertical shear design was ensured.

[0057] The method proposed in the present invention can be easily compiled into an application program, which greatly facilitates the use of engineering designers.

[0058] In addition to the above-described purposes, features and advantages, the present invention has other purposes, features and advantages. The present invention will be further described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The drawings constituting a part of this application are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0060] Figure 1 It is an axonometric view of the composite structural beam of steel and UHPC;

[0061] Figure 2 yes Figure 1 Structural diagram of the middle vertical stirrup group;

[0062] Figure 3 yes Figure 1 Schematic diagram of the structure of the steel tenon and mortise;

[0063] Figure 4 It is a flow chart of the vertical shear capacity design method of the externally reinforced UHPC-T beam of the present invention;

[0064] Figure 5 is a schematic cross-sectional view of the composite structural beam in Example 1;

[0065] Figure 6 is a schematic diagram of the composite structural beam cross section in Example 1 after being converted into a single material cross section;

[0066] Figure 7 is a schematic diagram of shear stress distribution of the composite structural beam in Example 1;

[0067] Figure 8 is a simplified calculation diagram of shear force of the composite structural beam in Example 1;

[0068] Among them, 100, composite structure beam, 110, UHPC bridge deck, 111, bridge deck transverse reinforcement, 112, bridge deck longitudinal reinforcement, 120, UHPC rib, 121, lower open stirrups, 122, upper open stirrups, 123, the bottom layer of longitudinal reinforcement, 124, the second bottom layer of longitudinal reinforcement, 125, longitudinal distribution reinforcement, 126, transverse short reinforcement, 130, T-shaped steel beam, 131, steel bottom plate, 132, steel web, 133, steel tenon, 134, mortise. DETAILED DESCRIPTION

[0069] In order to facilitate the understanding of the present invention, the present invention will be described more fully below, and preferred embodiments of the present invention are provided. However, the present invention can be implemented in many different forms and is not limited to the embodiments described herein. On the contrary, the purpose of providing these embodiments is to make the understanding of the disclosure of the present invention more thorough and comprehensive.

[0070] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0071] Embodiment 1:

[0072] Figure 1-Figure 3 A composite structural beam of steel and UHPC (i.e., an externally reinforced UHPC-T-shaped beam) is illustrated. The composite structural beam 100 includes a UHPC bridge deck 110 and a composite rib (not shown in the figure) located on the bottom surface of the UHPC bridge deck 110. The composite rib includes a UHPC rib 120 and a T-shaped steel beam 130. The UHPC rib 120 is located between the UHPC bridge deck 110 and the T-shaped steel beam 130, that is, the UHPC rib 120 is cast together with the UHPC bridge deck 110 to form a T-shaped structure, and the upper edge of the T-shaped steel beam 130 is buried inside the lower end of the UHPC rib 120.

[0073] Furthermore, the T-shaped steel beam 130 includes a steel bottom plate 131 and a steel web 132 disposed on the steel bottom plate 131, the two forming a T-shaped structure, and the upper edge of the steel web 132 (i.e., the side close to the UHPC rib 120) is alternately provided with steel tenons 133 and mortises 134 along the longitudinal bridge direction. Figure 3 As shown, Figure 3 The gray area in the figure is the mortise 134, and the distance between two adjacent tenons 133 is , the height of the steel tenon (i.e. the depth of the mortise) is The steel tenon 133 and the mortise 134 are buried in the concrete at the lower end of the UHPC rib 120, and the distance between the lower edge of the UHPC rib 120 and the bottom edge of the mortise 134 is .

[0074] Furthermore, the UHPC rib 120 includes a rib concrete layer and a rib reinforcement skeleton located in the rib concrete layer, wherein the rib reinforcement skeleton includes a bottom layer of longitudinal reinforcement 123, a second bottom layer of longitudinal reinforcement 124, a longitudinal distribution reinforcement 125, a transverse short reinforcement 126 and a vertical stirrup group (not shown in the figure); the vertical stirrup group includes lower open stirrups 121 and upper open stirrups 122 alternately arranged along the longitudinal bridge direction, such as Figure 1 and Figure 2 As shown, the lower open stirrup 121 and the steel tenon 133 are arranged in a one-to-one correspondence, the upper open stirrup 122 and the mortise 134 are arranged in a one-to-one correspondence, the steel tenon 133 is inserted into the opening at the lower end of the lower open stirrup 121, the lower end of the upper open stirrup 122 is placed in the mortise 134, and transverse short steel bars 126 are provided on both sides of the lower end of the upper open stirrup 122, and the transverse short steel bars 126 are spaced from the lower end of the upper open stirrup 122 (that is, the two are not overlapped); the position of the lower end of the lower open stirrup 121 is lower than that of the upper open stirrup 122 At the lower end, the bottom layer of longitudinal steel bars 123 is used to connect the lower ends of the lower open stirrups 121 along the longitudinal direction, and the second bottom layer of longitudinal steel bars 124 is used to connect the lower ends of the upper open stirrups 122 along the longitudinal direction. Specifically, in this embodiment, the number of the bottom layer of longitudinal steel bars 123 and the second bottom layer of longitudinal steel bars 124 are both two, and they are symmetrically arranged on both sides of the steel web 132; a plurality of longitudinal distribution steel bars 125 are arranged inside the vertical stirrup group along the vertical direction, and specifically, a single longitudinal distribution steel bar 125 passes through the alternately arranged upper open stirrups 122 and lower open stirrups 121 along the longitudinal direction.

[0075] Furthermore, the UHPC bridge deck 110 includes a bridge deck concrete layer and a bridge deck steel bar skeleton located in the bridge deck concrete layer, the bridge deck steel bar skeleton includes an upper transverse steel bar group, a lower transverse steel bar group and a bridge deck longitudinal steel bar 112; a plurality of bridge deck longitudinal steel bars 112 are arranged at intervals along the transverse direction of the bridge, the upper transverse steel bar group is located on the upper side of the bridge deck longitudinal steel bars 112, the upper transverse steel bar group includes a plurality of bridge deck transverse steel bars 111 arranged at intervals along the longitudinal direction of the bridge, the bridge deck longitudinal steel bars 112 are overlapped with the bridge deck transverse steel bars 111 in the upper transverse steel bar group; the lower transverse steel bar group is located on the lower side of the bridge deck longitudinal steel bars 112, the lower transverse steel bar group includes a plurality of bridge deck transverse steel bars 111 arranged at intervals along the longitudinal direction of the bridge, and the bridge deck transverse steel bars 111 in the lower transverse steel bar group are not overlapped with the bridge deck longitudinal steel bars 112.

[0076] Furthermore, the upper end of the lower open stirrup 121 is connected to the bridge deck reinforcement skeleton, specifically, overlapped with the bridge deck longitudinal reinforcement 112 .

[0077] Preferably, the bridge deck concrete layer and the rib concrete layer are both cast using UHPC concrete, and the UHPC concrete is an ultra-high performance concrete having ultra-high durability and ultra-high mechanical properties.

[0078] Furthermore, the lower end of the UHPC rib 120 is thickened at the buried steel tenon 133 and the mortise 134 (i.e., a reinforced horseshoe is provided) to ensure that the transverse distance from the steel tenon to the edge of the UHPC rib 120 is not less than 5 times the height of the steel tenon, thereby improving the tolerance of the centering error between the steel web 132 and the UHPC rib 120, and at the same time providing bending space for the upper open stirrups and the lower open stirrups and reserving sufficient protective layer thickness for the stirrups, thereby improving the bonding ability between the steel web and the UHPC rib 120.

[0079] In order to ensure the safe application of UHPC and steel composite structural beams, this embodiment provides a vertical shear capacity design method for an externally reinforced UHPC-T beam (i.e., a composite structural beam), such as Figure 4 As shown, the design method includes the following steps:

[0080] S1. Obtain the design value of the vertical shear effect of the composite structural beam under the proposed structural size Design values ​​of the effects of bending moment ;

[0081] Specifically, the permanent action of the composite structural beam is determined according to the structural dimensions of the proposed composite structural beam, and the variable action is determined according to the use requirements and environmental conditions of the composite structural beam; then, the effect design value of the vertical shear force under the basic combination of action effects is obtained based on the effect design value of the permanent action and the effect design value of the variable action. Design values ​​of the effects of bending moment .

[0082] Among them, the determination method of permanent action and variable action can be referred to the prior art, and no further detailed description is given in this embodiment. Preferably, the effect design value of the composite structure beam under permanent action and the effect design value under variable action are determined according to the general bridge internal force calculation method, and the effect design value of the permanent action and the effect design value of the variable action in the "General Specification for Design of Highway Bridges and Culverts" (JTG D60-2015) are combined to obtain the effect design value of the basic combination of action effects.

[0083] S2. Design value based on the geometric parameters of the cross section of the composite structure beam and the effect of vertical shear force Design values ​​of the effects of bending moment , calculate the vertical shear force component borne by the UHPC rib plate and the vertical shear force component borne by the steel web ;

[0084] Preferably, step S2 in this embodiment is specifically as follows:

[0085] S2.1. Convert the cross section of the composite structural beam into a cross section of a single material, specifically:

[0086] Multiply the thickness of the UHPC rib plate in the cross section of the composite structure beam and the width of the UHPC bridge deck by , and obtain the cross section of a single material (i.e., steel web material), such as Figure 5 and Figure 6 As shown; Among them, the elastic modulus ratio , is the elastic modulus of the steel web, is the elastic modulus of UHPC concrete.

[0087] S2.2. Divide the section into several unit layers in the height direction, where the height of the section (i.e. the height of the composite structural beam) is h ;

[0088] S2.3. Determine the distance from the neutral axis NA to the top of the section , and calculate the moment of inertia of the cross section about the neutral axis NA ;

[0089] Preferably, in step S2.3, the design value is based on the effect of the bending moment The cross-section layering method is used to iteratively calculate the distance from the neutral axis NA of the overall cross-section to the top of the overall cross-section according to the cross-section axial force and bending moment equilibrium conditions. For the specific iterative method, please refer to the prior art, which will not be described in detail in this embodiment. For example, Chinese patent application with publication number CN118965548A discloses a design method for a composite structural beam of steel and UHPC, wherein paragraphs 0039 to 0054 disclose the method of determining the composite structural beam by iterative calculation. method.

[0090] Furthermore, the moment of inertia of the cross section about the neutral axis NA is For the calculation method of , please refer to the prior art and will not be described in detail in this embodiment.

[0091] S2.4, according to the moment of inertia and the design value of the effect of vertical shear Calculate the shear stress of each unit layer, and further calculate the shear force of each unit layer;

[0092] Specifically, the cross section Shear stress per unit layer for:

[0093] (1),

[0094] in, is the design value of the vertical shear effect, For the The width of the unit layer, Indicates The static moment of the location of the unit layer; among them, The neutral axis NA is the boundary. The sum of the area moments of all unit layers on the side where the unit layer is located (i.e. The sum of the area moments of the unit layers and the The sum of the area moments of the other unit layers on the same side of the unit layer), The area moment of each unit layer is expressed as , For the The area of ​​the unit layer, , For the The distance from the unit layer to the neutral axis NA, For the The height of each unit layer;

[0095] Furthermore, the cross section Shear force per unit layer For (i.e. The shear stress acts on the force on the

[0096] (2),

[0097] In summary, according to formula (1) and formula (2), the shear force of each unit layer in the cross section can be obtained, as follows: Figure 7 As shown, the vertical shear components of the UHPC ribs and steel webs can be calculated separately in the subsequent calculation.

[0098] S2.5. Obtain the vertical shear force component borne by the UHPC ribs and the vertical shear force component borne by the steel web ;

[0099] Specifically, the vertical shear force component borne by the UHPC ribs is for:

[0100] (3),

[0101] Furthermore, the vertical shear force component borne by the steel web is for:

[0102] (4),

[0103] in, It is the first UHPC rib plate The shear force of each unit layer, For the steel web Shear force of each unit layer.

[0104] It should be noted that since the shear stress on the UHPC bridge deck and the steel base plate is generally small, their contribution to shear resistance is generally not considered, that is, .

[0105] S3. Calculation of the characteristic value of vertical shear bearing capacity of UHPC ribbed slabs and the characteristic value of the vertical shear bearing capacity of the steel web ; if exists or , then adjust the structural dimensions of the composite structural beam and return to step S1, otherwise go to step S4; wherein, is the importance coefficient of the composite structural beam, is the material partial factor;

[0106] Specifically, the characteristic value of the vertical shear bearing capacity of the UHPC ribbed plate is for:

[0107] (5),

[0108] Furthermore, the characteristic value of the vertical shear bearing capacity of the steel web is for:

[0109] (6),

[0110] in, is the yield strength of the steel web, in MPa; is the thickness of the steel web, in mm; is the height of the steel web, in mm; is the thickness of the UHPC rib plate (referring to the actual thickness of the UHPC rib plate, i.e. the thickness before conversion), in mm; is the height of the UHPC rib, in mm; is the tensile elastic ultimate strength of UHPC concrete, in MPa; is the ultimate tensile strength of UHPC concrete, in MPa; It is the sum of the cross-sectional areas of all vertical segments of a single stirrup in the UHPC rib (the stirrup here refers to the upper open stirrup or the lower open stirrup. The upper open stirrup and the lower open stirrup are generally of the same specification, so the cross-sectional areas of the upper open stirrup and the lower open stirrup are the same; the upper open stirrup and the lower open stirrup in this embodiment are both double-limbed, that is, they have two vertical segments, but in some embodiments, the stirrup may be set to a single limb, that is, only one vertical segment), the unit is mm 2 ; is the spacing of stirrups in the UHPC rib plate, in mm; It is the yield strength of stirrups in UHPC ribs, in MPa.

[0111] Optimally, the importance coefficient of the composite structural beam is According to the importance of the bridge, the values ​​are 0.9, 1.0, and 1.1 respectively; the material partial coefficient Used to convert the calculated bearing capacity characteristic value into the corresponding bearing capacity design value, taking 1.25 as the value.

[0112] S4. Calculate the horizontal shear capacity per unit length of the steel tenons and mortises alternately arranged along the longitudinal direction of the bridge on the steel web. , according to the cross-sectional shear stress distribution height z and horizontal shear capacity per unit length Obtain the characteristic value of vertical shear bearing capacity controlled by horizontal shear capacity ;

[0113] Since the positions of the tenons and mortises are close to the neutral axis, the vertical shear stress at the positions of the tenons and mortises is relatively large in the height direction of the composite structural beam. According to the principle of shear force reciprocity, the horizontal shear capacity per unit length of the tenons and mortises in the length direction of the composite structural beam is will be the maximum vertical shear force that the UHPC rib plate can withstand per unit height. Since the vertical shear stress is mainly borne by the steel web and the UHPC rib plate, and the vertical shear stress of the steel web is generally greater than that of the UHPC rib plate, it is safe to consider the vertical shear stress distribution at a height of z , the width is On a rectangle, such as Figure 8 As shown, .

[0114] Horizontal shear resistance per unit length The calculation of should consider the minimum values ​​of the two failure modes of steel tenon failure and mortise failure, specifically:

[0115] Calculate the horizontal shear bearing capacity characteristic value corresponding to the shear failure of the steel tenon , unit N:

[0116] (7),

[0117] Calculate the characteristic value of horizontal shear bearing capacity corresponding to the shear failure of the mortise , unit N:

[0118] (8),

[0119] Calculation of the characteristic value of the horizontal shear capacity between layers of composite structural beams , unit N:

[0120] (9),

[0121] Calculate the horizontal shear capacity per unit length :

[0122] (10),

[0123] Characteristic value of vertical shear capacity controlled by horizontal shear capacity for:

[0124] · (11),

[0125] in, The longitudinal spacing of the steel tenons, in mm; is the thickness of the steel web, in mm; is the yield strength of the steel web, in MPa; is the shape coefficient of the mortise, which is related to the shape of the steel tenon. For example, the MCL type key is ; is the standard value of cube compressive strength of UHPC concrete, in MPa; is the strengthening coefficient of horizontal reinforcement in the mortise, wherein the horizontal reinforcement in the mortise includes the horizontal section of the transverse short steel bars and the upper opening stirrups, , It is the sum of the cross-sectional areas of the horizontal reinforcement in the mortise, including the horizontal sections of the short transverse reinforcement and the upper opening stirrups; The area of ​​the mortise, such as MCL type key ; is the elastic modulus of the steel tenon (i.e., steel web), in MPa; is the elastic modulus of UHPC concrete, in MPa.

[0126] S5. If Then adjust the structural dimensions of the composite structural beam and return to step S1, otherwise the design is terminated.

[0127] The method of this embodiment avoids the deficiency of shear resistance of simply superimposing UHPC ribs and steel webs, and takes into account the differences in shear force distribution ratio and load-bearing history of the two materials, thereby preventing over-design caused by ignoring the contribution of UHPC ribs and avoiding the risk of overestimation caused by simple superposition.

[0128] The method of this embodiment clearly identifies the particularity of the position of the tenon and mortise being close to the neutral axis, and uses the horizontal shear resistance of the tenon and mortise as a limiting condition for the vertical shear resistance. By considering the bearing capacity of the tenon and mortise, the reliability of the structural design is improved.

[0129] The method of this embodiment can take into account the influence of the change in the stress mechanism after the UHPC rib plate cracks. Specifically: if the effect design value of the bending moment The tensile part of UHPC is in the elastic section. The position of the neutral axis NA will not change with the increase of is a fixed value; as If the UHPC ribs are further increased, after the UHPC ribs are softened or cracked under tension, according to the section axial force and bending moment equilibrium conditions, the neutral axis NA will move upward, that is, The static moment and inertia moment of the upper and lower parts of the neutral axis NA change continuously, which causes the bending moment to affect the shear force distribution. It is the design value based on the effect of bending moment The cross-sectional layering method is used to iteratively confirm the The method of this embodiment can take into account the effect design value of the bending moment under different stress conditions. The impact of the changes was taken into account, and the redistribution of shear force between the UHPC ribs and the steel webs was considered. By considering the redistribution of force, the safety of the vertical shear design was ensured.

[0130] Application examples:

[0131] In this case, based on the specific structural dimensions of a composite structural beam, the above design method is used to verify the vertical shear capacity of the composite structural beam, as follows:

[0132] According to the effect design value of permanent action and the effect design value of variable action, the effect design value of vertical shear force under the basic combination of action effects is obtained. , design value of the effect of bending moment .

[0133] Elastic modulus of steel web , elastic modulus of UHPC concrete , , convert UHPC material into steel and obtain the converted section. Iterative calculation based on the section layering method mm, moment of inertia ; Calculate the vertical shear force components borne by the UHPC ribs and steel webs respectively , .

[0134] Get the thickness of UHPC ribs , the height of UHPC ribs =770 mm , the sum of the cross-sectional areas of all vertical segments of a single stirrup in the UHPC rib , the spacing of stirrups in UHPC ribs s= 75 mm , Yield strength of stirrups in UHPC ribbed slabs , UHPC tensile elastic limit strength and ultimate tensile strength They are , According to formula (5), the vertical shear bearing capacity characteristic value of UHPC ribbed plate is calculated as .

[0135] Obtaining the yield strength of the steel web , Steel web height , steel web thickness =19mm, the characteristic value of the vertical shear bearing capacity of the steel web is calculated according to formula (6): ;

[0136] , less than , meeting the requirements.

[0137] , less than , meeting the requirements.

[0138] Get the longitudinal spacing of the steel tenons , steel web thickness =19mm, yield strength of steel web (Q355 material) According to formula (7), the horizontal shear bearing capacity characteristic value corresponding to the shear failure of the steel tenon is calculated as ;

[0139] according to Get the shape coefficient of the mortise =2.17, standard value of cubic compressive strength of UHPC concrete The diameter of the upper opening stirrup is 10mm, the diameter of the transverse short steel bar in the mortise is 12mm, and the sum of the cross-sectional areas of the horizontal steel bars in the mortise is ,according to Get the area of ​​the mortise , the elastic modulus of the steel tenon (i.e. steel web) , elastic modulus of UHPC concrete ,according to Calculate the reinforcement ratio in the mortise According to formula (8), the horizontal shear bearing capacity characteristic value corresponding to the shear failure of the mortise is calculated as ;

[0140] According to formula (9), the characteristic value of the interlayer horizontal shear bearing capacity of the composite structure beam is calculated as follows: =252.9 Horizontal shear capacity per unit length of shear connector ; Shear stress distribution height , the characteristic value of vertical shear bearing capacity controlled by horizontal shear capacity =1686×1.2=2023kN.

[0141] =1.0×1.25×716.8=896kN, less than It meets the requirements. But it can be seen that Much smaller than and The sum is 3360.5 kN, which further illustrates the necessity of adopting the verification method of this embodiment.

[0142] Embodiment 2:

[0143] The present embodiment provides a vertical shear capacity design system for an externally reinforced UHPC-T-beam, the system comprising a memory (i.e., a storage medium) and a processor, the memory storing computer instructions, the computer instructions being configured to execute the vertical shear capacity design method for an externally reinforced UHPC-T-beam in Example 1 when running, and the processor executing the vertical shear capacity design method for an externally reinforced UHPC-T-beam in Example 1 when running the computer instructions stored in the memory; through the design system of the present embodiment, after the designer inputs the proposed structural dimensions into the design system, it can verify whether the current structural dimensions meet the safety requirements.

[0144] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for designing the vertical shear capacity of an externally reinforced UHPC-T beam, characterized in that: include: S1. Obtain the design value of the vertical shear effect of the composite structural beam under the proposed structural size Design values ​​of the effects of bending moment ; S2. Design value based on the geometric parameters of the cross section of the composite structure beam and the effect of vertical shear force and the design value of the effect of the bending moment , calculate the vertical shear force component borne by the UHPC rib plate and the vertical shear force component borne by the steel web ; S3. Calculation of the vertical shear bearing capacity characteristic value of UHPC ribbed slab and the characteristic value of vertical shear bearing capacity of steel web ; if exists or , then adjust the structural dimensions of the composite structural beam and return to step S1, otherwise go to step S4; wherein, is the importance coefficient of the composite structural beam, is the material partial factor; S4. Calculate the horizontal shear capacity per unit length of the steel tenons and mortises alternately arranged along the longitudinal direction of the bridge on the steel web. , according to the cross-sectional shear stress distribution height z and horizontal shear capacity per unit length Obtain the characteristic value of vertical shear bearing capacity controlled by horizontal shear capacity ; S5. If Then adjust the structural dimensions of the composite structural beam and return to step S1, otherwise the design is terminated.

2. The vertical shear capacity design method of the externally reinforced UHPC-T beam according to claim 1 is characterized in that: The step S2 specifically comprises: S2.

1. Convert the cross section of the composite structural beam into a cross section of a single material; S2.2, divide the cross section into several unit layers in the height direction; S2.

3. Design value based on the effect of bending moment The distance from the neutral axis NA to the top of the section is obtained iteratively using the section layering method. , and calculate the moment of inertia of the cross section about the neutral axis NA ; S2.4, according to the moment of inertia and the design value of the effect of vertical shear Calculate the shear stress of each unit layer, and further calculate the shear force of each unit layer; S2.

5. Obtain the vertical shear force component borne by the UHPC ribs and the vertical shear component borne by the steel web .

3. The vertical shear capacity design method of the externally reinforced UHPC-T beam according to claim 2 is characterized in that: In step S2.1, the cross section of the composite structural beam is converted into a cross section of a single material, specifically: Multiply the thickness of the UHPC rib plate in the cross section of the composite structure beam and the width of the UHPC bridge deck by , and obtain the cross section of a single material; among them, the elastic modulus ratio , is the elastic modulus of the steel web, is the elastic modulus of UHPC concrete.

4. The vertical shear capacity design method of the externally reinforced UHPC-T beam according to claim 2 is characterized in that: In step S2.4, the Shear stress per unit layer for: （1）， Section Shear force per unit layer for: （2）， in, For the The width of the unit layer, Indicates The static moment of the location of the unit layer, For the The area of ​​the unit layer, For the The height of the unit layer.

5. The vertical shear capacity design method of externally reinforced UHPC-T beam according to claim 2 is characterized in that: Vertical shear force component borne by the UHPC ribs in step S2.5 for: （3）， Vertical shear force component borne by the steel web for: （4）， in, It is the first UHPC rib plate The shear force of each unit layer, For the steel web Shear force of each unit layer.

6. The vertical shear capacity design method of externally reinforced UHPC-T beam according to claim 1 is characterized in that: In step S4, the horizontal shear capacity per unit length of the steel tenons and mortise alternately arranged along the longitudinal bridge direction on the steel web is calculated. , specifically: Calculate the horizontal shear bearing capacity characteristic value corresponding to the shear failure of the steel tenon : （7）， Calculate the characteristic value of horizontal shear bearing capacity corresponding to the shear failure of the mortise : （8）， Calculation of the characteristic value of the horizontal shear capacity between layers of composite structural beams : （9）， Calculate the horizontal shear capacity per unit length : （10）， in, The longitudinal arrangement spacing of the steel tenons; is the thickness of the steel web; is the yield strength of the steel web; is the shape coefficient of the mortise; is the standard value of cube compressive strength of UHPC concrete; It is the horizontal reinforcement strengthening coefficient in the mortise.

7. The vertical shear capacity design method of an externally reinforced UHPC-T beam according to claim 6 is characterized in that: Characteristic value of vertical shear capacity controlled by horizontal shear capacity for: （11）。 8. The vertical shear capacity design method of externally reinforced UHPC-T beam according to claim 1 is characterized in that: Characteristic value of vertical shear bearing capacity of UHPC rib plate in step S3 for: （5）， Characteristic value of vertical shear capacity of steel web for: （6）， in, is the yield strength of the steel web; is the thickness of the steel web; is the height of the steel web; is the thickness of the UHPC rib; is the height of the UHPC rib; is the tensile elastic ultimate strength of UHPC concrete; is the ultimate tensile strength of UHPC concrete; It is the sum of the cross-sectional areas of all vertical segments of a single stirrup in the UHPC rib plate; is the spacing of stirrups in the UHPC rib plate; is the yield strength of stirrups in UHPC ribs.

9. A vertical shear capacity design system for externally reinforced UHPC-T beams, characterized in that: The system includes a memory and a processor. When the processor runs the computer instructions stored in the memory, it executes the vertical shear capacity design method of the externally reinforced UHPC-T beam according to any one of claims 1 to 8.

10. A storage medium, characterized in that: The storage medium stores computer instructions, and the computer instructions are configured to execute the vertical shear capacity design method of the externally reinforced UHPC-T beam according to any one of claims 1 to 8 when running.

Images