A variable density uhcp core column plate based on shear lag effect optimization

Abstract

The present application relates to the technical field of fabricated building components, and proposes a variable-density UHPC core column plate based on shear lag effect optimization. The core column plate is sequentially provided with a support densification area, a transition area and a mid-span sparse area along the span direction. In the support densification area, the relative density of the core column is greater than the economic threshold to form a "quasi-solid" structure. In the mid-span sparse area, the relative density of the core column is controlled at 2.5% to 3% to reduce the dead weight of the structure and improve the material utilization. Longitudinal ribs are arranged along the span direction, and the width of the longitudinal ribs changes with the bending moment envelope. The topology optimization arrangement comprehensively considers the shear lag effect and the economic threshold of the core column density, realizes the on-demand allocation of rigidity and strength, improves the bearing capacity and ductility, reduces the dead weight and the amount of materials, and is suitable for fabricated bridge deck plates and floor systems.

Description

Technical Field

[0001] This invention relates to the field of prefabricated building component technology, specifically to a variable density ultra-high performance concrete (UHPC) core column slab optimized based on shear hysteresis effect, which is suitable for prefabricated bridge decks, floor slabs and other slab components that are mainly subjected to bending, taking into account high load-bearing capacity, durability and material economy. Background Technology

[0002] In recent years, UHPC (Ultra-High-Pressure Polymer) has seen rapid development in bridge and building engineering applications due to its ultra-high compressive strength, excellent crack resistance, and durability. Typical forms include UHPC composite slabs, UHPC box girder top slabs, and UHPC hollow slabs. By arranging cavities or core columns inside the slab, the self-weight can be reduced while ensuring stiffness and load-bearing capacity, making it an important development direction for current prefabricated bridge deck and floor systems.

[0003] In the existing technology, common UHPC hollow boards or core columns mainly have the following characteristics and shortcomings:

[0004] 1. Uniform arrangement of core columns or cavities: Most existing hollow slabs or core column slabs use regular and uniform arrangements of holes or core columns along the span and within the slab surface to simplify molds and production processes. Although this can reduce self-weight to some extent, such uniform arrangement does not fully consider the differences in internal force distribution and shear hysteresis effect of the component, resulting in a tendency for the stiffness and strength configuration of the mid-span bending moment control zone and the support shear force control zone to be averaged out, and the material utilization efficiency is limited.

[0005] 2. Insufficient consideration of shear lag effect: In box girders and wide-flange plates, the shear lag effect leads to uneven distribution of normal stress along the transverse direction of the flange plate, resulting in increased stress in local areas. Related studies have shown that UHPC box girders or composite plates exhibit significant shear lag even in the elastic stage. However, the topology design of existing hollow slabs and core column plates is mostly aimed at simplifying stiffness, and rarely optimizes stiffness and density based on the shear lag effect. Therefore, there is still a risk of stress concentration in high shear areas such as the support area.

[0006] 3. Economic Issues Regarding Core Column Relative Density: Studies on core column panels or honeycomb panel components show that when the core column relative density (the proportion of core column concrete volume to the total component volume) exceeds a certain threshold, the increase in load-bearing capacity is no longer proportional to the amount of additional material used, meaning material utilization decreases. Related experimental and numerical analysis results indicate that when the core column relative density exceeds approximately 5%, the increase in load-bearing capacity per unit volume of material tends to weaken, while the component's self-weight continues to increase, resulting in a decline in overall economic efficiency. Simultaneously, experiments also show that component failure is mostly concentrated in the bending control zone (near mid-span), but the high shear force and localized bearing pressure in the support area still require close attention.

[0007] 4. Identical Construction of Bending Moment Control Zone and Shear Control Zone: In traditional design, the mid-span pure bending zone and the support high shear zone often use plates of the same thickness, longitudinal ribs of the same cross-section, and core columns or holes of the same density, only meeting different stress requirements by configuring longitudinal tensile reinforcement of different areas. This construction method does not combine the strain distribution characteristics under the "plane section assumption" with the shear hysteresis effect, and lacks targeted optimization of the spatial distribution of cross-sectional stiffness, resulting in problems such as excessive thickness and density in the mid-span region and insufficient lateral force transmission paths in the support region.

[0008] 5. Insufficient application of topology optimization in engineering construction: Although some academic studies have explored the effects of different combinations of core column density, rib width, and plate thickness on load-bearing capacity, stiffness, and crack control through finite element analysis and topology optimization methods, most conclusions remain at the level of parameter sensitivity analysis. There is still a lack of technically feasible solutions for transforming implicit conclusions such as the "influence of core column and rib width on load-bearing capacity" and the "economic threshold of core column density" into explicit structural forms and parameter ranges that can be directly applied to engineering layout.

[0009] Therefore, existing UHPC hollow slab or core column slab technologies mainly suffer from the following technical problems: the span and longitudinal stiffness distribution lacks "on-demand allocation" to match the actual internal forces, resulting in similar structures in the mid-span bending control zone and the support high shear zone, and materials are not specifically allocated to key stress-bearing parts; the core column or hole density is mostly uniformly distributed across the entire span, without distinguishing the different needs of the bending moment control zone and the shear control zone. When the core column density is increased to a certain level to meet the local bearing pressure and shear resistance of the support zone, the material is increased across the entire span, resulting in large material usage and heavy self-weight, and the increase in density beyond the economic threshold has limited effect on improving the bearing capacity; most existing solutions do not combine the shear hysteresis effect with the variable density of the core column and the variable cross-section of the longitudinal ribs, and there is still a lack of a UHPC core column slab structure that comprehensively optimizes the stiffness distribution in both the span and thickness directions.

[0010] Therefore, it is necessary to provide a new variable-density UHPC core column plate based on shear hysteresis effect optimization. Through the coordinated design of zoning along the span direction, variable-spacing core columns and variable-section longitudinal ribs, a high-stiffness, high-shear-resistance and reliable force transmission path is formed in the support area, and lightweight and efficient bending load is achieved in the mid-span area. This breaks through the idea of ​​uniform arrangement and simple thickening or stiffening in the existing technology, significantly improves material utilization and structural performance, and enhances the novelty and inventiveness of the invention. Summary of the Invention

[0011] This invention proposes a variable-density UHPC core-column slab based on shear hysteresis optimization, aiming to solve the following problems existing in UHPC hollow slabs or core-column slabs: the internal force distribution in the span direction is mismatched with the arrangement of core columns and longitudinal ribs, resulting in similar structures in the bending moment control zone and shear control zone, and low material utilization; core columns or cavities are mostly arranged uniformly across the entire span, and when the core column density is increased to meet the high shear force and local bearing pressure in the support area, it is inevitable that material will also be added in the pure bending zone at the mid-span, resulting in a large self-weight, and the increase in bearing capacity is limited after exceeding the economic threshold of the relative density of the core column; the shear hysteresis effect is more significant in wide slabs and flange slabs, but existing structures rarely consider the shear hysteresis effect in conjunction with the variable density of core columns and the variable cross-section of longitudinal ribs, and the force transmission path and stiffness distribution lack topology optimization design ideas; existing research mostly stays at the level of parametric analysis of the influence of core column density and rib width on bearing capacity, without providing zoning arrangements, variable cross-section rules and parameter ranges that can be directly adopted in engineering, making it difficult to promote and apply in engineering practice.

[0012] The purpose of this invention is to divide the UHPC core plate into a support-reinforced zone, a transition zone, and a mid-span sparse zone along the span direction, and to use different core column spacings and selectable cross-sectional dimensions in different zones. At the same time, by combining the bending moment envelope control to gradually change the width of the longitudinal ribs along the span, the relative density of the core columns is controlled below the economic threshold in the mid-span region, while a "quasi-solid" high-stiffness and high-shear band is formed in the high shear zone of the support. This establishes a stiffness distribution and force transmission path that matches the distribution of bending moment and shear force, thereby significantly reducing self-weight and material usage while improving the load-bearing capacity and ductility, and enhancing the overall economy and assemblability of the structure.

[0013] To achieve the above objectives, the present invention provides a variable-density UHPC core plate optimized based on shear hysteresis effect, the preferred embodiment of which can be found in the appendix. Figure 1 ~Attached Figure 4 The core plate mainly includes: the upper flange plate. Lower flange Several UHPC core pillars arranged along the thickness direction of the plate Longitudinal UHPC ribs continuously arranged along the span direction First support encryption zone ; Sparse region across the middle Second support encryption zone Optional transition area settings End-mounted assembly connection structure and wet joint Reinforcement and additional structural steel bars wait.

[0014] (1) Overall structure and zoning design

[0015] like Figure 1 and Figure 2As shown, the UHPC core plate of the present invention forms an effective span L along the span direction between the first support end and the second support end. Within this range, the plate is divided into three or four functional zones according to the bending moment and shear force distribution of the components under typical simply supported or continuously supported conditions:

[0016] First support encryption zone Second support encryption area These are arranged near the supports at both ends to resist large support shear forces, support reaction force transmission, and potential negative bending moments (in continuous systems). The length of the reinforced zone is preferably 0.15L to 0.25L, and can be optimized according to the magnitude of the support reaction force, the shear span ratio, and the actual stress conditions.

[0017] Cross-sparse region Located near the mid-span of the structural member, this area is the main bending moment control zone. In the case of a simply supported beam, it is the zone of maximum positive bending moment. In a continuous beam system, the location and length of the positive bending moment control zone can be determined based on the bending moment envelope. The preferred length of the mid-span sparse zone is... This results in bending moment dominating the region while shear force is relatively small.

[0018] transition zone (Optional): Located between the support-reinforced zone and the mid-span sparse zone, this transition zone ensures a smooth transition in core column density and longitudinal rib cross-sectional dimensions, preventing stress concentration caused by abrupt changes in stiffness. The total length of the transition zone is... ,in , , These represent the lengths of the encrypted support zone on both sides and the sparse zone in the middle of the span, respectively.

[0019] Through the above-mentioned zoning arrangement, the components achieve functional transitions from "bending moment control zone – transition zone – shear control zone" in the span direction, providing a spatial basis for subsequent core column variable density and longitudinal rib variable cross section.

[0020] (2) Variable spacing core column arrangement

[0021] One of the core aspects of this invention is to differentiate the spacing and density of core columns in different zones based on the economic threshold of the relative density of the core columns.

[0022] Core column arrangement in the support encryption zone (quasi-solid design): such as Figure 2 As shown, in the encryption area of ​​the first support Second support encryption area Inside, UHPC core Spacing along both the span direction and the width direction of the plate A regular layout is preferred, ideally forming an array of approximately regular squares or rhombuses. This can be achieved by reducing the spacing. This results in a core column relative density exceeding the economic threshold (approximately 5%) determined through experiments or numerical analysis, and locally forming a "quasi-solid" structure. "Quasi-solid" refers to a relatively small residual cavity or lightweight material area between the core columns, with overall stiffness and shear capacity approaching that of a solid UHPC sheet of the same volume. Within this area, the core column cross-sectional dimensions can remain unchanged or be appropriately increased to improve local compressive and shear capacity. Simultaneously, utilizing the high compressive strength, high shear strength, and high toughness of UHPC material, it effectively resists high shear forces at supports, peak local compressive stress caused by support reactions, and stress redistribution within the flanges due to shear lag, thereby increasing safety margin.

[0023] Core pillar arrangement across sparse regions (economic control): such as Figure 2 and Figure 3 As shown, in the sparse region of the middle span Inside, UHPC core According to spacing The rules are set up, and the following conditions are met: And control the relative density of the core pillars within the mid-sparse region. exist: Within this range, the density is below the aforementioned economic threshold of approximately 5%, aiming to minimize material usage and self-weight while ensuring the bending stiffness and positive bending moment bearing capacity of the components. In the sparse mid-span region, the stress on the components is mainly controlled by bending moment, with relatively small shear forces. Furthermore, since the shear lag effect in the mid-span region is relatively insignificant compared to the support region, the longitudinal and transverse stiffness configurations can be appropriately reduced without significantly compromising overall safety. Reducing the number of core columns to decrease self-weight is beneficial for reducing the design load on the main beam or supporting components.

[0024] Transition zone core column arrangement (smooth variable density): such as Figure 2 As shown, in the transition region Inside, the UHPC core column spacing is determined by the support reinforcement zone. Smooth transition to the mid-sparse region It is preferable to adopt a linear or piecewise linear variation law, for example: ,in, The coordinates are along the span direction. and These represent the start and end points of the transition zone. By gradually increasing the core spacing, the relative density of the cores is gradually reduced from a high value to a target range of 2.5%–3%, avoiding abrupt changes in stiffness and mass distribution, which helps reduce stress concentration and crack propagation risks. In some embodiments, to simplify the mold, a segmented constant spacing approach can be adopted, that is, two or more segments with constant spacing are set within the transition zone, each segment having a spacing value between... and between.

[0025] (3) Longitudinal rib variable cross section design

[0026] Another key aspect of this invention is the use of longitudinal UHPC ribs. The variable cross-section design constructs a stiffness distribution that adapts to the bending moment envelope diagram, enabling the component to better exert its bending load-bearing potential under the "plane section assumption" and form a continuous force transmission path in conjunction with the variable density of the core column.

[0027] Basic arrangement of longitudinal ribs: such as Figure 3 As shown, one or more longitudinal UHPC ribs can be arranged along the width of the plate. Each longitudinal rib extends through the upper flange in the thickness direction. With lower flange With UHPC core It is cast monolithically. The height of the longitudinal ribs is usually similar to or slightly smaller than the slab thickness, and its main design variable is the width along the span direction. .

[0028] Design principle of longitudinal rib width varying with bending moment: such as Figure 4 As shown, the bending moment envelope diagram is based on the component under the design load condition. The present invention proposes a longitudinal rib width It can be determined according to the following functional relationship: ,in: The coordinates are along the span direction; Design the bending moment value at this section; This represents the absolute value of the maximum design bending moment across the entire span. This is the minimum longitudinal rib width within the span, used to ensure minimum structural stiffness; This is an adjustment factor related to the component height, reinforcement conditions, and structural requirements.

[0029] Through the above relationships, the following effects can be achieved: in the region of maximum positive bending moment at mid-span or the region of maximum negative bending moment at the support of a continuous beam, At that time, the width of the longitudinal rib is close to This forms a high bending stiffness section in the bending moment control zone; in the shear force control zone, the bending moment is smaller, and the width of the longitudinal ribs tends to be close to... Meanwhile, the high-density core columns in the support reinforcement zone provide shear stiffness and bearing capacity, achieving a division of labor between bending and shear. In the transition zone, the width of the longitudinal ribs changes slowly with the bending moment, coordinating with the change in core column density to form a continuous force transmission path from the bending moment control zone to the shear force control zone, reducing the adverse effects of sudden changes in cross-sectional stiffness on cracks and stress concentration.

[0030] In practice, to facilitate mold making and construction, the above continuous function can be discretized into several constant values ​​or step-like changes. That is, a uniform longitudinal rib width value is used in different partitions, but these width values ​​are still arranged from large to small according to the bending moment, thereby achieving a simplified variable cross-section design in engineering.

[0031] The fusion structure of longitudinal ribs and encrypted core pillars: such as Figure 2 As shown, in the support encryption area , Inner, longitudinal ribs The width gradually increases near the support end and is associated with dense UHPC core posts. The ribs and core columns interweave and connect to form a locally high-stiffness, high-shear-resistance "rib-core column coupling zone". This coupling zone smoothly transmits the support reaction force to the mid-span moment control zone along the span direction, and disperses the stress concentration caused by the shear hysteresis effect along the width direction within the plate surface, thereby improving the overall internal force redistribution capacity.

[0032] (4) Core column cross-section and material configuration

[0033] Core column cross-section: UHPC core column The cross-section can be circular, polygonal, or rounded rectangular. For example... Figure 3 As shown, a circular cross-section is preferred to facilitate mold standardization and casting process control. In some embodiments, in order to improve the local bearing capacity of the support area without significantly increasing the complexity of the mold, a larger diameter core column can be used in the dense support area, while a slightly smaller diameter core column can be used in the sparse area at mid-span, or the diameter can be kept unchanged while only the spacing is adjusted.

[0034] UHPC material performance requirements: Upper flange plate Lower flange Core column With longitudinal ribs All components are integrally cast from UHPC. The UHPC is preferably selected with a compressive strength of not less than 150 MPa and a flexural strength of not less than 20 MPa, and is reinforced with a low water-cement ratio, highly reactive mineral admixtures, high-strength micro-aggregates, and steel fibers. By improving the synergistic effect of the concrete matrix and fibers, the crack resistance in the shear section and near the borehole wall is enhanced, and the variable-density core column improves the ductility and crack control of the components.

[0035] Reinforcement and connection details: such as Figure 3 As shown, on the upper flange plate and lower flange The longitudinal tensile reinforcement and distribution reinforcement are arranged according to the design requirements. Furthermore, shear stirrups, punching shear reinforcement, or shear keys can be added within the support reinforcement zone to meet the code requirements for minimum reinforcement ratio and shear bearing capacity. Circumferential or diagonal structural reinforcement can be arranged around the core column to improve the borehole wall's crack resistance. Prefabricated connection structures and wet joints are provided at the slab ends. It is used to reliably connect the UHPC core column plate with the main beam, secondary beam or adjacent plate unit to form an integral bridge deck or floor system.

[0036] (5) Combination with shear hysteresis effect and economic threshold

[0037] In terms of design concept, this invention explicitly utilizes the following two types of research conclusions and transforms them into implementable engineering structural features:

[0038] Shear lag effect on stiffness distribution: The shear lag effect leads to uneven distribution of normal stress along the width of wide plates or flange plates, resulting in higher stress in areas near the main beam or ribs. This invention addresses this by arranging high-density core columns and widened longitudinal ribs near the supports, matching the concentrated internal force areas along the plate width with high-stiffness, high-load-bearing paths, thus enhancing the flange plate's ability to transfer loads to the main beam. Simultaneously, in the mid-span region, where shear force is relatively small and the shear lag effect is less significant than in the support area, a lower core column density and smaller rib width can be used to reduce material usage.

[0039] Engineering Transformation of the Economic Threshold for Core Column Relative Density: Existing experiments and numerical analyses have shown that when the relative density of the core column exceeds approximately 5%, the gain in bearing capacity with increasing density gradually weakens, while self-weight and material costs continue to increase linearly, leading to a decrease in material utilization. This invention controls the core column density within the range of 2.5% to 3% in the sparse region of the mid-span, i.e., below the economic threshold, to ensure efficient material utilization. In the dense support region, to meet the requirements of high shear, local compressive stress, and shear hysteresis effects, the core column density is intentionally allowed to exceed this threshold, forming an optimized scheme of "exchanging local material enrichment for overall safety and stiffness." Through zonal design, the concept of "over-allocation in critical areas and material saving in non-critical areas" is effectively realized.

[0040] Compared with existing UHPC plate components that use uniformly arranged core columns or uniform cavities across the entire span, the present invention has the following significant advantages:

[0041] 1. Stiffness and strength are allocated as needed, resulting in high material utilization efficiency: By dividing the core column density and longitudinal rib width into zones and using variable cross-section design along the span direction, the stiffness distribution of the moment control zone, shear force control zone, and transition zone is matched with the internal force conditions, effectively utilizing the high strength and high toughness of UHPC and avoiding material waste caused by average configuration across the entire span.

[0042] 2. Balancing support shear and mid-span moment control, overall load-bearing capacity and ductility are improved: The "quasi-solid" structure in the support-reinforced zone significantly enhances local shear and punching shear resistance, reducing the risk of cracks near the supports; in the sparse mid-span zone, bending moment capacity is controlled through longitudinal rib cross-section variations and flange reinforcement, while the high tensile strength and fiber-reinforced toughening properties of UHPC improve later-stage ductility. Overall, the member not only exhibits improved ultimate load-bearing capacity but also a more ductile failure mode, contributing to structural safety.

[0043] 3. Reduced self-weight, facilitating prefabricated construction and minimizing superstructure design: By reducing the core column density in the mid-span region and optionally reducing the core column cross-sectional dimensions, the self-weight of the slab unit is significantly reduced while ensuring stiffness and load-bearing capacity. This reduction in self-weight helps to decrease the cross-sectional dimensions of the main beams and the design internal forces of the supporting components, and also facilitates the hoisting and transportation of large prefabricated components, making it suitable for prefabricated construction of long-span bridges and large-span floor slabs.

[0044] 4. Designed in conjunction with shear hysteresis effect to improve internal force redistribution and fatigue performance: The high-density core column in the support area and the widened longitudinal rib form a high-stiffness force transmission path along the width of the plate, which effectively disperses the local stress concentration caused by shear hysteresis. This is beneficial to improving the fatigue performance of the structure under repeated loads such as vehicle loads and wind loads, as well as the crack control capability during the service stage.

[0045] 5. Clear structural form, facilitating standardized design and factory production: This invention is based on the core concept of "zoning + variable density + variable cross-section," but in practice, different spacing and width combinations can be achieved using a limited number of standardized molds. For example, the support area uses a standard mold. Standard molds are used in the cross-section area. The transition zone uses a limited number of transition spacings to achieve simple and reliable industrial production without increasing the complexity of the process.

[0046] 6. Novelty and inventiveness: This invention is not a simple splicing of existing uniform core column plates and variable cross-section beams. Instead, based on a comprehensive analysis of the "economic threshold of core column density" and "the influence law of core column and longitudinal rib on stress and deformation" in the literature, it proposes a synergistic topology optimization arrangement of zoned variable density and longitudinal rib variable cross-section. It clearly transforms academic conclusions into engineering-implementable construction details and parameter ranges, which have substantial technical features and significant progress, and are conducive to obtaining patent authorization. Attached Figure Description

[0047] To more clearly illustrate the technical solution of the present invention, the present invention will be further described below with reference to the accompanying drawings, in which:

[0048] Figure 1 This is a schematic diagram of the overall structure of the variable density UHPC core plate of the present invention (top view and simplified three-dimensional diagram).

[0049] Figure 2 This is a schematic longitudinal cross-sectional view of the variable density UHPC core plate of the present invention along the span direction;

[0050] Figure 3 This is a schematic cross-sectional view of the variable density UHPC core plate of the present invention;

[0051] Figure 4 This is a schematic diagram showing the relationship between the longitudinal rib width and the bending moment envelope of the present invention.

[0052] Figure 1 A schematic diagram of the overall structure of the variable density UHPC core plate of the present invention is shown. It can be seen that the plate consists of an upper flange plate... and lower flange This constitutes the basic bending section; several longitudinal UHPC ribs are evenly arranged inside the plate. UHPC core columns are installed along the span direction and along the thickness direction. The panels are arranged in a regular array with varying spacing within different zones; assembly connections and wet joint structures are located at the ends of the panels. It is used to connect with the main beam or adjacent plate units. The functional zoning along the span direction is visible in the diagram: the two ends are the first support reinforcement zones. Second support encryption area The middle section is a sparse region. A transition zone can be set between the support encryption zone and the mid-span sparse zone. .

[0053] Figure 2 This is a cross-sectional diagram along the longitudinal direction (span direction), highlighting the zonal design and variable spacing arrangement of the core columns: in the first support reinforcement zone Second support encryption area Inside, UHPC core The spacing is It has a relatively high density, approaching a "quasi-solid" structure; in the sparse region of the span... Inside, UHPC core The spacing is ,and The relative density is controlled within the range of 2.5% to 3%; transition zone Inside, the core spacing is from Gradually transition to It can be linear or piecewise linear; longitudinal UHPC ribs The width is larger in the mid-span region, gradually changing towards the support end and merging with the high-density core column area to form a continuous force transmission path; prefabricated connections and wet joint structures are visible at the plate ends. This facilitates component assembly.

[0054] Figure 3 This is a schematic cross-sectional view, highlighting the combined section form of the flange, longitudinal ribs, and UHPC core column: Upper flange. With lower flange Through longitudinal UHPC ribs and UHPC core The entire structure is connected to form a box-shaped or ribbed composite section; UHPC core column Arranged in rows and columns along the width of the plate, its cross-section can be circular or other equivalent cross-sectional forms; longitudinal ribs One or more strips can be arranged along the width of the slab, and their width and height can be controlled according to design requirements; reinforcement and structural steel bars are provided in the upper and lower flanges. It is used to withstand tensile stress, control cracks, and enhance overall ductility.

[0055] Figure 4 The longitudinal rib width is schematically shown. With bending moment envelope Correspondence: The horizontal axis represents the coordinate along the span direction. The vertical axis represents the bending moment envelope. With longitudinal rib width The curve shows that Follow The longitudinal rib width increases with the increase of bending moment, reaching its maximum value at the point of maximum bending moment and decreasing in the region near the support with smaller bending moment; this schematic diagram reflects the longitudinal rib width design principle adopted in this invention, namely: Through this functional relationship, the longitudinal rib stiffness can be allocated as needed based on the bending moment envelope. Detailed Implementation

[0056] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. Those skilled in the art should understand that equivalent substitutions or adjustments to the dimensional parameters, material ratios, and construction processes in the following embodiments, without departing from the concept of the present invention, are all within the scope of protection of the present invention.

[0057] Example 1: Variable density UHPC core plate for simply supported bridge deck

[0058] This embodiment illustrates a typical application of the variable-density UHPC core plate of the present invention in the deck of a simply supported small box girder highway bridge. (Reference) Figures 1-4 This core column plate is used as a bridge deck assembly unit plate between the main beams of the bridge.

[0059] 1. Basic geometric dimensions

[0060] Effective span: Let the clear span of the bridge deck between two adjacent main beams be . Slab width: The width of a single precast slab is... Perpendicular to the centerline of the main beam; Plate thickness: Total thickness is Among them: upper flange thickness Lower flange thickness The height of the middle rib and core column area is approximately Longitudinal UHPC ribs Three ribs are arranged along the width of the plate, with a uniform spacing of approximately The rib height is consistent with the plate thickness, that is, it connects from the lower surface of the lower flange plate to the upper surface of the upper flange plate, so as to achieve overall stress by integral casting.

[0061] 2. Partition Length Division

[0062] According to the design internal force analysis results, the bending moment and shear force envelope of the simply supported bridge deck under the combination of standard vehicle load and pavement dead load have the following characteristics: the bending moment is the largest at mid-span, and the bending moment control section is located in the range of approximately 0.4L to 0.6L at mid-span; the shear force is the largest at the support, and the shear force lag effect leads to significant stress concentration in the flange plate near the main beam.

[0063] This embodiment uses the following partition length: First support encryption zone :length Second support encryption zone :length ; Sparse region across the middle :length Symmetrically arranged in the middle of the span; transition zone It is set on both sides, and the length of each side is: From the left support to the right support, along the span direction, the following are the first support reinforcement zones: (0~0.6 m) → Left transition zone (0.6–0.9 m) → Sparse region in the middle of the span (0.9~2.1 m) → Right transition zone (2.1~2.4 m) → Second support reinforcement zone (2.4–3.0 m).

[0064] 3. Examples of UHPC material properties and formulation

[0065] The UHPC used in this embodiment meets the following performance indicators: 28-day cubic compressive strength. Flexural strength Splitting tensile strength Elastic modulus .

[0066] Referencing common UHPC mix proportions (by mass), an example is shown below (for illustrative purposes only, not as a limitation): Cement (P.O42.5): 1.00; Silica fume: 0.25–0.30; Ultrafine mineral powder: 0.20–0.25; Quartz sand (0.1–2.0 mm): 1.10–1.20; Water-cement ratio High-efficiency water-reducing agent: 1.0%–2.0% of the mass of cementitious materials; diameter Steel fibers with an aspect ratio of approximately 13, at a dosage of 2% to 3% (volume fraction).

[0067] By introducing steel fibers, the crack resistance and tensile bearing capacity of the plate and core column are improved, so that the local stress concentration under variable density arrangement can still be within the range of crack development control.

[0068] 4. Core column arrangement and density calculation

[0069] 4.1 Core Post Geometric Parameters

[0070] The core column cross-section is circular; the core column diameter is uniformly set to... The core column is effectively connected to the upper and lower flange plates, with a height of approximately [missing information]. However, since it is integrally formed with the flange plate during casting, it can be considered as penetrating the plate thickness.

[0071] 4.2 Core column arrangement in the support reinforcement zone ( )

[0072] First support encryption zone Second support encryption area Inner: Spacing of core columns along the span direction: Spacing between core posts along the width of the plate: .

[0073] Taking the volume calculation of a component as an example, let the length under consideration be... The total volume of the plate segment is: The number of core posts per unit length is approximately: The volume of a single core column is: The total volume of the core column within a unit length plate segment is: Relative density (for example only, actual density may vary slightly): In this embodiment, the relative density of the core column in the support area is much greater than the economic threshold of about 5%, forming a "quasi-solid" local high-stiffness and high-shear-resistance zone to resist the local compressive stress under the action of high shear force and support reaction force of the support.

[0074] 4.3 Core column arrangement in the sparse region of the middle span ( )

[0075] In the sparse region of the middle To control the relative density of the core pillars within the range of 2.5% to 3%, the spacing is determined according to the following steps: The target relative density is set as follows: Assuming the same core diameter is still used in the mid-span region And initially set the same spacing along the width and span of the board. The number of core pillars per unit length of plate segment is: The total volume of the core column per unit length of plate segment is: Relative density: ,make ,have to: Substitute , ,get: Based on the standardization and layout rules of the mold, this embodiment takes the following spacing for the core pillars along the span direction: or Spacing between core posts along the width of the plate: .according to calculate: , , Slightly higher than 3%, can or Slightly increase to 0.42–0.45 m, making The density was reduced to the range of 2.5% to 3%. It can be seen that the relative density of the core column in the sparse region of the mid-span is significantly lower than that in the support region. Compared with the uniform density design across the entire span, this effectively reduces the self-weight and material usage.

[0076] 4.4 Core Column Arrangement in the Transition Zone

[0077] Transition zones on the left and right sides Inside, a segmented linear transition is achieved using a two-level spacing: near the support reinforcement zone (approximately 0.15 m in length): , ; Near the sparse region in the middle of the span (approximately 0.15 m in length): , In this way, within the two transition zones, the core column density smoothly decreases from a high value in the support-reinforced zone to a low value in the mid-span sparse zone, avoiding the adverse effects of sudden stiffness changes.

[0078] 5. Longitudinal Rib Variable Cross-Section Design and Calculation

[0079] Longitudinal UHPC ribs In this embodiment, the height is the same as the plate thickness, and the width is... The functional relationship is approximated by piecewise constants: ,in: This is used to ensure minimum structural stiffness; The result was obtained through trial calculations and optimization using finite element analysis. This represents the bending moment envelope of a simply supported slab under design conditions. This represents the maximum positive bending moment at mid-span.

[0080] Based on the bending moment distribution of a simply supported slab, it can be approximated as follows: Mid-span region: 0.4L~0.6L At a distance of 0.2L from the support: (Approximate as a simply supported beam with a quadratic moment distribution); at a distance of 0.1L from the support: Support: .

[0081] Accordingly, this embodiment is simplified to the following segmented rib width setting (taking a single longitudinal rib as an example):

[0082] Cross-sparse region (0.9~2.1 m):

[0083] transition zone (0.6–0.9 m, 2.1–2.4 m): about halfway between the mid-span (approximately 0.75L). ,Pick: Near the support halfway (approximately 0.25L to 0.30L). ,Pick: The actual construction is simplified as follows: A uniform approach is adopted within the transition zone. ;

[0084] Support encryption zone (0~0.6 m, 2.4~3.0 m): the side closest to the span (0.2L from the support). The calculated width is approximately: Near the support, Theoretically However, in order to integrate with the high-density core column group to form a "rib-core column coupling zone", this embodiment uniformly adopts in the support reinforcement zone. Within 0.2 m of the support, the punching shear resistance can be enhanced by widening the flange or by implementing local thickening measures.

[0085] By using the above segmentation settings, an approximate "longitudinal rib variable cross section design based on bending moment variation" can be achieved in engineering using a limited number of rib width molds.

[0086] 6. Reinforcement Arrangement and Construction Measures

[0087] In this embodiment, to meet the code requirements for minimum reinforcement ratio, crack control, and overall ductility, the upper and lower flange plates... and longitudinal ribs Necessary reinforcement and structural reinforcement are arranged in the middle. .

[0088] upper flange Longitudinal tensile reinforcement with a diameter of 12 mm and a spacing of 150 mm is arranged along the span direction; distribution reinforcement with a diameter of 8 mm and a spacing of 200 mm is arranged along the width direction of the slab; the spacing of the distribution reinforcement in the support reinforcement zone can be increased to 150 mm.

[0089] lower flange In a simply supported positive bending moment structure, the lower flange is the main tension zone. Longitudinal main reinforcement with a diameter of 14 mm and a spacing of 125 mm is arranged along the span direction; distributed reinforcement with a diameter of 8 mm and a spacing of 200 mm is arranged along the width direction of the slab; negative bending moment secondary reinforcement is appropriately added in the sparse zone at the mid-span to control the crack width at the mid-span.

[0090] Longitudinal ribs Two to four longitudinal steel bars with a diameter of 12 mm are arranged along the height direction inside the rib; closed stirrups or transverse tie bars with a diameter of 8 mm and a spacing of 150 mm are arranged inside the rib to restrain the UHPC and maintain the integrity of the rib section; the stirrup density can be increased near the rib end in the support reinforcement zone to improve shear and punching shear resistance.

[0091] Reinforcing steel around the core column: in the core column The perimeter is reinforced with circumferential or square closed reinforcing bars, with a diameter of 6 to 8 mm, mainly used to control the development of cracks at the connection between the core column and the flange plate; the spacing of the circumferential reinforcing bars is 100 to 150 mm, and the spacing is appropriately increased according to the magnitude of the shear force.

[0092] End connection and wet joint construction The precast slab has a pre-reserved extension section of reinforcing steel at the end, which facilitates mutual anchoring with the pre-embedded reinforcing steel on the adjacent slab or main beam in the wet joint on site; the wet joint can be filled with high-performance grout or UHPC grout to ensure that the strength of the connection area is not lower than that of the slab itself; if a dry connection is used, shear keys and precision bolt holes can be set at the end to form a detachable connection.

[0093] 7. Manufacturing Process Steps

[0094] Taking factory prefabrication as an example, the manufacturing steps of the variable density UHPC core column board in this embodiment are as follows:

[0095] (1) Mold design and manufacturing: according to Figures 1-3 The structural arrangement includes upper and lower flange forming surfaces in the steel mold or combined mold; replaceable core column forming core rods are set in the mold, corresponding to different spacings and arrangements in the support densification zone, transition zone and mid-span sparse zone; adjustable baffles or combined templates with adjustable longitudinal rib width are set to achieve segmented forming of rib width.

[0096] (2) Reinforcing steel cage processing and binding: Process the upper and lower flange plate reinforcing steel mesh and longitudinal rib reinforcing steel cage according to the design drawings; place the reinforcing steel cage in the lower formwork and use spacers to ensure the thickness of the protective layer; reserve perforations or partially bypass the reinforcing steel at the core column position to ensure sufficient spacing between the core column and the reinforcing steel; bind the structural reinforcing steel around the core column and weld or bind it to the flange plate reinforcing steel and longitudinal rib reinforcing steel.

[0097] (3) Core rod installation for core column forming: According to the zoning design, install the core rod in the mold according to the following steps. , Place core rods at the interval between the core rods and the transition zone; check the position, verticality, and sealing of the core rods to prevent grout from flowing across the surface or forming honeycomb during pouring.

[0098] (4) UHPC mixing and pouring: According to the design mix ratio, dry and wet mixing of UHPC is carried out in a forced mixer. The mixing time and sequence are controlled to ensure that the steel fibers are evenly dispersed. The mixed UHPC is poured into the mold from one end or multiple points. The pouring method is adopted to avoid cold joints. During the pouring process, an immersion vibrator and an external vibrating table are used to vibrate together to ensure that the concrete fills the space around the rib groove and core column. However, the vibration time should be controlled to prevent the fibers from sinking or segregating.

[0099] (5) Surface leveling and initial curing: After the UHPC is poured, the upper surface is moderately scraped and smoothed. If a rough interface is required with the upper paving layer, the surface can be roughened before initial setting. Cover with plastic film and control the temperature and humidity during the initial setting stage according to the UHPC mix ratio and ambient temperature.

[0100] (6) Steam or standard curing: When using steam curing, the temperature can be slowly raised to 60-90℃ within 12-24 hours, kept constant for 24 hours, and then slowly cooled down. After demolding, it is transferred to standard curing. When using standard curing, the temperature should be maintained at 20±2℃ and the relative humidity ≥95%, and the curing time should be no less than 7 days to ensure early strength.

[0101] (7) Demolding and core rod removal: After the curing time reaches the specified time, remove the template and carefully pull out the core rod of the core column; check the quality of the core column hole wall and the flange plate surface. For local defects, high-strength repair mortar can be used for repair.

[0102] (8) Quality inspection and delivery: Inspect the geometric dimensions, appearance quality, concrete strength and steel reinforcement protective layer thickness of the precast slabs; conduct random checks on the density and position of the core columns to ensure that the zonal variable density arrangement meets the design requirements; after passing the inspection, stack and transport the precast slabs for on-site installation.

[0103] 8. On-site installation and load-bearing performance description

[0104] In the simply supported box girder bridge deck system, the variable density UHPC core column plate in this embodiment is constructed through end connection. It connects to the main beam and adjacent plate units. Through finite element numerical analysis and comparative tests, the following stress performance characteristics can be obtained: In the mid-span region, the longitudinal ribs with variable cross-sections and sparsely arranged core columns jointly bear the bending moment, resulting in a relatively uniform stress distribution in the flange plates; in the support region, the high-density core columns and widened longitudinal ribs form a high-stiffness force transmission path, enabling the local reaction force of vehicle wheel loads to be quickly transferred to the top plate of the main beam, reducing the bending tensile stress of the flange plates near the supports; compared with the uniform core column density scheme across the entire span, this embodiment can reduce the self-weight of the plate units by approximately 10% to 20% while ensuring the same bearing capacity, and the design load of the upper main beam is correspondingly reduced; since the shear hysteresis effect is more significant near the supports, this embodiment adopts a "quasi-solid" structure in this region, which can significantly reduce the peak transverse stress of the flange plates and improve fatigue performance.

[0105] Example 2: Application of continuous slabs in prefabricated floor slabs

[0106] This embodiment illustrates an application scenario of the variable density UHPC core column plate of the present invention in prefabricated building floor slabs, focusing on the differentiated design in the negative bending moment zone (above the support) and the positive bending moment mid-span zone.

[0107] 1. Project Background

[0108] A prefabricated office building uses steel or concrete beams with an 8.0 m span to support UHPC precast floor slabs. The floor slabs are arranged in two continuous spans, with a clear span of [missing information]. Floor slab width The floor slab must meet the office building's service load of 3.5 kN / m² and a certain amount of variable office equipment load. The continuous slab generates a large negative bending moment near the inner supports, while the mid-span is the positive bending moment control zone. Therefore, different core columns and longitudinal ribs must be arranged in the negative bending moment zone at the supports and the positive bending moment zone at the mid-span, respectively.

[0109] 2. Zoning principle and design of negative bending moment zone

[0110] Approximately [length] is arranged on each side above the inner support. The "negative bending moment support reinforcement zone" serves as the first and second support reinforcement zones. Extended meaning; in the region of maximum positive bending moment at mid-span (approximately Set up a sparse region across the middle. Approximately The rest are transition zones. It is used to achieve a smooth transition from the negative bending moment control zone to the positive bending moment control zone.

[0111] In the negative bending moment region, the upper flange is mainly under tension, while the lower flange is under compression; in the positive bending moment region, the situation is reversed. Therefore, in terms of reinforcement arrangement: in the negative bending moment region at the inner support, the upper flange has more longitudinal tensile reinforcement, while the reinforcement of the lower flange can be reduced; in the positive bending moment region at mid-span, the lower flange has denser longitudinal tensile reinforcement, and the upper flange mainly bears compressive stress.

[0112] Regarding the core column arrangement, the shear force in the negative bending moment zone is also relatively large. Therefore, high-density core columns and wider longitudinal ribs are still used to form a coupling zone between the tensile stiffness of the upper flange and the shear stiffness of the support. The remaining core column spacing and longitudinal rib cross-section design can basically refer to Example 1, except for the bending moment envelope... The negative bending moment peak needs to be considered, and the functional relationship needs to be adjusted. Make symmetrical or asymmetrical adjustments.

[0113] Example 3: Design Method and Parameter Selection Process

[0114] To facilitate the application of this invention by those skilled in the art in different engineering projects, a relatively general design method and parameter selection process are given below.

[0115] Step 1: Determine the plate's geometric parameters and design loads

[0116] The span length is determined based on the intended use and the form of the superstructure. , board width Total thickness Determine the design load combination, including dead load, variable load, vehicle load, temperature and shrinkage / creep effects, etc.; select the UHPC material grade and target strength level.

[0117] Step 2: Obtain the internal force envelope and shear hysteresis effect

[0118] Linear elastic analysis or finite element analysis is performed on the plate-beam system to obtain the bending moment envelope. and shear envelope For wide plates or box girder top plates, considering the shear lag effect, the equivalent width method, shear lag element or fine finite element model analysis can be used to obtain the normal stress distribution of the flange plate.

[0119] Step 3: Divide the space into functional zones

[0120] according to and Determine the length range of the moment control zone and shear force control zone; determine the length of the support reinforcement zone. , Generally taken Determine the length of the sparse region in the middle. Generally take The remaining portion is designated as a transition zone. And can be symmetrical or slightly offset according to actual needs.

[0121] Step 4: Determine the core diameter and density target

[0122] Select the core column diameter based on structural and construction requirements, plate thickness, and mold standards. (e.g., 60–100 mm); Based on literature and experimental results, determine the economic threshold for the core post. Set target density in the sparse region of the span. Set the target density in the support encryption zone. It can be higher than 5%, depending on the specific calculation of shear and local bearing pressure.

[0123] Step 5: Back-calculate the core spacing

[0124] In terms of unit board length Based on this, the general formula for the relative density of the core column is: ,in The number of core pillars per unit length. For the volume of a single core column. If the spacing along the plate width and span is respectively... ,but: Substituting the values, we get: Therefore, the target density for different partitions can be calculated in reverse. The value is rounded and adjusted in conjunction with mold standardization and layout rules.

[0125] Step 6: Determine the cross-section of the longitudinal ribs

[0126] According to the bending moment envelope Selected reference section bending moment Determine the minimum rib width (Based on minimum structural stiffness and casting process); coefficients are determined through preliminary calculations or iterative analysis. This makes the rib width in Within the range of variation, it meets the requirements for stiffness and flexural bearing capacity; according to This yields the theoretically continuous function; Discretized into several constant or stepped widths, it facilitates mold making and construction.

[0127] Step 7: Overall Experience Calculation and Optimization

[0128] Finite element analysis is performed based on the determined core column density and rib cross section to verify the bending of the normal cross section, the shear of the inclined cross section, fatigue, crack control and deflection; the local bearing pressure and punching shear capacity of the support densification zone are checked, and the core column diameter or density, rib width and local flange thickening are adjusted if necessary; under the premise of meeting the bearing capacity and service performance, the density or rib width of the sparse zone in the middle of the span can be appropriately reduced to further optimize the material utilization rate.

[0129] Example 4: Deformation and Crack Control During Construction and Use

[0130] In the implementation of this invention, the following measures can be combined to further improve the deformation and crack control performance:

[0131] 1. Pre-camber setting

[0132] During prefabrication, a certain pre-camber can be preset in the template along the span direction to offset part of the deflection, which is especially effective in long-span slabs or heavy-duty bridge decks.

[0133] 2. Limit the demolding age and stress level.

[0134] Do not install under stress before the UHPC reaches 60% to 70% of its design strength to avoid excessive cracking caused by early shrinkage and creep.

[0135] 3. Post-cast layer and composite structure

[0136] A 40-60 mm post-cast layer can be set on the bridge deck or floor surface to work in conjunction with the UHPC core column plate of this invention. The post-cast layer can use ordinary C40-C50 concrete to optimize the cost. Through interface treatment and shear connection, the post-cast layer and the UHPC plate share the stress, further reducing the stress level and crack width of the single plate.

[0137] 4. Durability and Protection

[0138] UHPC's low permeability significantly improves durability without the need for traditional waterproofing layers. For wet joints at the ends, protective coatings or steel cladding can be applied to enhance the durability and fatigue resistance of the connection.

[0139] As can be seen from the above embodiments, the "zoning + variable density + variable cross section" UHPC core column plate scheme proposed in this invention can significantly improve material utilization and reduce structural self-weight while ensuring load-bearing capacity and stiffness. It also fully considers the shear hysteresis effect and the economic threshold of core column density, making it a new type of prefabricated plate component structure with good engineering promotion value.

Claims

1. A variable-density UHPC core plate optimized based on shear hysteresis effect, characterized in that, include: A precast UHPC slab, with an effective span formed between the opposite first and second support ends along the span direction. Several UHPC core columns arranged along the thickness direction and longitudinal UHPC ribs connected to the core columns; the UHPC core column plate is divided into the following sections along the span direction: a first support-reinforced zone, a mid-span sparse zone, and a second support-reinforced zone, with a transition zone optionally provided in the middle connecting the support-reinforced zone and the mid-span sparse zone; wherein: 1) within the support-reinforced zone, the UHPC core columns are arranged according to the spacing The regular arrangement of the core pillars results in a relative density higher than a preset economic threshold, forming a near-solid local high-stiffness, high-shear-resistance zone; 2) Within the mid-span sparse region, the UHPC core pillars are arranged according to the spacing... Arrange according to rules, and satisfy And the relative density of the core column in the sparse region of the span is controlled at 2.5% to 3%; 3) the longitudinal UHPC ribs are continuously arranged along the span direction, and their width As the span-direction bending moment envelope diagram changes, the reference width is taken at the location of the maximum bending moment at mid-span. It gradually increases towards the supports on both sides until it connects and merges with the dense core column array in the support densification zone, thus forming a continuous force transmission path that transitions from the mid-span bending moment control zone to the support shear control zone.

2. The variable density UHPC core plate according to claim 1, characterized in that: The lengths of the first support encryption area and the second support encryption area are respectively The length of the sparse region in the middle is The rest is a transition zone, which causes the density of the core column within the span to vary in segments along the span direction.

3. The variable density UHPC core plate according to claim 1 or 2, characterized in that: The core spacing within the transition zone is determined by the support reinforcement zone. Towards the sparse region The relative density of the core column changes linearly or piecewise linearly, and the relative density of the core column smoothly transitions from a high value to a target density of 2.5% to 3%.

4. The variable density UHPC core plate according to any one of the preceding claims, characterized in that: The width of the longitudinal UHPC rib Determined according to the following formula: in, For the cross-directional coordinates, This is the bending moment value at that location. The maximum bending moment within the span, The minimum rib width within the span, This is an adjustment coefficient related to the member height and reinforcement conditions, thereby enabling the longitudinal rib section to be configured as needed according to the bending moment requirement.

5. The variable density UHPC core plate according to any one of the preceding claims, characterized in that: The cross-section of the UHPC core column is circular, polygonal, or rounded rectangle. The diameter or equivalent side length of the core column in the support reinforcement zone is not less than the diameter or equivalent side length in the mid-span sparse zone, so as to improve the local bearing capacity and shear resistance of the support zone.

6. The variable density UHPC core plate according to any one of the preceding claims, characterized in that: The plate includes an upper flange and a lower flange. The UHPC core and longitudinal UHPC ribs reliably connect the upper and lower flanges to form an integral bending member. The upper flange is under compression and the lower flange is under tension or vice versa, to meet the structural requirements of different force directions.

7. The variable density UHPC core plate according to any one of the preceding claims, characterized in that: The UHPC material has a compressive strength of not less than 150 MPa and a flexural strength of not less than 20 MPa. It is reinforced with a low water-cement ratio, high-strength micro-aggregates and steel fibers to improve the crack resistance and ductility of the shear section.

8. The variable density UHPC core plate according to any one of the preceding claims, characterized in that: The economic threshold for the relative density of the core column is determined based on the ratio of bearing capacity to self-weight and material utilization rate through experiments or numerical analysis. When the relative density of the core column is greater than about 5%, the increase in bearing capacity is relatively reduced. In this invention, the density is controlled below this threshold in the sparse region at the mid-span, while the density is allowed to exceed this threshold in the dense region at the support to meet the requirements of shear and local bearing pressure.

9. The variable density UHPC core plate according to any one of the preceding claims, characterized in that: The variable density UHPC core column slab is a prefabricated component with prefabricated wet joints or dry connection nodes at its ends along the width direction. These are used to connect with beams, diaphragms, or adjacent slab units to form a bridge deck or floor slab system.

10. The application of a variable density UHPC core column panel as described in any of the preceding claims in prefabricated bridge deck panels or prefabricated building floor slabs, characterized in that: The bearing reinforcement zone is arranged near the bridge bearings or in the secondary beam support area of ​​the floor slab, and the mid-span sparse zone is arranged in the mid-span area, so as to reduce the structural self-weight and improve the material utilization rate while meeting the requirements of bearing capacity and stiffness.

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