Space curve prestress composite beam column and design method thereof

Abstract

The invention relates to a space curve prestress composite beam column and a design method thereof. The bottom of the space curve composite beam column is vertically upward, the tail end overhanging part is approximately horizontal, and the middle part is connected with the horizontal prestressed concrete closed beam to form a space structure. The horizontal closed prestressed beam and the space curve composite beam column support each other, the constraint boundary condition of the space curve composite beam column is changed, and the internal force distribution and magnitude of the space curve composite beam column are changed. According to the space curve composite beam column with the horizontal closed prestressed beam, the anti-cracking and anti-bending performance of a component is improved, and the deformation performance of the component is also improved. Therefore, the structure is particularly suitable for large cantilever structures with high deformation and bearing capacity.

Description

Technical Field

[0001] The present invention relates to a prestressed composite beam-column with a spatial curve and a design method thereof. Background Art

[0002] In recent years, with the improvement of construction technology in China, the corresponding construction level has become higher and higher. The architectural shapes have also become more and more diverse. A variety of prestressed components have emerged. Among them, there is a component whose force-bearing has both the compressive force-bearing characteristics of a concrete column and the tensile force-bearing characteristics of a cantilever beam. The axis of the component is neither a traditional oblique line nor a quadratic parabola. Therefore, in the original prestressed concrete structure design method, it is difficult to determine the bearing capacity when the beam-column presents a complex curve. In addition, when the overhang is too large, it is difficult to ensure the anti-cracking deformation of the component.

[0003] By optimizing the position and quantity of prestressed closed beams, as well as the stiffness of the closed beams and the quantity of prestressed tendons, the distribution of the shell and its restraint distribution can be adjusted and improved, thereby reducing the stress distribution and achieving the control of the deformation of the complex shell. The combination of bonded and unbonded tendons can realize the regulation of prestress and the adjustment and replacement of unbonded tendons in the later stage. The combination of slow-bonded and unbonded tendons can realize the full-life adjustability, controllability and replaceability of prestress including the construction stage and the service stage, and maintain higher durability. Summary of the Invention

[0004] The present invention aims to provide a prestressed composite beam-column with a spatial curve and a design method thereof, and introduce the innovative concept of an indirect prestressed structure. The horizontal closed prestressed beam and the spatial curve composite beam-column support each other, changing the constraint boundary conditions of the spatial curve composite beam-column, changing the internal force distribution and magnitude of the spatial curve composite beam-column, thereby improving the mechanical properties and ultimate bearing capacity of the spatial curve composite beam-column. This effect of the horizontal closed prestressed beam is called the indirect prestress effect.

[0005] In the present invention, the bottom of the spatial curve composite beam-column is vertically upward, the end overhanging part is close to horizontal, and the middle is connected to the horizontal prestressed concrete closed beam to form a spatial structure. This spatial curve composite beam-column with a horizontal closed prestressed beam not only improves the anti-cracking and flexural resistance performance of the component, but also improves the deformation performance of the component. Therefore, it is particularly suitable for large overhanging structures with high requirements for deformation and bearing capacity.

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

[0007] A prestressed composite beam-column with a spatial curve and a design method thereof, including a spatial curve composite beam-column 1 and a middle closed beam 2. The spatial curve composite beam-column 1 is fixed at the bottom, close to the fixed end and close to vertical, the end is close to horizontal, and the middle is connected to the horizontal prestressed concrete closed beam. The center line of the spatial curve composite beam-column 1 can be expressed by the equation z = ayα It is described as +c(α<0). Unbonded prestressed steel bars are arranged at the upper part, and the curve of the prestressed tendon is z = ay α +b(α<0). In the middle closed beam 2, prestressed steel bars (bonded, unbonded, and slow-bonded bars) are arranged at both the top and bottom of the beam.

[0008] Furthermore, the design method of the space curve composite beam-column is realized through the following steps:

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

[0010] Step 2: Estimate the cross-sectional area A of the longitudinal prestressed tendon at the upper part of the cantilever beam p Estimate

[0011] Step 3: Calculate the normal force q caused by the prestressed tendon n ;

[0012] Step 4: Calculate the tangential force q caused by the prestressed tendon τ ;

[0013] Step 5: Determine the total bending moment value M caused by the normal force q n , tangential force q τ and the external load;

[0014] Step 6: Check the flexural bearing capacity;

[0015] Step 7: Check the shear bearing capacity.

[0016] Furthermore, the prestressed tendon curve described in Step 1 is z = ay α +b. The specific method for determining the curvature K:

[0017] First, find the first derivative z' and the second derivative z" of the curve, and then obtain the curvature of the curve

[0018] Furthermore, the calculation of the prestressed normal force described in Step 2 is as follows: q n = N p K; where: N p is the tension of the prestressed tendon;

[0019] Furthermore, the calculation of the prestressed tangential force described in Step 3 is as follows: q τ = μN p K; where:

[0020] μ is the friction coefficient between the prestressed tendon and the duct wall;

[0021] Furthermore, use the formula for calculating the flexural bearing capacity of the rectangular cross-section prestressed concrete flexural member:

[0022]

[0023] α1f c bx=f y A s -f y 'A s '+f py A p

[0024] Where: M is the design value of bending moment; α1 is the coefficient of rectangular stress diagram. For concrete not higher than C50, α1 = 1.0; for C80 concrete, α1 = 0.94; the value in between is taken by linear interpolation method; b is the width of rectangular section; f c is the design value of axial compressive strength of concrete; x is the height of concrete compression zone; h0 is the effective height of section, which is the distance from the resultant force point of all tensile reinforcement to the compression edge of section; f y is the design value of tensile strength of non-prestressed reinforcement; f′ y is the design value of compressive strength of non-prestressed reinforcement; A s is the cross-sectional area of longitudinal ordinary reinforcement in the tensile zone; A s ′ is the cross-sectional area of longitudinal ordinary reinforcement in the compression zone; A p is the area of prestressed reinforcement arranged in the tensile zone;

[0025] Furthermore, the specific content of Step 7 is as follows:

[0026] V=α cv f t bh0+f yv A sv h0 / s

[0027] Where: V is the design value of shear force; α cv is the coefficient of shear bearing capacity of concrete for inclined section, and for general flexural members, it is taken as 0.7. f yv is the design value of tensile strength of non-prestressed reinforcement; A sv is the total cross-sectional area of each limb of stirrups arranged in the same section; f t is the design value of axial tensile strength of concrete; s is the stirrup spacing in the member length direction.

[0028] The present invention analyzes the curve of prestressed tendons, takes the calculated tangential and normal forces as external loads and applies them to complex beam-columns with a spatial curve axis, and obtains the calculation formula for the flexural bearing capacity of the normal section of post-tensioned unbonded prestressed concrete with a rectangular section. Description of the Drawings

[0029] Figure 1 is the front view of the spatial curve composite beam-column with an end overhang;

[0030] Figure 2 are the tangential force and normal force received by the spatially curved composite beam-column with an end overhang in the design;

[0031] Figure 3 is the simplified calculation diagram for the flexural bearing capacity of the spatially curved composite beam-column with an end overhang in the design; Specific implementation mode

[0032] The present invention will be further described in detail below with reference to the accompanying drawings.

[0033] 1. First, find the first derivative z' and the second derivative z" of the curve, and then obtain the curvature of the curve Obtain the curvature K of the prestressed tendon curve;

[0034] 2. Estimate the cross-sectional area A of the longitudinal prestressed tendons in the upper part of the cantilever beam p Estimation. Design according to unbonded, and determine the total area of prestressed tendons according to the requirements of the serviceability limit state and crack control. The prestressed concrete is calculated in the uncracked state; during construction and service, under the design load and the action of prestress, estimate the area A of the unbonded tendons p ; The calculation is as follows:

[0035] The normal stresses of concrete generated by external loads and prestress are respectively:

[0036]

[0037] Among them: σ ck is the normal stress of the concrete at the tensile edge for crack resistance check under the standard combination of loads; M k is the maximum bending moment design value of the beam section under the standard combination of loads; I is the moment of inertia of the gross cross-section of the concrete member, y is the distance from the centroid of the concrete cross-section to the upper edge of the member; σ pc is the stress generated by prestress after deducting all prestress losses; A n is the net cross-sectional area, e pn is the distance from the centroid of the net cross-section to the point of action of prestress; y n is the distance from the centroid of the net cross-section to the upper surface. σ p2 is the normal stress of the concrete cross-section caused by the secondary internal force of prestress. Since this member is a cantilever member, this item is zero during estimation.

[0038] The prestressing force of the post-tensioned prestressed member is:

[0039] N p =σ pe A p

[0040] Among them σ peIt is the effective prestress of the prestressed reinforcement in the tensile zone of the concrete, and 0.80 times the tensile control stress is taken in the estimation stage.

[0041] From σ ck -σ pc =f tk Calculate the cross-sectional area of the prestressed reinforcement as:

[0042]

[0043] 3. Calculate the normal force q n , q n =N p K; where: N p is the tensile force of the prestressed reinforcement;

[0044] 4. Calculate the tangential force q τ , q τ =μN p K; where: μ is the friction coefficient between the prestressed reinforcement and the duct wall;

[0045] 5. Determine the normal force q n , tangential force q τ and the total bending moment value M caused by the external load;

[0046] 6. Check the flexural bearing capacity;

[0047] α1f c bx = f y A s -f y 'A s '+f py A p

[0048] where: M is the design value of the bending moment; α1 is the coefficient of the rectangular stress diagram. For concrete not higher than C50, α1 = 1.0; for C80 concrete, α1 = 0.94; the value in between is taken by linear interpolation; b is the width of the rectangular section; f c is the design value of the axial compressive strength of the concrete; x is the height of the concrete compression zone; h0 is the effective height of the section, which is the distance from the resultant force point of all the tensile reinforcement to the compression edge of the section; f y is the design value of the tensile strength of the non-prestressed reinforcement; f′ y is the design value of the compressive strength of the non-prestressed reinforcement; A s is the cross-sectional area of the longitudinal ordinary reinforcement in the tensile zone; A s ′ is the cross-sectional area of the longitudinal ordinary reinforcement in the compression zone; A p is the area of the prestressed reinforcement arranged in the tensile zone;

[0049] 7. Shear bearing capacity check.

[0050] V = α cv f t bh0 + f yv A sv h0 / s

[0051] In the formula: V is the shear design value; α cv is the shear bearing capacity coefficient of concrete for inclined section. For general flexural members, it is taken as 0.7. f yv is the design value of the tensile strength of non-prestressed steel bars; A sv is the total cross-sectional area of all limbs of stirrups configured in the same cross-section; f t is the design value of the axial tensile strength of concrete; s is the stirrup spacing in the member length direction.

[0052] Thus, the design calculation work is completed.

[0053] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claimed rights.

Claims

1. A prestressed composite beam-column with a spatial curve and its design method, comprising a spatial curve composite beam-column (1) and a middle closed beam (2). The spatial curve composite beam-column (1) is fixed at the bottom, the part near the fixed end is close to vertical, the cantilever part at the end is close to horizontal, and it is connected to the prestressed concrete closed beam in the middle and horizontal. The center line of the spatial curve composite beam-column (1) can be described by the equation z = ay α + c (α < 0), and unbonded prestressed steel bars are arranged near the upper surface inside the component. The curve of the post-tensioned prestressing tendon is z = ay α + b (α < 0). Prestressed steel bars (bonded, unbonded, and slow-bonded bars) are arranged at both the top and bottom of the middle closed beam (2).

2. The prestress design method of the space curve composite beam-column according to claim 1, characterized in that: The design method of the space curve composite beam-column is realized through the following steps: Step 1: Determine the curvature K of the curve of the prestressed tendon of the space curve composite beam-column; Step 2: Estimate the cross-sectional area A of the longitudinal prestressed tendons at the upper part of the cantilever beam p Estimate. Design according to the unbonded method. Determine the total area of prestressed tendons based on the requirements of the serviceability limit state and according to crack control. Calculate the prestressed concrete in the uncracked state; under the construction and service conditions, estimate the area A of the unbonded tendons under the action of design loads and prestress p The calculation is as follows: The normal stresses of concrete generated by external loads and prestress are respectively: Where: σ ck is the normal stress of the concrete at the tensile edge for crack resistance check under the standard combination of loads; M k is the design value of the maximum bending moment of the beam section under the standard combination of loads; I is the moment of inertia of the gross cross-section of the concrete member, and y is the distance from the centroid of the concrete cross-section to the upper edge of the member; σ pc is the stress generated by prestress after deducting all prestress losses; A n is the net cross-sectional area, e pn is the distance from the centroid of the net cross-section to the point of action of the prestress; y n is the distance from the centroid of the net cross-section to the upper surface. σ p2 is the normal stress of the concrete cross-section caused by the secondary internal force of prestress. Since this member is a cantilever member, this item is zero during estimation. The prestressing force of the post-tensioned prestressed member is: N p = σ pe A p where σ pe is the effective prestress of the prestressed reinforcement in the tensile zone of the concrete, and 0.80 times the tensile control stress is taken in the estimation stage. From σ ck -σ pc = f tk Calculate the cross-sectional area of the prestressed steel bars as follows: Step 3: Calculate the normal force q caused by the prestressing tendon n = N p K; where: N p is the tensile force of the prestressing tendon; Step 4: Calculate the tangential force q caused by the prestressing tendon τ , q τ = μN p K; where: μ is the friction coefficient between the prestressing tendon and the duct wall; Step 5: Determine the normal force q n and tangential force q τ caused by the prestressing tendon, and the total bending moment value M caused by the external load; Step 6: Check the flexural bearing capacity; Step 7: Check the shear bearing capacity.

3. The prestress design method of the space curve composite beam-column according to claim 2, characterized in that: The prestressed tendon curve described in Step 1 is z = ay α + c. The specific determination method of the curvature K is as follows: First, find the first derivative z' and the second derivative z" of the curve, and then obtain the curvature of the curve Obtain the curvature K of the prestressing tendon curve 4. The prestress design method of the space curve composite beam-column according to claim 3, characterized in that: The normal prestress force described in Step 2 is calculated as follows: q n = N p K; where: N p is the tension of the prestressing tendon.

5. The prestress design method of the space curve composite beam-column according to claim 4, characterized in that: The calculation of the prestressed tangential force described in Step 3 is as follows: q n = μN p K; where: μ is the friction coefficient between the prestressed tendon and the duct wall.

6. The prestress design method of the space curve composite beam-column according to claim 5, characterized in that: The details of Step 6 are as follows: Use the formula for calculating the ultimate flexural capacity of the rectangular cross-section prestressed concrete flexural member: α1f c bx = f y A s -f y 'A s '+f py A p Where: M is the design value of bending moment; α1 is the coefficient of rectangular stress diagram. For concrete not higher than C50, α1 = 1.0; for C80 concrete, α1 = 0.94; the value in between is obtained by linear interpolation; b is the width of the rectangular cross-section; f c is the design value of the axial compressive strength of concrete; x is the height of the concrete compression zone; h0 is the effective height of the cross-section, which is the distance from the resultant force point of all tensile reinforcement to the compression edge of the cross-section; f y is the design value of the tensile strength of non-prestressed reinforcement; f' y is the design value of the compressive strength of non-prestressed reinforcement; A s is the cross-sectional area of longitudinal ordinary reinforcement in the tensile zone; A s ′ is the cross-sectional area of longitudinal ordinary reinforcement in the compression zone; A p is the area of prestressed reinforcement arranged in the tensile zone.

7. The prestress design method of the space curve composite beam-column according to claim 6, characterized in that: The details of Step 7 are as follows: V = α cv f t bh0 + f yv A sv h0 / s Where: V is the shear design value; α cv is the coefficient of the shear bearing capacity of concrete for inclined sections, and for general flexural members, it is taken as 0.

7. f yv is the design value of the tensile strength of non-prestressed steel bars; A sv is the total cross-sectional area of all limbs of stirrups arranged in the same cross-section; f t is the design value of the axial tensile strength of concrete; s is the stirrup spacing in the member length direction.

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