Simplified determination method for optimal depth-to-width ratio of upper structure of continuous rigid frame aqueduct

Abstract

The invention discloses a simplified determination method for the optimal depth-to-width ratio of an upper structure of a continuous rigid frame aqueduct, and the method comprises the following steps: drawing different depth-to-width ratio schemes, and carrying out the structural modeling through engineering simulation software; analyzing structure effects of vertical effects of different depth-to-width ratio schemes to obtain normalized indexes of the different depth-to-width ratio schemes under the vertical effects; analyzing the structure effect of the transverse action of the different depth-to-width ratio schemes to obtain normalized indexes under the transverse action of the different depth-to-width ratio schemes; drawing structure effect diagrams of different depth-to-width ratio schemes under transverse and vertical effects by taking the depth-to-width ratio as a horizontal coordinate and taking the normalized index as a longitudinal axis; and determining the optimal depth-to-width ratio according to the principle of the minimum structural comprehensive effect under the transverse and vertical effects. Complex scheme total price comparison is simplified into mechanical effect comparison, and the calculation amount of scheme comparison is greatly reduced.

Description

Technical Field

[0001] The present invention belongs to the field of aqueduct design in water conservancy projects, and particularly relates to a simplified method for determining the optimal depth-width ratio of the upper structure of a continuous rigid frame aqueduct. Background Art

[0002] A continuous rigid frame aqueduct is a canal system building in the water conservancy and hydropower industry. It adopts the technology of rigid connection between the upper aqueduct structure system and the lower piers, which makes it possible to construct aqueducts with extremely large spans. The aqueduct body is generally rectangular or U-shaped, and adopts the "bridge-aqueduct integration" to effectively combine the load-bearing structure and the water passage body, which can effectively reduce the self-weight of the structure. Combined with the development and application of prestressed technology, it can ensure its longitudinal flexural stiffness and transverse torsional stiffness.

[0003] The depth-width ratio of the aqueduct body is the ratio of the width to the depth of the water passage section of the aqueduct. A reasonable depth-width ratio can ensure good hydraulic conditions for the upper aqueduct body, and ensure good mechanical properties of the upper structure and the lower piers, and further ensure the optimal project cost.

[0004] In previous designs, the depth-width ratio of the aqueduct was selected according to experience. From the perspective of water passing capacity, the depth-width ratio should be selected according to the conditions of the best hydraulic section (the depth-width ratio H / B of the best hydraulic section of a rectangular aqueduct body is 0.5); but from the perspective of mechanical properties, a larger depth-width ratio of the beam-type aqueduct body is beneficial to increasing the longitudinal stiffness of the aqueduct body. Therefore, a narrow and deep section with a depth-width ratio greater than 0.5 is generally adopted. For a rectangular aqueduct, generally H / B = 0.6 - 0.8, for a U-shaped aqueduct, generally H / B = 0.7 - 0.9. For a larger-span aqueduct body, the depth-width ratio can be even larger to reduce the longitudinal stress of the aqueduct body, but it should be noted that increasing the height of the aqueduct body will increase the lateral wind pressure, which is not conducive to lateral stability.

[0005] The above methods are all empirical values, lacking a quantitative analysis and determination method for the depth-width ratio of the aqueduct. Especially for a rigid frame aqueduct with a large width, the above empirical values lack empirical reference. Therefore, it is necessary to study and propose a method for determining the optimal depth-width ratio of the upper structure of a rigid frame aqueduct.

[0006] Theoretically speaking, when selecting the design depth-width ratio of the aqueduct, different values can be proposed, and the mechanical properties of the upper and lower structures at different depth-width ratios can be calculated respectively, the structural dimensions can be determined respectively, the steel bars, prestressed anchor cables and foundation treatment plans can be calculated, and the respective project costs can be calculated, and finally the optimal depth-width ratio can be selected. However, this method has a large amount of calculation, and there are also many main span ratios, aqueduct thicknesses, section form selections, etc. that need to be analyzed. Just for one parameter, so many selection and analysis are required, which is unrealistic for the design of aqueduct buildings. Based on the above problems, through analysis and research, the present invention proposes a simplified method for determining the optimal depth-width ratio of the upper structure of a continuous rigid frame aqueduct. Summary of the Invention

[0007] The object of the present invention is to provide a simplified method for determining the optimal depth-width ratio of the upper structure of a continuous rigid-frame aqueduct, which simplifies the comparison of the total prices of complex schemes into the comparison of mechanical effects, greatly simplifying the computational workload of scheme comparison.

[0008] To achieve the above object, the technical solution adopted by the present invention is as follows:

[0009] A simplified method for determining the optimal depth-width ratio of the upper structure of a continuous rigid-frame aqueduct, comprising the following steps:

[0010] S1. Draw schemes with different depth-width ratios and carry out structural modeling using engineering simulation software;

[0011] S2. Analyze the structural effects of different depth-width ratio schemes under vertical actions to obtain the normalized indexes of different depth-width ratio schemes under vertical actions;

[0012] S3. Analyze the structural effects of different depth-width ratio schemes under lateral actions to obtain the normalized indexes of different depth-width ratio schemes under lateral actions;

[0013] S4. With the depth-width ratio as the abscissa and the normalized index as the ordinate, draw the structural effect diagrams of different depth-width ratio schemes under lateral and vertical actions;

[0014] S5. Determine the optimal depth-width ratio according to the principle of the minimum comprehensive structural effect under lateral and vertical actions.

[0015] Preferably, the specific steps of S1 are as follows:

[0016] S101. Carry out hydraulic analysis to determine the longitudinal slope of the aqueduct;

[0017] S102. Draw up schemes with different depth-width ratios and determine the cross-sectional area, shape and size of the water passage;

[0018] S103. Draw schemes with different depth-width ratios;

[0019] S104. For schemes with different depth-width ratios, carry out structural modeling using engineering simulation software.

[0020] Preferably, the specific steps of S2 are as follows:

[0021] S201. Analyze the weight of the main beam, the moment at the pier top, the maximum shear force, the moment at the mid-span and the deflection at the mid-span of different depth-width ratio schemes under vertical actions according to two working conditions, namely the design working condition and the increased working condition;

[0022] S202. Normalize the data in S201 to obtain the normalized indexes of different depth-width ratio schemes under vertical actions.

[0023] Preferably, the specific steps of S3 are as follows:

[0024] S301. Analyze the results of the lateral displacement and lateral acceleration under the lateral action of different depth-width ratio schemes respectively according to two working conditions: crosswind working condition and earthquake working condition.

[0025] S302. Normalize the data in S301 to obtain the normalized indexes under the lateral action of different depth-width ratio schemes.

[0026] Preferably, in S202, the specific formula for normalization is as follows:

[0027]

[0028] where X norm is the index after normalization, X is the index to be normalized, X max is the maximum value of the index under different depth-width ratio schemes, and X min is the minimum value of the index under different depth-width ratio schemes.

[0029] Preferably, the specific steps of S5 are as follows: Take the main girder weight, pier top moment, maximum shear force, mid-span moment, and lateral acceleration under the earthquake working condition as the main indexes, and take the mid-span deflection caused by self-weight and the lateral displacement caused by crosswind load as the secondary indexes. Select the relatively concentrated interval according to the principle of smaller normalized indexes to determine the optimal depth-width ratio.

[0030] The beneficial effect of the present invention is that it simplifies the comparison of complex scheme total prices into the comparison of mechanical effects, greatly simplifying the calculation amount of scheme comparison. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is the flow chart of the method of the present invention.

[0032] Figure 2 is the schematic diagram of the designed cross-section of different depth-width ratio schemes.

[0033] Figure 3 is the comparison diagram of the interfaces of the Timoshenko beam element before and after deformation.

[0034] Figure 4 is the modeling effect diagram of the Timoshenko beam element.

[0035] Figure 5 is the finite element model diagram of Design Section 1.

[0036] Figure 6 is the analysis diagram of the structural comprehensive effect under the lateral and vertical actions of different depth-width ratio schemes.

[0037] In the figure, t1 is the web thickness, t2 is the middle partition thickness, t3 is the top plate thickness, and t4 is the bottom plate thickness. DETAILED DESCRIPTION OF THE INVENTION

[0038] To make the objectives, technical solutions and advantages of the present invention clearer, the following will clearly and completely describe the technical solutions of the present invention in conjunction with the drawings and embodiments of the present invention.

[0039] As Figure 1 shown, a simplified method for determining the optimal depth-width ratio of the upper structure of a continuous rigid-frame aqueduct includes the following steps:

[0040] S1. Draw schemes with different depth-width ratios and conduct structural modeling using engineering simulation software.

[0041] S101. Conduct hydraulic analysis to determine the longitudinal slope of the aqueduct.

[0042] The hydraulic calculation method of the aqueduct adopts the formula for uniform flow in open channels. According to the topographic conditions, the longitudinal slope is initially selected in the range of 1 / 500 to 1 / 2000, and the design flow rate and head loss are calculated by trial until the longitudinal slope meets the requirements of flow passing and head loss.

[0043] S102. Draw up schemes with different depth-width ratios and determine the cross-sectional area, shape and dimensions of the water passage.

[0044] The cross-section of the continuous rigid-frame aqueduct is of two types: rectangular and U-shaped. The present invention proposes to select 3 (such as 0.6, 0.8, 1.1) to 5 different depth-width ratios (0.6, 0.7, 0.8, 0.9, 1.0) from them. According to the uniform flow in open channels, the corresponding cross-sectional dimensions of the water passage, namely the width B and the depth H, can be calculated.

[0045] The calculation method of the cross-sectional area of the rectangular water passage is BH, and the calculation method of the cross-sectional area of the U-shaped water passage is (πBB / 8 + BH - BB / 2)

[0046] S103. Draw schemes with different depth-width ratios.

[0047] The rigid-frame aqueduct has a "variable box and variable cross-section" section. The mid-span section is a single-box section, which is determined only by the cross-section of the water passage. The bottom slab of the section gradually thickens towards the two side support parts. When the thickness of the bottom slab is insufficient to meet the structural requirements at a certain section, the section becomes a two-box section.

[0048] According to the different depth-width ratio schemes drawn up in S102, the web thickness, middle partition thickness, top slab thickness and bottom slab thickness of each scheme are determined according to experience. To study the influence of the size and shape of the cross-section of the water passage on the overall structural effect, the thicknesses of different depth-width ratio schemes are simplified and considered according to a unified value. At the same time, the lower structure is kept the same, and schemes with different depth-width ratios are drawn.

[0049] S104. For different depth-width ratio schemes, conduct structural modeling using engineering simulation software.

[0050] For different depth-width ratio schemes, finite element modeling and analysis are carried out using MADIS software.

[0051] The beam elements of the model are based on Timoshenko's beam theory. Shear deformation can be considered during analysis, making the calculation of structures such as deep beams and thin-walls more accurate.

[0052] During finite element modeling and analysis, only the overall structural response changes caused by the change of the box girder section are concerned, and the boundary conditions are simplified as follows: The bottom of the pier is fixed, and general support constraints are used at both ends.

[0053] S2. Analyze the structural effects of vertical and lateral actions for different depth-width ratio schemes, and obtain the normalized indexes under vertical actions for different depth-width ratio schemes.

[0054] S201. According to two working conditions, namely the design working condition (self-weight + design flow) and the increased working condition (self-weight + increased flow), analyze the main beam weight, pier top moment, maximum shear force, mid-span moment, and mid-span deflection under vertical actions for different depth-width ratio schemes.

[0055] S202. Normalize the data of S201 to obtain the normalized indexes under vertical actions for different depth-width ratio schemes.

[0056] Since the units of the above indexes are different and the numerical differences are large. To avoid the amplification of the influence of a certain index, the data is normalized to facilitate the comprehensive comparison of multiple indexes. Under the design working condition and the increased working condition, the structural effects of the above vertical actions, including the main beam weight, pier top moment, maximum shear force, mid-span moment, and mid-span deflection, are normalized respectively.

[0057] The specific formula for normalization is as follows:

[0058]

[0059] Among them, X norm is the index after normalization, X is the index to be normalized, such as the main beam weight, pier top moment, maximum shear force, mid-span moment, mid-span deflection, lateral displacement, and lateral acceleration of a certain depth-width ratio scheme, X max is the maximum value of the index under different depth-width ratio schemes, such as the maximum value of the main beam weight, X min is the minimum value of the index under different depth-width ratio schemes, such as the minimum value of the main beam weight.

[0060] Through normalization, the numerical ranges of the main beam weight, pier top moment, maximum shear force, mid-span moment, mid-span deflection, lateral displacement, and lateral acceleration all become relative values related to the maximum and minimum values, becoming dimensionless parameters that can reflect the mechanical effects, with a range of 0 to 1.

[0061] S201 and S202 analyzed the different load effects under vertical actions. The load effects mainly reflect the geometric and mechanical characteristics of the aqueduct body structure under different depth-width ratio schemes. A large self-weight value represents a large amount of concrete work, while the larger the pier top moment, maximum shear force, mid-span moment, and mid-span deflection, the more steel bars or prestressed anchor cables need to be configured, indicating that the mechanical conditions of the structure are worse.

[0062] S3: Analyze the structural effects of lateral actions for different depth-width ratio schemes to obtain the normalized indicators under lateral actions of different depth-width ratio schemes.

[0063] S301: According to two working conditions, namely the crosswind working condition (self-weight + crosswind) and the seismic working condition (self-weight + seismic force), analyze the lateral displacement and lateral acceleration results under lateral actions of different depth-width ratio schemes respectively.

[0064] S302: Normalize the data of S301 to obtain the normalized indicators under lateral actions of different depth-width ratio schemes.

[0065] The normalization process adopts the specific formula for normalization in S202, which will not be described in detail here.

[0066] S301 and S302 analyzed the different load effects under lateral actions. The load effects mainly reflect the mechanical effects of different depth-width ratio schemes on the lower structure of the aqueduct. The larger the lateral displacement and lateral acceleration, the more steel bars or prestressed anchor cables need to be configured, indicating that the mechanical conditions of the structure are worse.

[0067] S4: With the depth-width ratio as the abscissa and the normalized indicators such as the main beam weight, pier top moment, maximum shear force, mid-span moment, mid-span deflection, lateral displacement, and lateral acceleration as the ordinate, draw the structural effect diagrams under lateral and vertical actions of different depth-width ratio schemes.

[0068] S5: Determine the optimal depth-width ratio according to the principle of the minimum comprehensive structural effect under lateral and vertical actions.

[0069] Considering the full action (self-weight + design flow + crosswind + earthquake), the differences in structural effects are obvious. The results of each normalized indicator show that among the results of different depth-width ratio schemes, the larger the normalized indicator of the main beam weight, the greater the project cost, while the larger the normalized indicators of the pier top moment, maximum shear force, mid-span moment, and mid-span deflection, the worse the mechanical conditions. This technology takes into account the requirements of each indicator, and takes the main beam weight, pier top moment, maximum shear force, mid-span moment, mid-span deflection, and lateral acceleration under seismic working conditions as the main indicators, and the vertical deflection caused by self-weight and the lateral displacement caused by crosswind load as the secondary indicators. Select a relatively concentrated interval according to the principle of smaller normalized indicators to determine the optimal depth-width ratio.

[0070] The present invention is further verified and illustrated through the following experimental examples:

[0071] S1. Draw different depth-width ratio schemes and carry out structural modeling using engineering simulation software.

[0072] S101. For a certain aqueduct, the design flow rate is increased to 48.35 m 3 / s. Combining with the terrain and through hydraulic analysis, the designed longitudinal slope is 1:4000.

[0073] S102. According to the hydraulic analysis, a U-shaped water-crossing section is adopted, and the following 5 depth-width ratio schemes are initially proposed, as shown in Table 1.

[0074] Table 1 Results of different depth-width ratio schemes

[0075]

[0076] S103. The upper structure of the aqueduct is a continuous steel structure of 67m + 120m + 67m. The upper part adopts a single-box double-chamber (upper and lower chambers) variable cross-section and the upper box girder for water passage. The lower part all adopts double-limb hollow thin-walled piers.

[0077] As Figure 2 shown, according to experience, the web thickness t1, the middle partition thickness t2, the top plate thickness t3, and the bottom plate thickness t4 of each scheme are determined. Taking the two-box section as an example, the schematic diagram is shown in Figure 2 . For the convenience of comparison, the web, middle partition, top plate, and bottom plate thicknesses of each scheme are kept consistent. Taking the maximum section at the pier as the control section, the design section data of different depth-width ratio schemes are drawn in Table 2.

[0078] Table 2 Design section data table of different depth-width ratio schemes

[0079]

[0080] S104. Use the MADIS software to carry out finite element modeling and analysis of the aqueduct.

[0081] The model beam element is based on the beam theory of Timoshenko. Shear deformation can be considered during analysis, and the calculation of deep beams, thin-walled structures, etc. is more accurate.

[0082] For the comparison diagram of the interface before and after the deformation of the Timoshenko beam element, see Figure 3 , and for the modeling effect diagram of the Timoshenko beam element, see Figure 4 .

[0083] During the finite element modeling and analysis, only the change in the overall structural response caused by the change in the box girder section is concerned. The boundary conditions are simplified as follows: The bottom of the pier is fixed, and the two ends are constrained by general supports. Taking Design Section 1 as an example, the specific model is as follows Figure 5 shown:

[0084] S2. Analyze the structural effects of the vertical and horizontal actions of different depth-width ratio schemes, and obtain the normalized indexes under the vertical actions of different depth-width ratio schemes.

[0085] S201. Analyze the weight of the main beam, the moment at the pier top, the maximum shear force, the moment at the mid-span, and the mid-span deflection under different vertical loads of different depth-width ratio schemes according to three loads: self-weight load, design flow rate, and increased flow rate.

[0086] The internal force effects of each control section under the self-weight load are shown in Table 3.

[0087] Table 3. Table of internal force effects and structural lateral effects of control sections under self-weight load

[0088]

[0089]

[0090] The internal force effects of each control section under the water load of the design flow rate are shown in Table 4.

[0091] Table 4. Table of internal force effects of control sections under the water load of the design flow rate (excluding self-weight)

[0092]

[0093] The internal force effects of each control section under the water load of the increased flow rate are shown in Table 5.

[0094] Table 5. Table of internal force effects of control sections under the water load of the increased flow rate (excluding self-weight)

[0095]

[0096] S202. To avoid the amplification of the influence of a certain index, normalize the data. The normalized results of each load effect under different working conditions are shown in Tables 6 to 8.

[0097] Table 6. Table of normalized self-weight effect

[0098]

[0099] Table 7. Table of normalized design flow rate effect

[0100]

[0101] Table 8. Table of normalized increased flow rate effect

[0102]

[0103] S3. Analyze the structural effects of the horizontal actions of different depth-width ratio schemes, and obtain the normalized indexes under the horizontal actions of different depth-width ratio schemes.

[0104] S301. Analyze the lateral displacement and lateral acceleration results under lateral action for different depth-width ratio schemes under the crosswind condition (self-weight + crosswind) and the seismic condition (self-weight + seismic force) respectively. See Tables 9 and 10.

[0105] Table 9 Internal force effect table of control sections under seismic action

[0106]

[0107] Table 10 Internal force effect table of control sections under crosswind load

[0108]

[0109]

[0110] S302. Normalize the data in S301. See Table 11.

[0111] Table 11 Normalized result table of crosswind and seismic action effects

[0112]

[0113] S4. Take the depth-width ratio as the abscissa and the normalized indexes such as the main beam weight, pier top moment, maximum shear force, mid-span moment, mid-span deflection, lateral displacement, and lateral acceleration as the ordinate to draw the structural effect diagrams under lateral and vertical actions for different depth-width ratio schemes. See Figure 6 . It can be seen that compared with the increased condition, since the self-weight load plays a dominant role in the design condition, therefore, the most unfavorable increased condition is used as the vertical action effect and compared with the lateral load for comprehensive analysis.

[0114] S5. Considering the full action (self-weight + design flow + crosswind + earthquake), the structural effect differences are obvious and the dispersion is relatively large. The relatively concentrated interval is 0.72 - 0.83. In fact, the mid-span deflection caused by self-weight can be not regarded as a necessary control factor because it can be handled by increasing the camber during the construction stage. In addition, compared with the lateral displacement caused by crosswind load, the lateral acceleration results under seismic action are dominant. Thus, considering the comprehensive vertical and lateral characteristic indexes, the optimal depth-width ratio interval for the research object under full action is 0.72 - 0.83. To sum up, the optimal depth-width ratio of 0.79 is finally selected.

Claims

1. A simplified method for determining the optimal depth-width ratio of the superstructure of a continuous rigid frame aqueduct, characterized in that, It includes the following steps: S1. Draw different depth-width ratio schemes and carry out structural modeling using engineering simulation software; S2. Analyze the structural effects of vertical actions for different depth-width ratio schemes to obtain the normalized indexes under vertical actions of different depth-width ratio schemes; S3. Analyze the structural effects of horizontal actions for different depth-width ratio schemes to obtain the normalized indexes under horizontal actions of different depth-width ratio schemes; S4. Take the depth-width ratio as the abscissa and the normalized index as the ordinate to draw the structural effect diagrams under horizontal and vertical actions of different depth-width ratio schemes; S5. Determine the optimal depth-width ratio according to the principle of the minimum comprehensive structural effect under horizontal and vertical actions.

2. The simplified determination method for the optimal depth-width ratio of the upper structure of a continuous rigid frame aqueduct according to claim 1, wherein The specific steps of S1 are as follows: S101. Carry out hydraulic analysis to determine the longitudinal slope of the aqueduct; S102. Draw up different depth-width ratio schemes and determine the cross-sectional area, shape and dimensions of the water passage; S103. Draw different depth-width ratio schemes; S104. For different depth-width ratio schemes, carry out structural modeling using engineering simulation software.

3. The simplified determination method for the optimal depth-width ratio of the upper structure of the continuous rigid frame aqueduct according to claim 1, wherein, The specific steps of S2 are as follows: S201. Analyze the weight of the main beam, the moment at the pier top, the maximum shear force, the moment at the mid-span and the mid-span deflection under vertical actions of different depth-width ratio schemes under two working conditions, namely the design working condition and the increased working condition; S202. Normalize the data in S201 to obtain the normalized indexes under vertical actions of different depth-width ratio schemes.

4. The simplified determination method for the optimal depth-width ratio of the upper structure of the continuous rigid-frame aqueduct according to claim 3, characterized in that The specific steps of S3 are as follows: S301. Analyze the lateral displacement and lateral acceleration results under horizontal actions of different depth-width ratio schemes under two working conditions, namely the cross-wind working condition and the earthquake working condition, respectively; S302. Normalize the data in S301 to obtain the normalized indexes under horizontal actions of different depth-width ratio schemes.

5. The simplified determination method for the optimal depth-width ratio of the upper structure of a continuous rigid frame aqueduct according to claim 3, characterized in that In S202, the specific formula for normalization is as follows: Among them, X norm is the index after normalization, X is the index to be normalized, X max is the maximum value of the index under different depth-width ratio schemes, X min is the minimum value of the index under different depth-width ratio schemes.

6. The simplified determination method of the optimal depth-width ratio of the upper structure of the continuous rigid frame aqueduct according to claim 4, characterized in that The specific steps of S5 are as follows: Take the weight of the main beam, the moment at the pier top, the maximum shear force, the moment at the mid-span and the lateral acceleration under the earthquake working condition as the main indexes, and take the mid-span deflection caused by self-weight and the lateral displacement caused by cross-wind load as the secondary indexes. Select the relatively concentrated interval according to the principle of the smaller normalized index to determine the optimal depth-width ratio.

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