Method for determining flexural capacity of steel shell-UHPC composite beam considering diaphragm effect

Abstract

A steel shell-UHPC composite beam flexural capacity determination method considering the role of the partition, relates to the field of building design. The steel shell-UHPC composite beam flexural capacity determination method considering the role of the partition is to construct the steel shell-UHPC composite beam structure with partition after four-point loading bending test, determine the failure mechanism, failure characteristics and crack propagation law of the steel shell-UHPC composite beam structure with partition under the action of bending load, establish the cross-section stress diagram of the steel shell-UHPC composite beam structure with partition and calculate the ultimate bending moment. The steel shell-UHPC composite beam structure with partition is established to analyze its failure mechanism, failure characteristics and crack propagation law under the action of bending load, and based on the cross-section stress diagram of the steel shell-UHPC composite beam structure with partition, the ultimate bending moment calculation formula is established to calculate the ultimate bending moment, which can greatly simplify the calculation process while ensuring the calculation accuracy.

Description

Technical Field

[0001] This application relates to the field of architectural design, and more specifically, to a method for determining the flexural bearing capacity of a steel shell-UHPC composite beam that takes into account the effect of a partition. Background Technology

[0002] Ultra-high performance concrete (UHPC) is widely used due to its advantages such as ultra-high strength, high durability, high crack resistance, and self-leveling properties. Steel-shell-concrete composite structures, by replacing ordinary concrete with UHPC, can improve load-bearing capacity and impact resistance. The internal structure of the steel-shell-UHPC composite uses longitudinally and transversely arranged steel partitions to divide the steel shell into compartments, effectively constraining the deformation of the external steel plate during the UHPC pouring stage, improving the stability of the steel shell, and facilitating construction. Simultaneously, the external steel plate of the steel-shell-UHPC composite structure can fully utilize its material properties, sharing bending stress with the UHPC. Furthermore, the steel-shell-UHPC composite structure uses modified clothoid MCL-shaped combination pins, eliminating the flanges of the steel connectors and openings in the web to allow the combination pins to embed into the UHPC and share the load, not only connecting the UHPC to the external steel plate but also increasing the rigidity of the external steel plate.

[0003] Currently, there is a lack of mechanical performance analysis methods for steel shell-UHPC composite beams with longitudinal / transverse diaphragms. The influence of the arrangement of longitudinal and transverse diaphragms on their bending bearing capacity is not considered, and corresponding calculation methods are lacking, which seriously affects the design, construction, and use of steel shell-UHPC composite structures. Summary of the Invention

[0004] The purpose of this application is to provide a method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of diaphragms. This method analyzes the failure mechanism, damage characteristics, and crack propagation law of a steel shell-UHPC composite beam structure with diaphragms under bending loads, and establishes a formula for calculating the ultimate bending moment based on the cross-sectional stress diagram of the steel shell-UHPC composite beam structure with diaphragms. This method can greatly simplify the calculation process while ensuring calculation accuracy.

[0005] This application is implemented as follows:

[0006] This application provides a method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of diaphragms, including the following steps:

[0007] Construct a steel shell-UHPC composite beam structure with diaphragms;

[0008] A four-point loading bending test was conducted on the constructed steel shell-UHPC composite beam structure with diaphragm to determine the failure mechanism, failure characteristics and crack propagation law of the steel shell-UHPC composite beam structure with diaphragm under bending load.

[0009] Establish the cross-sectional stress diagram of the steel shell-UHPC composite beam structure with diaphragm and calculate the ultimate bending moment.

[0010] In some alternative embodiments, the steel shell-UHPC composite beam structure with partitions includes a steel shell and ultra-high performance concrete filled inside the steel shell. Multiple longitudinal partitions and / or multiple transverse partitions are connected inside the steel shell, and multiple longitudinal MCL-shaped combination pins and multiple transverse MCL-shaped combination pins are connected to the outer steel plate of the steel shell.

[0011] In some alternative implementations, when establishing the cross-sectional stress diagram of the diaphragm-equipped steel shell-UHPC composite beam structure, the height of the UHPC compression zone of the diaphragm-equipped steel shell-UHPC composite beam structure is calculated based on the principle of force equilibrium and deformation compatibility conditions. x Then, the ultimate bending moment is calculated based on the moment balance of the cross-section of the steel shell-UHPC composite beam structure with diaphragm.

[0012] In some alternative implementations, when establishing the cross-sectional stress diagram of the diaphragm-equipped steel shell-UHPC composite beam structure... ， When no diaphragm is installed at mid-span or shear studs are installed on the mid-span diaphragm, the internal force is provided by the longitudinal MCL-shaped combination pins in the compression zone. The upper steel plate provides internal force. The longitudinal diaphragm in the pressure zone provides internal force. The UHPC in the pressure zone provides internal force. The sum equals the internal force provided by the lower steel plate. The longitudinal diaphragm in the tension zone provides internal force. The longitudinal MCL-shaped combination pin in the tension zone provides internal force. The tension zone UHPC provides internal force The sum is used to calculate the height of the UHPC pressure zone. x .

[0013] When constructing the cross-sectional force diagram of a steel shell-UHPC composite beam structure with diaphragms, if a transverse diaphragm is installed at mid-span, the internal force is provided by the longitudinal MCL-shaped composite pins in the compression zone. The upper steel plate provides internal force. The longitudinal diaphragm in the pressure zone provides internal force. The UHPC in the pressure zone provides internal force. The sum equals the internal force provided by the lower steel plate. The longitudinal diaphragm in the tension zone provides internal force. The longitudinal MCL-shaped combination pin in the tension zone provides internal force. The sum is used to calculate the height of the UHPC pressure zone. x .

[0014] In some alternative implementations, when constructing the cross-sectional force diagram of the steel shell-UHPC composite beam structure with diaphragms, when the mid-span transverse diaphragm has an opening, the neutral axis is above the opening, and all UHPC within the opening is under tension. Internal forces are provided by the longitudinal MCL-shaped combination pins in the compression zone. The upper steel plate provides internal force. The longitudinal diaphragm in the pressure zone provides internal force. The UHPC in the pressure zone provides internal force. The sum equals the internal force provided by the lower steel plate. The longitudinal diaphragm in the tension zone provides internal force. The longitudinal MCL-shaped combination pin in the tension zone provides internal force. The tensile force provided by the UHPC in the tension zone The sum is used to calculate the height of the UHPC pressure zone. x .

[0015] In some alternative implementations, when constructing the cross-sectional force diagram of the steel shell-UHPC composite beam structure with diaphragms, when the mid-span transverse diaphragm has an opening and the neutral axis is inside the opening, the UHPC portion inside the opening is under tension and the portion under compression. The internal force is provided by the longitudinal MCL-shaped combination pins in the compression zone. The upper steel plate provides internal force. The longitudinal diaphragm in the pressure zone provides internal force. The UHPC in the pressure zone provides internal force. The sum equals the internal force provided by the lower steel plate. The longitudinal diaphragm in the tension zone provides internal force. The longitudinal MCL-shaped combination pin in the tension zone provides internal force. The internal force is provided by the UHPC in the tension zone. The sum is used to calculate the height of the UHPC pressure zone. x .

[0016] In some alternative implementations, when calculating the ultimate bending moment based on the section moment equilibrium of the diaphragm-steel shell-UHPC composite beam structure, if no diaphragm is provided at mid-span or if shear studs are provided on the mid-span diaphragm, the ultimate bending moment is calculated based on the diaphragm-steel shell-UHPC composite beam structure. Provide bending moment for longitudinal MCL-shaped combination pins in the compression zone The UHPC in the compression zone provides bending moment. The longitudinal diaphragm in the compression zone provides bending moment. The lower steel plate provides bending moment. The longitudinal diaphragm in the tension zone provides bending moment. The longitudinal MCL-shaped combination pin in the tension zone provides bending moment. The upper steel plate provides bending moment. The UHPC in the tension zone provides bending moment. The sum is used for calculation.

[0017] In some alternative implementations, when calculating the ultimate bending moment based on the section moment balance of the diaphragm-steel shell-UHPC composite beam structure, if a transverse diaphragm is installed at mid-span, the ultimate bending moment is calculated based on the diaphragm-steel shell-UHPC composite beam structure. Provide bending moment for longitudinal MCL-shaped combination pins in the compression zone The UHPC in the compression zone provides bending moment. The longitudinal diaphragm in the compression zone provides bending moment. The lower steel plate provides bending moment. The longitudinal diaphragm in the tension zone provides bending moment. The longitudinal MCL-shaped combination pin in the tension zone provides bending moment. and the upper steel plate provide bending moment The sum is used for calculation.

[0018] In some alternative implementations, when calculating the ultimate bending moment based on the section moment equilibrium of the diaphragm-steel shell-UHPC composite beam structure:

[0019] With an opening in the mid-span diaphragm and the neutral axis above the opening, the ultimate bending moment of the steel shell-UHPC composite beam structure with diaphragm is calculated. Provide bending moment for longitudinal MCL-shaped combination pins in the compression zone The UHPC in the compression zone provides bending moment. The longitudinal diaphragm in the compression zone provides bending moment. The lower steel plate provides bending moment. The longitudinal diaphragm in the tension zone provides bending moment. The longitudinal MCL-shaped combination pin in the tension zone provides bending moment. The upper steel plate provides bending moment. The bending moment provided by the UHPC in the tension zone of the mid-span diaphragm opening Calculate the sum;

[0020] With an opening in the mid-span diaphragm and the neutral axis within the opening, the ultimate bending moment of the steel shell-UHPC composite beam structure with diaphragm is determined. Provide bending moment for longitudinal MCL-shaped combination pins in the compression zone The UHPC in the compression zone provides bending moment. The longitudinal diaphragm in the compression zone provides bending moment. The lower steel plate provides bending moment. The longitudinal diaphragm in the tension zone provides bending moment. The longitudinal MCL-shaped combination pin in the tension zone provides bending moment. The upper steel plate provides bending moment. The bending moment provided by the UHPC in the tension zone of the mid-span diaphragm opening The sum is used for calculation.

[0021] In some alternative implementations, the uniform ultimate bending moment based on the UHPC tensile contribution rate is calculated for the diaphragm-coated steel shell-UHPC composite beam structure using the following formula. :

[0022] ;

[0023] In the formula, Provides bending moment for the longitudinal MCL-shaped combination pin in the compression zone; Provide bending moment for the UHPC in the compression zone; Provide bending moment for the longitudinal diaphragm in the compression zone; Provide bending moment for the lower steel plate; Provide bending moment for the upper steel plate; Provide bending moment for the longitudinal diaphragm in the tension zone; Provides bending moment for longitudinal MCL-shaped combination pins in the tension zone; , This represents the effective tensile area of ​​the UHPC. This refers to the area of ​​the UHPC in the tension zone without diaphragms. ; This is the distance between the neutral axis and the center of the tension zone of the UHPC; This represents the tensile strength of UHPC.

[0024] The beneficial effects of this application are as follows: The method for determining the flexural bearing capacity of a steel-shell-UHPC composite beam considering the effect of diaphragms provided in this application involves constructing a steel-shell-UHPC composite beam structure with diaphragms, conducting a four-point loading flexural test on the constructed diaphragm-equipped steel-shell-UHPC composite beam structure, determining the failure mechanism, damage characteristics, and crack propagation law of the diaphragm-equipped steel-shell-UHPC composite beam structure under bending load, proposing a cross-sectional stress diagram of the diaphragm-equipped steel-shell-UHPC composite beam structure, and calculating the ultimate bending moment. This method, by establishing a steel-shell-UHPC composite beam structure with diaphragms and analyzing its failure mechanism, damage characteristics, and crack propagation law under bending load, and establishing a formula for calculating the ultimate bending moment based on the cross-sectional stress diagram of the diaphragm-equipped steel-shell-UHPC composite beam structure, significantly simplifies the calculation process while ensuring the accuracy of the ultimate bending moment calculation for the diaphragm-equipped steel-shell-UHPC composite beam structure. Attached Figure Description

[0025] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0026] Figure 1 A flowchart illustrating the method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of a diaphragm, provided in an embodiment of this application.

[0027] Figure 2 A three-dimensional spatial perspective view of the steel shell-UHPC composite beam structure with diaphragm constructed in the method for determining the flexural bearing capacity of the steel shell-UHPC composite beam considering the effect of the diaphragm provided in the embodiments of this application;

[0028] Figure 3 A schematic diagram of the SUSCB-1 structure designed in the method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of a diaphragm, provided in the embodiments of this application;

[0029] Figure 4 A schematic diagram of the SUSCB-2 structure designed in the method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of a diaphragm, as provided in the embodiments of this application;

[0030] Figure 5 A schematic diagram of the SUSCB-3 structure designed in the method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of a diaphragm, provided in the embodiments of this application;

[0031] Figure 6 A schematic diagram of the SUSCB-4 structure designed in the method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of a diaphragm, provided in the embodiments of this application;

[0032] Figure 7 A schematic diagram of the SUSCB-5 structure designed in the method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of a diaphragm, provided in the embodiments of this application;

[0033] Figure 8 A schematic diagram of the SUSCB-6 structure designed in the method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of a diaphragm, provided in the embodiments of this application;

[0034] Figure 9 A schematic diagram of the SUSCB-7 structure designed in the method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of a diaphragm, as provided in the embodiments of this application;

[0035] Figure 10 A schematic diagram of the SUSCB-8 structure designed in the method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of a diaphragm, provided in the embodiments of this application;

[0036] Figure 11 A schematic diagram of a displacement gauge installed on a steel-shell-UHPC composite beam structural specimen with diaphragms in the method for determining the flexural bearing capacity of a steel-shell-UHPC composite beam considering the effect of diaphragms provided in the embodiments of this application.

[0037] Figure 12 A schematic diagram of a structure in which strain gauges are installed on the upper steel plate of a steel shell-UHPC composite beam specimen with diaphragms, in the method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of diaphragms provided in the embodiments of this application.

[0038] Figure 13 A schematic diagram of a steel shell-UHPC composite beam specimen with diaphragms, provided in the method for determining the flexural bearing capacity of the steel shell-UHPC composite beam considering the effect of the diaphragm, in an embodiment of this application;

[0039] Figure 14 The method for determining the flexural bearing capacity of a steel-shell-UHPC composite beam considering the effect of diaphragms provided in the embodiments of this application is a mid-span load-deflection curve for a steel-shell-UHPC composite beam structural specimen with longitudinal diaphragms when longitudinal diaphragms are set;

[0040] Figure 15 The method for determining the flexural bearing capacity of a steel-shell-UHPC composite beam considering the effect of diaphragms provided in the embodiments of this application is a mid-span load-deflection curve for a steel-shell-UHPC composite beam structural specimen with diaphragms when no longitudinal diaphragms are provided;

[0041] Figure 16 The method for determining the flexural bearing capacity of a steel-shell-UHPC composite beam considering the effect of diaphragms provided in the embodiments of this application includes stress distribution diagrams at the mid-span section of a steel-shell-UHPC composite beam structure with diaphragms when there are no transverse diaphragms and when shear studs are arranged on the transverse diaphragms.

[0042] Figure 17 The stress distribution diagram at the mid-span section of the steel shell-UHPC composite beam structure with diaphragms when transverse diaphragms are set in the method for determining the flexural bearing capacity of the steel shell-UHPC composite beam considering the effect of diaphragms provided in the embodiments of this application;

[0043] Figure 18 The method for determining the flexural bearing capacity of a steel-shell-UHPC composite beam considering the effect of diaphragms provided in this application provides a stress distribution diagram of the neutral axis at the mid-span section above the opening of the diaphragm in the steel-shell-UHPC composite beam structure with diaphragms when the diaphragm has an opening;

[0044] Figure 19 The stress distribution diagram of the neutral axis at the mid-span section within the opening of the diaphragm in the diaphragm of the steel shell-UHPC composite beam structure with diaphragm, when the diaphragm has an opening, in the method for determining the flexural bearing capacity of the steel shell-UHPC composite beam considering the effect of the diaphragm provided in the embodiments of this application.

[0045] Figure 20 The method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of a diaphragm, as provided in the embodiments of this application, calculates the ratio of the calculated value to the experimental result.

[0046] In the diagram: 100, steel shell-UHPC composite beam structure with diaphragm; 110, upper steel plate; 120, lower steel plate; 130, side steel plate; 140, end steel plate; 150, longitudinal diaphragm; 160, transverse diaphragm; 170, longitudinal MCL-shaped combination pin; 180, transverse MCL-shaped combination pin. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0048] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0049] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0050] In the description of this application, it should be noted that the terms "center," "upper," "lower," "left," "right," "vertical," "horizontal," "inner," and "outer," etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of this application is in use. They are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this application. In addition, the terms "first," "second," and "third," etc., are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0051] Furthermore, terms such as "horizontal," "vertical," and "sag" do not imply that components must be absolutely horizontal or suspended, but rather that they can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal relative to "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0052] In the description of this application, it should also be noted that, unless otherwise expressly specified and limited, the terms "set up," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances.

[0053] In this application, unless otherwise expressly specified and limited, "above" or "below" the second feature can include direct contact between the first and second features, or contact between the first and second features through another feature between them. Furthermore, "above," "over," and "on top" of the second feature includes the first feature being directly above or diagonally above the second feature, or simply indicates that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature includes the first feature being directly below or diagonally below the second feature, or simply indicates that the first feature is at a lower horizontal level than the second feature.

[0054] The following describes in further detail the features and performance of the method for determining the flexural bearing capacity of the steel shell-UHPC composite beam considering the effect of the diaphragm, with reference to embodiments.

[0055] like Figure 1 As shown in the embodiment of this application, a method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of a diaphragm is provided, which includes the following steps:

[0056] Step S1: To study the bending performance of the diaphragm-equipped steel shell-UHPC composite beam, the structural design of the diaphragm-equipped steel shell-UHPC composite beam is first carried out, and the diaphragm-equipped steel shell-UHPC composite beam structure is constructed; wherein, as... Figure 2As shown, the steel shell-UHPC composite beam structure 100 with diaphragms includes a steel shell composed of an upper steel plate 110, a lower steel plate 120, two side steel plates 130, and two end steel plates 140, and ultra-high performance concrete (UHPC) filled inside the steel shell. Longitudinal diaphragms 150 and transverse diaphragms 160 are connected inside the steel shell. Longitudinal MCL-shaped combination pins 170 and transverse MCL-shaped combination pins 180 are connected to the outer steel plates of the steel shell at intervals. In other optional embodiments, the steel shell-UHPC composite beam structure with diaphragms may also include only longitudinal diaphragms 150 or only transverse diaphragms 160.

[0057] When designing the steel shell-UHPC composite beam structure with diaphragms, the steel shell-UHPC composite beam structure with diaphragms was divided into two groups based on the arrangement of the longitudinal and transverse diaphragms. One group was equipped with longitudinal diaphragms, and the other group was not equipped with longitudinal diaphragms. The eight specimens in the two groups were named SUSCB-1, SUSCB-2, SUSCB-3, SUSCB-4, SUSCB-5, SUSCB-6, SUSCB-7, and SUSCB-8, respectively.

[0058] like Figure 3 As shown, SUSCB-1 is equipped with both spaced-apart diaphragms and mid-span diaphragms.

[0059] like Figure 4 As shown, the SUSCB-2 eliminates the mid-span diaphragm compared to the SUSCB-1.

[0060] like Figure 5 As shown, the SUSCB-3 has two holes in the mid-span diaphragm, each measuring 100mm × 140mm, based on the SUSCB-1.

[0061] like Figure 6 As shown, SUSCB-4 is based on SUSCB-1 and has 8 pairs of shear studs with a horizontal and vertical spacing of 80mm, a diameter of 16mm and a length of 80mm on the transverse diaphragm. The shear studs are designed to be fully pull-out resistant.

[0062] like Figure 7 As shown, SUSCB-5 adds longitudinal diaphragms to the SUSCB-1.

[0063] like Figure 8 As shown, the SUSCB-6 adds longitudinal diaphragms to the SUSCB-2.

[0064] like Figure 9 As shown, SUSCB-7 adds longitudinal diaphragms to SUSCB-5, while also opening holes in the transverse diaphragms, with dimensions of 200mm × 140mm.

[0065] like Figure 10 As shown, the SUSCB-8 adds longitudinal diaphragms to the SUSCB-4.

[0066] The steel shell-UHPC composite beam structure with diaphragms has a length of 4000mm, a clear span of 3700mm, and a height and width of 330mm. The thickness of each diaphragm, as well as the thickness of the upper steel plate, lower steel plate, two side steel plates, and two end steel plates, is 9.75mm. The thickness of the MCL-shaped combination pins is 7.5mm. The spacing between the transverse MCL-shaped combination pin connectors is 240mm.

[0067] Step S2: The diaphragm-equipped steel shell-UHPC composite beam structure was subjected to an ultimate bending moment test using a four-point loading method to determine the failure mechanism, damage characteristics, and crack propagation law of the diaphragm-equipped steel shell-UHPC composite beam structure under bending load.

[0068] Load test: A steel distribution beam was placed on the diaphragm-equipped steel shell-UHPC composite beam structure specimen, and a four-point bending loading test was conducted on the diaphragm-equipped steel shell-UHPC composite beam structure. The load borne by the diaphragm-equipped steel shell-UHPC composite beam structure was measured by the force sensor equipped with the 1000t electro-hydraulic servo structural testing machine.

[0069] Deflection test: Displacement gauges with a range of 100 mm were placed at the mid-span, the centers of the two loading positions, and the supports of the steel shell-UHPC composite beam structure specimen with diaphragms, and numbered LVDT1-LVDT5 respectively. Figure 11 As shown. Displacement gauges LVDT1 and LVDT5 mainly record the vertical displacement at the support location, LVDT3 is used to measure the mid-span displacement as a function of load, and LVDT2 and LVDT4 are used to measure the vertical displacement at the loading point of the steel shell-UHPC composite beam.

[0070] Strain test: Five strain gauges were placed at the mid-span of both the upper and lower steel plates of the diaphragm-equipped steel shell-UHPC composite beam structure. The upper steel plates were numbered T1-T5, and the lower steel plate strain gauges were numbered B1-B5. Figure 12 and Figure 13 As shown, the strain gauges are spaced 60mm apart to measure the tensile and compressive strain of the steel plate under load. Five strain gauges are equidistantly arranged within the height range of the UHPC at the mid-span cross-section of the diaphragm-equipped steel shell-UHPC composite beam structure to measure the strain of the UHPC at different cross-sectional heights under load. The concrete strain gauges are BX120-80AA model, with a grid width × grid length of 3mm × 80mm; the steel strain gauges are BX120-3AA model, with a grid width × grid length of 3mm × 2mm; the resistance of all strain gauges is 120Ω.

[0071] The four-point bending loading test procedure is as follows:

[0072] Before the formal loading, a preload of 10% of the estimated ultimate load was applied to debug the equipment and sensors, ensure their normal operation, and eliminate gaps between components such as supports and distribution beams. Then, the formal loading was carried out. Before reaching 80% of the estimated ultimate load, load-controlled loading was used at a loading rate of 10 kN / min, followed by displacement-controlled loading at a loading rate of 0.8 mm / min. Crack propagation and specimen deformation were recorded throughout the process until the end of the test.

[0073] The experimental phenomena are as follows:

[0074] All diaphragm-coated steel-shell UHPC composite beam structural members exhibited bending failure. The crack development process and distribution were essentially the same for each diaphragm-coated steel-shell UHPC composite beam structure, with cracks primarily vertically distributed and concentrated in the pure bending segment at failure. In the initial loading stage, the initial cracks occurred at the transverse MCL-shaped composite pins. As the load increased, the cracks gradually extended upwards, exhibiting a tree-like shape. Furthermore, cracks also appeared between the transverse MCL-shaped composite pins, gradually extending upwards, but notably, these cracks were shorter or appeared as independent cracks. As the load continued to increase, while the cracks gradually extended upwards, cracks also gradually appeared between the transverse MCL-shaped composite pins. During the yielding stage of the diaphragm-coated steel-shell UHPC composite beam structure, a gap formed between the transverse MCL-shaped composite pins and the UHPC contact surface, becoming increasingly pronounced with increasing load. A steel ruler was used to measure the gap, which could be directly inserted into the gap between the transverse MCL-shaped composite pins and the UHPC. The gap width was approximately 2 mm.

[0075] The experimental results are analyzed as follows:

[0076] In the initial loading stage, the vertical displacement changes linearly with the load, and the tensile UHPC has not yet cracked. When 20% of the ultimate load is reached, bending cracks gradually appear in the tensile UHPC, but the curve still maintains a linear growth, as shown in the figure. Figure 14 and Figure 15As shown, with the continued increase in load, vertical cracks appeared at each transverse MCL-shaped composite pin in the pure bending section and continued to develop. The transverse MCL-shaped composite pins separated from the UHPC contact surface, and the slope of the curve gradually decreased with the continued increase in load. Gaps appeared at the contact surface between the diaphragm and the UHPC, and the member entered the plastic stage. With continued loading, the cracks expanded rapidly, and vertical cracks also appeared in the UHPC between the transverse MCL-shaped composite pins in the tension zone, and the vertical deflection of the member increased significantly. In the final stage of loading, the gaps between the transverse MCL-shaped composite pin-UHPC contact surface and the diaphragm-UHPC contact surface continued to increase. The ultimate bearing capacity of the steel shell-UHPC composite beam structure with diaphragm still showed an increasing trend, but the rate of increase was extremely slow, and the overall structure had good ductility.

[0077] Step S3: Establish the cross-sectional force equations for the steel shell-UHPC composite beam structure with diaphragms and calculate the ultimate bending moment;

[0078] First, we make the following assumptions:

[0079] (1) Plane section assumption;

[0080] (2) The steel reaches its yield strength, and the UHPC material reaches its ultimate stress state;

[0081] (3) Ignore the effect of relative slip at the steel-UHPC interface on the bending bearing capacity;

[0082] (4) The stress in the compression zone concrete is triangularly distributed, and the tensile stress of the tension zone UHPC is also taken into account.

[0083] I. Calculate the height of the UHPC compression zone in a steel shell-UHPC composite beam structure with diaphragms based on the principle of force equilibrium and deformation compatibility conditions. x ;

[0084] 1. For example Figure 16 The diagram shows the stress distribution at the mid-span section of a steel shell-UHPC composite beam structure with diaphragms, with and without diaphragms and with shear studs on the diaphragms. When there are no diaphragms at mid-span or shear studs are installed on the mid-span diaphragms, the following force balance formula is satisfied:

[0085] (1)

[0086] In the formula, Provides internal force for the longitudinal MCL-shaped combination pins in the pressure zone. ; Provide internal force to the upper steel plate, ; Provides internal forces to the longitudinal diaphragms in the pressure zone; Provide internal forces to the UHPC in the compression zone. ; Provides internal force to the lower steel plate. ; Provide internal forces to the longitudinal diaphragm in the tension zone. ; Provides internal force for the longitudinal MCL-shaped combination pin in the tension zone. ; Provide internal force to the UHPC in the tension zone, ;

[0087] in, For the thickness of MCL-type combination pins, The height of the lower steel rib of the MCL-type combination pin. The compressive yield strength of the MCL-shaped composite pin. The thickness of the upper steel plate. The longitudinal number of MCL-shaped combination pins in the pressure zone. The thickness of the longitudinal diaphragm. The height of the UHPC pressure zone. The compressive yield strength of the longitudinal diaphragm. The height of the UHPC section. The tensile yield strength of the longitudinal diaphragm. For the tensile yield strength of the MCL-shaped composite pin, The longitudinal number of MCL-shaped combination pins in the tension zone. This represents the axial compressive strength of the UHPC. b represents the yield strength of the upper steel plate; b represents the width of the steel shell-UHPC composite beam structure specimen with diaphragm. The axial compressive strength of UHPC; The yield strength of the lower steel plate; This refers to the thickness of the lower steel plate. The tensile yield strength of the MCL-shaped composite pin; The tensile strength of UHPC; The effective height of the contact surface between the MCL-shaped combination pin and the UHPC;

[0088] 2. For example Figure 17 The diagram shows the stress distribution at the mid-span section of a steel shell-UHPC composite beam structure with diaphragms. When diaphragms are installed at the mid-span, the following force balance formula is satisfied:

[0089] ;

[0090] In the formula, Provides internal force for the longitudinal MCL-shaped combination pin in the pressure zone; Provides internal force to the upper steel plate; Provides internal forces to the longitudinal diaphragms in the pressure zone; Provides internal forces to the UHPC in the compression zone; Provides internal force to the lower steel plate; Provides internal forces to the longitudinal diaphragm in the tension zone; Provides internal force for the longitudinal MCL-shaped combination pin in the tension zone;

[0091] 3. When the transverse diaphragm at the mid-span is perforated, the calculation formula for the bending bearing capacity of the steel shell-UHPC composite beam is divided into two cases: the neutral axis is inside the hole and the neutral axis is above the hole.

[0092] Figure 18 The diagram shows the stress distribution at the mid-span section of a steel shell-UHPC composite beam structure with a diaphragm, where the neutral axis is located above the diaphragm opening. The UHPC within the mid-span diaphragm opening is entirely under tension, satisfying the following force equilibrium formula:

[0093] (3)

[0094] In the formula, Provides internal force for the longitudinal MCL-shaped combination pin in the pressure zone; Provides internal force to the upper steel plate; Provides internal forces to the longitudinal diaphragms in the pressure zone; Provides internal forces to the UHPC in the compression zone; Provides internal force to the lower steel plate; Provides internal forces to the longitudinal diaphragm in the tension zone; Provides internal force for the longitudinal MCL-shaped combination pin in the tension zone; The tensile force provided by the UHPC tension zone when the neutral axis is above the opening in the mid-span diaphragm. , The tensile strength of UHPC; The area of ​​the opening in the mid-span diaphragm;

[0095] like Figure 19 The diagram shows the stress distribution at the mid-span section of a steel shell-UHPC composite beam structure with a diaphragm when the diaphragm has an opening. The neutral axis is located within the mid-span diaphragm opening, and the UHPC portion within the opening is under tension while the portion under compression satisfies the following force equilibrium formula:

[0096] (4)

[0097] In the formula, Provides internal force for the longitudinal MCL-shaped combination pin in the pressure zone; Provides internal force to the upper steel plate; Provides internal forces to the longitudinal diaphragms in the pressure zone; Provides internal forces to the UHPC in the compression zone; Provides internal force to the lower steel plate; Provides internal forces to the longitudinal diaphragm in the tension zone; Provides internal force for the longitudinal MCL-shaped combination pin in the tension zone; To provide internal forces to the tension zone UHPC when the neutral axis is within the opening in the mid-span transverse diaphragm, ; The tensile strength of UHPC; This represents the effective tensile area of ​​the UHPC.

[0098] II. The ultimate bending moment of the steel shell-UHPC composite beam structure with diaphragm is obtained based on the moment equilibrium of the cross section:

[0099] During the steel plate cutting process, the steel pins in the MCL-shaped combination pins interlock and their areas are symmetrical along the center line. Therefore, when determining the effective height of the contact surface between the MCL-shaped combination pins and the UHPC, the geometric center line is taken as the effective height, and the contribution of the lower steel ribs of the MCL-shaped combination pins to the bending bearing capacity is included in the calculation of the outer steel plate.

[0100] 1. When there is no diaphragm at mid-span or the mid-span diaphragm is fitted with shear studs, the following bending moment calculation formula shall be satisfied:

[0101] (5)

[0102] In the formula, The ultimate bending moment of the steel shell-UHPC composite beam structure with diaphragms; Provides bending moment for the longitudinal MCL-shaped combination pin in the compression zone. ; Provide bending moment for the compression zone UHPC, ; Provide bending moment for the longitudinal diaphragm in the compression zone. ; Provide bending moment for the lower steel plate. ; Provide bending moment for the longitudinal diaphragm in the tension zone. ; Provides bending moment for the longitudinal MCL-shaped combination pin in the tension zone. ; Provide bending moment for the upper steel plate. ; Provide bending moment for the UHPC in the tension zone. ;

[0103] When shear studs are arranged in the mid-span diaphragm, since the full pull-out connection was considered in the experimental design, the flexural bearing capacity of the steel shell-UHPC composite beam structure with diaphragm is calculated using the same formula as that without diaphragm.

[0104] When a transverse diaphragm is installed at the mid-span, the following bending moment calculation formula must be satisfied:

[0105] (6)

[0106] In the formula, The ultimate bending moment of the steel shell-UHPC composite beam structure with diaphragms; Provides bending moment for the longitudinal MCL-shaped combination pin in the compression zone; Provide bending moment for the UHPC in the compression zone; Provide bending moment for the longitudinal diaphragm in the compression zone; Provide bending moment for the lower steel plate; Provide bending moment for the longitudinal diaphragm in the tension zone; Provides bending moment for longitudinal MCL-shaped combination pins in the tension zone; Provide bending moment for the upper steel plate;

[0107] When an opening is made in the mid-span diaphragm, the following bending moment calculation formula must be satisfied:

[0108] i. When the neutral axis is above the opening in the mid-span diaphragm (the UHPC inside the opening in the mid-span diaphragm is under tension):

[0109] (7)

[0110] In the formula, The ultimate bending moment of the steel shell-UHPC composite beam structure with diaphragms; Provides bending moment for the longitudinal MCL-shaped combination pin in the compression zone; Provide bending moment for the UHPC in the compression zone; Provide bending moment for the longitudinal diaphragm in the compression zone; Provide bending moment for the lower steel plate; Provide bending moment for the longitudinal diaphragm in the tension zone; Provides bending moment for longitudinal MCL-shaped combination pins in the tension zone; Provide bending moment for the upper steel plate; Provide bending moment for the UHPC under tension inside the hole. , ;

[0111] ii. The neutral shaft is located within the opening in the mid-span diaphragm (the UHPC portion within the opening in the mid-span diaphragm is under tension, and the portion is under compression):

[0112] (8)

[0113] In the formula, The ultimate bending moment of the steel shell-UHPC composite beam structure with diaphragms; Provides bending moment for the longitudinal MCL-shaped combination pin in the compression zone; Provide bending moment for the UHPC in the compression zone; Provide bending moment for the longitudinal diaphragm in the compression zone; Provide bending moment for the lower steel plate; Provide bending moment for the longitudinal diaphragm in the tension zone; Provides bending moment for longitudinal MCL-shaped combination pins in the tension zone; Provide bending moment for the upper steel plate; Provide bending moment for the UHPC under tension inside the hole. ; ;

[0114] III. The tensile force provided by the UHPC varies depending on the different arrangements of the mid-span diaphragms. Therefore, the calculation of flexural bearing capacity is divided into the above four cases. To quantitatively represent the influence of the UHPC in the tension zone on the flexural bearing capacity and to unify the calculation formulas for the above four working conditions, the concept of UHPC tensile contribution rate is proposed, resulting in a unified ultimate bending moment calculation formula for diaphragm-supported steel shell-UHPC composite beam structures based on the UHPC tensile contribution rate:

[0115] (9)

[0116] In the formula, The ultimate bending moment of the steel shell-UHPC composite beam structure with diaphragms; Provides bending moment for the longitudinal MCL-shaped combination pin in the compression zone; Provide bending moment for the UHPC in the compression zone; Provide bending moment for the longitudinal diaphragm in the compression zone; Provide bending moment for the lower steel plate; Provide bending moment for the longitudinal diaphragm in the tension zone; Provides bending moment for longitudinal MCL-shaped combination pins in the tension zone; Provide bending moment for the upper steel plate; , Contribution rate of UHPC tensile stress; ; This refers to the area of ​​the UHPC in the tension zone without diaphragms. ; The bending moment provided for a tension UHPC; This is the distance between the neutral axis and the center of the tension zone of the UHPC;

[0117] In addition, for steel shell-UHPC composite beam structures with diaphragms but without longitudinal diaphragms, the stress diagram corresponding to the longitudinal diaphragms is removed in the above calculation method, and the corresponding part of the longitudinal diaphragms is removed in the above ultimate bending moment calculation formula, while the rest remains unchanged.

[0118] Comparison of calculation method and experimental results for the steel shell-UHPC composite beam structure with diaphragm provided in this application embodiment:

[0119] To verify the correctness of the proposed theoretical model, the ratio of the calculated values ​​of the calculation method for the diaphragm-equipped steel shell-UHPC composite beam structure provided in the embodiments of this application to the experimental results was compared. Figure 20 As shown, the average error of the proposed theoretical model is 3%, and the COV is 0.01. Within the range of changes in the parameters of the components studied, the calculated values ​​of the proposed theoretical model are in good agreement with the experimental values.

[0120] The embodiments described above are some, but not all, of the embodiments of this application. The detailed description of the embodiments of this application is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

Claims

1. A method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of diaphragms, characterized in that, Includes the following steps: Construct a steel shell-UHPC composite beam structure with partitions; the steel shell-UHPC composite beam structure with partitions includes a steel shell and ultra-high performance concrete filled in the steel shell, the steel shell is connected with multiple longitudinal partitions and / or multiple transverse partitions, and the outer steel plate of the steel shell is connected with multiple longitudinal MCL-shaped combination pins and multiple transverse MCL-shaped combination pins. A four-point loading bending test was conducted on the constructed steel shell-UHPC composite beam structure with diaphragm to determine the failure mechanism, failure characteristics and crack propagation law of the steel shell-UHPC composite beam structure with diaphragm under bending load. Establish the cross-sectional stress diagram of the steel shell-UHPC composite beam structure with diaphragm and calculate the ultimate bending moment; When constructing the cross-sectional stress diagram of a diaphragm-equipped steel shell-UHPC composite beam structure, the height of the UHPC compression zone in the diaphragm-equipped steel shell-UHPC composite beam structure is calculated based on the principle of force equilibrium and deformation compatibility conditions. x Then, the ultimate bending moment is calculated based on the moment balance of the cross-section of the steel shell-UHPC composite beam structure with diaphragm. When no diaphragm is installed at mid-span or shear studs are installed on the mid-span diaphragm, the internal force is provided by the longitudinal MCL-shaped combination pins in the compression zone. The upper steel plate provides internal force. The longitudinal diaphragm in the pressure zone provides internal force. The UHPC in the pressure zone provides internal force. The sum equals the internal force provided by the lower steel plate. The longitudinal diaphragm in the tension zone provides internal force. The longitudinal MCL-shaped combination pin in the tension zone provides internal force. The tension zone UHPC provides internal force The sum is used to calculate the height of the UHPC pressure zone. x ; When a transverse diaphragm is installed at the mid-span, the internal force is provided by the longitudinal MCL-shaped combination pins in the compression zone. The upper steel plate provides internal force. The longitudinal diaphragm in the pressure zone provides internal force. The UHPC in the pressure zone provides internal force. The sum equals the internal force provided by the lower steel plate. The longitudinal diaphragm in the tension zone provides internal force. The longitudinal MCL-shaped combination pin in the tension zone provides internal force. The sum is used to calculate the height of the UHPC pressure zone. x ; When the transverse diaphragm is perforated, the neutral shaft is above the perforation. When all the UHPC inside the perforation is under tension, the internal force is provided by the longitudinal MCL-shaped combination pin in the compression zone. The upper steel plate provides internal force. The longitudinal diaphragm in the pressure zone provides internal force. The UHPC in the pressure zone provides internal force. The sum equals the internal force provided by the lower steel plate. The longitudinal diaphragm in the tension zone provides internal force. The longitudinal MCL-shaped combination pin in the tension zone provides internal force. The tensile force provided by the UHPC in the tension zone The sum is used to calculate the height of the UHPC pressure zone. x ; When the transverse diaphragm has a hole and the neutral shaft is inside the hole, the UHPC portion inside the hole is under tension and the portion under compression. The internal force is provided by the longitudinal MCL-shaped combination pin in the compression zone. The upper steel plate provides internal force. The longitudinal diaphragm in the pressure zone provides internal force. The UHPC in the pressure zone provides internal force. The sum equals the internal force provided by the lower steel plate. The longitudinal diaphragm in the tension zone provides internal force. The longitudinal MCL-shaped combination pin in the tension zone provides internal force. The UHPC in the tension zone provides internal force. The sum is used to calculate the height of the UHPC pressure zone. x .

2. The method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of diaphragms according to claim 1, characterized in that, When calculating the ultimate bending moment based on the section moment equilibrium of a steel shell-UHPC composite beam structure with diaphragms, if there are no diaphragms at mid-span or if shear studs are installed on the mid-span diaphragms, the ultimate bending moment of the steel shell-UHPC composite beam structure with diaphragms is calculated. Provide bending moment for longitudinal MCL-shaped combination pins in the compression zone The UHPC in the compression zone provides bending moment. The longitudinal diaphragm in the compression zone provides bending moment. The lower steel plate provides bending moment. The longitudinal diaphragm in the tension zone provides bending moment. The longitudinal MCL-shaped combination pin in the tension zone provides bending moment. The upper steel plate provides bending moment. The UHPC in the tension zone provides bending moment. The sum is used for calculation.

3. The method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of diaphragms according to claim 2, characterized in that, When calculating the ultimate bending moment based on the section moment equilibrium of a steel shell-UHPC composite beam structure with diaphragms, if a transverse diaphragm is installed at mid-span, the ultimate bending moment of the steel shell-UHPC composite beam structure with diaphragms should be calculated. Provide bending moment for longitudinal MCL-shaped combination pins in the compression zone The UHPC in the compression zone provides bending moment. The longitudinal diaphragm in the compression zone provides bending moment. The lower steel plate provides bending moment. The longitudinal diaphragm in the tension zone provides bending moment. The longitudinal MCL-shaped combination pin in the tension zone provides bending moment. and the upper steel plate provide bending moment The sum is used for calculation.

4. The method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of diaphragms according to claim 3, characterized in that, When calculating the ultimate bending moment based on the moment equilibrium of the cross-section of a steel shell-UHPC composite beam structure with diaphragms: With an opening in the mid-span diaphragm and the neutral axis above the opening, the ultimate bending moment of the steel shell-UHPC composite beam structure with diaphragm is calculated. Provide bending moment for longitudinal MCL-shaped combination pins in the compression zone The UHPC in the compression zone provides bending moment. The longitudinal diaphragm in the compression zone provides bending moment. The lower steel plate provides bending moment. The longitudinal diaphragm in the tension zone provides bending moment. The longitudinal MCL-shaped combination pin in the tension zone provides bending moment. The upper steel plate provides bending moment. The bending moment provided by the UHPC in the tension zone of the mid-span diaphragm opening Calculate the sum; With an opening in the mid-span diaphragm and the neutral axis within the opening, the ultimate bending moment of the steel shell-UHPC composite beam structure with diaphragm is determined. Provide bending moment for longitudinal MCL-shaped combination pins in the compression zone The UHPC in the compression zone provides bending moment. The longitudinal diaphragm in the compression zone provides bending moment. The lower steel plate provides bending moment. The longitudinal diaphragm in the tension zone provides bending moment. The longitudinal MCL-shaped combination pin in the tension zone provides bending moment. The upper steel plate provides bending moment. The bending moment provided by the UHPC in the tension zone of the mid-span diaphragm opening The sum is used for calculation.

5. The method for determining the flexural bearing capacity of a steel shell-UHPC composite beam considering the effect of a diaphragm, as described in claim 2, 3, or 4, is characterized in that... The uniform ultimate bending moment based on the tensile contribution rate of UHPC in a steel shell-UHPC composite beam structure with diaphragms is calculated using the following formula. : ； In the formula, Provides bending moment for the longitudinal MCL-shaped combination pin in the compression zone; Provide bending moment for the compression zone UHPC; Provide bending moment for the longitudinal diaphragm in the compression zone; Provide bending moment for the lower steel plate; Provide bending moment for the upper steel plate; Provide bending moment for the longitudinal diaphragm in the tension zone; Provides bending moment for longitudinal MCL-shaped combination pins in the tension zone; , This represents the effective tensile area of ​​the UHPC. This refers to the area of ​​the UHPC in the tension zone without diaphragms. ; This is the distance between the neutral axis and the center of the tension zone of the UHPC; This represents the tensile strength of UHPC.

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