Rectangular hollow steel shell-UHPC (Ultra High Performance Concrete) combined bridge tower section optimization design method

Abstract

The invention discloses a rectangular hollow steel shell-UHPC (Ultra High Performance Concrete) combined bridge tower section optimization design method, which comprises the following steps: acquiring an envelope bending moment and a corresponding axial force according to axial force and bending moment combinations of a bridge tower under multiple working conditions: Mmax is the envelope bending moment of the bridge tower section; mi is the bending moment value of the section of the bridge tower under any working condition; f is the axial force corresponding to Mmax; the flexural capacity of the bridge tower section is calculated according to the expression that the ratio of M to Mmax is calculated, and if M / Mmax is larger than or equal to 1.0 and smaller than or equal to 1.5, it is confirmed that the bridge tower section meets the capacity requirement; otherwise, adjusting the size parameter of the section of the bridge tower, and repeating the calculation process until M / Mmax is more than or equal to 1.0 and less than or equal to 1.5. According to the method, the characteristic of interface damage is used as a design index of the section of the steel shell-UHPC combined bridge tower, the usage amount of the steel shell and the UHPC material in the section of the bridge tower can be effectively limited, and the engineering cost optimization of the bridge tower is achieved.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering, and in particular relates to a method for optimizing the cross-section design of a rectangular hollow steel shell-UHPC composite bridge tower. Background Technology

[0002] Steel-shell-concrete composite bridge towers are composite structures with steel shell segments as the main load-bearing component and internal concrete filling. Due to their advantages such as high load-bearing capacity, high ductility, and ease of construction, they have been successfully applied to a series of long-span bridge projects, including the Nanjing Jiangxinzhou Yangtze River Bridge, the Changtai Yangtze River Bridge, and the Anluo Yellow River Bridge. To further improve structural performance, traditional concrete can be replaced with ultra-high performance concrete (UHPC), forming steel-shell-UHPC composite bridge towers. While this new structure offers superior load-bearing performance, the high cost of UHPC materials significantly increases the overall project cost when used in large-scale bridge tower components. Therefore, in the design of steel-shell-UHPC composite bridge tower sections, it is necessary to control the amount and strength of both the steel shell and UHPC to achieve a reasonable match between material strength and structural requirements. Summary of the Invention

[0003] The purpose of this invention is to provide a method for optimizing the cross-section design of a rectangular hollow steel shell-UHPC composite bridge tower. Based on the capacity requirements of the bridge tower, the optimal strength and quantity of the steel shell and UHPC in the cross-section can be directly calculated, thereby optimizing the engineering cost of the bridge tower.

[0004] The objective of this invention is achieved through the following technical measures: a method for optimizing the cross-section design of a rectangular hollow steel shell-UHPC composite bridge tower, characterized by comprising the following steps:

[0005] S1. Obtain the envelope bending moment and its corresponding axial force from the combination of axial force and bending moment under multiple working conditions of the bridge tower:

[0006]

[0007] Among them, M max M is the envelope bending moment of the bridge tower section; i Let M be the bending moment value of the bridge tower section under any working condition; F is M. max The corresponding axial force;

[0008] S2. Determine the dimensional parameters of the bridge tower cross-section, including cross-section height H, cross-section width B, cross-section thickness T, steel shell thickness t, and steel shell yield strength f. y ;

[0009] S3. Under the plane section assumption, the strain distribution of the bridge tower section is defined by the characteristics of the limit failure according to the following formula:

[0010]

[0011] Where, ε y E represents the yield strain of the steel shell. s ε is the Young's modulus of elasticity of the steel shell. u denoted as ρ, where ρ is the crush strain of the UHPC; x is the height of the compression zone of the UHPC.

[0012] S4. Using formula (1), determine the dimensional parameters of the bridge tower section and formula (2) to construct the axial force equilibrium relationship under the limit failure of the bridge tower section. Introduce the simplification assumption of low wall thickness to obtain the expression for the axial force of the bridge tower section under the limit failure:

[0013] F = 4(2x - H)tf y +[BT+2x(xT)]f cv Formula⑶

[0014] Among them, f cv This represents the uniformly distributed compressive strength of UHPC.

[0015] S5. Combine formulas (2) and (3) to establish the uniformly distributed compressive strength f of UHPC. cv With crush strain ε u Relationship:

[0016]

[0017] S6. Solve for fcv and εu in formula (4);

[0018] S7. Based on the obtained fcv and εu, and combined with the dimensional parameters of the bridge tower section determined in step S2, calculate the flexural bearing capacity of the bridge tower section. The expression is as follows:

[0019]

[0020] Where M is the ultimate bending moment of the bridge tower section;

[0021] S8. Calculate M and M max If the ratio is 1.0≤M / Mmax≤1.5, it is confirmed that the bridge tower section meets the capacity requirements; otherwise, proceed to step S2, adjust the dimensional parameters of the bridge tower section, and repeat steps S3 to S8 until 1.0≤M / Mmax≤1.5.

[0022] This invention utilizes the characteristic of interface failure as a design index for the cross-section of a steel-shell-UHPC composite bridge tower, and calculates the optimal strength and amount of steel shell and UHPC in the cross-section. This effectively limits the amount of steel shell and UHPC materials used in the bridge tower cross-section, and can optimize the engineering cost of the bridge tower.

[0023] Step S6 of the present invention includes:

[0024] Constructing a constitutive model of the UHPC under pressure:

[0025]

[0026] ε cc =e k ε c Formula⑿

[0027]

[0028] f r =0.1f c ′ Formula ⒃

[0029] α c =0.005 + 0.0075c sr Formula⒄

[0030]

[0031] In the formula: f' c σ is the cylindrical compressive strength of UHPC; σ is the compressive stress of UHPC; ε is the compressive strain of UHPC; ε c E represents the compressive strain corresponding to the peak compressive strength. c ε is the elastic modulus of UHPC; cc β represents the compressive strain at the end of the platform segment. c The correlation coefficient for cross-sectional shape is 0.92 for a rectangular shape; A s A represents the area of ​​the steel shell. c The area is UHPC; the other parameters are process variables and have no actual physical meaning.

[0032] Then create f cv and ε u Constitutive relations:

[0033]

[0034] Finally, by combining formulas (7) and (18), f can be obtained. cv and ε u .

[0035] In step S8 of the present invention, when 1.0≤M / Mmax≤1.10, the bridge tower cross section meets the capacity requirements.

[0036] Compared with the prior art, the present invention has the following significant effects:

[0037] (1) The bridge tower section of the present invention has the highest theoretical flexural bearing capacity and flexural stiffness when the limit failure occurs under the condition of constant parameters. Conversely, when the bending moment, stiffness requirements and material properties are constant, the material usage of the section when the limit failure occurs is theoretically the least. The present invention uses the characteristic of interface failure as the design index of the steel shell-UHPC composite bridge tower section, which can effectively limit the amount of steel shell and UHPC materials used in the bridge tower section and reduce the engineering cost of the bridge tower.

[0038] (2) The present invention introduces a constrained constitutive model and an average strength calculation method based on crushing strain, which can accurately evaluate the compressive performance of UHPC under bending load in composite bridge tower sections.

[0039] (3) The low wall thickness assumption proposed in this invention greatly simplifies the calculation process of axial force and bending moment for composite bridge tower sections, making it easier for designers to quickly determine the cross-sectional dimensions of the bridge tower. Attached Figure Description

[0040] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0041] Figure 1 This is a cross-section and strain distribution diagram of the steel shell-UHPC composite bridge tower of the present invention;

[0042] Figure 2 This is a graph showing the relationship between the UHPC constitutive curve under pressure and the average strength of the present invention;

[0043] Figure 3 This is a comparison diagram of the design effects of different failure modes of the present invention.

[0044] In the figure: 1-Outer steel shell; 2-Inner steel shell; 3-Ultra-high performance concrete; 4-Yield strain of steel shell; 5-Crush strain of UHPC; 6-Height of UHPC compression zone; 7-Section width; 8-Section height; 9-Section thickness. Detailed Implementation

[0045] The present invention will now be described in detail with reference to the embodiments and accompanying drawings to help those skilled in the art better understand the inventive concept of the present invention. However, the scope of protection of the claims of the present invention is not limited to the following embodiments. For those skilled in the art, all other embodiments obtained without creative effort without departing from the inventive concept of the present invention are within the scope of protection of the present invention.

[0046] Figure 1The cross-section of the UHPC bridge tower is a rectangular hollow steel shell, consisting of an outer steel shell 1 and an inner steel shell 2, with ultra-high performance concrete 3 filling the space between them. Under ultimate failure, the strain distribution of the cross-section is determined by the yield strain 4 of the steel shell and the crushing strain 5 of the UHPC, and the height 6 of the UHPC compression zone is also defined. Furthermore, the design parameters of the cross-section, including cross-section widths 7, 8, and 9, are also indicated in the figure.

[0047] Figure 2 This is a graph showing the relationship between the constitutive curve of UHPC under compression and its average strength, which illustrates the average strength f of UHPC. cv The principle is that in [0, ε u Within the interval, the area enclosed by the constitutive curve and the x-axis is equal to the area enclosed by the mean intensity line and the x-axis.

[0048] Figure 3 The comparison diagrams show the effects of different failure modes. The basic principle is that the axial force-bending moment capacity curve of a compression-bending member has an outward-protruding shape, with the critical failure point corresponding to the maximum bending moment. The essence of section design is to use the capacity curve to enclose the internal force demand (F, M). max Using the boundary failure as the benchmark for enveloping the section is the most efficient method. In contrast, whether the envelopment is based on large or small eccentric failure, the bending performance of the section will be wasted.

[0049] This invention discloses a method for optimizing the cross-section design of a rectangular hollow steel shell-UHPC composite bridge tower, comprising the following steps:

[0050] S1. Bridge towers are compression-bending members, subjected to different combined axial forces and bending moments under various working conditions. First, based on the combination of axial forces and bending moments under multiple working conditions, the envelope bending moment and its corresponding axial force are obtained:

[0051]

[0052] Among them, M max M is the envelope bending moment of the bridge tower section; i Let F be the bending moment value of the bridge tower section under any working condition such as construction, operation, wind load, and seismic load; M is the bending moment value. max The corresponding axial force.

[0053] S2. Determine the dimensional parameters of the bridge tower cross-section, including cross-section height H, cross-section width B, cross-section thickness T, steel shell thickness t, and steel shell yield strength f. y ;

[0054] S3. Define the strain distribution of the section based on the characteristics of limit failure. Limit failure is a special failure condition of traditional reinforced concrete sections under bending loads. Its physical meaning is that the steel reinforcement yields under tension while the concrete collapses, representing that the bending section reaches its ultimate state simultaneously on both the tension and compression sides. However, in the steel shell-UHPC section, the physical meaning of limit failure changes to the simultaneous yielding of the steel shell and the collapse of the UHPC. Under the plane section assumption, the strain distribution of the section under limit failure conforms to:

[0055]

[0056] Where, ε y E represents the yield strain of the steel shell. s ε is the Young's modulus of elasticity of the steel shell. u denoted as ρ, where ρ is the crush strain of the UHPC; x is the height of the compression zone of the UHPC.

[0057] S4. Using formula (1), determine the dimensional parameters of the bridge tower section and formula (2) to construct the axial force equilibrium relationship under the limit failure of the bridge tower section. A simplified assumption of low wall thickness is introduced, stemming from the ultra-high compressive strength of the UHPC. This reduces the required wall thickness of the bridge tower section, making it much smaller than the section height. In this case, the inner and outer steel shells can be considered to have the same strain distribution. Based on this, the expression for the axial force of the bridge tower section under the limit failure is obtained:

[0058] F = 4(2x - H)tf y +[BT+2x(xT)]f cv Formula⑶

[0059] Among them, f cv This represents the uniformly distributed compressive strength of UHPC.

[0060] S5. Combine formulas (2) and (3) to establish the uniformly distributed compressive strength f of UHPC. cv With crush strain ε u Relationship:

[0061]

[0062] S6. Solve for f in formula (4) cv and ε u ;

[0063] S7. Based on the obtained f cv and ε u Based on the dimensional parameters of the bridge tower section determined in step S2, the flexural bearing capacity of the bridge tower section is calculated, and its expression is as follows:

[0064]

[0065] Where M is the ultimate bending moment of the bridge tower section;

[0066] S8. Calculate M and M max If the ratio of M / Mmax is 1.0 ≤ M / Mmax ≤ 1.5, then the bridge tower cross-section is confirmed to meet the capacity requirements; if the calculated M is less than or much greater than Mmax, then the bridge tower cross-section is considered to meet the capacity requirements. max This indicates that the proposed initial cross-sectional parameters are insufficient or too conservative. The corresponding parameters should be adjusted and the calculation process repeated until 1.0≤M / Mmax≤1.5.

[0067] Step S6 includes:

[0068] First, we introduce the compression constitutive model of UHPC. Considering the constraint effect of the steel shell on UHPC, and that this effect is basically the same as that of steel-tube concrete, the steel-tube confined concrete constitutive model is also the compression constitutive model of UHPC, as follows:

[0069]

[0070] ε cc =e k ε c Formula⑿

[0071]

[0072] f r =0.1f c ′ Formula ⒃

[0073] α c =0.005 + 0.0075c sr Formula⒄

[0074]

[0075] In the formula: f' c σ is the cylindrical compressive strength of UHPC; σ is the compressive stress of UHPC; ε is the compressive strain of UHPC; ε c E represents the compressive strain corresponding to the peak compressive strength. c ε is the elastic modulus of UHPC; cc β represents the compressive strain at the end of the platform segment. c The correlation coefficient for cross-sectional shape is 0.92 for a rectangular shape; A s A represents the area of ​​the steel shell. c The area is UHPC; the other parameters are process variables and have no actual physical meaning.

[0076] After confirming the compressive constitutive model of UHPC, it is also necessary to define the crushing strain of UHPC. In traditional concrete structure design (GB50010-2010), the strain value corresponding to the decrease of concrete compressive strength to 0.5 times peak strength is taken as the crushing strain of concrete. This invention refers to this setting and establishes f accordingly. cv and ε u Constitutive relations:

[0077]

[0078] Finally, by combining formulas (7) and (18), f can be obtained. cv and ε u Since the constitutive model has high complexity, it is difficult to solve it directly. Therefore, the trial-and-error method is recommended.

[0079] Example:

[0080] The internal force combination of a cable-stayed bridge tower is F = 533216 kN and M. max Taking a value of 1034872 kN·m as an example, the dimensional parameters of the bridge tower section are first determined as follows: B = 10m, H = 8m, T = 0.4m, f y =345MPa and t=16mm, and when E s At 200 GPa, ε y =0.001725, substituting the parameters into formula (4) yields:

[0081]

[0082] Combining the UHPC constitutive model under compression, f is obtained using the trial-and-error method. cv =45.9MPa, ε u =0.0088, from the compressive constitutive model of UHPC, we know f' c =72MPa, meaning the required cylindrical compressive strength of the UHPC is 72MPa. Substituting the parameters into formula (5), we obtain M = 1842536kN·m, which is significantly greater than M. max Furthermore, the calculated required UHPC compressive strength is only 72MPa, which fails to fully utilize the ultra-high compressive strength of UHPC. The dimensional parameters of the bridge tower section should be adjusted and the calculation process repeated.

[0083] The dimensions of the bridge tower cross-section were adjusted to B = 8m, H = 6m, and T = 0.3m, while keeping the other parameters unchanged. The calculation process was repeated to obtain f. cv =73.2MPa, ε u =0.0343, f' c=107MPa. At this point, the required cylindrical compressive strength of the UHPC is as high as 107MPa. Substituting the parameters into formula (5), we obtain M = 1063809kN·m. This value is slightly larger than M. max This resulted in a steel-UHPC composite bridge tower section that perfectly met the requirements and fully utilized the compressive strength of UHPC. The designed bridge tower section has a UHPC thickness of only 0.3m, less than 1 / 20 of the side length, and the UHPC area in the bridge tower section is 8.04m². 2 The steel shell area is 0.86m². 2 This achieves the design objective of lightweight and high-strength composite bridge towers.

Claims

1. A method for optimizing the cross-section design of a rectangular hollow steel shell-UHPC composite bridge tower, characterized in that... Includes the following steps: S1. Obtain the envelope bending moment and its corresponding axial force from the combination of axial force and bending moment under multiple working conditions of the bridge tower: Among them, M max M is the envelope bending moment of the bridge tower section; i Let M be the bending moment value of the bridge tower section under any working condition; F is M. max The corresponding axial force; S2. Determine the dimensional parameters of the bridge tower cross-section, including cross-section height H, cross-section width B, cross-section thickness T, steel shell thickness t, and steel shell yield strength f. y ; S3. Under the plane section assumption, the strain distribution of the bridge tower section is defined by the characteristics of the limit failure using the following formula: Where, ε y E represents the yield strain of the steel shell. s ε is the Young's modulus of elasticity of the steel shell. u denoted as ρ, where ρ is the crush strain of the UHPC; x is the height of the compression zone of the UHPC. S4. Using formula (1), determine the dimensional parameters of the bridge tower section and formula (2) to construct the axial force equilibrium relationship under the limit failure of the bridge tower section. Introduce the simplification assumption of low wall thickness to obtain the expression for the axial force F of the bridge tower section under the limit failure: F = 4(2x - H)tf y +[BT+2x(xT)]f cv Formula⑶ Among them, f cv This represents the uniformly distributed compressive strength of UHPC. S5. Combine formulas (2) and (3) to establish the uniformly distributed compressive strength f of UHPC. cv With crush strain ε u Relationship: S6. Solve for f in formula (4) cv and ε u ; S7. Based on the obtained f cv and ε u Based on the dimensional parameters of the bridge tower section determined in step S2, the flexural bearing capacity of the bridge tower section is calculated, and its expression is as follows: Where M is the ultimate bending moment of the bridge tower section; S8. Calculate M and M max If the ratio is 1.0≤M / Mmax≤1.5, it is confirmed that the bridge tower section meets the capacity requirements; otherwise, proceed to step S2, adjust the dimensional parameters of the bridge tower section, and repeat steps S3 to S8 until 1.0≤M / Mmax≤1.

5.

2. The method for optimizing the cross-section design of a rectangular hollow steel shell-UHPC composite bridge tower according to claim 1, characterized in that: Step S6 includes: First, construct the constitutive model of the UHPC under pressure: ε cc = e k ε c Official ⑿ f r =0.1f c ′Formula⒃α c =0.005 + 0.0075c sr Formula⒄ In the formula: f' c σ is the cylindrical compressive strength of UHPC; σ is the compressive stress of UHPC; ε is the compressive strain of UHPC; ε c E represents the compressive strain corresponding to the peak compressive strength. c ε is the elastic modulus of UHPC; cc β represents the compressive strain at the end of the platform segment. c The correlation coefficient for cross-sectional shape is 0.92 for a rectangular shape; A s A represents the area of ​​the steel shell. c The area is UHPC; the other parameters are process variables and have no actual physical meaning. Then create f cv and ε u Constitutive relations: Finally, by combining formulas (7) and (18), f can be obtained. cv and ε u .

3. The method for optimizing the cross-section design of a rectangular hollow steel shell-UHPC composite bridge tower according to claim 1 or 2, characterized in that: In step S8, when 1.0 ≤ M / Mmax ≤ 1.10, the bridge tower cross section meets the capacity requirements.

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