Design method for simple continuous track girder structure

Abstract

The objective of the present invention is to provide a method for designing a simple girder continuous structure system for track girders. [Solution] The present invention comprises a first track girder, a second track girder, and a simple girder continuous structure for connecting them, and the design method based on the structure includes the steps of determining the support section S1, selecting the steel plate and reinforcing bar S2, arranging the studs S3, calculating the safety factor of the crack width S4, calculating the safety factor of the bending strength S5, repeating the above steps to optimize the structure based on the minimum allowable safety factor defined by the designer S6, and completing the design of the structure system S7 when the obtained safety factor meets the requirements. The structure system can resist the tensile force in the large negative bending moment area, and does not encounter the difficult problem of tendon tension of the negative bending moment in the prior art, and the design method based on the structure quickly realizes the calculation of the force received by this type of structure and the optimization of the design, which is easy to be popularized and applied on a large scale.

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 a track girder. [Background technology]

[0002] As shown in Fig. 1, straddle-type monorail is a new type of rail transport system in which vehicles run across tracks. The track girders support the vehicles vertically and (Vehicle travel direction) Guidance of lateral direction (Vehicle width direction) This type of rail transport system is usually applied to urban rail transport with low to medium volume transport. The running wheels 52 of the straddle-type monorail vehicle run on the top surface of the track girder 55 of the straddle-type monorail bridge girder, and the guide wheels 53 and stabilizing wheels 54 run on the sides. The gravity of the car body 51 is mainly transmitted to the track girder through the running wheels. The track girder is a structure that combines the bridge girder that supports the load of the train and the rail on which the train runs, so the alignment of the precast, erected and completed bridge girder in the horizontal and vertical directions requires accuracy of 1 mm. Since it is difficult to ensure the accuracy of the track girder by on-site pouring, the construction method of "factory production, on-site assembly, and partial on-site pouring" was generally used.

[0003] At present, straddle-type monorails have been built or are in operation on several tracks in Chongqing, Yinchuan, Wuhu, etc., and the structural systems for the bridge girder span structure include the simple girder system, the continuous girder system, and the steel continuous rigid frame system. However, each system has a number of problems that have long remained unsolved, which 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 the simple girder system: (1) No secondary internal force is generated due to the effects of foundation settlement, concrete shrinkage and creep, temperature, etc.; (2) The difficulty of linear control during on-site erection is low, and linear adjustment is relatively easy. After the bridge girder is completed, the linear alignment of each hole can be adjusted; (3) The difficulty of on-site construction is low, the construction procedure is few, and the construction speed is fast, so it is very suitable for precast and assembled construction. Disadvantages: (1) Poor integrity, low rigidity, poor earthquake resistance, lateral collapse resistance, and torsional resistance; (2) Many expansion joints, high unit cost, poor travelability, and high tire wear; (3) The girder end angle of the simple girder is large, so the span is smaller than that of the continuous girder, and the piers are dense, which is not useful for avoiding underground pipelines, and the appearance is general; (4) Many expansion joints and supports, and the amount of curing and inspection work is large.

[0006] Second, advantages of the continuous girder system: (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 a rigid wet joint with dense rebar and tendon at the top of the intermediate pier on site, which requires a large amount of work for connecting rebars and results in low efficiency of precasting, assembly and construction. (2) In the new type of transportation system of straddle-type monorail, the ratio of live load on the track girder is much higher than that of conventional railway bridges, which makes it 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 dense rebars and dense rebar arrangement so that the crack width meets the requirements of the specifications. However, it is difficult to ensure the density of concrete with dense rebar arrangement. When controlling the stress in the negative bending moment area using the commonly used short tendon method of prestressing, it is necessary to open the upper part of the track girder on both sides of the intermediate pier. It is necessary to insert short tendons into the grooves, but 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 requires that the entire connecting girder be passed through after the precast girders of each span are erected, which makes the construction difficult and labor-intensive. Furthermore, passing a long tendon through the non-negative bending moment area is obviously a waste of materials, and further exacerbates the problem of excessive compressive stress on the top edge of the precast girder. When tensioning through a long tendon, the impact on the vertical and especially the lateral alignment of the precast girder is significant, and the requirements for tensioning work are also very high.

[0007] Third, advantages of the steel continuous frame system: (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 the monorail cars; (3) medium span, and good coordination between the pier height and span; (4) few expansion joints and fewer supports, reducing the amount of curing and maintenance work; (5) the horizontal force in the vertical direction is borne by multiple piers, which reduces the horizontal displacement of the pier top and the number of lower pile foundations. Disadvantages: (1) The structural system is greatly affected by uneven foundation settlement, concrete shrinkage, creep, temperature, etc.; (2) A rigid wet joint with dense reinforcing bars and tendons needs to be cast on-site at the top of the intermediate pier, 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 large, 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 trafficability will be significantly affected; (4) The requirements for linear control are very high, and all adjustments need to be completed before the bridge girder is completed, and the linearity cannot be adjusted after the bridge girder is completed.

[0008] In order to make up for the shortcomings of each of the above systems, a simple girder continuous structure system can be used, which can effectively overcome the shortcomings of simple girder and continuous girder, and combine the advantages of both to make the structure more rational. The simple girder continuous construction method uses the precast and erection method of simple girder, which is convenient for construction, easy to standardize structural dimensions, and can provide support for large-scale precast manufacturing, greatly improving construction efficiency. However, the simple girder continuous structure system of the traditional track girder has the following problems: when using traditional concrete girders, the tendons in the negative bending moment area at the top of the pier need to be tensioned on-site, making it difficult to control the linearity of the completed bridge girder of the track girder; when using traditional steel-concrete composite beams, there are unfavorable factors such as tension of the cast-in-place concrete deck in the negative bending moment area and compression of the lower edge of the steel girder in the negative bending moment area; and the proportion of the live load of the monorail bridge girder is very large, making it difficult to suppress the crack width of the concrete deck of the composite beam.

[0009] Therefore, there is a need for a simple girder continuous 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 the conventional technology, and there is an urgent need to propose a corresponding design method.

[0010] The present invention has been made in view of the above circumstances, and provides a design method for a simple girder continuous structure system of a track girder, which solves the problem that the current simple girder continuous structure system of a track girder has difficulty in resisting the tensile force in the large negative bending moment area, and it is difficult to solve the tendon tension problem of negative bending moment. At present, there is no clear design method for the simple girder continuous structure of a track girder, 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, which makes the structural design and calculation very difficult, and cannot be popularized and applied. Summary of the Invention [Problem to be solved by the invention]

[0011] In view of the above-mentioned problems, the present invention provides a calculation formula for the bending strength and crack width of a structure composed of steel plates and reinforcing bars, and provides a design method for a simple girder continuous structure system of a track girder, which makes it easier to actually design, popularize, and apply 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 comprises 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 comprise precast prestressed concrete members, and the simple girder continuous structure of the track girder is provided at the top of a continuous pier, The simple girder continuous structure of the track girder comprises a reinforcing bar, a steel plate, a post-cast wet joint, and a stud, the reinforcing bar is disposed in the first track girder and the second track girder, passes through the first track girder, and is connected to a side surface close to the second track girder, the stud is connected to the steel plate, and a top surface of the steel plate is flush with an upper surface of the first track girder and the second track girder, the steel plate is pre-embedded in the track girder before the prestress tendon of the track girder is fixed, and the post-cast wet joint is cast 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 structure 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 examining 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 area of ​​the rebar in the tension region required for the support section is A rr As a result, Steel plate and reinforcing bar selection step S2: 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 section is a cross section of the rectangular section and a cross section of the steel plate placed on the rectangular section. The height of the support 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 section and the bottom surface of the steel plate is s rp And then, Stud placement step S3: Based on the structural provisions and placement requirements of the steel concrete composite structure specification 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 of safety factor of crack width of simple girder continuous structure of track girder Step S4: The simple girder continuous structure 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 is 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, i.e., N pq =V x1 +V x2 +N x3 In the case of , the axial force of the reinforcing bar is 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 structure of the track girder is R W =0.2 / W cr and Calculation of the safety factor of bending strength of the simple girder continuous structure of the track girder Step S5: When checking the bending strength, the calculation is performed according to the most unfavorable situation in which the steel plate and the concrete are not bonded, that is, the axial bearing force N of the steel plate at the cross section of the support 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 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 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 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 min{R 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 continuity structural 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 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 with the same thickness as the steel plate and 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 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, width and vertical length dl, and one side of the cross section where the bending moment is zero. m The vertical tensile axial force on one side of the plate and the vertical shear force on the bottom surface are N xm Since we know that ≒ 0, TIFF0007661599000002.tif21166, where V xc (l) is the width B and thickness H of the point l in the vertical direction from the support cross section. p Concrete micro 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 width B and height H of the relevant part.

[0014] Preferably, TIFF0007661599000003.tif23166, next, V xp (l) is a small rectangular steel plate element with 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 part, 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 section at that location, E p , E c are the elastic modulus of the steel plate and the concrete, respectively.

[0015] Preferably, TIFF0007661599000004.tif23166, V xp (l), V pc (l), S p (l), I cr (l) is a steel plate micro rectangular parallelepiped element □ with a vertical distance of l from the support cross section. l Vertical shear force at the base of the bridge, vertical shear force at the entire cross section of the bridge, 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 cross section of the concrete girder in that location without cracks.

[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 Then, 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 of 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 concrete, the compressive strength of concrete, and the tensile strength of the stud, respectively.

[0019] Preferably, teeth are provided on the side of the precast prestressed concrete member, 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. Effect 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 structural system of a track girder, which resists the negative bending moment of the continuous girder through reinforcing bars, steel plates and post-cast wet joints, and the steel plates are fixed in the first and second precast track girders through studs, and the first and second track girders are prestressed reinforced concrete members, and the reinforcing bars pre-embedded in the first and second precast track girders before the post-cast wet joints are cast on site are connected to each other as a whole. The steel plates and reinforcing bars in this structural system can jointly resist the tensile force of the large negative bending moment area, and the problem of tendon tension of the negative bending moment in the prior art does not occur, and the application of steel plates can reduce the amount and diameter of reinforcing bars, which reduces the difficulty of sleeve connection, and further avoids the shortage of the continuous girder structural system, and improves the overall performance compared with the simple girder and steel continuous rigid frame structural system.

[0022] The structure in which the steel plate and the reinforced concrete girder jointly resist bending is obviously different from the conventional reinforced concrete girder and steel-concrete composite beam, so there is currently no clear design method, 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, which makes the structural design and calculation very difficult and cannot be popularized and applied. Therefore, the present invention proposes an analytical formula for calculating the bending strength and crack width for the simple girder continuous structural system of the track girder, which can effectively avoid the problems that the structural design is too difficult, too time-consuming, and inconvenient to optimize the amount of materials used, which requires calculation based on a refined nonlinear solid finite element model in the prior art, and can quickly realize the calculation of the force applied to this type of structure and the optimization of the design, and facilitate large-scale popularization and application. The present invention analyzes the simple girder continuous structure system of track girder, and combines it with the special requirements of the simple girder continuous structure system of track girder based on the basic principles of material mechanics and structural design, respectively analyzes the forces received by the steel plate and reinforced concrete in the simple girder continuous structure system of track girder, thereby optimizing the design and material usage of the simple girder continuous structure system of track girder. [Brief description of the drawings]

[0023] [Figure 1] FIG. 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. [Diagram 2] FIG. 2 is a schematic overall configuration diagram of the simple girder continuous structure system of the track girder of the present invention. [Diagram 3] FIG. 1 is a schematic overall configuration diagram of a simple continuous beam structure according to the present invention. [Figure 4] FIG. 11 is a general elevation view of a refined finite element model of a 2×30 m track girder in the second embodiment. [Diagram 5] FIG. 11 is a partial perspective 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. 11 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 interface where the cracks have occurred in a 2 × 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 interface where the crack has occurred in a 2 × 30 m track girder model when dr = 20 mm in the second embodiment. [Figure 9] 13 shows the crack analysis results of a 2×30m track girder under rebars with different diameters in the second embodiment. [Figure 10] 13 is a stress analysis result of a 2×30m track girder under rebars of different diameters in the second embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[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 Figs. 2 and 3, a design method for a simple girder continuous structure system of a track girder is provided. The simple girder continuous structure system of a track girder includes 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. The first track girder 1 and the second track girder 2 include precast prestressed concrete members. The simple girder continuous structure 4 of the track girder is provided on the top of a continuous pier 31, and includes a reinforcing bar 41, a steel plate 42, a post-cast wet joint 43, and a stud 44. The reinforcing bar 41 is provided between the first track girder 1 and the second track girder 2. The stud 44 is connected to the steel plate 42, the top surface of the steel plate 42 is flush with the top surface of the first track girder 1 and the second track girder 2, the steel plate 42 is pre-embedded in the track girder before the prestress tendon of the track girder is fixed, the post-cast wet joint 43 is cast between the first track girder 1 and the second track girder 2 to connect the first track girder 1 and the second track girder 2, the post-cast wet joint 43 is connected and fixed to the continuous pier 31 via the fixed support 311, and the vertical length of the post-cast wet joint 43 is L c It is.

[0026] In this embodiment, the simple girder continuous structure system of the track girder resists the negative bending moment of the continuous girder through the reinforcing bar 41, the steel plate 42 and the post-cast wet joint 43. The steel plate 42 is fixed in the precast first track girder 1 and the second track girder 2 through the stud 44. The first track girder 1 and the second track girder 2 are prestressed reinforced concrete members. The reinforcing bars 41 pre-embedded in the precast first track girder 1 and the second track girder 2 before the post-cast wet joint 43 is cast on site are connected to each other as a whole, so that the simple girder continuous structure system of the track girder can better transmit stress and withstand load. Furthermore, since the steel plate 42 is pre-embedded in the track girder before the prestressing tendon of the track girder is fixed, it further ensures that the end of the steel plate 42 and the track girder concrete are always in a compressed state, so that the phenomenon of gaps occurring at the contact surface between the end side of the steel plate 42 and the track girder concrete under the action of vehicle load can be avoided. The steel plate 42 and the reinforcing bar 41 in this structural system can jointly resist the tensile force in the large negative bending moment area, and the problem of tendon tension of the negative bending moment in the prior art does not occur, and the application of the steel plate 42 can also reduce the amount and diameter of the reinforcing bar 41, which reduces the difficulty of sleeve connection, and further avoids the shortage of the continuous girder structural system, and improves the overall performance compared with the simple girder and the steel continuous rigid frame structural system. In this embodiment, the simple girder continuous structural system of the adjacent track girders is connected via the separated pier 32, and there is an expansion joint 33 between the simple girder continuous structural system of the adjacent track girders, so that the simple girder continuous structural system has the advantages of both the simple girder system and the continuous girder system.

[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 the studs 44 are fastened to the reinforcing bars 41 through the gaps between the reinforcing bars 41 arranged in the width direction of the bridge girder. After providing teeth on the sides of the precast track girder, the shear resistance effect between the precast wet joints 43 can be significantly improved.

[0028] Based on the above-mentioned simple girder continuous structural system of track girder, the present invention proposes a design method for realizing the design of the simple girder continuous structural system of track girder and the optimization of material usage, which includes 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, the most unfavorable negative bending moment M of the support section 431 is calculated. 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 A rr As a result, Step S2: Selection of steel plate 42 and reinforcing bar 41: Based on the requirements for concrete pouring 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 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, and the support section 431 is a cross section of the rectangular section and a cross section of the steel plate 42 placed on the rectangular section. The height of the support 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 then, Stud 44 placement step S3: Based on the structural provisions and placement requirements of the steel concrete composite structure specification for studs 44, the minimum stud 44 spacing s under the steel plate 42 is determined.s , max stud diameter 44 d s , and maximum stud count n s Determine, Calculation of safety factor of crack width of simple girder continuous structure of track girder Step S4: The simple girder continuous structure 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 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, i.e., 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 (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 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 allowable value (0.2 mm) of a general reinforced concrete girder. Calculation of the safety factor of bending strength of the simple girder continuous structure of the track girder Step S5: When checking the bending strength, the calculation is performed according to the most unfavorable situation in which 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 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 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 Reduce the area of ​​the rebar to 41 A r Then, return to step S3 and redesign the simple girder continuous structure system of the track girder, and min{R 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 continuity structural system of the track girder is completed.

[0029] In this embodiment, based on the proposed simple girder continuous structure system of the track girder, which can resist the tensile force in the large negative bending moment area and does not require consideration of the tendon tension problem of the negative bending moment, a calculation and analytical formula for bending strength and crack width is proposed, and the design and material usage of the simple girder continuous structure system of the track girder are optimized according to the basic principles of material mechanics and structural design. In this design method, the joint bending resistance structure consisting of the steel plate 42 and the reinforced concrete girder in the simple girder continuous structure system of the track girder will have gaps between the steel plate 42 and the concrete of the track girder and slide under the long-term reciprocating fatigue action due to the live load of vehicles, etc., so that the simple girder continuous structure system of the track girder does not satisfy the assumption of the planar section. After cracks occur in the post-cast wet joints 43 of the concrete of the first track girder 1 and the second track girder 2, the crack width does not change linearly in the vertical direction, but the crack width is largest at the reinforcing bar 41, and the crack width gradually decreases in the vertical direction, so that the crack width and bending strength cannot be evaluated based on the conventional reinforced concrete girder or steel-concrete composite beam. In order to avoid the problems that the conventional technology requires calculation based on a refined nonlinear solid finite element model, the structural design is too difficult, takes too much time, and is difficult to optimize the amount of material used, the design method of the present invention is based on the basic principles of material mechanics and structural design and combines with the special requirements of the simple girder continuous structural system of the track girder, respectively analyzes the forces received by the steel plate and the reinforced concrete in the simple girder continuous structural system of the track girder, and realizes the design and optimization of the material used in the simple girder continuous structural system of the track girder.

[0030] In addition, when examining the crack width of the simple girder continuous structure 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. 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, that is, the material properties of both may not be exerted at the same time, and the safety factors of the material strength of both may be significantly different. When examining the bearing capacity of the simple girder continuous structure 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, and when examining the bearing capacity at this point, the plastic deformation of the simple girder continuous structure 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 bar 41 can both be fully exerted, so the bearing capacity of the simple girder continuous structure system of the track girder can be calculated simultaneously based on the design strength 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 on one side of the steel plate 42 and the end face on 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 of the plate and the vertical shear force on the bottom surface are N xmSince we know that ≒ 0, TIFF0007661599000005.tif19166, where V xc (l) is the width B and thickness H of the point l in the vertical direction from the support section 431 p Concrete micro 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 width B and height H of the relevant part.

[0032] In this embodiment, the axial force of the end surface of 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 by the microelement 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, concrete generally does not crack, 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 axial force can be calculated based on the basic theory of material mechanics and the microelement 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 The longitudinal 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 TIFF0007661599000006.tif21166, Vxp (l) is a small rectangular parallelepiped element of a steel plate 21 at a vertical distance of l from the support 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 part, 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 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 continuous structural system of the track girder. The precast track girders on both sides of the simple girder continuous structural system of the track girder are both prestressed concrete structures. Generally, cracks do not occur in concrete, so 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, considering that gaps occur between the steel plate 42 and the concrete, causing slippage and not satisfying the assumption of a planar cross section, S p When calculating (l), the calculation is based on the area moment of the steel plate 42 with respect to the neutral axis of the concrete girder cross section at the relevant location, and I c When calculating (l), a conservative calculation should be made based on the moment of inertia of the concrete girder cross section at that location.

[0035] TIFF0007661599000007.tif21166, 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 section 431. l Vertical shear force at the base of the bridge, vertical shear force at the entire cross section of the bridge, 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 the relevant location without cracks. The post-cast wet joint 43 in the simple girder continuous 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 the 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 should be calculated based on the cross section where the crack occurs. I 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 Then, 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 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 taken 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 for 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 to 8 show d r The crack occurrence state of the track girder model when the crack occurrence interface is 12mm and 20mm is shown. The DX direction displacement difference of the nodes on both sides of the crack occurrence interface reflects the crack width obtained by the finite element model of the simple girder continuous structure system. It can be seen that the crack width is the largest at the rebar 41 and gradually decreases in the vertical direction, which is significantly different from the situation in which the crack width changes linearly in the vertical direction after cracks occur at the post-cast wet joints 43 of a general concrete girder. Figure 9 shows the crack analysis result of the track girder under the rebars 41 of different diameters. According to Figure 9, it can be seen that the structure of the analytical calculation formula of the present invention and the result of the refined finite element model are relatively close under the rebars 41 of different diameters. This shows that the design using the calculation method of the present invention has higher accuracy. Figure 10 shows the stress analysis result of the track girder under the 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 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 is significantly different from the change in crack width after concrete cracks occur in general concrete girders, so it cannot be calculated and analyzed based on normal concrete girders. Figures 6 to 7 further prove that the design method proposed in the present invention has higher accuracy, and the design and material usage of the track girder simple girder continuous structural system can be optimized according to the design method during the use process, and the need for a complex and detailed finite element model during the use process of the track girder simple girder continuous structural system is avoided, and the quick design and optimization of the track girder simple girder continuous structural system is realized.

[0040] The above description is only the preferred embodiments 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 with zero bending moment 2 Second track girder 31 Continuous pier 311 Fixed bearing 32 Separate pier 33 Expansion joint 4. Simple digit sequence structure 41 Reinforcement 42 Steel plate 43 Post-cast wet joint 431 Support Section 44 Stud 51 Body 52 Running wheel 53 Guide Wheel 54 Stable wheel 55 Track girder of straddle-type monorail bridge girder

Claims

1. A method for designing a simple girder continuous structural system of a track girder, the simple girder continuous structural system of the 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 a top of a continuous pier, The simple girder continuous structure of the track girder comprises a reinforcing bar, a steel plate, a post-cast wet joint, and a stud, the reinforcing bar is disposed in the first track girder and the second track girder, passes through the first track girder, and is connected to a side surface close to the second track girder, the stud is connected to the steel plate, and a top surface of the steel plate is flush with an upper surface of the first track girder and the second track girder, the steel plate is pre-embedded in the track girder before the prestress tendon of the track girder is fixed, and the post-cast wet joint is cast 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 rear-mounted wet joint in the vertical direction (hereinafter, the direction of travel of the vehicle is referred to as the vertical direction) is L ｃ The design method of 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 specification 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 examining the crack width of the support, the most unfavorable negative bending moment M 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, L ｍ and the reinforcing bar area of ​​the tension region required for the support cross section is A ｒｒ As a result, 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 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, the thickness H of the steel plate ｐ , the longitudinal length L of the steel plate 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 then, Step S3 of arranging the studs: Based on the structural provisions and arrangement requirements of the steel concrete composite structure specification 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 structure of the track girder: The simple girder continuous structure of the track girder is divided into two parts 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 is 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 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 is 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 structure of the track girder can be calculated as 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 Then, 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 safety factor of the bending strength 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 the concrete are not bonded, that is, the axial bearing force N of the steel plate at the cross section of the support point 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 structure of the track girder is 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 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 zone of the reinforced concrete bending member, f ｃｄ is the design value of the concrete compressive strength, and the safety factor of the bending strength of the simple girder continuous structure 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 Then, 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 vertical length dl. ４ (Hereinafter, the infinitesimal rectangular parallelepiped element is shown by □) is a vertical tensile axial force on one side end face and a vertical shear force on the bottom face, and N ｘ５ and dV ｘ５ are □ ４ The above on one side ４ A concrete micro rectangular parallelepiped element with the same thickness and width and vertical length dl ５ The vertical tensile axial force on one side of the end surface and the vertical shear force on the bottom surface are also N ｘｍ and dV ｘｍ are the concrete minute rectangular parallelepiped elements □ with a width and a vertical length dl and the same thickness as the cross section where the bending moment is zero. 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 is clear that ≒ 0, Here, 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 micro 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 this part with width B and height H, S ｃ (l) is □ ｌ The area moment of the part of the cross section about the neutral axis of the width B and height H of the cross section is I ｃｃ 2. The design method for a simple girder continuous structure 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 above And then V ｘｐ (l) is a small rectangular steel plate element with 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 part, 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 section at that location, E ｐ , E ｃ The design method for a simple girder continuous structure system of a track girder according to claim 1, characterized in that:

4. The above And then 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 bridge, vertical shear force at the entire cross section of the bridge, 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 The design method for a simple girder continuous structure system of a track girder according to claim 1, characterized in that:

5. I ｃｒ (l)=0.8I ｃ (l) and I ｃ The design method for a simple girder continuous structure system of a track girder 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 no cracks occur.

6. The axial support force of the steel plate at the cross section of the support 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. The design method for a simple girder continuous structural system of a track girder according to any one of claims 1 to 5, characterized in that a tooth-shaped protrusion is provided on a side surface of the precast prestressed concrete member, and the stud is fastened to the reinforcing bar through a gap between the reinforcing bars arranged in the width direction of the bridge girder and connected to the reinforcing bar.

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