Method for determining midspan and lower edge curve of lower chord beam of open-web continuous rigid frame bridge

Abstract

The invention discloses a method for determining lower edge curves of midspan and lower chord beams of an open-web continuous rigid frame bridge. The method comprises the steps that the total height H between the upper chord beam and the lower chord beam in an open-web area, the height h1 of the lower chord beam in the open-web area, the height h2 of the upper chord beam in the open-web area, the beam height at the upper chord and lower chord convergence node, the midspan beam section range Lm and the midspan beam height h3 are determined; calculating a lower edge curve F (x) of a midspan beam section and a lower edge curve G (x) of a lower chord beam section in an open web area; calculating the function of the curve F (x) and the curve G (x) at the connection point of the upper and lower chord convergence nodes and the first-order derivative continuity of the function; according to the method, the lower edge curve of the mid-span beam section conforms to the stress characteristics of the mid-span beam section in cantilever construction; the curve of the lower edge of the lower chord beam section of the hollow area arches upwards, so that the self-weight of the lower chord beam section and the load transmitted by the upper chord are balanced; the structure transition between the midspan beam section and the open web area lower chord beam section is smooth, and the stress transmission is smooth; and the lower edge curves of the midspan beam section and the open-web area lower chord beam section are optimized, so that the structure of the open-web continuous rigid frame bridge is more reasonable.

Description

Technical Field

[0001] The present invention relates to the technical field of the structure of concrete open-web continuous rigid frame bridges, and particularly relates to a method for determining the lower edge curves of the mid-span and the lower chord beam of an open-web continuous rigid frame bridge. Background Art

[0002] The concrete open-web continuous rigid frame bridge type, also known as the arch-beam composite continuous rigid frame bridge, is a new modification of the conventional continuous rigid frame form. Its main idea is to increase the height of the box girder root and hollow out the web of the box girder root to reduce the self-weight and form a beam-arch composite mechanical effect, thereby improving the structural load-bearing efficiency and enhancing the bridge's spanning ability. The open-web continuous rigid frame bridge has the characteristics of balanced cantilever construction similar to the conventional continuous rigid frame bridge, as well as the advantages of low operation and maintenance costs and low project cost. Its economic span is between 220m and 400m, and it is expected to fill the gap between the applicable spans of conventional continuous rigid frame bridges and cable-stayed bridges. As of 2024, there are about 10 large-span open-web continuous rigid frame bridges built or under construction for highways, railways, urban roads, rail transit, etc., which reflects significant technical and economic advantages and broad application prospects.

[0003] The concrete open-web continuous rigid frame bridge has many advantages such as relatively light self-weight, large spanning ability, and beautiful shape. However, in practical applications, there is a problem that the force transition between the mid-span beam section and the lower chord beam section of the open-web area is not smooth. The structural design is usually relatively conservative, and the structural size is large, which not only affects the exertion of the engineering and economic advantages of this bridge type but also increases the construction difficulty of the lower chord, thus restricting the popularization, application, and development of the open-web continuous rigid frame bridge type structure. Summary of the Invention

[0004] Aiming at the above existing technical deficiencies, the purpose of the present invention is to provide a method for determining the lower edge curves of the mid-span and the lower chord beam of an open-web continuous rigid frame bridge, which can optimize the lower edge curves of the mid-span beam section and the lower chord beam section of the open-web area, make the structure of the open-web continuous rigid frame bridge more reasonable, more economical, and have a greater spanning ability.

[0005] To solve the above technical problems, the present invention adopts the following technical solutions:

[0006] The present invention provides a method for determining the lower edge curves of the mid-span and the lower chord beam of an open-web continuous rigid frame bridge, including the following steps:

[0007] S1. Determine the total height H between the upper chord beam and the lower chord beam in the open-web area, the height h of the lower chord beam in the open-web area 1 , the height h of the upper chord beam in the open-web area 2 , the beam height at the joint where the upper and lower chords meet, the range L of the mid-span beam section m and the height h of the mid-span beam 3 ;

[0008] S2. Calculate the range of the mid-span beam segment and the lower edge curve F(x) of the mid-span beam segment:

[0009]

[0010] Among them, c is the exponential of the lower edge curve function of the mid-span beam segment, with a value range of 1.8 to 2.0; x jt is the connection point position between the lower edge curve F(x) of the mid-span beam segment and the lower edge curve G(x) of the lower chord beam segment in the void area;

[0011] S3. Calculate and determine the function value and its first derivative of the curve F(x) at the connection point of the upper and lower chord convergence nodes:

[0012] y jt = F(x jt ) = h 1 + h 2 - h 3

[0013]

[0014] S4. Calculate and determine the coefficients of the 2.0 - 3.0 order polynomial function of the lower edge curve G(x) of the lower chord beam segment in the void area:

[0015]

[0016] Obtain the function of the lower edge curve G(x) of the lower chord beam segment in the void area:

[0017]

[0018] Among them, b is the exponential of the lower edge curve function of the mid-span beam segment, with a value range of 2.0 to 3.0; γ is the unit weight of the lower chord concrete, taking 26 kN / m 3 ; σ c is the control stress of the lower chord concrete, taking 0.4 - 0.6 times of the design axial compressive strength of the concrete;

[0019] S5. Check the second derivative of the lower edge curve G(x) of the lower chord beam segment in the void area, adjust the parameters of H, h 1 , h 2 and repeat the previous steps S1 - S4 to make the value of the second derivative of the lower edge curve G(x) of the lower chord beam segment in the void area satisfy not less than γ / σ c , and be within a certain range.

[0020] Preferably, in step S1, the total height H between the upper chord beam and the lower chord beam in the void area:

[0021]

[0022] Among them, L is the main span clear span of the open-web continuous rigid-frame bridge.

[0023] Preferably, in step S1, the height h of the lower chord beam in the open-web area 1 :

[0024]

[0025] Preferably, in step S1, the height h of the upper chord beam in the open-web area 2 :

[0026]

[0027] The height of the beam at the upper and lower chord meeting node is h 1 + h 2 .

[0028] Preferably, in step S1, the span of the mid-span beam section L m :

[0029] L m = (12 - 15)(h 1 + h 2 ).

[0030] Preferably, in step S1, the height h of the mid-span beam 3 :

[0031]

[0032] Preferably, the numerical value of the second derivative of the lower edge curve G(x) of the lower chord beam section in the open-web area is not greater than 3 - 5 times of γ / σ c , so that the upward curvature of the lower chord beam section is not too large, and the maximum eccentricity of the lower chord beam section under eccentric compression is controlled.

[0033] So far, the lower edge curve F(x) of the mid-span beam section and the lower edge curve G(x) of the lower chord beam section in the open-web area are determined, and the function and its first derivative of the curves F(x) and G(x) are continuous at the connection point of the upper and lower chord meeting nodes. The numerical value of the second derivative of the lower edge curve G(x) of the lower chord beam section in the open-web area is within a certain range, so that the structural transition between the mid-span beam section and the lower chord beam section in the open-web area is smooth, the stress transfer is smooth, the eccentricity of the lower chord beam section in the open-web area under eccentric compression is small, and the force is reasonable.

[0034] The beneficial effects of the present invention are as follows:

[0035] 1. The lower edge curve F(x) of the mid-span beam section adopts a parabola of 1.8 - 2.0 times, and the length of the mid-span beam section is 12 - 15 times the height of the beam at the upper and lower chord meeting nodes, which conforms to the mechanical characteristics of the mid-span beam section in cantilever construction, and the force is safe and reasonable;

[0036] 2. The lower edge curve G(x) of the lower chord beam section in the hollow area adopts a polynomial function of 2.0 - 3.0 orders, which meets the requirement of a small eccentricity in eccentric compression under the action of the internal force transmitted by the upper and lower chord connection nodes, the self-weight of the lower chord beam section, and the possible vertical force transmitted by the upper chord. The force on the lower chord beam section is safer and more reasonable.

[0037] 3. The functions and their first derivatives of the curve F(x) and the curve G(x) are continuous at the connection points of the upper and lower chord connection nodes, making the structural transition between the mid-span beam section and the lower chord beam section in the hollow area smooth and the stress transmission smooth, solving the problem of easy cracking of the concrete at the connection nodes and improving the safety and durability of the connection nodes.

[0038] 4. Control the numerical value of the second derivative of the lower edge curve G(x) of the lower chord beam section in the hollow area to be not less than γ / σ c and within a certain range, the upward arch of the lower chord beam section can balance its own weight and the load transmitted by the upper chord, and the upward arch curvature is not too large, so that the maximum eccentricity of the eccentric compression of the lower chord beam section is controlled.

[0039] 5. The lower edge curves of the mid-span beam section and the lower chord beam section in the hollow area are optimized, making the structure of the concrete-filled continuous rigid frame bridge more reasonable, more economical, and having a greater spanning ability. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the following drawings are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0041] Figure 1 It is a structural schematic diagram of a concrete-filled continuous rigid frame bridge provided by an embodiment of the present invention;

[0042] Figure 2 is Figure 1 a schematic diagram of the beam height and curve function coordinate system of the mid-span beam section and the lower chord beam section in the hollow area.

[0043] In the figure: 1. Upper chord beam section, 2. Lower chord beam section, 3. Upper and lower chord connection nodes, 4. Mid-span beam section, 5. Connection point, 6. Lower edge curve of the mid-span beam section, 7. Lower edge curve of the lower chord beam section. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0044] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0045] Taking Figure 1 the concrete open-web continuous rigid-frame bridge as an example, this embodiment provides a method for determining the lower edge curve of the mid-span and the lower chord beam of the open-web continuous rigid-frame bridge, including the following steps:

[0046] S1. Refer to Figure 2 to determine the total height H between the upper chord beam 1 and the lower chord beam 2 in the open-web area, the height h of the lower chord beam in the open-web area 1 , the height of the upper chord beam in the open-web area h 2 , the beam height at the upper and lower chord convergence node 3, the range L of the mid-span beam segment 4 m and the mid-span beam height h 3 ;

[0047] The total height H between the upper chord beam and the lower chord beam in the open-web area:

[0048]

[0049] Among them, L is the main span clear span of the open-web continuous rigid-frame bridge.

[0050] The height h of the lower chord beam in the open-web area 1 :

[0051]

[0052] The height h of the upper chord beam in the open-web area 2 :

[0053]

[0054] The beam height at the upper and lower chord convergence node is h 1 +h 2 .

[0055] The range L of the mid-span beam segment m :

[0056] L m =(12 - 15)(h 1 +h 2 ).

[0057] The mid-span beam height h 3 :

[0058]

[0059] S2. Calculate the range of the mid-span beam segment and the lower edge curve F(x) of the mid-span beam segment:

[0060]

[0061] Among them, c is the function exponent of the lower edge curve of the mid-span beam segment, with a value range of 1.8 to 2.0; x jt is the position of the connection point 5 between the lower edge curve F(x) of the mid-span beam segment and the lower edge curve G(x) of the lower chord beam segment in the open-web area;

[0062] S3. Calculate and determine the function value and its first derivative at the connection point of the curve F(x) at the upper and lower chord convergence node:

[0063] y jt = F(x jt ) = h 1 + h 2 - h 3

[0064]

[0065] S4. Calculate and determine the coefficients of the 2.0 - 3.0 order polynomial function of the lower edge curve G(x) of the lower chord beam segment in the open-web area:

[0066]

[0067] Obtain the function of the lower edge curve G(x) of the lower chord beam segment in the open-web area:

[0068]

[0069] Among them, b is the function exponent of the lower edge curve of the mid-span beam segment, with a value range of 2.0 to 3.0; γ is the unit weight of the lower chord concrete, taking 26 kN / m 3 ; σ c is the control stress of the lower chord concrete, taking 0.4 - 0.6 times of the design axial compressive strength of the concrete;

[0070] S5. Check the second derivative of the lower edge curve G(x) of the lower chord beam segment in the open-web area, adjust the parameters of H, h 1 , h 2 parameters, and repeat the previous steps S1 - S4 to make the value of the second derivative of the lower edge curve G(x) of the lower chord beam segment in the open-web area satisfy not less than γ / σ c , and be within a certain range.

[0071] The value of the second derivative of the lower edge curve G(x) of the lower chord beam segment in the open-web area is not greater than 3 - 5 times γ / σ c , so that the upward curvature of the lower chord beam segment is not too large, and the maximum eccentricity of the eccentric compression of the lower chord beam segment is controlled.

[0072] So far, the lower edge curve 5 of the mid-span beam segment, i.e., F(x), and the lower edge curve 6 of the lower chord beam segment in the open web area, i.e., G(x), are determined. And the function and its first derivative of the curve F(x) and the curve G(x) are continuous at the connection point of the upper and lower chord meeting nodes. The numerical value of the second derivative of the lower edge curve G(x) of the lower chord beam segment in the open web area is within a certain range, so that the structural transition between the mid-span beam segment and the lower chord beam segment in the open web area is smooth, and the stress transfer is smooth. The eccentricity of the lower chord beam segment in the open web area under eccentric compression is small and the force is reasonable.

[0073] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and its equivalent technologies, the present invention also intends to include these changes and modifications.

Claims

1. A method for determining the lower edge curve of the mid-span and lower chord beams of a hollow continuous rigid frame bridge, characterized in that: The steps include: S1. Determine the total height H between the upper and lower chord beams in the hollow area, the height h1 of the lower chord beam in the hollow area, the height h2 of the upper chord beam in the hollow area, the beam height at the junction of the upper and lower chords, and the range L of the mid-span beam section m and the mid-span beam height h3; S2. Calculate the range of the mid-span beam section and the lower edge curve F(x) of the mid-span beam section: Where c is the curve function index of the lower edge of the mid-span beam segment, ranging from 1.8 to 2.0; x jt It is the connection point between the lower edge curve F(x) of the mid-span beam segment and the lower edge curve G(x) of the lower chord beam segment in the hollow area; S3. Calculate and determine the function value and its first-order derivative of the curve F(x) at the connection point where the upper and lower chords meet: y jt =F(x jt )=h1+h2-h3 S4. Calculate and determine the coefficients of the 2.0-3.0 order polynomial function of the lower edge curve G(x) of the lower chord beam section in the hollow area: Get the function of the lower edge curve G(x) of the lower chord beam segment in the hollow area: Where b is the curve function index of the lower edge of the mid-span beam section, which takes a value of 2.0 to 3.0; γ is the concrete weight of the lower chord, which takes a value of 26 kn / m 3 ; σ c The control stress of the lower chord concrete is 0.4 to 0.6 times the axial compressive design strength of the concrete; S5. Check the second-order derivative of the lower edge curve G(x) of the lower chord beam section in the hollow area, adjust the H, h1, and h2 parameters, and repeat the above steps S1-S4 to make the second-order derivative value of the lower edge curve G(x) of the lower chord beam section in the hollow area satisfy not less than γ / σ c .

2. The method for determining the lower edge curve of the mid-span and lower chord beams of a hollow continuous rigid frame bridge according to claim 1, characterized in that: In step S1, the total height H between the upper chord beam and the lower chord beam in the hollow area is: Among them, L is the clear span of the main span of the open-type continuous rigid frame bridge.

3. The method for determining the lower edge curve of the mid-span and lower chord beams of a hollow continuous rigid frame bridge according to claim 2, characterized in that: In step S1, the height h1 of the lower chord beam in the hollow area is:

4. The method for determining the lower edge curve of the mid-span and lower chord beams of a hollow continuous rigid frame bridge as claimed in claim 3, characterized in that: In step S1, the height h2 of the upper chord beam in the hollow area is: The beam height at the junction of the upper and lower chords is h1+h2.

5. The method for determining the lower edge curve of the mid-span and lower chord beams of a hollow continuous rigid frame bridge as claimed in claim 3, characterized in that: In step S1, the mid-span beam segment range L m : L m =(12~15)(h1+h2)。 6. The method for determining the lower edge curve of the mid-span and lower chord beams of a hollow continuous rigid frame bridge as claimed in claim 5, characterized in that: In step S1, the mid-span beam height h3 is:

7. A method for determining the lower edge curve of the mid-span and lower chord beams of a hollow continuous rigid frame bridge as claimed in claim 6, characterized in that: The second-order derivative value of the lower edge curve G(x) of the lower chord beam section in the hollow area is not greater than 3 to 5 times γ / σ c , so that the upward curvature of the lower chord beam section will not be too large, and the maximum eccentricity of the eccentrically compressed lower chord beam section can be controlled.

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