Design method of simple girder continuous structure system of track girder

Abstract

To provide a design method for a simple girder continuous structural system of a track girder.SOLUTION: A simple girder continuous structural system of a track girder comprises a first raceway girder and a second raceway girder, and a simple girder continuous structure for connecting them. A design method based on the above structure includes fulcrum section determination step S1, steel plate and reinforcing bar selection step S2, stud arrangement step S3, crack width safety factor calculation step S4, bending strength safety factor calculation step S5, step S6 in which a designer repeats the above steps to optimize the structure based on the minimum allowable safety factor defined by the designer, and step S7 in which the design of the structure system is completed when the obtained safety factor satisfies a requirement. The structural system is capable of resisting tensile forces in the region of a large negative bending moment, and the design method based on the structure does not cause the difficulty of the tendon tension of the negative bending moment in the conventional art, and quickly realizes the calculation of the force received by this type of structure and the optimization of the design, and facilitates its large-scale popularization and application.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to the technical field of straddle-type monorail bridge girder design, and in particular to a design method for a simple girder continuous structure system of track girders. [Background technology]

[0002] As shown in Figure 1, straddle-type monorails are a new type of rail transit system in which vehicles straddle tracks. The track girders support the vehicles vertically, guide them longitudinally, and stabilize them laterally. This type of rail transit system is typically used for low- to medium-volume urban rail transit. The running wheels 52 of the straddle-type monorail vehicle run on the top surface of the track girders 55 of the straddle-type monorail bridge girder, while the guide wheels 53 and stabilizing wheels 54 run on the sides. The weight of the vehicle body 51 is primarily transmitted to the track girders via the running wheels. Because the track girders function as both the bridge girder that supports the train's load and the rails on which the train travels, horizontal and vertical alignment of the precast, erected, and completed bridge girders must be accurate to within one millimeter. Because it is difficult to ensure the accuracy of the track girders using on-site concrete, the typical construction method is "factory fabrication, on-site assembly, and partial on-site concrete casting."

[0003] Currently, straddle-type monorails have been constructed in Chongqing, Yinchuan, Wuhu, etc., or several tracks are in operation. The structural systems for bridge girder span structures include simple girder systems, continuous girder systems, and steel continuous rigid frame systems. However, each system has a number of long-standing unresolved problems that have limited the spread and application of straddle-type monorails.

[0004] The three systems mentioned above have the following advantages and disadvantages:

[0005] 1. Advantages of simple girder systems: (1) No secondary internal forces are generated due to foundation settlement, concrete shrinkage and creep, temperature, etc.; (2) Alignment control during on-site erection is easy, and alignment adjustment is relatively easy; the alignment of each girder can be adjusted after the bridge girder is completed; (3) On-site construction is easy, with few construction steps and fast construction speed, making it very suitable for precast and prefabricated construction. Disadvantages: (1) Poor integrity, low rigidity, and poor earthquake resistance, lateral collapse resistance, and torsional resistance; (2) Many expansion joints, high unit cost, poor roadability, and high tire wear; (3) The large girder end angle of simple girders results in smaller spans than continuous girders, and the piers are densely packed, making them ineffective for avoiding underground pipelines and unsightly; (4) Many expansion joints and supports require a lot of curing and inspection work.

[0006] Second, advantages of continuous girder systems: (1) good integrity, high rigidity, and certain earthquake and torsional resistance; (2) few expansion joints, good driving performance, and low tire wear; (3) medium span, good coordination between pier height and span; (4) few expansion joints and bearings, and medium amount of curing and maintenance work. Disadvantages: (1) It is necessary to cast in-situ a rigid wet joint with densely packed rebars and tendons at the top of the intermediate pier, which requires a large amount of rebar joining work and results in low precast, assembly, and construction efficiency. (2) In the new straddle-type monorail transportation system, the proportion of live load on the track girder is much higher than that of conventional railway bridges, making it very difficult to control the crack resistance in the negative bending moment area. To use a normal reinforced concrete structure, it is necessary to use a very high girder height or very densely packed rebars and densely arranged reinforcement so that the crack width meets the requirements of the specifications. However, densely arranged reinforcement makes it difficult to ensure the density of the concrete. When using the commonly used short-tender method of prestressing to control the stress in the negative bending moment area, openings are required at the top of the track girder on both sides of the intermediate pier. However, the concrete at the groove opening does not accumulate compressive stress when the bridge girder is completed, so the durability of this area, especially the interface between the old and new concrete, cannot be guaranteed. The rare method of passing a long tendon from the top edge to control the stress in the negative bending moment area involves passing the long tendon through the entire connecting girder after the precast girders of each span are erected. This makes the construction difficult and labor-intensive. Furthermore, passing a long tendon through the non-negative bending moment area is clearly a waste of material and exacerbates the problem of excessive compressive stress on the top edge of the precast girders. Tensioning through a long tendon has a significant impact on the vertical and especially lateral alignment of the precast girders, and also requires a very high level of tensioning work.

[0007] 3. Advantages of steel continuous frame systems: (1) good integrity, high rigidity, and strong earthquake and torsional resistance; (2) few expansion joints, good running performance, and less wear on the rubber tires of monorail vehicles; (3) medium span, good coordination between pier height and span; (4) few expansion joints and fewer supports, reducing the amount of curing and maintenance work; (5) since the horizontal force in the longitudinal direction is borne by multiple piers, the horizontal displacement of the pier top and the number of lower pile foundations can be reduced. Disadvantages: (1) The structural system is greatly affected by uneven foundation settlement, concrete shrinkage, creep, temperature, etc.; (2) It is necessary to cast in-situ rigid wet joints with densely packed reinforcing bars and tendons at the top of the intermediate piers, which requires a large amount of reinforcing bar joining work and low precast, assembly, and construction efficiency; (3) The proportion of live load on the track girder is excessively high, making it difficult to control the tensile stress in the negative bending moment area. If cracks occur in the negative bending moment area, maintenance will be very difficult and traffic performance will be significantly affected; (4) The requirements for alignment control are very high, and all adjustments must be completed at once before the bridge girder is completed, and the alignment cannot be adjusted after the bridge girder is completed.

[0008] To address the shortcomings of the above systems, a simple girder-continuous structure can be used. This structure effectively overcomes the shortcomings of both simple and continuous girders, combining the advantages of both to create a more streamlined structure. The simple girder-continuous structure utilizes simple girder precast and erection methods, making construction easier, facilitating standardization of structural dimensions, and supporting large-scale precast construction, significantly improving construction efficiency. However, when using conventional concrete girders, the tendons at the top of the piers must be pre-tensioned in situ in the negative bending moment region, making it difficult to control the alignment of the completed bridge girder. When using conventional steel-concrete composite beams, there are undesirable factors, such as tension in the cast-in-place concrete deck in the negative bending moment region and compression at the bottom edge of the steel girders. The live load of monorail bridge girders is very large, making it difficult to control crack width in the composite beam's concrete deck.

[0009] Therefore, there is a need for a simple girder continuity structural system for track girders that can resist large tensile forces in the negative bending moment region and does not have the negative bending moment control problems of conventional technology, and there is an urgent need to propose a corresponding design method.

[0010] The present invention has been made in consideration of the above circumstances, and provides a design method for a simple girder continuous structure system for track girders, which solves the problem that the current simple girder continuous structure system for track girders has difficulty in resisting tensile forces in the large negative bending moment area and has difficulty in solving the tendon tension problem of negative bending moments.However, there is currently no clear design method for the simple girder continuous structure of track girders, and the calculation of its bending strength and crack width lacks analytical formulas and can only be calculated based on a refined nonlinear solid finite element model, making the structural design and calculation very difficult and preventing its widespread application. Summary of the Invention [Problem to be solved by the invention]

[0011] The present invention focuses on the above-mentioned problems and provides a method for designing a simple girder continuous structural system for track girders, which provides formulas for calculating the bending strength and crack width of a structure composed of steel plates and reinforcing bars, and which facilitates the actual design, dissemination, and application of the structure. [Means for solving the problem]

[0012] In order to achieve the above object, the present invention provides the following technical means: A design method for a simple girder continuous structural system of a track girder, the simple girder continuous structural system of a track girder comprising a first track girder and a second track girder for connecting both sides, and a simple girder continuous structure for connecting the first track girder and the second track girder, the first track girder and the second track girder comprising precast prestressed concrete members, the simple girder continuous structure of the track girder being provided at the top of a continuous pier, The simple girder continuity structure of the track girder comprises reinforcing bars, steel plates, post-cast wet joints, and studs, the reinforcing bars are arranged in the first track girder and the second track girder, pass through the first track girder, and are connected to a side surface close to the second track girder, the studs are connected to the steel plates, and the top surfaces of the steel plates are flush with the upper surfaces of the first track girder and the second track girder, the steel plates are pre-embedded in the track girders before the prestressing tendons of the track girders are fixed, and the post-cast wet joints are installed between the first track girder and the second track girder to connect the first track girder and the second track girder, The vertical length of the post-cast wet joint is L c The design method for the simple girder continuous structural system of the track girder includes the following steps: Step S1: Based on the requirements of the straddle-type monorail specifications for the deflection of the track girder, the support section located at the span center section of the simple girder continuous structure system of the track girder and the continuous pier is determined. The support section is assumed to be a normal reinforced concrete solid rectangular section with a width B and a height H. When checking the crack width of the support, the most unfavorable negative bending moment M of the support section is determined. q and vertical shear force V q Calculate the most unfavorable negative bending moment M of the support section when checking the bending strength of the support section. d and vertical shear force V d Calculate the distance between the support section and the section on the left side of the support section where the bending moment is zero, and determine L m The rebar area of ​​the tension area required for the support cross section is calculated as A rr and Step S2: Selection of steel plate and reinforcing bar: Based on the requirements of concrete pouring and reinforcing bar connection, the minimum net distance s between the reinforcing bar and the upper edge of the support section is determined. r , maximum rebar diameter d r , total number of rebars n r Calculate the actual area A of the reinforcing bar. r =n r πd r 2 / 4, thickness of steel plate H p , the longitudinal length of the steel plate L p =2H, width B p=B, and the support cross section is a combination of the rectangular cross section and the steel plate cross section placed on top of the rectangular cross section. The height of the support cross section is H=H c +H p The distance between the center of gravity of the reinforcing bar at the upper edge of the support cross section and the bottom surface of the steel plate is s rp And Stud placement step S3: Based on the structural provisions and placement requirements of the steel concrete composite structure specifications for the studs, the minimum stud spacing s under the steel plate is s , maximum stud diameter d s , and the maximum total number of studs n s Determine Calculation of safety factor of crack width of simple girder continuous structure system of track girder Step S4: The simple girder continuous structure system of track girder is divided into two by the central axis of the continuous pier, and when checking the crack width, the axial force N of the steel plate of the support cross section pq is the longitudinal shear force V of the stud located on one side of the post-cast wet joint x1 , the longitudinal shear force V of the stud in the first track girder within one side range of the simple girder continuous structural system of the track girder x2 and the axial force N at the end of one side of the steel plate x3 Calculated based on the sum of N pq =V x1 +V x2 +N x3 In this case, the axial force of the reinforcing bar is N rq =(M q -N pq (HH p / 2-(1-0.87)(H c -s rp ))) / (0.87(H c -s rp ))+N pq A r / (BH p ) and N pq , N rq And from the crack width verification formula, the crack width W cr The safety factor of the crack width of the simple girder continuous structural system of the track girder is R W =0.2 / W cr and Calculation of the safety factor of the bending strength of the simple girder continuous structure system of the track girder Step S5: When checking the bending strength, calculate according to the most unfavorable situation that the steel plate and concrete are not bonded, that is, the axial bearing force N of the steel plate at the support cross section pu is the minimum value between the strength of the steel plate itself and the sum of the shear strength of all studs, and the bending strength M of the simple girder continuous structural system of the track girder u =N pu (HH p / 2-x / 2)+f rd A r (H c -s rp -x / 2), where f rd is the design value of the tensile strength of the reinforcing bar, x is the height of the concrete compression zone, and x=min{f rd A r / (f cd B), ξ b (H c -s rp )}, ξ b is the height of the relative limit area of ​​the bending member of the reinforced concrete, and the safety factor of the bending strength of the simple girder continuous structural system of the track girder is R M =M u / M d and Step S6: min{R W ,R M}>[R], [R] is the minimum allowable safety factor defined by the designer himself, and if it is 1.3 or more, the longitudinal length of the steel plate L p and thickness H p Reduce the rebar area A r Then, return to step S3, and redesign the simple girder continuous structure system of the track girder, and W ,R M If}≦[R], proceed to step S7; Step S7: min{R W ,R M If}≦1.2, increase H and return to step S2. <min{R W ,R M If}≦[R], the design of the simple girder continuous structure system of the track girder is completed.

[0013] Preferably, the N x3 =N x4 +dV x4 =(N x5 +dV x5 )+dV x4 =((N x6 +dV x6 )+dV x5 )+dV x4 =……=(N xm +dV xm )+……+dV x6 +dV x5 +dV x4 where N x4 and dV x4 are the longitudinal tensile axial force and the longitudinal shear force at the bottom of the end face of one side of the steel plate and the end face of one side of a concrete minute rectangular parallelepiped element □4, which has the same thickness as the steel plate and a width and longitudinal length dl, respectively, and N x5 and dV x5 are the longitudinal tensile axial force of one end face and the longitudinal shear force of the bottom face of a concrete minute rectangular parallelepiped element □5, which has the same thickness as the □4 on one side of the □4 and a width and longitudinal length dl, respectively. Similarly, N xm and dV xm are the concrete minute rectangular parallelepiped elements □ with the same thickness as the cross section where the bending moment is zero and the width and vertical length dl, respectively. m The vertical tensile axial force on one side end surface and the vertical shear force on the bottom surface are N xm Since it can be seen that ≒ 0, TIFF2025172672000002.tif21166, where V xc (l) is the width B and thickness H at the point l in the vertical direction from the support cross section. p Concrete minute rectangular parallelepiped element □ l Vertical shear force on the base of the cc (l) is the vertical shear force of the entire cross section of width B and height H at this point, S c (l) is □ l The area moment of the relevant part about the neutral axis of the entire cross section of width B and height H is I cc (l) is the moment of inertia of the entire cross section of the relevant part with width B and height H.

[0014] Preferably, the TIFF2025172672000003.tif23166, V xp (l) is a steel plate minute rectangular parallelepiped element □ at a vertical distance of l from the support cross section l Vertical shear force on the base of the pc (l) is the vertical shear force of the entire cross section of the relevant location, S p (l) is □ l The area moment of the concrete girder section at the relevant point about the neutral axis, I c (l) is the moment of inertia of the concrete girder cross section at that location, E p , E c are the elastic modulus of the steel plate and the concrete, respectively.

[0015] Preferably, the TIFF2025172672000004.tif23166, and V xp (l), V pc (l), S p (l), I cr (l) is a steel plate minute rectangular parallelepiped element □ at a vertical distance of l from the support cross section. l Vertical shear force at the base of the structure, vertical shear force at the entire cross section of the structure, l The area moment of the concrete girder section at the relevant location with respect to the neutral axis, and the moment of inertia of the cracked section of the concrete girder at the relevant location, E p , E c are the elastic modulus of the steel plate and the concrete, respectively.

[0016] Preferably, I cr (l)=0.8I c (l) and I c (l) is the moment of inertia of the section of the concrete girder at that location where cracks do not occur.

[0017] Preferably, the crack width in step S4 is W cr =K1K2γ(N pq +N rq ) / (A r +BH p )(80+(8+0.4d r) / ρ te 0.5 ) / E s and ρ te =A r / (2s rp B) and E s is the elastic modulus of the reinforcing bar, and the possible values ​​of K1, K2, and γ are 0.72, 1.5, and 1.1, respectively.

[0018] Preferably, the axial support force of the steel plate at the support cross section in step S5 is N pu =min{f pd BH p ,min{0.43(n s πd s 2 / 4)(E c f cd ) 0.5 , 0.7(n s πd s 2 / 4)f sd}}, where f pd , E c , f cd , f sd are the design values ​​of the tensile strength of the steel plate, the elastic modulus of the concrete, the compressive strength of the concrete, and the tensile strength of the stud, respectively.

[0019] Preferably, tooth-like protrusions are provided on the side surfaces of the precast prestressed concrete members, and the studs are passed through gaps between the reinforcing bars arranged in the width direction of the bridge girder and are connected to the reinforcing bars by fastening them. [Effects of the Invention]

[0020] The advantageous effects of the present invention are as follows:

[0021] The present invention provides a design method for a simple girder-continuous track girder structural system, which resists the negative bending moment of the continuous girder through reinforcing bars, steel plates, and post-cast wet joints. The steel plates are anchored in the first and second precast track girders with studs, and the first and second track girders are prestressed reinforced concrete members, with the pre-embedded reinforcing bars in the first and second precast track girders connected together before the post-cast wet joints are cast in place. The steel plates and reinforcing bars in this structural system can jointly resist the tensile force in the large negative bending moment area, eliminating the problem of tendon tensioning under negative bending moments encountered in prior art. The use of steel plates also reduces the amount and diameter of reinforcing bars, easing the difficulty of sleeve connections and avoiding the shortcomings of continuous girder structural systems, resulting in improved overall performance compared to simple girder and steel continuous rigid frame structural systems.

[0022] A structure in which steel plates and reinforced concrete girders jointly resist bending is significantly different from conventional reinforced concrete girders and steel-concrete composite beams, and therefore no clear design method currently exists. The calculation of its bending strength and crack width lacks analytical formulas and can only be calculated based on a refined nonlinear solid finite element model, making the structural design and calculation extremely difficult and preventing popularization and application. Therefore, this invention proposes analytical formulas for calculating the bending strength and crack width of the simple girder continuous structural system of this track girder, which effectively avoids the problems of the prior art requiring calculations based on a refined nonlinear solid finite element model, making the structural design too difficult, time-consuming, and inconvenient to optimize material usage. This allows for rapid calculation of the force applied to this type of structure and optimization of the design, facilitating large-scale popularization and application. The present invention analyzes the simple girder continuous structural system of track girders, and combines it with the special requirements of the simple girder continuous structural system based on the basic principles of material mechanics and structural design, analyzes the forces that the steel plates and reinforced concrete in the simple girder continuous structural system of track girders are subjected to, and realizes the optimization of the design and material usage of the simple girder continuous structural system of track girders. [Brief explanation of the drawings]

[0023] [Figure 1] 1 is a schematic diagram showing the positional relationship between a straddle-type monorail vehicle and a track girder in the background art of the present invention. FIG. [Figure 2] FIG. 1 is a schematic overall configuration diagram of a simple girder continuous structure system for track girders of the present invention. [Figure 3] 1 is a schematic overall configuration diagram of a simple continuous beam structure of the present invention. [Figure 4] FIG. 10 is a general elevation view of a refined finite element model of a 2×30 m track girder in the second embodiment. [Figure 5] FIG. 10 is a partial bird's-eye view of solid elements of a refined finite element model of a 2×30 m track girder before passivation treatment in the second embodiment. [Figure 6] FIG. 10 is a partial perspective view of solid elements of a refined finite element model of a 2×30 m track girder after passivation treatment in the second embodiment. [Figure 7] This shows the crack occurrence state and the nodal displacement at the crack occurrence interface of a 2 x 30 m track girder model when dr = 12 mm in the second embodiment. [Figure 8] This shows the crack occurrence state and the nodal displacement at the crack occurrence interface of a 2 x 30 m track girder model when dr = 20 mm in the second embodiment. [Figure 9] 10 shows the crack analysis results of a 2×30 m track girder under rebars with different diameters in the second embodiment. [Figure 10] 10 shows the stress analysis results of a 2×30 m track girder under rebars with different diameters in the second embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0024] The present invention will be described in more detail below with reference to test examples and specific embodiments. However, it should not be understood that the scope of the above subject matter of the present invention is limited to the following embodiments, and the technology implemented based on the content of the present invention is included in the scope of the present invention.

[0025] (First embodiment) As shown in Figures 2 and 3, this is a design method for a simple girder continuous structural system of a track girder, and the simple girder continuous structural system of a track girder comprises a first track girder and a second track girder 2 for connecting both sides, and a simple girder continuous structure 4 for connecting the first track girder 1 and the second track girder 2, and the first track girder 1 and the second track girder 2 comprise precast prestressed concrete members, and the simple girder continuous structure 4 of the track girder is provided on the top of a continuous pier 31 and comprises reinforcing bars 41, steel plates 42, post-cast wet joints 43, and studs 44, and the reinforcing bars 41 are connected to the first track girder 1 and the second track girder The studs 44 are connected to the steel plates 42, the top surfaces of which are flush with the upper surfaces of the first and second track girders 1 and 2, and the steel plates 42 are pre-embedded in the track girders before the prestressing tendons of the track girders are fixed. The post-cast wet joints 43 are cast between the first and second track girders 1 and 2 to connect the first and second track girders 1 and 2, and the post-cast wet joints 43 are connected and fixed to the continuous pier 31 via fixed bearings 311. The longitudinal length of the post-cast wet joints 43 is L. c is.

[0026] In this embodiment, the simple girder continuous structural system of the track girder resists the negative bending moment of the continuous girder through the reinforcing bars 41, steel plates 42, and post-cast wet joints 43. The steel plates 42 are fixed into the precast first track girders 1 and second track girders 2 through studs 44, and the first track girders 1 and second track girders 2 are prestressed reinforced concrete members. The pre-embedded reinforcing bars 41 in the precast first track girders 1 and second track girders 2 are connected together as a whole before the post-cast wet joints 43 are cast in place, so that the simple girder continuous structural system of the track girder can better transmit stress and withstand loads. Furthermore, because the steel plates 42 are pre-embedded in the track girders before the prestressing tendons of the track girders are fixed, it further ensures that the ends of the steel plates 42 and the track girder concrete are always in a compressed state, which prevents gaps from forming at the contact surfaces between the sides of the ends of the steel plates 42 and the track girder concrete under the action of vehicle load. The steel plates 42 and reinforcing bars 41 in this structural system can jointly resist the tensile force in the large negative bending moment area, eliminating the problem of tendon tensioning under negative bending moments as in the prior art, and the use of steel plates 42 also reduces the amount and diameter of reinforcing bars 41 used, easing the difficulty of sleeve connections and further avoiding the shortcomings of continuous girder structural systems, improving overall performance compared to simple girder and steel continuous rigid frame structural systems. Furthermore, in this embodiment, the simple girder continuous structural systems of adjacent track girders are connected via separated piers 32, and there is an expansion joint 33 between the simple girder continuous structural systems of adjacent track girders, so that the simple girder continuous structural system combines the advantages of both simple girder systems and continuous girder systems.

[0027] In a preferred embodiment, teeth are provided on the sides of the precast prestressed concrete members of the first track girder 1 and the second track girder 2, and studs 44 are passed through gaps in the reinforcing bars 41 arranged in the width direction of the bridge girder and fastened to the reinforcing bars 41 to connect them. After providing teeth on the sides of the precast track girders, the shear resistance effect between them and the post-cast wet joints 43 can be significantly improved.

[0028] Based on the above-mentioned simple girder continuous structural system of track girders, the present invention proposes a design method for realizing the design of the simple girder continuous structural system of track girders and the optimization of material usage, including the following steps: Step S1: Determine the support section 431. Based on the requirements of the straddle-type monorail specifications for the deflection of the track girder, determine the support section 431 located at the span center section of the simple girder continuous structure system of the track girder and the continuous pier 31. Assume that the support section 431 is a normal reinforced concrete solid rectangular section with a width B and a height H. When checking the crack width of the support, determine the most unfavorable negative bending moment M of the support section 431. q and vertical shear force V q Calculate the most unfavorable negative bending moment M of the support section 431 when checking the bending strength of the support section. d and vertical shear force V d Calculate the distance between the support section 431 and the section on the left side of the support section 431 where the bending moment is zero, and determine L m The area of ​​the reinforcing bar 41 required for the support section 431 is calculated as A rr and Step S2: Selection of steel plate 42 and reinforcing bar 41: Based on the requirements for concrete placement and reinforcing bar 41 connection, the minimum net distance s between the reinforcing bar 41 and the upper edge of the support section 431 is determined. r , maximum rebar diameter 41 d r , total number of rebars 41 n r Calculate the actual area A of the reinforcing bar 41. r =n r πd r 2 / 4, thickness H of steel plate 42 p , the longitudinal length L of the steel plate 42 p =2H, width B p =B is calculated, and the support cross section 431 is a cross section of the rectangular cross section and a cross section of the steel plate 42 placed on the rectangular cross section, and the height of the support cross section 431 is H=H c +H p The distance between the center of gravity of the reinforcing bar 41 at the upper edge of the support section 431 and the bottom surface of the steel plate 42 is s rp And Stud 44 placement step S3: Based on the structural provisions and placement requirements of the steel concrete composite structure specifications for studs 44, the minimum stud 44 spacing s under the steel plate 42 is determined.s , Maximum stud diameter 44 d s , and maximum stud 44 total number n s Determine Calculation of safety factor for crack width of simple girder continuous structural system of track girder Step S4: The simple girder continuous structural system of track girder is divided into two by the central axis of the continuous pier 31, and when checking the crack width, the axial force of the steel plate 42 of the support cross section 431 is N pq is the longitudinal shear force V of the stud 44 located on one side of the post-cast wet joint 43 x1 , the longitudinal shear force V of the stud 44 in the first track girder within one side range of the simple girder continuous structural system of the track girder x2 and the axial force N at the end of one side of the steel plate 42 x3 Calculated based on the sum of N pq =V x1 +V x2 +N x3 In this case, the axial force of the reinforcing bar 41 is N rq =(M q -N pq (HH p / 2-(1-0.87)(H c -s rp ))) / (0.87(H c -s rp ))+N pq A r / (BH p ) and N pq , N rq And the crack width W from the crack width verification formula cr The safety factor for the crack width of the simple girder continuous structure of the track girder is R W =0.2 / W cr and In the formula of step S4, 0.87 is the moment arm coefficient in the reinforcing bar 41 when cracks occur in a general reinforced concrete girder, and 0.2 is the crack width tolerance (0.2 mm) of a general reinforced concrete girder. Calculation of the safety factor of the bending strength of the simple girder continuous structure system of the track girder Step S5: When checking the bending strength, the calculation is performed according to the most unfavorable situation where the steel plate 42 and the concrete are not bonded, that is, the axial bearing force N of the steel plate 42 of the support section 431 puis the minimum value between the strength of the steel plate 42 itself and the sum of the shear strength of all the studs 44, and the bending strength M of the simple girder continuous structural system of the track girder u =N pu (HH p / 2-x / 2)+f rd A r (H c -s rp -x / 2), where f rd is the design value of the tensile strength of the reinforcing bar 41, x is the height of the concrete compression area, and x=min{f rd A r / (f cd B), ξ b (H c -s rp )}, ξ b is the height of the relative limit area of ​​the bending member of the reinforced concrete, and the safety factor of the bending strength of the simple girder continuous structural system of the track girder is R M =M u / M d and Step S6: min{R W ,R M}>[R], [R] is the minimum allowable safety factor defined by the designer himself, and if it is 1.3 or more, the longitudinal length L of the steel plate 42 p and thickness H p The area of ​​the rebar is reduced to 41. r Then, return to step S3 and redesign the simple girder continuous structure system of the track girder, and W ,R M If}≦[R], proceed to step S7; Step S7: min{R W ,R M If}≦1.2, increase H and return to step S2. <min{R W ,R M If}≦[R], the design of the simple girder continuous structure system of the track girder is completed.

[0029] In this embodiment, based on the proposed simple girder continuous structural system for track girders, which can resist tensile forces in the large negative bending moment region and does not require consideration of tendon tension issues due to negative bending moments, a calculation and analytical formula for bending strength and crack width is proposed, and the design and optimization of material usage for the simple girder continuous structural system for track girders are carried out according to the basic principles of material mechanics and structural design. In this design method, the joint bending-resisting structure consisting of the steel plate 42 and reinforced concrete girder in the simple girder continuous structural system for track girders will experience gaps and slippage between the steel plate 42 and the concrete of the track girder under long-term reciprocating fatigue action due to live loads such as those of vehicles, resulting in the simple girder continuous structural system for track girders not satisfying the assumptions of a planar cross section. After cracks occurred at 43 wet joints in the concrete of the first track girder 1 and the second track girder 2, the crack width did not change linearly in the vertical direction, but was largest at 41 reinforcing bars and gradually decreased in width in the vertical direction. Therefore, it is not possible to evaluate the crack width and bending strength based on conventional reinforced concrete girders or steel-concrete composite beams. To avoid the problems of the prior art requiring calculations based on a refined nonlinear solid finite element model, which makes the structural design too difficult, time-consuming, and difficult to optimize material usage, the design method of the present invention combines the basic principles of material mechanics and structural design with the special requirements of the simple-girder continuous structural system of the track girder to analyze the forces exerted on the steel plates and reinforced concrete in the simple-girder continuous structural system, thereby achieving the design and optimization of material usage of the simple-girder continuous structural system of the track girder.

[0030] In addition, when examining the crack width of the simple girder continuous structure system of the track girder, the axial force of the steel plate 42 is mainly determined by the parameters of the thickness and length of the steel plate 42 itself, that is, when the size of the steel plate 42 is determined, the force shared by the steel plate 42 is basically a constant value, and when the area of ​​the reinforcing bar 41 changes, the stress of the reinforcing bar 41 (stress σ of the reinforcing bar 41) rq =N rq / A r) changes significantly, but the force received by the steel plate 42 does not change significantly, i.e., the material properties of both may not be exerted simultaneously, and the safety factors of the material strength of both may be significantly different. When verifying the bearing capacity of the simple girder continuous structural system of the track girder, the bearing capacity of the steel plate 42 mainly depends on its own cross-sectional size and the arrangement of the studs 44. When verifying the bearing capacity at this point, it is considered that the plastic deformation of the simple girder continuous structural system of the track girder is more significant, and the shear strength of the studs 44 (or the strength of the steel plate 42 itself) and the tensile strength of the reinforcing bars 41 can both be fully exerted, so the bearing capacity of the simple girder continuous structural system of the track girder can be simultaneously calculated based on the design strengths of each.

[0031] In a preferred embodiment, N x3 =N x4 +dV x4 =(N x5 +dV x5 )+dV x4 =((N x6 +dV x6 )+dV x5 )+dV x4 =……=(N xm +dV xm )+……+dV x6 +dV x5 +dV x4 where N x4 and dV x4 are the longitudinal tensile axial force of the end face of one side of the steel plate 42 and the end face of one side of the concrete minute rectangular parallelepiped element □4, which has the same thickness as the steel plate 42 and a width and longitudinal length dl, and the longitudinal shear force of the bottom surface, respectively, and N x5 and dV x5 are the longitudinal tensile axial force of one end face and the longitudinal shear force of the bottom face of a concrete minute rectangular parallelepiped element □5, which has the same thickness as □4 on one side of □4 and a width and longitudinal length dl, respectively. Similarly, N xm and dV xm are the concrete minute rectangular parallelepiped elements □ with the same thickness as the cross section 11 where the bending moment is zero and the width and vertical length dl, respectively. m The vertical tensile axial force on one side end surface and the vertical shear force on the bottom surface are N xmSince it can be seen that ≒ 0, TIFF2025172672000005.tif19166, where V xc (l) is the width B and thickness H of the point where the vertical distance from the support cross section 431 is l p Concrete minute rectangular parallelepiped element □ l Vertical shear force on the base of the cc (l) is the vertical shear force of the entire cross section of width B and height H at this point, S c (l) is □ l The area moment of the relevant part about the neutral axis of the entire cross section of width B and height H is I cc (l) is the moment of inertia of the entire cross section of the relevant part with width B and height H.

[0032] In this embodiment, the axial force of the end surface on one side of the steel plate 42 and the axial force of the concrete in the track girder connected to the steel plate 42 are calculated using the infinitesimal element method. Since the first track girder 1 and the second track girder 2 on both sides of the simple girder continuous structure 4 of the track girder are both prestressed concrete structures, cracks generally do not occur in the concrete, and the end of the steel plate 42 and the concrete connected to the end of the steel plate 42 are equivalent to a rigid connection, and changes in axial force can be transmitted. Therefore, complex calculations based on a refined nonlinear solid finite element model are not required, and the N is calculated based on the basic theory of material mechanics and the infinitesimal element method. x3 Furthermore, since cracks do not usually occur in the precast track girders on both sides, parameters such as the moment of inertia are calculated based on a uniform, crack-free cross section.

[0033] When calculating the longitudinal shear force of the stud 44 in step S4, c Vertical shear force V of all studs 44 within the range of / 2 x1 , one side (L p -L c ) / 2 longitudinal shear force V of the stud 44 in the first track girder 1 x2 and the axial force N at the left end of the steel plate 42 x3 Since it is calculated based on the sum of TIFF2025172672000006.tif21166, and Vxp (l) is a minute rectangular parallelepiped element □ of a steel plate 21 at a vertical distance of l from the support cross section 431 l Vertical shear force on the base of the pc (l) is the vertical shear force of the entire cross section of the relevant location, S p (l) is □ l The area moment of the concrete girder section at the relevant point about the neutral axis, I c (l) is the moment of inertia of the concrete girder cross section at that location, E p , E c are the elastic modulus of the steel plate 42 and the elastic modulus of the concrete, respectively.

[0034] In this embodiment, V x2 is the longitudinal shear force of all studs 44 in the first track girder 1 within one side range of the simple girder continuity structural system of the track girder. The precast track girders on both sides of the simple girder continuity structural system of the track girder are both prestressed concrete structures, and cracks do not generally occur in concrete. Therefore, the concrete girder parameters of the first track girder 1 and the second track girder 2 are calculated based on a cross section without cracks. However, taking into consideration that gaps may occur between the steel plate 42 and the concrete, causing slippage and not satisfying the assumption of a flat cross section, S p When calculating (l), the calculation is based on the area moment of the steel plate 42 relative to the neutral axis of the concrete girder cross section at that location, and I c When calculating (l), a conservative calculation is made based on the moment of inertia of the concrete girder cross section at that location.

[0035] TIFF2025172672000007.tif21166, and V xp (l), V pc (l), S p (l), I cr (l) is a minute rectangular parallelepiped element □ of a steel plate 42 at a vertical distance of l from the support cross section 431. l Vertical shear force at the base of the structure, vertical shear force at the entire cross section of the structure, l The area moment of the concrete girder section at the relevant location with respect to the neutral axis, and the moment of inertia of the cracked section of the concrete girder at the relevant location, E p, E c are the elastic modulus of the steel plate 42 and the elastic modulus of the concrete, respectively.

[0036] In a preferred embodiment, I cr (l)=0.8I c (l) and I c (l) is the moment of inertia of the section of the concrete girder at that location without cracks. The post-cast wet joint 43 in the simple continuous girder structure 4 of the track girder is a poured ordinary reinforced concrete structure, and in this embodiment, V x1 is the longitudinal shear force of all studs 44 on one side of the post-cast wet joint 43. When checking the crack width, the post-cast wet joint 43 will obviously crack under the action of external force, so the parameters of the concrete girder must be calculated based on the cross section where the crack occurs. cr When calculating (l), I c (l) is reduced by a factor of 0.8 for calculation.

[0037] Also, the crack width in step S4 is W cr =K1K2γ(N pq +N rq ) / (A r +BH p )(80+(8+0.4d r ) / ρ te 0.5 ) / E s and ρ te =A r / (2s rp B) and E s is the elastic modulus of the reinforcing bar 41, and possible values ​​of K1, K2, and γ are 0.72, 1.5, and 1.1, respectively. Here, K1, K2, and γ are all amplification factors of the strain of the reinforcing bar 41 when calculating the crack width of a general concrete structure. The axial bearing capacity of the steel plate 41 at the support cross section 431 in step S5 is N pu =min{f pd BH p ,min{0.43(n s πd s 2 / 4)(E c f cd )0.5 , 0.7(n s πd s 2 / 4)f sd}}, where f pd , E c , f cd , f sd are the design value of the tensile strength of the steel plate 42, the elastic modulus of the concrete, the design value of the compressive strength of the concrete, and the design value of the tensile strength of the stud 44, respectively.

[0038] (Second embodiment) In order to verify the technical effect of the present invention, a 2 x 30 m straddle-type monorail track girder using the simple girder continuous structural system of the present invention is used as an example, and a refined "girder-solid" nonlinear finite element model (nonlinear solid elements are used in the negative bending moment region, and space beam elements are used in the remaining part) is shown in Figures 4 to 6, and the calculation results under the actual design load of the straddle-type monorail are shown in Figures 7 to 10. Figures 7 and 8 show d r Figure 9 shows the cracking behavior of the track girder model for axial displacements of 12 mm and 20 mm. The difference in DX displacement between the nodes on both sides of the cracking interface reflects the crack width obtained using the finite element model of the simple girder continuous structural system. The crack width is largest at the rebar 41 and gradually decreases in the vertical direction. This is significantly different from the typical crack width observed in a typical concrete girder, where cracks occur at the wet joints 43 after post-casting, and then change linearly in the vertical direction. Figure 9 shows the crack analysis results for the track girder under rebars 41 of different diameters. Figure 9 shows that the structure of the analytical calculation formula of the present invention and the results of the refined finite element model are relatively similar for rebars 41 of different diameters. This demonstrates that the design using the calculation method of the present invention has higher accuracy. Figure 10 shows the stress analysis results for the track girder under rebars of different diameters. It can be seen that the results of the analytical calculation formula of the present invention and the refined finite element model are relatively close under the conditions of reinforcing bars 41 with different diameters, and both reflect the phenomenon that when the area of ​​the reinforcing bar 41 changes, the stress of the reinforcing bar 41 changes obviously, but the stress of the steel plate 42 does not change obviously.

[0039] As can be seen from the crack occurrence state, crack analysis, and stress analysis of the track girder finite element model of the present invention in the second embodiment, the simple girder continuous structural system provided by the present invention cannot be calculated or analyzed based on a normal concrete girder because the change in crack width after concrete crack occurrence is significantly different from that of a typical concrete girder. Figures 6 and 7 further demonstrate the higher accuracy of the design method proposed by the present invention, and the design and material usage of the track girder continuous structural system can be optimized in accordance with this design method during use, thereby avoiding the need for a complex and detailed finite element model during use of the track girder continuous structural system, and realizing rapid design and optimization of the track girder continuous structural system.

[0040] The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention. Any modifications, equivalent replacements and improvements made within the scope of the spirit and principle of the present invention shall be included in the protection scope of the present invention. [Explanation of symbols]

[0041] 1 First track girder 11 Sections where bending moment is zero 2 Second track girder 31 Continuous pier 311 Fixed bearing 32 Separated pier 33 Expansion joint 4 Simple digit continuous structure 41 Reinforced concrete 42 Steel plate 43 Post-cast wet joint 431 Support cross section 44 studs 51 Body 52 Running wheel 53 Guide Wheel 54 Stable wheel 55 Track girder of straddle-type monorail bridge girder

Claims

1. A design method for a simple girder continuous structural system of a track girder, the simple girder continuous structural system of a track girder comprising a first track girder and a second track girder for connecting both sides, and a simple girder continuous structure for connecting the first track girder and the second track girder, the first track girder and the second track girder comprising precast prestressed concrete members, and the simple girder continuous structure of the track girder being provided at the top of a continuous pier, The simple girder continuity structure of the track girder comprises reinforcing bars, steel plates, post-cast wet joints, and studs, the reinforcing bars are arranged in the first track girder and the second track girder, pass through the first track girder, and are connected to a side surface close to the second track girder, the studs are connected to the steel plates, and the top surfaces of the steel plates are flush with the upper surfaces of the first track girder and the second track girder, the steel plates are pre-embedded in the track girders before the prestressing tendons of the track girders are fixed, and the post-cast wet joints are installed between the first track girder and the second track girder to connect the first track girder and the second track girder, The length of the post-cast wet joint in the vertical direction is L ｃ and the design method for the simple girder continuous structure system of the track girder is as follows: Step S1 for determining the support section: Based on the requirements of the straddle-type monorail specifications for the deflection of the track girder, the support section located at the span center section of the simple girder continuous structure system of the track girder and the continuous pier is determined. The support section is assumed to be a normal reinforced concrete solid rectangular section with a width B and a height H. When checking the crack width of the support, the most unfavorable negative bending moment M of the support section is determined. ｑ and vertical shear force V ｑ Calculate the most unfavorable negative bending moment M of the support section when checking the bending strength of the support section. ｄ and vertical shear force V ｄ Calculate the distance between the support section and the section where the bending moment on the left side of the support section is zero, and determine L ｍ The reinforcing bar area of ​​the tension region required for the support cross section is calculated as A ｒｒ and Step S2 of selecting the steel plate and the reinforcing bar: Based on the requirements of concrete pouring and reinforcing bar connection, the minimum net distance s between the reinforcing bar and the upper edge of the support section ｒ , maximum rebar diameter d ｒ , total number of rebars n ｒ and calculate the actual area A of the reinforcing bar. ｒ = n ｒ πd ｒ ２ / 4, the thickness H of the steel plate ｐ , the longitudinal length L of the steel plate ｐ =2H, width B ｐ =B is calculated, and the support cross section is a combination of the rectangular cross section and the steel plate cross section placed on top of the rectangular cross section, and the height of the support cross section is H = H ｃ +H ｐ , the distance between the center of gravity of the reinforcing bar at the upper edge of the support cross section and the bottom surface of the steel plate is s ｒｐ And Step S3 of arranging the studs: Based on the structural provisions and arrangement requirements of the steel concrete composite structure specifications for the studs, the minimum stud spacing s under the steel plate is determined. ｓ , maximum stud diameter d ｓ , and the maximum total number of studs n ｓ Determine Calculation step S4 of the safety factor of the crack width of the simple girder continuous structural system of the track girder: The simple girder continuous structural system of the track girder is divided into two by the central axis of the continuous pier, and when checking the crack width, the axial force N of the steel plate of the support cross section ｐｑ is the longitudinal shear force V of the stud located on one side of the post-cast wet joint ｘ１ , the longitudinal shear force V of the stud in the first track girder within one side range of the simple girder continuous structural system of the track girder ｘ２ and the axial force N at the end of one side of the steel plate ｘ３ Calculate based on the sum of N ｐｑ =V ｘ１ +V ｘ２ +N ｘ３ In this case, the axial force of the reinforcing bar N ｒｑ = (M ｑ -N ｐｑ (H-H ｐ / 2-(1-0.87) (H ｃ -s ｒｐ ))) / (0.87(H ｃ -s ｒｐ )) + N ｐｑ A ｒ / (BH ｐ ) and N ｐｑ , N ｒｑ And from the crack width verification formula, the crack width W ｃｒ The safety factor of the crack width of the simple girder continuous structural system of the track girder is R Ｗ = 0.2 / W ｃｒ and the crack width is W ｃｒ =K １ K ２ γ (N ｐｑ +N ｒｑ ) / (A ｒ +BH ｐ )(80+(8+0.4d ｒ ) / ρ ｔｅ ０．５ ) / E ｓ and ρ ｔｅ = A ｒ / (2s ｒｐ B) and E ｓ is the elastic modulus of the reinforcing bar, K １ , K. ２ , γ can take values ​​of 0.72, 1.5, and 1.1, respectively. Calculation step S5 of the bending strength safety factor of the simple girder continuous structure system of the track girder: When checking the bending strength, the calculation is performed according to the most unfavorable situation that the steel plate and concrete are not bonded, that is, the axial bearing force N of the steel plate at the support cross section ｐｕ is the minimum value between the strength of the steel plate itself and the sum of the shear strength of all the studs, and the bending strength M of the simple girder continuous structural system of the track girder ｕ = N ｐｕ (H-H ｐ / 2-x / 2) + f ｒｄ A ｒ (H ｃ -s ｒｐ −x / 2), where f ｒｄ is the design value of the tensile strength of the reinforcing bar, x is the height of the concrete compression zone, and x = min {f ｒｄ A ｒ / (f ｃｄ B), ξ ｂ (H ｃ -s ｒｐ ), ξ ｂ is the height of the relative limit zone of the reinforced concrete bending member, f ｃｄ is the design value of concrete compressive strength, and the safety factor of bending strength of the simple girder continuous structural system of the track girder is R Ｍ = M ｕ / M ｄ and Step S6: min{R Ｗ , R Ｍ }>[R], [R] is the minimum allowable safety factor defined by the designer himself, and if it is 1.3 or more, the longitudinal length L of the steel plate ｐ and thickness H ｐ and reduce the reinforcing bar area A ｒ is reduced, and the process returns to step S3, and the design of the simple girder continuous structure system of the track girder is carried out again, and min{R Ｗ , R Ｍ }≦[R], proceed to step S7, Step S7: min{R Ｗ , R Ｍ }≦1.2, increase H, return to step S2, and Ｗ , R Ｍ }≦[R], the design of the simple girder continuous structure system of the track girder is completed. A design method for a simple girder continuous structure system of a track girder, comprising the steps of:

2. The N ｘ３ = N ｘ４ +dV ｘ４ = (N ｘ５ +dV ｘ５ ) + dV ｘ４ = ((N ｘ６ +dV ｘ６ ) + dV ｘ５ ) + dV ｘ４ =……=(N ｘｍ +dV ｘｍ ) +... + dV ｘ６ +dV ｘ５ +dV ｘ４ where N ｘ４ and dV ｘ４ are the end face of one side of the steel plate and a concrete minute rectangular parallelepiped element □ having the same thickness as the steel plate and a width and a length in the vertical direction of dl. ４ The longitudinal tensile axial force on one side end surface and the longitudinal shear force on the bottom surface are N ｘ５ and dV ｘ５ are respectively ４ The above □ on one side ４ A concrete minute rectangular parallelepiped element □ with the same thickness as ５ The longitudinal tensile axial force on one side end surface and the longitudinal shear force on the bottom surface are also N ｘｍ and dV ｘｍ are the concrete minute rectangular parallelepiped elements □ of one side of the cross section where the bending moment is zero and the thickness of the cross section where the bending moment is zero, and the width and length in the vertical direction are dl. ｍ The vertical tensile axial force on one side end surface and the vertical shear force on the bottom surface are N ｘｍ Since it can be seen that ≒ 0, where V ｘｃ (l) is the width B and thickness H of the point at a vertical distance of l from the support cross section ｐ Concrete minute rectangular parallelepiped element □ ｌ Vertical shear force on the base, V ｃｃ (l) is the vertical shear force of the entire cross section of this location with width B and height H, S ｃ (l) is □ ｌ The area moment of the width B and height H of the relevant part about the neutral axis of the entire cross section, I ｃｃ 2. A design method for a simple girder continuous structural system of track girders according to claim 1, characterized in that (l) is the moment of inertia of the entire cross section of the width B and height H of the relevant location.

3. The aforementioned , and V ｘｐ (l) is a small rectangular parallelepiped element of a steel plate at a vertical distance of l from the support cross section. ｌ Vertical shear force on the base, V ｐｃ (l) is the vertical shear force of the entire cross section of the relevant location, S ｐ (l) is □ ｌ The area moment of the concrete girder section at the relevant point with respect to the neutral axis, I ｃ (l) is the moment of inertia of the concrete girder cross section at that location, E ｐ , E ｃ 2. The design method for a simple continuous girder structure system of track girders according to claim 1, wherein σ and σ are the elastic modulus of the steel plate and the concrete, respectively.

4. The aforementioned And V ｘｐ (l), V ｐｃ (l), S ｐ (l), I ｃｒ (l) is the steel plate minute rectangular parallelepiped element □ at a vertical distance of l from the support cross section. ｌ Vertical shear force at the base of the structure, vertical shear force at the entire cross section of the structure, ｌ The area moment of the concrete girder section at the relevant location with respect to the neutral axis, and the moment of inertia of the cracked section of the concrete girder at the relevant location, E ｐ , E ｃ 2. The design method for a simple continuous girder structure system of track girders according to claim 1, wherein σ and σ are the elastic modulus of the steel plate and the concrete, respectively.

5. I ｃｒ (l) = 0.8 I ｃ (l) and I ｃ 5. A design method for a simple continuous girder structure system of track girders according to claim 4, characterized in that (l) is the moment of inertia of a cross section of the concrete girder at the relevant location where cracks do not occur.

6. The axial support force of the steel plate at the support cross section in step S5 is N ｐｕ =min{f ｐｄ BH ｐ ,min{0.43(n ｓ πd ｓ ２ / 4) (E ｃ f ｃｄ ) ０．５ , 0.7 (n ｓ πd ｓ ２ / 4)f ｓｄ }}, where f ｐｄ , E ｃ , f ｃｄ , f ｓｄ are the design value of the tensile strength of the steel plate, the elastic modulus of concrete, the design value of the compressive strength of concrete, and the design value of the tensile strength of the stud, respectively.

7. 6. A design method for a simple continuous girder structural system of track girders according to any one of claims 1 to 5, characterized in that tooth-like protrusions are provided on the side surfaces of the precast prestressed concrete members, and the studs are fastened to and connected to the reinforcing bars by passing through gaps between the reinforcing bars arranged in the width direction of the bridge girder.

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