An indirect prestressed complex double-layer concrete shell and its design method

Abstract

The present invention relates to an indirect prestressed complex double-layer concrete shell and a design method thereof. The bottoms of the upper shell and the lower shell of the complex shell are vertically upward, the end cantilevered parts are close to horizontal, and concrete ribs are arranged between the two shells. The middle part of the shell is connected to the horizontal prestressed concrete closed beam to form a spatial structure. The horizontal closed prestressed beam and the complex shell support each other, which changes the constraint boundary conditions of the complex shell and changes the internal force distribution and size of the complex shell. This complex shell with a horizontal closed prestressed beam not only improves the crack resistance and bending resistance of the component, but also improves the deformation performance of the component. Therefore, it is particularly suitable for large cantilever structures with high deformation and bearing capacity.

Description

Technical Field

[0001] The invention relates to an indirect prestressed complex double-layer concrete shell and a design method thereof. Background Art

[0002] In recent years, with the improvement of construction technology in my country, the corresponding construction level has also been getting higher and higher. Single-layer concrete shells are also becoming more and more diverse. From the perspective of force characteristics: some concrete shells have both the compressive force characteristics of concrete columns and the tensile force characteristics of cantilever beams; from the perspective of form: the center line of the shell is neither a traditional oblique line nor a quadratic parabola, but appears in the form of a complex curve. In addition, if the cantilever of the shell is too large, it is difficult to ensure the crack resistance and deformation of the component. Summary of the invention

[0003] The present invention aims to provide an indirect prestressed complex double-layer concrete shell and a design method thereof, and introduces the innovative concept of indirect prestressed structure. The horizontal closed prestressed beam and the complex shell support each other, which changes the constraint boundary conditions of the complex shell, changes the internal force distribution and size of the complex shell, and thus improves the stress performance and ultimate bearing capacity of the complex shell. This effect of the horizontal closed prestressed beam is called indirect prestressing effect.

[0004] The closed beam can be a circular ring or a closed beam of any curve. The number of closed beams can be more than one or more. By optimizing the position and number of prestressed closed beams, the stiffness of the closed beams and the number of prestressed tendons, the distribution of the complex shell and its constraint distribution can be adjusted and improved, thereby reducing the stress distribution and controlling the deformation of the complex shell. The combination of bonded and non-bonded tendons can achieve the regulation of prestress and the adjustment and replacement of non-bonded tendons in the later stage. The combination of slow-bonding and non-bonded tendons can achieve the full life cycle of prestressing, including the construction stage and the use stage, which can maintain higher durability.

[0005] The upper shell and the bottom of the lower shell of the complex shell in the present invention are vertically upward, the end cantilevered part is close to horizontal, and a concrete rib is arranged between the two shells. The middle part of the shell is connected to the horizontal prestressed concrete closed beam to form a spatial structure. This complex shell with a horizontal closed prestressed beam not only improves the crack resistance and bending resistance of the component, but also improves the deformation performance of the component. Therefore, it is particularly suitable for large cantilever structures with high deformation and bearing capacity.

[0006] To achieve the above object, the present invention adopts the following scheme:

[0007] An indirect prestressed complex double-layer concrete shell and a design method thereof, comprising an upper shell 1, a lower shell 2, a rib plate 3, and a closed beam 4. The upper shell 1 and the lower shell 2 are fixed at the bottom, close to vertical near the fixed end, close to horizontal at the end, and the middle and horizontal prestressed concrete closed beams are connected. The middle closed beam 4 is provided with unbonded prestressed steel bars at the top and bottom of the beam, and the center line of the closed beam is described by the equation z=f(x).

[0008] Furthermore, the design method of the complex shell is implemented by the following steps:

[0009] Step 1: Determine the curvature K of the prestressed tendon curve;

[0010] Step 2: Calculate the normal force q caused by the prestressed tendons n =N p K; Where: N p is the tension of the prestressed tendons;

[0011] Step 3: Calculate the tangential force q caused by the prestressed tendons τ ,q τ =μN p K; where: μ is the friction coefficient between the prestressed tendons and the hole wall;

[0012] Step 4: Determine the normal force q caused by the prestressing tendon n , tangential force q τ The total bending moment value M caused by the external load is obtained from M, and the shell stress σ is obtained from M. (Steps 1 to 4 can also be implemented by finite element program).

[0013] Step 5: Shell reinforcement calculation;

[0014] Furthermore, the prestressed tendon curve described in step 1 is z=f(x), and the specific method for determining the curvature K is:

[0015] First, find the first-order derivative z' and the second-order derivative z" of the curve, and then get the curvature of the curve Get the curvature K of the prestressed tendon curve;

[0016] Furthermore, the prestressed normal force described in step 2 is calculated as follows: q n =N p K; Where: N p is the tension of the prestressed tendons;

[0017] Furthermore, the prestressed tangential force described in step 2 is calculated as follows: τ =μN p K; where: μ is the friction coefficient between the prestressed tendons and the hole wall;

[0018] Furthermore, step five is described as follows: using the concrete effective stress graph to calculate the reinforcement of the complex shell. :

[0019] A s =(Ab-0.6A t bf t ) / f y

[0020] Where: A s The cross-sectional area of ​​the ordinary steel bar under tension is; A is the total area of ​​the principal tensile stress diagram; A t The area of ​​the graph where the principal tensile stress is less than the design value of the tensile strength of the concrete axis; b is the width of the calculated section; f is the area of ​​the graph where the principal tensile stress is less than the design value of the tensile strength of the concrete axis; y It is the design value of tensile strength of non-prestressed steel bars.

[0021] The present invention analyzes the prestressed tendon curve, applies the calculated tangential and normal forces as external loads to the complex single-layer concrete shell, and obtains a calculation formula for the bending bearing capacity of the concrete positive section of the complex single-layer concrete shell (with bonding, non-bonding, and slow-bonding tendons).

[0022] After adopting this system, the material usage of the structure is reduced by about 15%, which is more economical. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 It is the main view of the complex shell with the end cantilevered; DETAILED DESCRIPTION

[0024] The present invention is further described in detail below with reference to the accompanying drawings.

[0025] Step 1: First, find the first-order derivative z' and the second-order derivative z" of the curve, and then get the curvature of the curve Get the curvature K of the prestressed tendon curve;

[0026] Step 2: Calculate the normal force q caused by the prestressed tendons n =N p K; Where: N p is the tension of the prestressed tendons;

[0027] Step 3: Calculate the tangential force q caused by the prestressed tendons τ ,q τ =μN p K; where: μ is the friction coefficient between the prestressed tendons and the hole wall;

[0028] Step 4: Determine the normal force q caused by the prestressing tendon n , tangential force q τ The total bending moment value M caused by the external load is obtained from M, and the shell stress σ is obtained from M. (Steps 1 to 4 can also be implemented by finite element program).

[0029] Step 5: Shell reinforcement calculation;

[0030] A s =(Ab-0.6A t bf t ) / f y

[0031] Where: A s The cross-sectional area of ​​the ordinary steel bar under tension is; A is the total area of ​​the principal tensile stress diagram; A t The area of ​​the graph where the principal tensile stress is less than the design value of the tensile strength of the concrete axis; b is the width of the calculated section; f is the area of ​​the graph where the principal tensile stress is less than the design value of the tensile strength of the concrete axis; y It is the design value of tensile strength of non-prestressed steel bars.

[0032] Thus, the design calculation work is completed.

[0033] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art who is familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. An indirect prestressed complex double-layer concrete shell and a design method thereof, comprising an upper shell (1), a lower shell (2), a rib plate (3), and a closed beam (4). The upper shell (1) and the lower shell (2) are fixed at the bottom, the parts close to the fixed ends are nearly vertical, the cantilevered parts at the ends are nearly horizontal, and the middle and horizontal prestressed concrete closed beams are connected. The rib plate (3) is a concrete slab. The closed beam (4) is provided with prestressed steel bars (bonded, non-bonded, and slow-bonded bars) at the top and bottom of the beam, and the prestressed bars of the closed beam are described by the curve equation z=f(x).

2. The prestressed design method for a complex shell according to claim 1, characterized in that: The design method of the complex shell is implemented by the following steps: Step 1: Determine the curvature K of the prestressed tendon curve; Step 2: Calculate the normal force q caused by the prestressed tendons n =N p K; Where: N p is the tension of the prestressed tendons; Step 3: Calculate the tangential force q caused by the prestressed tendons τ ,q τ =μN p K; where: μ is the friction coefficient between the prestressed tendons and the hole wall; Step 4: Determine the normal force q caused by the prestressing tendon n , tangential force q τ The total bending moment value M caused by the external load is obtained from M, and the shell stress σ is obtained from M. (Steps 1 to 4 can also be implemented by finite element program). Step 5: Calculation of shell reinforcement.

3. The prestressed design method for a complex shell according to claim 2, characterized in that: The prestressed tendon curve described in step 1 is z=f(x), and the specific method for determining the curvature K is: First, find the first-order derivative z' and the second-order derivative z" of the curve, and then get the curvature of the curve Get the curvature K of the prestressed tendon curve.

4. The prestressed design method for a complex shell according to claim 3 is characterized in that: The prestressing normal force described in step 2 is calculated as follows: q n =N p K; Where: N p is the tension of the prestressed tendons.

5. The prestressed design method for a complex shell according to claim 4, characterized in that: The prestressed tangential force described in step 3 is calculated as follows: q τ =μN p K; where: μ is the friction coefficient between the prestressed tendons and the hole wall.

6. The prestressed design method for a complex shell according to claim 5, characterized in that: Step 4 is as follows: Determine the normal force q caused by the prestressed tendon n , tangential force q τ The total bending moment value M caused by the external load is obtained; the stress σ of the shell is obtained from M.

7. The prestressed design method for a complex shell according to claim 6, characterized in that: Step 5 is as follows: The ordinary steel bars of the shell are calculated as follows: A s =(Ab-0.6A t bf t ) / f y Where: A s The cross-sectional area of ​​the ordinary steel bar under tension is; A is the total area of ​​the principal tensile stress diagram; A t The area of ​​the graph where the principal tensile stress is less than the design value of the tensile strength of the concrete axis; b is the width of the calculated section; f is the area of ​​the graph where the principal tensile stress is less than the design value of the tensile strength of the concrete axis; y It is the design value of tensile strength of non-prestressed steel bars.

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