Oblique tendon prestressed concrete composite floor slab and design method thereof

Abstract

The application discloses a kind of oblique direction out muscle prestressed concrete composite floor and design method thereof, including concrete prefabricated bottom plate, plate top reinforcement arranged on the upper end of composite cast-in-place layer, and horse stool bar component connecting prefabricated bottom plate and cast-in-place component, non-prestressed reinforcement end is obliquely extended from the top of side end of bottom plate, and is connected with horizontal reverse bending section plate top reinforcement by bending section, and the extended reinforcement of adjacent bottom plate is anchored at joint, and multiple groups of horse stool bars are arranged at intervals to form space grid, replace traditional truss reinforcement, the anisotropic rigidity of composite floor is corrected by rigidity adjustment coefficient, and deflection is calculated by establishing flexure differential equation, and reinforcement is designed by classification in combination with composite floor structure parameters.The maximum applicable span of the composite floor can be expanded to 9 meters, the oblique cross reinforcement on the side of the plate and the horse stool bar jointly form a composite surface anti-sliding structure, the steel content of non-bending reinforcement of the component is reduced, the material cost is reduced, the hoisting formwork construction is not needed, the assembly efficiency is high, and the bending capacity reaches or approaches the cast-in-place plate with the same thickness.

Description

Technical Field

[0001] This invention relates to the field of prefabricated concrete structure technology, specifically to a prestressed concrete composite floor slab with inclined reinforcement and its design method. Background Technology

[0002] Composite floor slabs are composed of precast concrete base slabs and post-cast concrete layers, forming an important horizontal structure in prefabricated concrete buildings. Their selection directly impacts the building's structural quality, construction convenience, and project cost. Currently, the national standard "Technical Specification for Prefabricated Concrete Structures" (JGJ 1-2014) recommends two types of precast concrete base slabs and their inter-slab joint combinations. After being superimposed and cast in place, these form two types of composite floor slabs with different load-bearing properties, suitable for one-way and two-way slabs respectively. The first type of composite slab has no reinforcing bars on the sides of the precast concrete base slab, allowing for standardized molds and high production efficiency. During assembly, adjacent base slabs are pressed together, and straight additional reinforcing bars are placed around the joint, forming what is known as a "separated joint" or "tight joint." This type of joint is simple in construction and efficient, but due to its poor load-bearing capacity, it is not suitable for two-way composite floor slabs. The second type of composite slab has straight reinforcing bars on both sides of the precast concrete base slab, which are then extended into the overlapping post-cast strip between adjacent base slabs for lap anchoring, and combined with other measures to form a so-called "integral joint".

[0003] Due to its superior load-bearing performance, the "Technical Specification for Prefabricated Concrete Structures" (JGJ 1-2014) designates it as the side connection for two-way composite floor slabs. However, its shortcomings in engineering practice, such as non-standard perforation molds, increased production costs, interference between side reinforcement bars, and low construction efficiency during factory prefabrication and on-site assembly of the base slab, have exposed numerous problems. Furthermore, both types of composite floor slabs rely on truss or stirrup reinforcement to achieve shear resistance at the composite surface, significantly increasing the steel content of structural reinforcement and raising direct material costs; therefore, their technical and economic performance needs improvement.

[0004] Furthermore, the maximum applicable span of traditional concrete composite floor slabs is generally no more than 6m. However, in recent years, some large public building projects such as shopping malls, schools, and hotels have put forward higher requirements for the span of floor slabs in order to pursue building headroom, layout of large spaces, and flexible partitioning. However, conventional concrete composite floor slabs are limited by some material properties and are often difficult to verify through deflection and crack width under their normal service limit state. Summary of the Invention

[0005] To overcome the shortcomings of traditional composite floor slabs in the prior art, such as small applicable spans, insufficient force transmission in separated joints, complex structure of integral joints, low production and assembly efficiency, and difficulty in ensuring quality, this invention provides a type of inclined reinforced prestressed concrete composite floor slab. Through innovative reconstruction and improvement of the existing technology, it enhances the crack resistance and bending resistance of precast concrete slabs, while simplifying the production process, reducing production costs, and improving construction quality.

[0006] The second objective of this invention is to provide a design method applicable to the aforementioned inclined reinforced prestressed concrete composite floor slabs. This method takes into account the anisotropic stress characteristics that differ from cast-in-place floor slabs, and develops exclusive design methods for single- and two-way slabs, providing a theoretical basis and design reference for large-scale engineering promotion.

[0007] The technical solution of the present invention to solve the above-mentioned technical problems is: This invention proposes a prestressed concrete composite floor slab with inclined reinforcement, increasing the maximum applicable span of the composite slab to 9m through the application of prestressing technology. The bottom slab of this composite floor slab uses inclined reinforcement on the slab side instead of the traditional straight reinforcement on the slab side, which, together with the stirrups on the outer side of the joint, forms an anti-slip mechanism on the composite surface. Based on the bottom slab structure, a novel close-fitting joint is further proposed, which has a simple structure, high assembly efficiency, and excellent force transmission performance. The flexural bearing capacity at the joint is essentially equivalent to that of cast-in-place concrete, establishing a connection technology for constructing a two-way composite floor slab system.

[0008] Furthermore, this invention provides a proprietary design method for novel composite floor slabs. Compared to directly using cast-in-place structural design methods, this method fully considers the weakening effect of joints on the flexural stiffness of composite floor slabs, and can more objectively consider the impact of anisotropic stiffness distribution on the actual stress performance of the structure, making more reasonable and accurate predictions of key mechanical indicators such as the structure's load-bearing capacity and displacement. Specifically, it includes: A prestressed concrete composite floor slab with inclined reinforcement includes prestressed steel bars 2 and non-prestressed steel bars 3 connected perpendicularly to each other. It is characterized by further including a precast concrete base slab 7, a stirrup assembly 1, and a top reinforcement bar 5. The top reinforcement bar 5 is located at the upper end of the composite cast-in-place layer 8. The stirrup assembly 1 connects the top reinforcement bar 5 and the prestressed steel bars 2 to form an integral reinforced structure. The non-prestressed steel bars 3 are inserted into the precast concrete base slab 7 and arranged along the short span direction of the precast concrete base slab 7. The ends of the non-prestressed steel bars 3 extend from the top of the side end of the precast concrete base slab 7 and extend obliquely to connect with the top steel bar 5 of the slab. The extended ends of the non-prestressed steel bars 3 of adjacent precast concrete base slabs 7 are staggered along the joints of the composite floor slabs.

[0009] The inclined prestressed concrete composite floor slab has the following features: the ends of the non-prestressed steel bars 3 include interconnected bent extension sections and horizontal connecting sections. The bent extension sections are inclined toward the adjacent precast concrete base slab 7 and extend above the adjacent precast concrete base slab 7. The horizontal connecting sections are set in the opposite direction to the bent extension sections and are connected to the top steel bars 5 of the slab by bending in reverse.

[0010] The inclined prestressed concrete composite floor slab has multiple sets of stirrup assemblies 1, which are arranged along the short span direction of the precast concrete base slab 7. Each stirrup assembly 1 includes multiple stirrups that are spaced apart and connected to each other along the long span direction of the precast concrete base slab 7.

[0011] The inclined prestressed concrete composite floor slab further includes a first reinforcing steel assembly located at the joint of the composite floor slab. The first reinforcing steel assembly includes a first additional steel bar 4 and a first distributed steel bar 6. The first additional steel bar 4 is arranged vertically at the close joint of the precast concrete base slab 7. The first distributed steel bar 6 is arranged at intervals along the length of the first additional steel bar 4, and each of the first distributed steel bars 6 is vertically connected to the upper surface of the first additional steel bar 4.

[0012] The inclined prestressed concrete composite floor slab further includes a second reinforcing steel assembly arranged on the outer periphery of the composite floor slab. The second reinforcing steel assembly includes a second distributed steel bar 9 and a second additional steel bar 10 that are perpendicular to each other. One end of the second additional steel bar 10 is anchored into the post-cast concrete of the support beam 11, and the other end is located between the stirrup assembly 1 and the composite cast-in-place layer 8.

[0013] The present invention also provides a design method applicable to the above-mentioned inclined reinforced prestressed concrete composite floor slab, as detailed below: Step 1: Determine whether the composite floor slab is designed as a one-way slab or a two-way slab based on the ratio between the long side and the short side of the composite slab. Estimate the current cross-sectional dimensions of the composite slab and determine the structural parameters of the precast concrete base slab 7 based on the estimated cross-sectional dimensions of the composite slab. The structural parameters include any one or more of the following: the distance between the bending point of the non-prestressed steel bar 3 and the side of the precast concrete base slab 7; the bending angle of the non-prestressed steel bar 3; and the reverse bending length of the non-prestressed steel bar 3. Step 2: Calculate the design load value under the load combination controlled by permanent load based on the estimated cross-sectional dimensions of the composite slab and the structural parameters of the precast concrete base slab 7. p Design values ​​of loads under quasi-permanent load combination p’ ; Step 3: Calculate the bending moment and shear force of the composite slab. Determine whether the composite slab is designed as a one-way slab or a two-way slab based on the ratio between the long and short sides of the composite slab. When designed as a one-way slab, calculate the bending moment and shear force of the composite slab based on the design values ​​of the load combination controlled by the permanent load. When designed as a two-way slab, calculate the positive bending moment within the span and the negative bending moment at the supports of the composite slab based on the bending differential equation of the orthotropic prestressed two-way composite slab, based on the design values ​​of the load combination controlled by the permanent load. Step 4: Calculate the maximum deflection within the span of the composite slab based on the load design values ​​under the quasi-permanent load combination. oh ; Step 5, based on the bending moment of the composite plate M Calculate the flexural reinforcement of the bottom slab, the reinforcement of the joints within the span, and the reinforcement of the composite slab support section separately; Step 6: Determine whether the maximum deflection ω within the span of the composite slab and the maximum crack width at the bottom and top of the composite slab are within the design specification requirements. If not, adjust the thickness of the composite slab or the reinforcement of the bending steel bars, and return to Step 1 until the maximum deflection ω within the span of the composite slab and the maximum crack width at the bottom and top of the composite slab are both within the design specification requirements, thus completing the design. When designed as a one-way slab, before determining the maximum deflection ω within the span of the composite slab and the maximum crack width at the bottom and top of the composite slab, it also includes determining whether the shear capacity of the inclined section is within the design specification requirements based on the shear force V. If not, control and adjust the thickness of the composite slab until the shear capacity is within the design specification requirements.

[0014] The deflection limit should comply with the relevant provisions on structural durability in the current national standard "Code for Design of Concrete Structures" (GB50010-2010). The crack control level is level three. The maximum crack width at the bottom of the composite slab is calculated based on the maximum positive bending moment within the span, and the maximum crack width at the top of the slab is calculated based on the maximum negative bending moment at the support edge. The flexural capacity of the composite slab section and the shear capacity of the inclined section are calculated using the methods in "Code for Design of Concrete Structures" (GB50010-2010).

[0015] Specifically, in step 1, when the ratio of the long side to the short side of the composite floor slab is ≤2, it is designed as a two-way slab; when the ratio of the long side to the short side is >2, it is designed as a one-way slab.

[0016] The structural parameters of the precast concrete base slab 7 in step 1 are based on the total thickness of the composite slab. Specifically, this includes: when 150mm ≤ When < 200mm, α It is 150°. a It is 50mm. The thickness is 100mm; the concrete grade of the precast concrete base slab 7 is not lower than C30, and the concrete grade of the composite cast-in-place layer 8 is not lower than C25; when 200mm ≤ When < 250mm, α It is 135°. a It is 40mm. The thickness is 70mm; the concrete grade of the precast concrete base slab 7 is not lower than C35, and the concrete grade of the composite cast-in-place layer 8 is not lower than C30; when 250mm ≤ When ≤300mm, α It is 120°. a It is 30mm. The thickness is 50mm; the concrete grade of the precast concrete base slab 7 is not lower than C40, and the concrete grade of the composite cast-in-place layer 8 is not lower than C35. Among these: a The distance between the starting point of the non-prestressed steel bar bend 3 and the side of the precast concrete base slab 7. α For non-prestressed steel bars, the bending angle is 3. The inverse bending length of non-prestressed steel bars is 3.

[0017] Specifically, in step 4, when designed as a one-way slab, the method for calculating the maximum deflection ω within the span of the composite slab is as follows: When designed as a two-way slab, the maximum deflection ω within the span of the composite slab is calculated as follows: Establish and solve the flexure differential equation. The deflection calculation coefficients for composite plates under different boundary conditions are obtained, and the deflection of the composite plate is calculated accordingly. The specific formula is as follows: The calculation coefficients for the deflection of the composite plate under different boundary conditions are obtained by calculation: in, B s For the short-term stiffness of the composite slab in the non-prestressed direction, B This refers to the long-term stiffness of the composite slab in the non-prestressed direction. E c The elastic modulus of concrete. The moment of inertia of the composite slab at mid-span section, This is the stiffness adjustment coefficient in the non-prestressed direction. D 0 represents the flexural stiffness of a cast-in-place floor slab of uniform thickness. D 1. Bending stiffness of composite slab in the prestressing direction. D 2 This refers to the flexural stiffness of the composite slab in the non-prestressed direction. D 3 represents the torsional stiffness of the composite plate; For the torsional stiffness of the composite plate, Poisson's ratio for concrete G Shear modulus This represents the total thickness of the composite slab. oh Let the deflection be at any point within the composite plate. i To account for the influence coefficient of long-term load on the increase of deflection, oh This represents the maximum deflection within the span of the composite slab. The deflection coefficient for the composite plate is given. For the span of the composite slab, p’ The design value of the load under the quasi-permanent load combination.

[0018] Specifically, in step 5, the diameter of the first additional reinforcing bar 4 should be 12mm, and the anchorage length should be... .

[0019] When the first additional steel bar 4 is under tension, the reinforcement ratio of the first additional steel bar 4 per unit width of the slab should be greater than the reinforcement ratio of the non-prestressed steel bar 3 in the precast concrete base slab 7, and the reinforcement design should be carried out according to the following formula: When the first additional reinforcing bar 4 is under compression, the cross-sectional area of ​​the first additional reinforcing bar 4 should satisfy the following formula: in, The anchorage length of the tension reinforcement should be determined in accordance with the relevant provisions of the "Code for Design of Concrete Structures" (GB50010-2010). A s1 The cross-sectional area of ​​the non-prestressed steel reinforcement in the precast concrete base slab 7 is shown in section 3. A s2 The cross-sectional area of ​​the first additional reinforcing bar is 4. This represents the total thickness of the composite slab. The thickness of the composite cast-in-place layer is 8 mm. The effective height of the entire cross-section of the composite slab. For the effective height of the superimposed cast-in-place layer, The distance from the resultant point of the non-prestressed steel reinforcement 3 in the precast concrete base slab 7 to the bottom of the slab. The distance from the resultant point of the first additional reinforcement bar 4 to the overlapping surface.

[0020] Compared with the prior art, the present invention has the following advantages and beneficial effects: Develop a prestressed concrete precast slab with obliquely protruding reinforcement on the slab side. Expand the maximum applicable span of composite floor slabs to 9 meters, extending their application space and scope. Improve upon the traditional method of straight reinforcement on the side of composite floor slabs by utilizing standardized molds to simplify the production process, reduce production costs, and simultaneously improve component quality.

[0021] A new anti-shear slip structure for composite surfaces was developed, which uses diagonally intersecting steel bars on the slab side to limit the lifting effect of new and old concrete at the joint, and combines them with the stirrups on the outside of the joint to form an anti-slip mechanism for the composite surface, completely replacing the traditional truss steel bars, reducing the steel content of non-bending steel bars in the components, and lowering direct material costs.

[0022] A novel close-joint structure adapted to the aforementioned new type of precast concrete base slab was developed. This novel close-joint structure is simple, has a low steel content in non-bending reinforcement, eliminates the need for formwork construction, and boasts high assembly efficiency. Furthermore, its bending load-bearing capacity reaches or approaches that of a cast-in-place slab of equal thickness, exhibiting superior force transmission performance, thus establishing a connection technology for constructing two-way composite floor slabs.

[0023] Based on a new type of precast concrete base slab and a new type of close-joint structure, a new type of prestressed concrete composite floor slab is constructed. Considering its anisotropic stress characteristics, which are significantly different from cast-in-place floor slabs, a dedicated design method is developed for both single-sided and two-sided slabs, providing a theoretical basis and design reference for large-scale engineering promotion. Attached Figure Description

[0024] Figure 1 Schematic diagram of precast concrete base slab Figure 2 Sectional view of precast concrete base slab XX Figure 3 Construction diagram of side joints of precast concrete base slab Figure 4 Schematic diagram of the splicing of the base plate and surrounding beams Figure 5 for Figure 4 Plan view of joint at point A Figure 6 for Figure 4 BB section view Figure 7 for Figure 4 Cross section at CC Figure 8 Diagram of tight-fitting joint construction Figure 9 Plan layout for stirrups Figure 10 For the detailed drawing of the stirrup reinforcement Figure 11 Flowchart for one-way board design Figure 12 Flowchart for two-way board design Figure 13 Load-deflection curve The labels in the diagram represent: 1. Stirrup assembly; 2. Prestressed steel reinforcement; 3. Non-prestressed steel reinforcement; 4. First additional reinforcement; 5. Top reinforcement of slab; 6. First distribution reinforcement; 7. Precast concrete base slab; 8. Composite cast-in-place layer; 9. Second distribution reinforcement; 10. Second additional reinforcement; 11. Support beam. Detailed Implementation

[0025] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0026] Example 1 Combination such as Figure 1-10 As shown, a prestressed concrete composite floor slab with inclined reinforcement includes prestressed steel bars 2 and non-prestressed steel bars 3 connected perpendicularly to each other. The slab is characterized by further including a precast concrete base slab 7, a stirrup assembly 1, and a top reinforcement 5. The top reinforcement 5 is located at the upper end of the composite cast-in-place layer 8. The stirrup assembly 1 connects the top reinforcement 5 and the prestressed steel bars 2 to form an integral reinforced structure. The non-prestressed steel bars 3 are inserted into the precast concrete base slab 7 and arranged along the short span direction of the precast concrete base slab 7. The ends of the non-prestressed steel bars 3 extend from the top of the side end of the precast concrete base slab 7 and extend obliquely to connect with the top steel bar 5 of the slab. The extended ends of the non-prestressed steel bars 3 of adjacent precast concrete base slabs 7 are staggered along the joints of the composite floor slabs.

[0027] The end of the non-prestressed steel bar 3 includes a bent extension section and a horizontal connecting section connected to each other. The bent extension section is inclined towards the adjacent precast concrete base slab 7 and extends to the top of the adjacent precast concrete base slab 7. The horizontal connecting section is set in the opposite direction to the bent extension section and is connected to the top steel bar 5 of the slab in a reverse bend.

[0028] The stirrup assembly 1 consists of multiple sets, which are arranged along the short span direction of the precast concrete base slab 7. Each stirrup assembly 1 includes multiple stirrups that are spaced apart and connected to each other along the long span direction of the precast concrete base slab 7.

[0029] It also includes a first reinforcing steel assembly located at the joint of the composite floor slab. The first reinforcing steel assembly includes a first additional steel bar 4 and a first distributed steel bar 6. The first additional steel bar 4 is arranged vertically at the close joint of the precast concrete base slab 7. The first distributed steel bar 6 is arranged at intervals along the length of the first additional steel bar 4, and each of the first distributed steel bars 6 is vertically connected to the upper surface of the first additional steel bar 4.

[0030] It also includes a second reinforcing steel assembly arranged on the outer periphery of the composite floor slab. The second reinforcing steel assembly includes a second distributed steel bar 9 and a second additional steel bar 10 that are perpendicular to each other. One end of the second additional steel bar 10 is anchored into the post-cast concrete of the support beam 11, and the other end is located between the stirrup assembly 1 and the composite cast-in-place layer 8.

[0031] Specifically, in this embodiment, the precast concrete base slab 7 has a thickness of 70mm; the first distribution reinforcement 6 has a diameter of 6mm and a spacing of 150mm, and the first distribution reinforcement 6 and the first additional reinforcement 4 are connected by spot welding. The stirrup assembly 1 is arranged at both ends of the long span of the precast concrete base slab 7, with the arrangement section length being 1 / 4 of the slab span; the bottom is set below the non-prestressed reinforcement 3, and the top extends to the top reinforcement 5 of the slab. The stirrup 1 has a diameter of 6mm, a spacing of 400mm, a concave and convex length of 200mm, and a straight section length of 100mm at the outer end.

[0032] like Figure 11 As shown, the present invention also provides a design method for a unidirectional composite floor slab applicable to the above-mentioned inclined reinforced prestressed concrete composite floor slab. The design method assumes the following calculations before design: When the ratio of the long side to the short side of a prestressed concrete composite floor slab with diagonal reinforcement is not greater than 2, it should be designed as a two-way slab; when the ratio of the long side to the short side is greater than 2, it should be designed as a one-way slab.

[0033] The inclined reinforced prestressed concrete composite slab prevents the precast base slab from lifting and relative slippage with structural measures. The additional reinforcement can fully utilize its material strength, and the entire cross section of the composite slab is effective. Therefore, the calculation methods in the current national standard "Code for Design of Concrete Structures" (GB50010-2010) can be used to calculate the flexural bearing capacity of the composite slab's normal section and verify its shear bearing capacity of the inclined section.

[0034] Closely spaced joints weaken the flexural bearing capacity of the cross section. Therefore, when designing additional reinforcement, the design value of the bending moment of the joint section should be 10% greater than the design value of the bending moment of the entire cross section of the composite slab, and the calculated height of the section should be taken as the thickness of the composite cast-in-place layer.

[0035] Closely spaced joints weaken the shear control section at the support edge; therefore, only the contribution of the composite cast-in-place layer to the shear capacity of the inclined section is considered.

[0036] The weakening effect of close-fitting joints on the non-prestressed flexural stiffness of composite slabs necessitates the introduction of a non-prestressed stiffness adjustment coefficient into the calculation formula for the non-prestressed flexural stiffness of composite slabs. .

[0037] The design methodology specifically includes: Step 1: Estimate the current cross-sectional dimensions of the composite slab, and determine the structural parameters of the precast concrete base slab 7 based on the estimated cross-sectional dimensions of the composite slab. The structural parameters include the distance between the bending point of the non-prestressed steel bar 3 and the side of the precast concrete base slab 7, the bending angle of the non-prestressed steel bar 3, and the reverse bending length of the non-prestressed steel bar 3.

[0038] Step 1.1 Estimate the cross-sectional dimensions of the composite slab Specifically, the cross-sectional dimensions of the composite slab include length, width, and total thickness, determined by the following principles: the length of the composite floor slab is 2.1m to 9m; the width is... ,in The spacing between secondary beams is taken as a module of 50mm; the total thickness of the composite floor slab. Choose a diameter of 150mm to 300mm.

[0039] Understandably, other methods can also be used to estimate the cross-sectional dimensions of composite slabs based on actual needs.

[0040] Step 1.2: Determine the structural parameters of the precast concrete base slab. Specifically, it can be based on the total thickness of the composite plate. The structural parameters and material properties of the precast concrete base slab 7 are determined according to the following principles: the determination principle is based on the total thickness of the composite slab. Specifically, when 150mm ≤ When < 200mm, α It is 150°. a It is 50mm. The thickness is 100mm; the concrete grade of the precast concrete base slab 7 is not lower than C30, and the concrete grade of the composite cast-in-place layer 8 is not lower than C25; when 200mm ≤ When < 250mm, α It is 135°. a It is 40mm. The thickness is 70mm; the concrete grade of the precast concrete base slab 7 is not lower than C35, and the concrete grade of the composite cast-in-place layer 8 is not lower than C30; when 250mm ≤ When ≤300mm, α It is 120°. a It is 30mm. The thickness is 50mm; the concrete grade of the precast concrete base slab 7 is not lower than C40, and the concrete grade of the composite cast-in-place layer 8 is not lower than C35. Among them: [The text abruptly ends here, likely due to an incomplete sentence or missing information.] Figure 6-10 As shown, a The distance between the starting point of the non-prestressed steel bar bend 3 and the side of the precast concrete base slab 7. α For non-prestressed steel bars, the bending angle is 3. The horizontal reverse bending length of non-prestressed steel bar 3.

[0041] Understandably, other methods can also be used to determine the structural parameters of the precast concrete base slab 7 based on actual needs.

[0042] Step 2: Calculate the design load value under the load combination controlled by permanent load based on the estimated cross-sectional dimensions of the composite slab and the structural parameters of the precast concrete base slab (7). p Design values ​​of loads under quasi-permanent load combination p’ .

[0043] Specifically, during internal force analysis, load combinations can be performed according to the most unfavorable arrangement of live loads on the slab. The arrangement method can refer to the relevant provisions in the "Practical Handbook for Static Calculation of Building Structures" (Third Edition).

[0044] The internal force analysis of the composite slab is performed based on the load combination controlled by permanent loads. The load combination formula is as follows: When performing serviceability limit state verification, the maximum crack width and deflection are calculated based on the quasi-permanent load combination. The load combination formula is as follows: in: For the first A quasi-permanent value coefficient; For the first Partial factors for each dead load For the first Live load partial factor, For the first One standard value of dead load, For the first A standard value for live load, The number of constant loads participating in the combination, The number of live loads participating in the combination. The design value of dead load under the load combination controlled by permanent load. The design value of live load under the load combination controlled by permanent loads. The design value of the load under the load combination controlled by permanent load. The design value of dead load under quasi-permanent load combination, The design value of live load under quasi-permanent load combination. The design values ​​of the loads under the quasi-permanent load combination are given. , , , , The specific values ​​should comply with the relevant provisions in the current national standard "Code for Design of Building Structures" (GB50009-2012).

[0045] The above formulas can be used to calculate the design load values ​​under load combinations controlled by permanent loads. p Design values ​​of loads under quasi-permanent load combination p' .

[0046] Step 3: According to the one-way slab design, the design load values ​​are determined based on the load combination controlled by permanent loads. p Calculate the bending moment of the composite slab M With shear force V .

[0047] Specifically, when using a one-way slab design, the bending moment of the composite slab is calculated. M With shear force V， The bending moment of the composite slab can be calculated by referring to the relevant internal force coefficients in the "Practical Handbook for Static Calculation of Building Structures" (Third Edition). M and shear force V .

[0048] Step 4, based on the load design values ​​under the quasi-permanent load combination. p’ Calculate the maximum deflection within the span of the composite slab oh ; When using a one-way slab design, the maximum deflection within the span of the composite slab oh The calculation method is as follows: The formula for calculating the flexural stiffness of a one-way composite slab section is: Therefore, the formula for calculating its maximum deflection is: Where Bs is the short-term stiffness of the composite slab in the non-prestressed direction, B is the long-term stiffness of the composite slab in the non-prestressed direction, and Ec is the elastic modulus of concrete. The moment of inertia of the composite slab at mid-span section, This is the stiffness adjustment coefficient in the non-prestressed direction. For the flexural stiffness of cast-in-place floor slabs of uniform thickness, Flexural stiffness of composite slabs in the prestressing direction. This refers to the flexural stiffness of the composite slab in the non-prestressed direction. i To account for the influence coefficient of long-term load on deflection increase, ω is the maximum deflection within the span of the composite slab. The deflection coefficient for the composite plate is given. For the span of the composite slab, The design value of the load under the quasi-permanent load combination.

[0049] Specifically, the stiffness adjustment coefficient in the non-prestressed direction The calculation method is as follows: First, according to the design bending moment M With shear force V The reinforcement of the composite slab was designed according to the one-way slab principle. A finite element analysis model was established using ABAQUS software based on the actual geometric configuration, span, reinforcement, and other foundation conditions of the composite slab. The load-deflection curve of the composite slab was obtained according to the one-way slab analysis. The modeling method is as follows: Material constitutive model: The concrete constitutive model adopts the plastic damage model, and the element adopts C3D8R solid element; the constitutive models of ordinary steel bars and prestressed tendons adopt the ideal elastic-plastic model and the bilinear model proposed in the "Code for Design of Concrete Structures" (GB50010-2010), respectively, and the element adopts T3D2 truss element.

[0050] Material interaction: Because the composite slab of this invention can completely prevent tearing damage between the old and new concrete at the composite surface through structural measures, the bond slip between the steel reinforcement and the concrete can be disregarded. The interaction between the steel reinforcement and the concrete is an embedded relationship; the contact relationship between the precast concrete base slab 7 and the composite cast-in-place layer 8 is set as a tie connection.

[0051] Mesh division: The concrete unit mesh size is 50mm, and the steel reinforcement unit size is 20mm.

[0052] Boundary conditions: Rigid supports are arranged on the edge of the composite slab, the support beam 11 is bound to the bottom of the slab, the reference point is arranged at the center of the four-sided support beam 11, the coupling relationship between the two is established, and the corresponding linear and angular displacements of the coupling point are restricted to achieve the simply supported boundary conditions.

[0053] Prestressing application and loading method: The prestressing application process is simulated in ABAQUS using the cooling method. The calculation formula is as follows: in, ΔT For temperature difference; E S This refers to the elastic modulus of the steel reinforcement in the tension zone of the cross section, and the specific value should be taken according to the requirements of the table in the "Code for Design of Concrete Structures" (GB50010-2010). This represents the actual prestress after the breakage. βThis is the coefficient of linear expansion of the reinforcing steel. .

[0054] Applying prestress and simulating test loading conditions can be accomplished in three steps: S1 uses Model change to suspend the composite concrete unit, steel reinforcement unit and rigid support under the component, and applies prestress to the prestressed steel reinforcement in the precast concrete base slab 7 by defining temperature changes. S2, activate the suspended unit and the initial boundary conditions to ensure that the first step only applies prestress to the precast concrete base plate 7; S3, a reference point coupled to the loading surface is set directly above the center of the distribution beam, and the concentrated load is applied to the reference point. The load-deflection curve obtained through finite element analysis is used to determine the mid-span displacement. L Secant stiffness at / 200 is converted to actual bending stiffness of composite slab. D 1. Compare its bending stiffness with that of cast-in-place floor slabs of equal thickness. D The non-prestressed direction stiffness adjustment coefficient is obtained by comparing it with 0. The specific formula is as follows: in: L For the span of the composite slab; D 1. Bending stiffness of the prestressed slab; D 0 represents the bending stiffness of cast-in-place floor slabs of uniform thickness. For specific calculation methods, please refer to the "Code for Design of Concrete Structures" (GB50010-2010).

[0055] Step 5, based on the bending moment of the composite slab M Calculate the reinforcement details for the bending steel bars of the bottom slab and the reinforcement details for the support sections of the composite slab.

[0056] Specifically, the reinforcement of the bottom slab for bending resistance can be designed and configured according to the following process: Step 5.1: Reinforce the bottom slab with flexural steel bars according to a single-reinforced rectangular section; Step 5.2: Determine whether the current configuration of the bottom slab bending reinforcement ratio is greater than the preset minimum bottom slab bending reinforcement ratio. If it is less than or equal to the preset minimum bottom slab bending reinforcement ratio, then proceed to step 5.4 after reinforcement according to the minimum reinforcement ratio; if it is greater than the preset minimum bottom slab bending reinforcement ratio, then proceed to step 5.3. Step 5.3: Determine whether the current configured bottom slab bending reinforcement ratio is less than the preset maximum bottom slab bending reinforcement ratio. If it is less than the preset maximum bottom slab bending reinforcement ratio, proceed directly to step 5.4. If the reinforcement ratio is greater than or equal to the preset maximum flexural reinforcement ratio of the bottom slab, the flexural reinforcement of the bottom slab should be redesigned according to the doubly reinforced rectangular section. After the redesign, the flexural reinforcement ratio of the bottom slab needs to be determined again. If the reinforcement ratio is less than or equal to the preset minimum slab bending reinforcement ratio, then proceed to step 5.4 after reinforcement is carried out according to the minimum reinforcement ratio; if the reinforcement ratio is greater than the preset minimum slab bending reinforcement ratio but less than the preset maximum slab bending reinforcement ratio, then proceed directly to step 5.4; if the reinforcement ratio is greater than or equal to the maximum slab bending reinforcement ratio, then the total thickness of the composite slab needs to be increased, and the process should be restarted from step 1. Step 5.4: Design the reinforcement of the joints within the span and the reinforcement of the joints at the supports.

[0057] More specifically, when designing the flexural reinforcement of the base slab, the flexural reinforcement of the base slab is first designed according to the single-reinforced section. The flexural reinforcement of the base slab is the non-prestressed reinforcement 3. If the reinforcement ratio of the flexural reinforcement of the base slab meets the requirement of being greater than... r min and less than r max If the reinforcement ratio does not meet the requirement of being greater than 1, proceed to the next step; r min If the reinforcement is done according to the minimum reinforcement ratio, proceed to the next step; where... r max and r min The maximum and minimum reinforcement ratios of the tensile reinforcement in the bottom slab when designed as a single-reinforced rectangular section.

[0058] If the reinforcement ratio of the bottom slab bending reinforcement is greater than the minimum reinforcement ratio designed according to the single-reinforced section in the code, but not less than the maximum reinforcement ratio designed according to the single-reinforced section in the code, then the bottom slab bending reinforcement shall be designed according to the double-reinforced section. When designing the flexural reinforcement of the bottom slab according to the doubly reinforced section, if the flexural reinforcement ratio of the bottom slab meets the requirement of being greater than r min and less than r max If the reinforcement ratio does not meet the requirement of being greater than 1, proceed to the next step; r min If the minimum reinforcement ratio is used, proceed to the next step; if the flexural reinforcement ratio of the bottom slab is greater than... r min However, it does not satisfy the condition of being less than r max After increasing the total thickness of the composite slab by a module of 50mm, return to step one and redesign until the requirements are met before proceeding to the next step. r max , r minThe maximum and minimum reinforcement ratios of the tensile reinforcement in the bottom slab when designed with a doubly reinforced rectangular section as specified in the Code for Design of Concrete Structures (GB50010-2010).

[0059] Further design of reinforcement details for internal joints; Specifically, the reinforcement of the intra-span joints, also known as the intra-span close-joint reinforcement, refers to the reinforcement of the first additional steel bar 4. The first additional steel bar 4 has a diameter of 12mm and an anchorage length of [missing information]. ,in The values ​​should comply with the relevant provisions in the "Code for Design of Concrete Structures" (GB50010-2010). When the first additional reinforcement 4 is under tension, the reinforcement ratio of the first additional reinforcement 4 per unit width of the slab should be greater than the reinforcement ratio of the non-prestressed reinforcement 3 in the precast concrete base slab 7. The reinforcement design can be carried out according to the following formula: When the first additional reinforcing bar 4 is under compression, the cross-sectional area of ​​the first additional reinforcing bar 4 should satisfy the following formula:

[0060] in: A s1 The cross-sectional area of ​​the non-prestressed steel reinforcement in the precast concrete base slab 7 is shown in section 3. A s2 The cross-sectional area of ​​the first additional reinforcing bar is 4. This represents the total thickness of the composite slab. The thickness of the composite cast-in-place layer is 8 mm. The effective height of the entire cross-section of the composite slab. For the effective height of the superimposed cast-in-place layer, The distance from the resultant point of the non-prestressed steel reinforcement 3 in the precast concrete base slab 7 to the bottom of the slab. The distance from the resultant point of the first additional reinforcement bar 4 to the overlapping surface.

[0061] Further design of the reinforcement of the composite slab support section; Specifically, the effective height of the support section is taken as the thickness of the composite cast-in-place layer 8, and the second additional steel bar 10 serves as the bottom steel bar of the section. Its reinforcement design refers to the rectangular section design method in the existing technology.

[0062] Step 6, based on shear force V Determine if the shear capacity of the inclined section meets the preset design requirements. If not, adjust the thickness of the composite slab until the preset design requirements are met. Determine the maximum deflection within the span of the composite slab. oh Maximum crack width ω between the bottom and top of the composite slab maxDoes it meet the preset requirements? If yes, otherwise adjust the thickness of the composite slab or the reinforcement of the bending steel bars, and return to step 1 until the maximum deflection within the span of the composite slab is achieved. oh Maximum crack width ω between the bottom and top of the composite slab max All meet the preset design requirements.

[0063] Step 6.1, verify the shear capacity of the inclined section. Specifically, for one-way slab design, this also includes verifying the shear capacity of the inclined section, based on the shear force. V Determine whether the shear capacity of the inclined section meets the preset design requirements. If not, adjust the thickness of the composite slab until the preset design requirements are met.

[0064] For example, the formula for verifying the shear capacity of a one-way composite slab with an inclined section is as follows: in, For the influence coefficient of section height, when At that time, take , This represents the design value of the tensile strength of the composite concrete layer. For the width of the board, For the effective height of the superimposed cast-in-place layer, V The design value of shear force under load combinations controlled by permanent loads.

[0065] If the verification does not meet the requirements, increase the total thickness of the composite plate by 50mm as the module and return to the first step to redesign until the requirements are met before proceeding to the next step.

[0066] Step 6.2, verify the deflection of the composite plate; Specifically, determine the maximum deflection within the span of the composite slab. oh Does it meet the preset design requirements? If the maximum deflection within the span of the composite slab is... oh If the preset requirements are not met, the total thickness of the composite slab is increased. For example, if the deflection calculation does not meet the requirements, the total thickness of the composite slab is increased by 50mm as the module, and the process returns to step one to redesign until the requirements are met before proceeding to the next step.

[0067] Step 6.3: Calculate the maximum crack width between the bottom and top of the composite slab; Specifically, determine the maximum crack width between the bottom and top of the composite slab. oh max Does it meet the preset design requirements? If the maximum crack width between the bottom and top of the composite slab is... oh maxIf the preset requirements are not met, first reduce the diameter and spacing of the reinforcing bars. If the preset requirements are still not met, increase the reinforcement ratio of the bending reinforcing bars. Return to step 1. If the design requirements are met, exit.

[0068] For example, crack control levels can be divided into three levels. The maximum crack width at the bottom of the composite slab is calculated by taking the maximum positive bending moment within the span of the composite slab, and the maximum crack width at the top of the composite slab is calculated by taking the maximum negative bending moment at the support edge. oh max The maximum crack width limit should be met as specified in the Code for Design of Concrete Structures (GB50010-2010). oh lim If the crack width calculation does not meet the requirements, the diameter of the reinforcing bars should be reduced according to the principle of equal area replacement, and the spacing of the reinforcing bars should be reduced before recalculation. If the requirements are met, the design is completed. If the requirements are still not met, the reinforcement ratio of the non-prestressed reinforcing bars in the bending reinforcement should be increased and the design should be returned to step six and recalculated until the requirements are met.

[0069] Example 2 A type of inclined prestressed two-way concrete composite floor slab includes non-prestressed steel bars 3, stirrup assembly 1, first additional steel bars 4, and first distribution steel bars 6, as shown below. Figure 1-10 As shown, the stirrup assembly 1 is arranged at the top along the long span direction of the precast concrete base slab 7; the first additional reinforcing bar 4 is centrally located at the close joint of the precast concrete base slab 7; the first distributed reinforcing bar 6 is arranged above the first additional reinforcing bar 4; the non-prestressed reinforcing bar 3 is arranged along the short span direction of the precast concrete base slab 7, with its end bent upwards and extending out from the top of the side of the precast concrete base slab 7, then bent horizontally in reverse, and its end extends obliquely to the opposite side of the overlapping cast-in-place layer 8 for anchoring. Specifically, the thickness of the precast concrete base slab 7 is 70mm; the diameter of the first distributed reinforcing bar 6 is 6mm, the spacing is 150mm, and the first distributed reinforcing bar 6 and the first additional reinforcing bar 4 are connected by spot welding.

[0070] Specifically, the stirrup assembly 1 is arranged at both ends of the long span of the precast concrete base slab 7, with the length of the arrangement section being 1 / 4 of the slab span; the bottom is set below the non-prestressed steel bar 3, and the top extends to the top steel bar 5 of the slab. Specifically, the stirrup has a diameter of 6mm, a spacing of 400mm, a concave and convex length of 200mm, and a straight section length of 100mm at the outer end.

[0071] Specifically, the inclined prestressed concrete composite floor slab further includes a second distribution reinforcement 9 and a second additional reinforcement 10. The second distribution reinforcement 9 is arranged perpendicular to the second additional reinforcement 10. The second additional reinforcement 10 is anchored into the post-cast concrete of the support beam 11. The second additional reinforcement 10 is arranged perpendicular to the support beam 11 at the top of the precast concrete base slab 7. Specifically, the second additional reinforcement 10 is anchored into the post-cast concrete of the support beam 11 by an indirect lap joint.

[0072] like Figure 12 As shown, the present invention also provides a design method for a two-way composite floor slab applicable to the above-mentioned inclined reinforced prestressed concrete composite floor slab, specifically including: Step 1: Estimate the current cross-sectional dimensions of the composite slab, and determine the structural parameters of the precast concrete base slab 7 based on the estimated cross-sectional dimensions of the composite slab. The structural parameters include the distance between the bending point of the non-prestressed steel bar 3 and the side of the precast concrete base slab 7, the bending angle of the non-prestressed steel bar 3, and the reverse bending length of the non-prestressed steel bar 3.

[0073] Specifically, estimate the cross-sectional dimensions of the composite slab, including its length, width, and total thickness. The principles for determining these dimensions are: the length of the composite floor slab should be 2.1m to 9m; the width should be... ,in The spacing between secondary beams is taken as a module of 50mm; the total thickness of the composite floor slab. Choose a diameter of 150mm to 300mm.

[0074] Specifically, it can be based on the total thickness of the composite plate. The structural parameters and material properties of the precast concrete base slab 7 are determined according to the following principles: when 150mm ≤ When < 200mm, α It is 150°. a It is 50mm. The thickness is 100mm; the concrete grade of the precast concrete base slab 7 is not lower than C30, and the concrete grade of the composite cast-in-place layer 8 is not lower than C25; when 200mm ≤ When < 250mm, α It is 135°. a It is 40mm. The thickness is 70mm; the concrete grade of the precast concrete base slab 7 is not lower than C35, and the concrete grade of the composite cast-in-place layer 8 is not lower than C30; when 250mm ≤ When ≤300mm, α It is 120°. a It is 30mm. The thickness is 50mm; the concrete grade of the precast concrete base slab 7 is not lower than C40, and the concrete grade of the composite cast-in-place layer 8 is not lower than C35. Among them: [The text abruptly ends here, so the translation stops as well.] Figure 4-10 As shown, a The distance between the starting point of the non-prestressed steel bar bend 3 and the side of the precast concrete base slab 7. α For non-prestressed steel bars, the bending angle is 3. The horizontal reverse bending length of the non-prestressed steel bar is 3.

[0075] Step 2: Calculate the design load value under the load combination controlled by permanent load based on the estimated cross-sectional dimensions of the composite slab and the structural parameters of the precast concrete base slab (7). p Design values ​​of loads under combination of quasi-permanent loads p’ .

[0076] Specifically, the internal forces of the composite slab are analyzed based on the load combination controlled by permanent loads. The load combination formula is as follows: When performing serviceability limit state verification, the maximum crack width and deflection are calculated based on the quasi-permanent load combination. The load combination formula is as follows: in: For the first A quasi-permanent value coefficient; For the first Partial factors for each dead load For the first Live load partial factor, For the first One standard value of dead load, For the first A standard value for live load, The number of constant loads participating in the combination, The number of live loads participating in the combination. The design value of dead load under the load combination controlled by permanent load. The design value of live load under the load combination controlled by permanent loads. The design value of the load under the load combination controlled by permanent load. The design value of dead load under quasi-permanent load combination, The design value of live load under quasi-permanent load combination. The design values ​​of the loads under the quasi-permanent load combination are given. , , , , The specific values ​​should comply with the relevant provisions in the current national standard "Code for Design of Building Structures" (GB50009-2012).

[0077] Step 3: According to the two-way slab design, the design load value is determined based on the load combination controlled by permanent loads. p Calculate the bending moment of the composite slabM。

[0078] Step 3.1: Based on the specific construction conditions, the design is divided into single-zone two-way slab and multi-zone two-way slab designs; When designing a multi-zone two-way slab, the multi-zone two-way slab is transformed into a single-zone two-way slab for structural analysis by simplifying the most unfavorable arrangement of live loads and support conditions.

[0079] Step 3.2, calculate the positive bending moment within the span of the composite slab. M With support negative bending moment M' : Specifically, the internal forces of the single-cell two-way composite slab are analyzed using the method of elasticity mechanics. Based on the anisotropic thin plate theory in elasticity mechanics, the ratio of the bending stiffness of the composite slab in the prestressed direction to that in the non-prestressed direction is introduced. Establish the deflection differential equation for a single-grid orthotropic prestressed two-way composite slab: in, D 1. Bending stiffness of composite slab in the prestressing direction. D 2 This refers to the flexural stiffness of the composite slab in the non-prestressed direction. D 3 represents the torsional stiffness of the composite plate; For the torsional stiffness of the composite plate Poisson's ratio for concrete G Shear modulus This represents the total thickness of the composite slab. oh Let be the deflection at any point within the composite plate.

[0080] The Matlab program was used to solve the deflection differential equation, calculate the internal force coefficients, and calculate the bending moment of the composite slab based on the bending moment calculation coefficients. The specific formulas are as follows: in: This represents the ratio of the flexural stiffness of the composite slab in the prestressed direction to that in the non-prestressed direction. 、 These are the calculation coefficients for the positive bending moment within the span in the prestressed and non-prestressed directions of the composite slab, respectively. 、 Calculation coefficients for negative bending moments at supports in the prestressed and non-prestressed directions of composite slabs. The design value of the load under the load combination controlled by permanent load. For the span of the composite slab, Poisson's ratio for concrete , They are respectively Design values ​​of positive bending moments within the span in the prestressed and non-prestressed directions of the composite slab. , They are respectively Design values ​​of negative bending moments at supports in the prestressed and non-prestressed directions of the composite slab. , They are respectively Design values ​​of positive bending moments within the span in the prestressed and non-prestressed directions of the composite slab. , They are respectively Design values ​​of negative bending moments at supports in the prestressed and non-prestressed directions of the composite slab.

[0081] Step 4, based on the load design values ​​under the quasi-permanent load combination. p’ Calculate the maximum deflection within the span of the composite slab oh ; Specifically, according to the two-way slab design, the maximum deflection within the span of the composite slab is... oh According to the load design value under the quasi-permanent load combination p’ The calculations were obtained from the deflection coefficient of the composite slab, the span of the composite slab, and the bending stiffness of the composite slab in the non-prestressed direction.

[0082] More specifically, the detailed process for calculating the maximum deflection is as follows: Solve the aforementioned deflection differential equation, and then use Matlab to calculate the deflection coefficients. Based on this, the deflection of the composite plate can be calculated using the following formula: in, The deflection coefficient for the composite plate is given. For the span of the composite slab, The design value of the load under the quasi-permanent load combination. D 2 This refers to the flexural stiffness of the composite slab in the non-prestressed direction. , This is the stiffness adjustment coefficient in the non-prestressed direction. E CThe elastic modulus of concrete. Let be the moment of inertia of the composite slab section.

[0083] Step 5, based on the bending moment of the composite plate M Calculate the reinforcement of the bottom slab under bending, the reinforcement of the composite slab support section, and the reinforcement of the composite slab support section respectively.

[0084] Specifically, when designing the bending reinforcement of the base slab, the bending reinforcement of the base slab is first designed according to the single-reinforced section. The bending reinforcement of the base slab is the non-prestressed reinforcement 3. If the reinforcement ratio of the bending reinforcement of the base slab meets the requirement of being greater than... r min and less than r max If the reinforcement ratio does not meet the requirement of being greater than 1, proceed to the next step; r min If the reinforcement is done according to the minimum reinforcement ratio, proceed to the next step; where... r max and r min The maximum and minimum reinforcement ratios of the tensile reinforcement in the bottom slab when designed with a single-reinforced rectangular section as specified in the Code for Design of Concrete Structures (GB50010-2010).

[0085] If the reinforcement ratio of the bottom slab bending reinforcement is greater than the minimum reinforcement ratio designed for a single-reinforced section in the code, but not less than the maximum reinforcement ratio designed for a single-reinforced section in the code, then the bottom slab bending reinforcement design shall be carried out according to a doubly reinforced section. When designing the flexural reinforcement of the bottom slab according to the doubly reinforced section, if the flexural reinforcement ratio of the bottom slab meets the requirement of being greater than r min and less than r max If the reinforcement ratio does not meet the requirement of being greater than 1, proceed to the next step; r min If the minimum reinforcement ratio is used, proceed to the next step; if the flexural reinforcement ratio of the bottom slab is greater than... r min However, it does not satisfy the condition of being less than r max After increasing the total thickness of the composite slab by a module of 50mm, return to step one and redesign until the requirements are met before proceeding to the next step. r max , r min The maximum and minimum reinforcement ratios of the tensile reinforcement in the bottom slab when designed with a doubly reinforced rectangular section as specified in the Code for Design of Concrete Structures (GB50010-2010).

[0086] Further design of reinforcement for the internal close-joint joints; Specifically, the reinforcement of the close-fitting joints within the span, i.e., the reinforcement of the first additional steel bar 4, should have a diameter of 12mm and an anchorage length of [missing information]. ,in The values ​​should comply with the relevant provisions in the "Code for Design of Concrete Structures" (GB50010-2010). When the first additional reinforcement 4 is under tension, the reinforcement ratio of the first additional reinforcement 4 per unit slab width should be greater than the reinforcement ratio of the non-prestressed reinforcement 3 in the precast concrete base slab 7, and the reinforcement design should be carried out according to the following formula: When the first additional reinforcing bar 4 is under compression, the cross-sectional area of ​​the first additional reinforcing bar 4 should satisfy the following formula: in, A s1 The cross-sectional area of ​​the non-prestressed steel reinforcement in the precast concrete base slab 7 is shown in section 3. A s2 The cross-sectional area of ​​the first additional reinforcing bar is 4. This represents the total thickness of the composite slab. The thickness of the composite cast-in-place layer is 8 mm. The effective height of the entire cross-section of the composite slab. For the effective height of the superimposed cast-in-place layer, The distance from the resultant point of the non-prestressed steel reinforcement 3 in the precast concrete base slab 7 to the bottom of the slab. The distance from the resultant point of the first additional reinforcement bar 4 to the overlapping surface.

[0087] Further design of the reinforcement of the composite slab support section; Specifically, the effective height of the support section is taken as the thickness of the composite cast-in-place layer 8, and the second additional steel bar 10 serves as the bottom steel bar of the section. Its reinforcement design can adopt the rectangular section design method in the existing technology.

[0088] Step 6: Determine the maximum deflection within the span of the composite slab. oh Maximum crack width between the bottom and top of the composite slab oh max Does it meet the preset requirements? If yes, otherwise adjust the thickness of the composite slab or the reinforcement of the bending steel bars, and return to step 1 until the maximum deflection within the span of the composite slab is achieved. oh Maximum crack width between the bottom and top of the composite slab oh max All meet the preset design requirements, and when designed as a one-way slab, the requirements are also included based on shear force. V Determine whether the shear capacity of the inclined section meets the preset design requirements. If not, adjust the thickness of the composite slab until the preset design requirements are met.

[0089] 6.1 Verify the deflection of the composite slab; Specifically, determine the maximum deflection within the span of the composite slab. oh Does it meet the preset design requirements? If the maximum deflection within the span of the composite slab is... oh If the preset requirements are not met, the total thickness of the composite slab should be increased. For example, the deflection limit should comply with the relevant provisions on structural durability in the current national standard "Code for Design of Concrete Structures" (GB50010-2010). If the deflection calculation does not meet the requirements, the total thickness of the composite slab should be increased by 50mm (configurable) as the module, and the process should return to step one and redesign until the requirements are met before proceeding to the next step.

[0090] Step 6.2, verify the maximum crack width between the bottom and top of the composite slab; Specifically, determine the maximum crack width between the bottom and top of the composite slab. oh max Does it meet the preset design requirements? If the maximum crack width between the bottom and top of the composite slab is... oh max If the preset requirements are not met, first reduce the diameter and spacing of the reinforcing bars. If the preset requirements are still not met, increase the reinforcement ratio of the bending reinforcing bars. Return to step 1. If the design requirements are met, exit.

[0091] For example, crack control levels can be divided into three levels. The maximum crack width at the bottom of the composite slab is calculated by taking the maximum positive bending moment within the span of the composite slab, and the maximum crack width at the top of the composite slab is calculated by taking the maximum negative bending moment at the support edge. oh max The maximum crack width limit should be met as specified in Table 3.4.5 of the Code for Design of Concrete Structures (GB50010-2010). oh lim The specific calculations shall be performed according to the formulas in the "Code for Design of Concrete Structures" (GB50010-2010).

[0092] If the crack width calculation does not meet the requirements, the diameter of the reinforcing bars should be reduced according to the principle of equal area replacement, and the spacing of the reinforcing bars should be reduced before recalculation. If the requirements are met, the design is completed. If the requirements are still not met, the reinforcement ratio of the non-prestressed reinforcing bars in the bending reinforcement should be increased and the design should be returned to step seven and recalculated until the requirements are met.

[0093] Example 3 To further illustrate the performance of the present invention, the following embodiments are provided, in which key mechanical parameters of a prestressed concrete composite slab with inclined reinforcement (hereinafter referred to as composite slab A) are calculated and analyzed, and a cast-in-place slab and a standard composite slab are compared and analyzed accordingly. The geometric dimensions, peripheral support conditions, and longitudinal reinforcement ratio of the bottom reinforcement of the cast-in-place slab are the same as those of composite slab A in this embodiment. The concrete strength grade is C30, and it is cast in one piece without joints or overlapping surfaces. It is referred to as cast-in-place slab A below. The bottom plate dimensions, composite layer thickness, peripheral support conditions, concrete strength grade, joint location, and first additional reinforcement at the joint of the standard composite slab are the same as those of composite slab A in this embodiment. The only difference is that it adopts the separated joint structure recommended in the "Technical Specification for Precast Concrete Structures" (JGJ1-2014), and the precast concrete bottom plate has no reinforcement on the side. It is referred to as composite slab B below.

[0094] Example: Using the above-mentioned inclined reinforced prestressed concrete composite slab and its design method, a four-sided simply supported single-section slab is designed. The slab dimensions are 6800mm × 6800mm × 150mm, and it is composed of four 6800mm × 1700mm × 70mm inclined reinforced prestressed concrete precast base slabs 7 closely joined together. Figure 4-10 As shown, the thickness of the composite cast-in-place layer 8 is 80mm.

[0095] 1. Design materials Based on the length-to-width ratio of the floor slab, it should be designed as a single-section, two-way slab. The precast concrete base slab 7 uses C40 concrete, and the composite cast-in-place layer 8 uses C30 concrete. In the composite slab, the non-prestressed steel reinforcement 3 uses HRB400 grade steel; the prestressed reinforcement uses… Spiral ribbed steel wire , , The live load in the design is taken according to the "Load Code for Design of Building Structures" (GB5000 9-2012). The concrete protective layer is 20mm thick. Among other things: This refers to the standard value of the ultimate strength of prestressed steel bars. This is the design value of the tensile strength of prestressed steel bar 2; This is to control the stress during tensioning.

[0096] 2. Load Combination Load combinations controlled by permanent loads: Quasi-permanent load combination:

[0097] 3. Solve for internal forces and deflection coefficients (1) The load-deflection curve of the composite slab under loading was simulated using ABAQUS finite element software. The finite element model dimensions were 6800mm × 1000mm × 150mm, and the thickness of the cast-in-place layer of the composite slab was 80mm. The reinforcement design of this model should refer to the one-way slab reinforcement design in the design method of this patent; when calculating internal forces, the flexural bearing capacity of the section should be multiplied by 0.5 for reduction. The specific modeling and analysis results are as follows: Figure 13 As shown.

[0098] (2) The load-deflection curve obtained through finite element analysis is based on the mid-span displacement reaching L Secant stiffness at / 200 is converted to the actual bending stiffness of the composite slab. Compare it with the flexural stiffness of cast-in-place floor slabs of equal thickness Compared to the obtained non-prestressed direction stiffness adjustment coefficient .in L This refers to the span of the composite slab.

[0099] (3) Based on the theory of anisotropic thin plates, the ratio of the bending stiffness of the prestressed direction to the non-prestressed direction of the composite plate is introduced. Establish the deflection differential equation for a single-segment prestressed two-way composite slab: , Based on steps five and six of the two-way slab design method, the bending moment coefficient in the prestressing direction is calculated using MATLAB. Bending moment coefficient in non-prestressed direction Deflection coefficient .

[0100] 4. Internal force calculation and reinforcement design of cross-sections within the span Where: As is the cross-sectional area of ​​the steel reinforcement; , For structural reinforcement.

[0101] in: , For structural reinforcement.

[0102] 5. Comparison of Calculation Results Table 3 compares the ultimate load and deflection of the embodiment with those of cast-in-place slabs of equal size and reinforcement ratio, and composite slabs with separate joints of equal span. The ultimate load of the inclined-reinforced prestressed concrete composite slab is close to that of the cast-in-place slab, but the deflection is 29.3% higher. This indicates that since the design method for cast-in-place slabs does not consider the orthotropic stiffness of the slab, directly applying this method to design the inclined-reinforced prestressed concrete composite slab will lead to dangerously biased deformation calculation results. The ultimate load of the inclined-reinforced prestressed concrete composite slab is 42.70% higher than that of the standard closely spaced composite slab, while the deflection is much smaller than that of the standard separated-joint composite slab, proving that the joint force transmission mechanism of the composite slab in this invention is reliable and applicable to two-way slabs.

[0103] In summary, the composite slab joint structure of this invention has superior force transmission performance compared to the standard separated joint, and the bending bearing capacity at the joint is basically equivalent to that of cast-in-place slabs. However, it is not applicable to the deflection calculation and analysis methods of cast-in-place slabs. The exclusive design method developed by this invention can more realistically reflect the bidirectional anisotropic stiffness distribution of the composite slab, so the calculated deflection is closer to the actual stress characteristics of the floor slab, and it is safer than the deflection design theory of cast-in-place floor slabs.

Claims

1. A prestressed concrete composite floor slab with inclined reinforcement, comprising prestressed steel bars (2) and non-prestressed steel bars (3) connected perpendicularly to each other, characterized in that, It also includes a precast concrete base slab (7), a stirrup assembly (1), and a top slab reinforcement (5), wherein the top slab reinforcement (5) is located at the upper end of the composite cast-in-place layer (8); the stirrup assembly (1) is connected between the top slab reinforcement (5) and the prestressed reinforcement (2) to form an integral reinforced structure; The non-prestressed steel bars (3) are inserted into the precast concrete base slab (7) and arranged along the short span direction of the precast concrete base slab (7). The ends of the non-prestressed steel bars (3) extend from the top of the side end of the precast concrete base slab (7) and extend obliquely to connect with the top steel bars (5) of the slab. The extended ends of the non-prestressed steel bars (3) of adjacent precast concrete base slabs (7) are staggered along the joints of the composite floor slabs.

2. The inclined reinforced prestressed concrete composite floor slab according to claim 1, characterized in that, The end of the non-prestressed steel bar (3) includes a bent extension section and a horizontal connecting section connected to each other. The bent extension section is inclined toward the adjacent precast concrete base plate (7) and extends to the top of the adjacent precast concrete base plate (7). The horizontal connecting section is set in the opposite direction to the bent extension section and is connected to the top steel bar (5) of the plate in reverse bend.

3. The inclined reinforced prestressed concrete composite floor slab according to claim 1, characterized in that, The stirrup assembly (1) consists of multiple sets, which are arranged along the short span direction of the precast concrete base slab (7). Each stirrup assembly includes multiple stirrups that are spaced apart and connected to each other along the long span direction of the precast concrete base slab (7).

4. The inclined reinforced prestressed concrete composite floor slab according to any one of claims 1 to 3, characterized in that, It also includes a first reinforcing steel assembly located at the joint of the composite floor slab. The first reinforcing steel assembly includes a first additional steel bar (4) and a first distribution steel bar (6). The first additional steel bar (4) is arranged vertically at the close joint of the precast concrete base slab (7). The first distribution steel bar (6) is arranged at intervals along the length direction of the first additional steel bar (4), and each of the first distribution steel bars (6) is vertically connected to the upper surface of the first additional steel bar (4).

5. The inclined reinforced prestressed concrete composite floor slab according to claim 1, characterized in that... It also includes a second reinforcing steel assembly arranged on the outer periphery of the composite floor slab. The second reinforcing steel assembly includes a second distributed steel bar (9) and a second additional steel bar (10) that are perpendicular to each other. One end of the second additional steel bar (10) is anchored into the post-cast concrete of the support beam (11), and the other end is located between the stirrup assembly (1) and the composite cast-in-place layer (8).

6. A design method for a prestressed concrete composite floor slab with inclined reinforcement according to any one of claims 1-5, characterized in that, include: Step 1: Determine whether the composite floor slab is designed as a one-way slab or a two-way slab based on the ratio between the long side and the short side of the composite slab, estimate the current cross-sectional dimensions of the composite slab, and determine the structural parameters of the precast concrete base slab (7) based on the estimated cross-sectional dimensions of the composite slab. The structural parameters include any one or more of the following: the distance between the bending point of the non-prestressed steel bar (3) and the side of the precast concrete base slab (7), the bending angle of the non-prestressed steel bar (3), and the reverse bending length of the non-prestressed steel bar (3). Step 2: Calculate the design load value under the load combination controlled by permanent load based on the estimated cross-sectional dimensions of the composite slab and the structural parameters of the precast concrete base slab (7). p Design values ​​of loads under quasi-permanent load combination p’ ; Step 3: Calculate the bending moment and shear force of the composite slab. Determine whether the composite slab is designed as a one-way slab or a two-way slab based on the ratio between the long and short sides of the composite slab. When designed as a one-way slab, calculate the bending moment and shear force of the composite slab based on the design values ​​of the load combination controlled by the permanent load. When designed as a two-way slab, calculate the positive bending moment within the span and the negative bending moment at the supports of the composite slab based on the bending differential equation of the orthotropic prestressed two-way composite slab, based on the design values ​​of the load combination controlled by the permanent load. Step 4: Calculate the maximum deflection within the span of the composite slab based on the load design values ​​under the quasi-permanent load combination. ω ; Step 5, based on the bending moment of the composite plate M Calculate the flexural reinforcement of the bottom slab, the reinforcement of the joints within the span, and the reinforcement of the composite slab support section separately; Step 6: Determine whether the maximum deflection ω within the span of the composite slab and the maximum crack width at the bottom and top of the composite slab are within the range required by the design specifications. If not, adjust the thickness of the composite slab or the reinforcement of the bending steel bars, and return to Step 1 until the maximum deflection ω within the span of the composite slab and the maximum crack width at the bottom and top of the composite slab are both within the range required by the design specifications, then the design is complete. When designed as a one-way slab, before determining the maximum deflection ω within the span of the composite slab and the maximum crack width at the bottom and top of the composite slab, it also includes determining whether the shear capacity of the inclined section is within the range required by the design specifications based on the shear force V. If not, control and adjust the thickness of the composite slab until the shear capacity is within the range required by the design specifications.

7. The design method for inclined reinforced prestressed concrete composite floor slabs according to claim 6, characterized in that, In step 1, the structural parameters of the precast concrete base slab (7) are determined based on the estimated cross-sectional dimensions of the composite slab, specifically including: When 150mm ≤ When < 200mm, α It is 150°. a It is 50mm. The concrete grade of the precast concrete base slab (7) shall not be lower than C30, and the concrete grade of the composite cast-in-place layer (8) shall not be lower than C25. When 200mm ≤ When < 250mm, α It is 135°. a It is 40mm. The concrete grade of the precast concrete base slab (7) shall not be lower than C35, and the concrete grade of the composite cast-in-place layer (8) shall not be lower than C30. When 250mm ≤ When ≤300mm, α It is 120°. a It is 30mm. The concrete grade of the precast concrete base slab (7) shall not be lower than C40, and the concrete grade of the composite cast-in-place layer (8) shall not be lower than C35. in: a The distance between the bend point of the non-prestressed steel bar (3) and the side of the precast concrete base slab (7) α For non-prestressed steel bars (3) bending angle, The horizontal reverse bending length of non-prestressed steel bar (3) This represents the total thickness of the composite floor slab.

8. The design method for inclined reinforced prestressed concrete composite floor slabs according to claim 6, characterized in that, In step 4, when designed as a one-way slab, the method for calculating the maximum deflection ω within the span of the composite slab is as follows: When designed as a two-way slab, the maximum deflection within the span of the composite slab is... ω The calculation method is as follows: Establish the deflection differential equation and calculate the deflection coefficients of the composite plate under different boundary conditions. in, B s For the short-term stiffness of the composite slab in the non-prestressed direction, B This refers to the long-term stiffness of the composite slab in the non-prestressed direction. E c The elastic modulus of concrete. The moment of inertia of the composite slab at mid-span section, This is the stiffness adjustment coefficient in the non-prestressed direction. D 0 represents the flexural stiffness of a cast-in-place floor slab of uniform thickness. D 1. Bending stiffness of composite slab in the prestressing direction. D 2 This refers to the flexural stiffness of the composite slab in the non-prestressed direction. θ To account for the influence coefficient of long-term load on the increase of deflection, ω This represents the maximum deflection within the span of the composite slab. The deflection coefficient for the composite plate is given. For the span of the composite slab, The design value of the load under the quasi-permanent load combination.

9. The design method for inclined reinforced prestressed concrete composite floor slabs according to claim 6, characterized in that, Step 5 includes: Step 5.1: Reinforce the bottom slab with flexural steel bars according to a single-reinforced rectangular section; Step 5.2: Determine whether the current configuration of the bottom slab bending reinforcement ratio is greater than the preset minimum bottom slab bending reinforcement ratio. If it is less than or equal to the preset minimum bottom slab bending reinforcement ratio, then proceed to step 5.4 after reinforcement according to the minimum reinforcement ratio; if it is greater than the preset minimum bottom slab bending reinforcement ratio, then proceed to step 5.

3. Step 5.3: Determine whether the current configured bottom slab bending reinforcement ratio is less than the preset maximum bottom slab bending reinforcement ratio. If it is less than the preset maximum bottom slab bending reinforcement ratio, proceed directly to step 5.

4. If the reinforcement ratio is greater than or equal to the preset maximum flexural reinforcement ratio of the bottom slab, the flexural reinforcement of the bottom slab should be redesigned according to the doubly reinforced rectangular section. After the redesign, the flexural reinforcement ratio of the bottom slab needs to be determined again. If the reinforcement ratio is less than or equal to the preset minimum slab bending reinforcement ratio, then proceed to step 5.4 after reinforcement is carried out according to the minimum reinforcement ratio; if the reinforcement ratio is greater than the preset minimum slab bending reinforcement ratio but less than the preset maximum slab bending reinforcement ratio, then proceed directly to step 5.4; if the reinforcement ratio is greater than or equal to the maximum slab bending reinforcement ratio, then the total thickness of the composite slab needs to be increased, and the process should be restarted from step 1. Step 5.4: Design the reinforcement of the joints within the span and the reinforcement of the joints at the supports.

10. The design method for inclined reinforced prestressed concrete composite floor slabs according to claim 6, characterized in that, Step 5 also includes: When the first additional steel bar (4) is under tension, the reinforcement ratio of the first additional steel bar (4) per unit width of the slab should be greater than the reinforcement ratio of the non-prestressed steel bar (3) in the precast concrete base slab (7), and the reinforcement design should be carried out according to the following formula: When the first additional reinforcing bar (4) is under compression, the cross-sectional area of ​​the first additional reinforcing bar (4) should satisfy the following formula: in, A s1 The cross-sectional area of ​​the non-prestressed steel reinforcement (3) in the precast concrete base slab (7) is given. A s2 The cross-sectional area of ​​the first additional reinforcing bar (4) is... This represents the total thickness of the composite slab. For the thickness of the composite cast-in-place layer (8), The effective height of the entire cross-section of the composite slab. For the effective height of the superimposed cast-in-place layer (8), The distance from the resultant point of the non-prestressed steel bars (3) in the precast concrete base slab (7) to the bottom of the slab. The distance from the resultant point of the first additional reinforcement (4) to the overlapping surface.

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