Model test design method suitable for large-span steel-concrete composite beam bridge deck continuous structure

Abstract

The invention belongs to the field of civil (bridge) engineering, and particularly discloses a model test design method suitable for a large-span steel-concrete composite beam bridge deck continuous structure, which comprises the following steps: determining the section size of a reduced scale model according to neutral axis similarity and structural rigidity similarity criteria; and determining design parameters of the end connecting plate of the reduced scale model according to a bridge deck continuous structure local tensile stiffness similarity criterion. The method can accurately reflect neutral axis similarity, structural stiffness similarity and bridge deck continuous structure local tensile stiffness similarity criteria between the reduced scale model and an actual structure, and effectively improves the accuracy of a model test.

Description

Technical Field

[0001] The present invention belongs to the field of civil engineering (bridge) and specifically relates to a model test design method suitable for a continuous structure of a large-span steel-concrete composite beam bridge deck. The method can accurately reflect the similarity of the neutral axis, the similarity of the structural stiffness, and the similarity of the local tensile stiffness of the continuous structure of the bridge deck between the scaled model and the actual structure, and effectively improve the accuracy of the model test. Background Art

[0002] Simply supported steel-concrete composite beams have the advantages of good economic benefits, simple structure, clear force, and fast construction speed, and are widely used in bridge construction. However, simply supported beams have many expansion joints, which reduce the flatness of the bridge deck, and vehicles are prone to "jumping" at the expansion joints. In order to ensure driving comfort, the number of expansion joints should be reduced as much as possible, and a continuous bridge deck structure should be set at the beam end, such as the attached Figure 1 As shown in the figure, the continuous structure of the bridge deck is subjected to large tensile stress locally under the action of external loads, which is prone to damage and has high mechanical performance requirements. Therefore, it is necessary to study this part.

[0003] At present, "seamless bridges" with continuous deck structures have been widely used at home and abroad. However, the span is generally small. For example, according to surveys, the common span of "seamless bridges" in the United States is less than 40m. When the span of the bridge is small, the beam height is also small. At this time, the connecting plate of the continuous structure of the bridge deck is closer to the neutral axis of the section, and the tension it bears is also small. However, as the span of the bridge increases, the distance between the connecting plate of the continuous structure of the bridge deck and the neutral axis of the section increases, and its force characteristics are closer to those of a tension member, and the tension it bears increases significantly with the increase of the bridge span and beam height, as shown in the attached figure. Figure 2 At present, there is no research on long-span (span greater than 50m) continuous steel-concrete composite beam bridges. Therefore, it is necessary to design a special scaled model test based on the stress characteristics of long-span continuous steel-concrete composite bridges to verify the applicability of the continuous local structure of the bridge deck. Summary of the invention

[0004] In order to accurately reflect the local stress characteristics of the continuous structure of the bridge deck and improve the accuracy of the scaled model test, the purpose of the present invention is to provide a model test design method suitable for the continuous structure of the large-span steel-concrete composite beam bridge deck. The scaled model design method of the bridge deck continuous bridge proposed by the method is based on the similarity of the neutral axis, the similarity of the structural stiffness, and the similarity of the local tensile stiffness of the continuous structure of the bridge deck, so as to determine the specific size of the scaled model.

[0005] In order to achieve the above-mentioned invention object, the present invention provides the following technical solution: a model test design method suitable for continuous construction of large-span steel-concrete composite beam bridge deck, comprising:

[0006] Determine the cross-sectional dimensions of the scaled model based on the similarity of the neutral axis and the similarity of the structural stiffness;

[0007] According to the similarity criterion of local tensile stiffness of continuous structure of bridge deck, the design parameters of the end connecting plate of scaled model are determined.

[0008] Optionally, determining the cross-sectional dimensions of the scaled model according to the similarity criteria of neutral axes and structural stiffness includes:

[0009] According to the similarity criterion of the neutral axis of the cross section, the y-axis of the scaled model and the actual bridge cross section are ensured. 0 / y s and 0 / y c The value is close;

[0010] Among them, y 0 is the height of the neutral axis of the cross section; s y is the distance between the neutral axis of the cross section and the centroid of the stress-bearing reinforcement in the connecting plate; c is the distance between the neutral axis of the cross section and the top of the connecting plate;

[0011] According to the stiffness similarity criterion, ensure that the stiffness index β of the scaled model and the actual bridge are similar;

[0012]

[0013] Furthermore, the derivation process of formula (3) includes:

[0014] The beam end rotation angle θ is selected as the structural stiffness similarity index. When a bridge with a span of L is subjected to a vertical force P in the middle of the span, the beam end rotates by an angle θ. At this time, the beam end rotation angle θ is calculated according to formula (1):

[0015]

[0016] Stress of bottom plate of mid-span steel beam σ b Calculate according to formula (2):

[0017]

[0018] Where E is the elastic modulus of the material; I is the moment of inertia of the section.

[0019] Optionally, determining the design parameters of the end connecting plate of the scaled model according to the similarity criterion of the local tensile stiffness of the continuous structure of the bridge deck includes:

[0020] According to the similarity criterion of the local tensile stiffness of the connecting plate, the design parameters of the scaled model are adjusted so that γ real and γ target near;

[0021]

[0022] Where: γ real is the scaling ratio of the actual tensile stiffness of the connecting plate of the scaled model, γ target k′ is the scaling ratio of the tensile stiffness of the target connecting plate of the scaled model; link , I′, h′, L′ are the tensile stiffness of the connecting plate, section moment of inertia, section height and model span of the scaled model respectively; k link , I, h, and L are the tensile stiffness of the connecting plate, the moment of inertia of the section, the height of the section, and the span of the bridge of the actual continuous bridge deck.

[0023] Furthermore, the derivation process of formula (11) and formula (12) includes:

[0024] By applying a unit rotation angle at the end of the simply supported beam, the beam end rotation stiffness k of the simply supported beam bridge is obtained by the force method. r for:

[0025]

[0026] Under the action of bending moment M, the beam end rotates by angle θ, and the connecting plate generates tension T. The bending moment M and tension T are calculated according to formulas (5) and (6) respectively:

[0027] M=k r θ (5)

[0028] T=k link ·h·θ (6)

[0029] Where h is the height of the beam section;

[0030] According to the similarity criterion of the local tensile stiffness of the connecting plate, the ratio of M / T should be similar. Combining equations (4), (5) and (6), we can obtain:

[0031]

[0032] To ensure that the M / T values ​​of the scaled model and the actual bridge structure are similar, according to formula (7):

[0033]

[0034] k′ link and k link Calculate according to the following formula:

[0035]

[0036]

[0037] In the formula, A′ sand L′ link are the cross-sectional area of ​​the longitudinal reinforcement and the unbonded length of the longitudinal reinforcement of the scaled model connection plate; A s and L link are the cross-sectional area of ​​the longitudinal reinforcement and the unbonded length of the longitudinal reinforcement of the connecting plate of the actual bridge structure, respectively.

[0038] Compared with the prior art, the present invention has at least the following beneficial effects: the present invention proposes a scaled model test design method that can reflect the local stress characteristics of the continuous structure of the bridge deck. Through the "similarity" criteria such as similarity of the neutral axis of the cross section, similarity of the structural stiffness, and similarity of the local tensile stiffness of the continuous structure of the bridge deck, the continuous structure of the bridge deck is scaled to a smaller size, so that the scaled model can not only reflect the stress characteristics of the continuous structure of the bridge deck, but also reduce the size and scale of the test piece. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The drawings described herein are used to provide a further understanding of the present application and constitute a part of the present application. The illustrative embodiments of the present application and their descriptions are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0040] Figure 1 This is a schematic diagram of the continuous local structure of the bridge deck;

[0041] Figure 2 It is a schematic diagram of the continuous structure cross section of the bridge deck;

[0042] Figure 3 A schematic diagram of the geometric relationship of the continuous construction cross section of the bridge deck;

[0043] Figure 4 This is a schematic diagram of the bridge's stress and deformation;

[0044] Figure 5 This is a schematic diagram of the calculation of the rotational stiffness of the simply supported beam bridge end;

[0045] Figure 6 This is a schematic diagram of the forces at the ends of a continuous bridge deck;

[0046] Figure 7 Schematic diagram of the cross-sectional dimensions of the continuous bridge deck and the end of the scaled model. DETAILED DESCRIPTION

[0047] In order to facilitate ordinary technicians in the field to understand and implement the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and implementation examples. It should be understood that the implementation examples described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0048] Example 1

[0049] A model test design method applicable to the continuous structure of a large-span steel-concrete composite beam bridge deck includes:

[0050] Since the distance between the neutral axis of the section and the continuous connecting plate of the bridge deck directly determines the force mode of the connecting plate, specifically, when the connecting plate is closer to the neutral axis of the section, the connecting plate is closer to the eccentric tension member, and when the connecting plate is farther from the neutral axis of the section, the connecting plate is closer to the axial tension member.

[0051] According to the similarity criterion of the neutral axis of the cross section, it is necessary to ensure that the y 0 / y s and 0 / y c The values ​​are close, that is, the error range is within 5%, where y 0 is the height of the neutral axis of the cross section; s is the distance between the neutral axis of the cross section and the steel layer in the connecting plate; c is the distance between the neutral axis of the cross section and the top of the connecting plate, as shown in the attached figure. Figure 3 shown.

[0052] Furthermore, the scaled model and the actual bridge should meet the structural stiffness similarity criterion. Since the beam end rotation angle can directly reflect the overall stiffness of the bridge structure, and the beam end rotation angle is directly related to the overall structure of the continuous bridge deck and the force of the local connecting plate, the beam end rotation angle θ is selected as the structural stiffness similarity index. Figure 4 As shown in the figure, when a bridge with a span of L is subjected to a vertical force P in the middle of the span, the beam end will rotate by an angle θ. At this time, the beam end rotation angle θ is calculated according to the following formula:

[0053]

[0054] Stress of bottom plate of mid-span steel beam σ b Calculate according to formula (2):

[0055]

[0056] Where E is the elastic modulus of the material; I is the moment of inertia of the section.

[0057] Therefore, according to the stiffness similarity criterion, the stiffness index β (as shown in formula (3)) of the scaled model and the actual bridge should be close, that is, the error range is within 5%.

[0058]

[0059] Furthermore, by applying a unit rotation at the ends of the simply supported beam (excluding the connecting plate), as shown in the attached Figure 5 As shown, the “force method” can be used to obtain the beam end rotation stiffness k of a simply supported beam bridge. r for:

[0060]

[0061] The local stress state at the end of the continuous beam bridge deck is shown in the attached figure. Figure 6 As shown in the figure, under the action of bending moment M, the beam end rotates at an angle θ, and the connecting plate generates a tensile force T. The bending moment M and the tensile force T are calculated according to formulas (5) and (6) respectively:

[0062] M=k r θ (5)

[0063] T=k link ·h·θ (6)

[0064] Where h is the height of the beam section.

[0065] According to the similarity criterion of the local tensile stiffness of the connecting plate, the ratio of M / T should be similar. In addition, by combining equations (4), (5) and (6), we can obtain:

[0066]

[0067] To ensure that the M / T values ​​of the scaled model and the actual bridge structure are similar, according to formula (7):

[0068]

[0069] Where γ is the scaling ratio of the tensile stiffness of the scaled model connection plate to the tensile stiffness of the actual bridge connection plate, k l ' ink , I′, h′, L′ are the tensile stiffness of the connecting plate, section moment of inertia, section height and model span of the scaled model respectively; k link , I, h, L are the tensile stiffness of the connecting plate, the moment of inertia of the section, the section height and the span of the bridge for the actual continuous bridge deck. And, k′ link and k link Calculate according to the following formula:

[0070]

[0071] In the formula, A′ s and L′ link are the cross-sectional area of ​​the longitudinal reinforcement and the unbonded length of the longitudinal reinforcement of the scaled model connection plate; A s and L link are the cross-sectional area of ​​the longitudinal reinforcement and the unbonded length of the longitudinal reinforcement of the connecting plate of the actual bridge structure, respectively.

[0072] Furthermore, the left side of formula (8) is the scaling ratio γ of the actual tensile stiffness of the connecting plate of the scaled model real , and the right side of formula (8) is the scaling ratio γ of the tensile stiffness of the target connecting plate of the scaled model target :

[0073]

[0074] According to the similarity criterion of the local tensile stiffness of the connecting plate, the design parameters of the scaled model should be adjusted so that γ real and γ target Close, that is, the error range is within 5%.

[0075] Example 2

[0076] The following takes a 60m span continuous steel box composite beam bridge as an example to illustrate the specific implementation process of the scaled model test design method for a large span continuous bridge deck structure proposed in Example 1 of the present invention. The end section of the bridge (model) is shown in the attached figure. Figure 7 As shown. Among them, b 0 is the width of the concrete bridge deck; b 1 b is the overhang width of the concrete bridge deck; 2 b is the overhang width of the lower flange of the steel beam; 4 b is the width of the lower flange of the steel beam between the webs on both sides; c is the thickness of the concrete bridge deck; h 0 is the net height of the web of the steel beam; t f is the thickness of the upper flange of the steel beam; t b is the thickness of the lower flange of the steel beam; t w is the web thickness of the steel beam; α is the web inclination angle of the steel beam; b f is the width of the upper flange of the steel beam;

[0077] According to the scale model test design method proposed in the present invention, the design procedure of the scale model is divided into two steps:

[0078] (1) According to the similarity of neutral axis and structural stiffness, the cross-sectional dimensions of the scaled model are determined, as shown in Table 1. As can be seen from Table 1, the y 0 / y c and 0 / y s It is similar to the real bridge structure and meets the neutral axis similarity criterion; the stiffness index β calculated according to the scaled model size is similar to the real bridge structure and meets the structural stiffness similarity criterion;

[0079] (2) According to the similarity criterion of local tensile stiffness of the continuous structure of the bridge deck, the design parameters of the end connection plate of the scaled model are determined, as shown in Table 2. According to the design parameters of the connection plate of the scaled model determined in Table 2 and the design parameters of the connection plate of the real bridge structure, the actual tensile stiffness scaling ratio γ of the connection plate of the scaled model is calculated according to formula (11): real is 0.12, and the tensile stiffness scaling ratio γ of the target connecting plate of the scaled model is calculated according to formula (12):target is 0.125, which is close to each other and meets the requirement of similarity criterion of local tensile stiffness of continuous structure of bridge deck.

[0080] In summary, the design of a scaled model of a 60m span continuous steel box composite beam bridge was completed.

[0081] Table 1 Cross-sectional dimensions of the scaled model of the bridge deck continuous structure

[0082]

[0083]

[0084] Table 2 Design parameters of the connecting plate of the scaled model of the continuous structure of the bridge deck

[0085]

[0086] The above embodiments are only used to illustrate the present invention and are not intended to limit the technical solutions described in the present invention. Although the present invention has been described in detail with reference to the above embodiments, the present invention is not limited to the above specific implementation methods. Therefore, any modification or equivalent replacement of the present invention; and all technical solutions and improvements thereof that do not depart from the spirit and scope of the invention are included in the scope of the claims of the present invention.

Claims

1. A model test design method suitable for continuous construction of large-span steel-concrete composite beam bridge decks, characterized in that: include: Determine the cross-sectional dimensions of the scaled model based on the similarity of the neutral axis and the similarity of the structural stiffness; According to the similarity criterion of local tensile stiffness of continuous structure of bridge deck, the design parameters of the end connecting plate of scaled model are determined.

2. The model test design method for continuous construction of large-span steel-concrete composite beam bridge deck according to claim 1 is characterized in that: Determining the cross-sectional dimensions of the scaled model according to the similarity of the neutral axis and the similarity of the structural stiffness comprises: According to the similarity criterion of the neutral axis of the cross section, the y0 / y s and y0 / y c The value is close; Where y0 is the height of the neutral axis of the cross section; y s y is the distance between the neutral axis of the cross section and the centroid of the stress-bearing reinforcement in the connecting plate; c is the distance between the neutral axis of the cross section and the top of the connecting plate; According to the stiffness similarity criterion, ensure that the stiffness index β of the scaled model and the actual bridge are similar; 3. The model test design method for continuous structure of large-span steel-concrete composite beam bridge deck according to claim 2 is characterized in that: The derivation process of formula (3) includes: The beam end rotation angle θ is selected as the structural stiffness similarity index. When a bridge with a span of L is subjected to a vertical force P in the middle of the span, the beam end rotates by an angle θ. At this time, the beam end rotation angle θ is calculated according to formula (1): Stress of bottom plate of mid-span steel beam σ b Calculate according to formula (2): Where E is the elastic modulus of the material; I is the moment of inertia of the section.

4. The model test design method for continuous construction of large-span steel-concrete composite beam bridge deck according to claim 1 is characterized in that: The design parameters of the end connecting plate of the scaled model are determined according to the similarity criterion of the local tensile stiffness of the continuous structure of the bridge deck, including: According to the similarity criterion of the local tensile stiffness of the connecting plate, the design parameters of the scaled model are adjusted so that γ real and γ target near; Where: γ real is the scaling ratio of the actual tensile stiffness of the connecting plate of the scaled model, γ target k′ is the scaling ratio of the tensile stiffness of the target connecting plate of the scaled model; link , I′, h′, L′ are the tensile stiffness of the connecting plate, section moment of inertia, section height and model span of the scaled model respectively; k link , I, h, and L are the tensile stiffness of the connecting plate, the moment of inertia of the section, the height of the section, and the span of the bridge of the actual continuous bridge deck.

5. The model test design method for continuous construction of large-span steel-concrete composite beam bridge decks according to claim 4 is characterized in that: The derivation process of formula (11) and formula (12) includes: By applying a unit rotation angle at the end of the simply supported beam, the beam end rotation stiffness k of the simply supported beam bridge is obtained by the force method. r for: Under the action of bending moment M, the beam end rotates by angle θ, and the connecting plate generates tension T. The bending moment M and tension T are calculated according to formulas (5) and (6) respectively: M=k r i (5) T=k link ·h·θ (6) Where h is the height of the beam section; According to the similarity criterion of the local tensile stiffness of the connecting plate, the ratio of M / T should be similar. Combining equations (4), (5) and (6), we can obtain: To ensure that the M / T values ​​of the scaled model and the actual bridge structure are similar, according to formula (7): k′ link and k link Calculate according to the following formula: In the formula, A′ s and L′ link are the cross-sectional area of ​​the longitudinal reinforcement and the unbonded length of the longitudinal reinforcement of the scaled model connection plate; A s and L link are the cross-sectional area of ​​the longitudinal reinforcement and the unbonded length of the longitudinal reinforcement of the connecting plate of the actual bridge structure, respectively.

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