CN103246766B - The actual moment of flexure projectional technique of girder of beam bridge and beam bridge Bearing Capacity Evaluation method - Google Patents

Abstract

Translated fromChinese

本发明公开了一种梁桥的主梁实际弯矩推算方法及承载能力评定方法。其中的弯矩推算方法是以平均实测裂缝高度为依据，从相应的横截面弯矩—裂缝高度图中读取实测裂缝所在横截面的弯矩值，所述的弯矩-裂缝高度图是通过对桥梁截面进行截面非线性全过程分析而得到的。承载能力评定方法是采用本发明公开的弯矩推算方法计算待评定桥梁上关键截面处弯矩值后，利用基于裂缝特征得到的修正系数Z₃来对梁桥的承载能力进行快速评定，对于通过本发明方法评定未通过的桥梁，可以选择使用荷载试验进一步进行承载能力评定。采用本发明的桥梁弯矩计算方法可以快速计算其相应截面的弯矩，从而减少荷载试验的次数，或更加准确地评定桥梁承载能力。The invention discloses a method for calculating the actual bending moment of a main girder of a girder bridge and a method for evaluating the bearing capacity. The bending moment calculation method is based on the average measured crack height, and the bending moment value of the cross section where the measured crack is located is read from the corresponding cross-sectional bending moment-crack height diagram. The bending moment-crack height diagram is obtained by It is obtained by analyzing the section nonlinear whole process of the bridge section. The bearing capacity evaluation method is to use the bending moment calculation method disclosed in the present invention to calculate the bending moment value at the key section of the bridge to be evaluated, and then use the correction coefficient Z3 obtained based_on the crack characteristics to quickly evaluate the bearing capacity of the beam bridge. For the bridges that fail to pass the evaluation by the method of the present invention, the load test can be selected to further evaluate the bearing capacity. The bridge bending moment calculation method of the invention can quickly calculate the bending moment of its corresponding section, thereby reducing the number of load tests or evaluating the bearing capacity of the bridge more accurately.

Description

Translated fromChinese

梁桥的主梁实际弯矩推算方法及梁桥承载能力评定方法Calculation Method of Actual Bending Moment of Main Girder of Girder Bridge and Evaluation Method of Bearing Capacity of Girder Bridge

技术领域technical field

本发明涉及一种基于裂缝高度的混凝土梁桥的主梁弯矩推算方法及混凝土梁桥承载能力评定方法。The invention relates to a method for estimating the main girder bending moment of a concrete girder bridge based on the crack height and a method for evaluating the bearing capacity of the concrete girder bridge.

背景技术Background technique

采用《公路桥梁承载能力检测评定规程》中的规范体系法对混凝土梁桥承载能力进行评定时，对每一个评定对象都要进行结构检算，甚至需要进行荷载试验，过程比较繁杂，技术要求高。When evaluating the bearing capacity of concrete girder bridges using the standard system method in the "Regulations for Testing and Evaluation of Bearing Capacity of Highway Bridges", structural inspection and calculation are required for each evaluation object, and even load tests are required. The process is complicated and the technical requirements are high. .

规范体系法主要包括桥梁技术状况调查和荷载试验，通过桥梁技术状况调查得到检算系数Z₁，带入《公路桥梁承载能力检测评定规程》中公式（7.3.1）中计算，根据计算的结果判断是否需要进行荷载试验：The code system method mainly includes bridge technical condition investigation and load test. The checking coefficient Z₁ is obtained through the bridge technical condition investigation and brought into the formula (7.3.1) in the "Highway Bridge Bearing Capacity Test and Evaluation Regulations" for calculation. According to the calculated results To determine whether a load test is required:

当γ₀S≤R(f_d,ξ_cα_dc,ξ_sα_ds)Z₁(1-ξ_e)时，被评定梁桥无需进行荷载试验；When γ₀ S≤R(f_d ,ξ_c α_dc ,ξ_s α_ds )Z₁ (1-ξ_e ), the rated girder bridge does not need to carry out load test;

当γ₀S＞R(f_d,ξ_cα_dc,ξ_sα_ds)Z₁(1-ξ_e)时，被评定梁桥需进行荷载试验，通过荷载试验得到检算系数Z₂，将该检算系数Z₂作为公式（7.3.1）中检算系数Z₁的取值对梁桥的承载能力进行评定。When γ₀ S > R(f_d , ξ_c α_dc , ξ_s α_ds ) Z₁ (1-ξ_e ), the rated girder bridge needs to be subjected to a load test, and the checking coefficient Z₂ is obtained through the load test, and the The checking coefficient Z₂ is used as the value of the checking coefficient Z₁ in the formula (7.3.1) to evaluate the bearing capacity of the girder bridge.

γ₀S≤R(f_d,ξ_cα_dc,ξ_sα_ds)Z₁(1-ξ_e)（7.3.1）γ₀ S≤R(f_d ,ξ_c α_dc ,ξ_s α_ds )Z₁ (1-ξ_e ) (7.3.1)

公式（7.3.1）中：γ₀：结构的重要性系数；S：荷载效应函数；R(·)：抗力效应函数；f_d：材料强度设计值；a_dc：构件混凝土几何参数值；a_ds：构件钢筋几何参数值；Z₁：承载能力检算系数；ξ_e：承载能力恶化系数；ξ_c：配筋混凝土结构的截面折减系数；ξ_s：钢筋的截面折减系数。In formula (7.3.1): γ₀ : importance coefficient of structure; S: load effect function; R(·): resistance effect function; f_d : design value of material strength; a_dc : geometric parameter value of member concrete; a_ds : Geometric parameter value of member reinforcement; Z₁ : Checking coefficient of bearing capacity; ξ_e : Deterioration coefficient of bearing capacity; ξ_c : Section reduction coefficient of reinforced concrete structure; ξ_s : Section reduction coefficient of steel bar.

通过桥梁技术状况调查得到检算系数Z₁存在比较大的人为主观性，没有考虑结构的受力情况，对于判别桥梁是否需要进行荷载试验的情况存在比较大的人为主观性。尤其是当出现误判的情况下，导致对整座桥梁承载能力的评定出现错误。The inspection coefficient Z1 obtained through the bridge technical condition investigation has_a relatively large human subjectivity, without considering the stress of the structure, and there is relatively large human subjectivity in judging whether the bridge needs to be subjected to a load test. Especially when there is a misjudgment, it will lead to errors in the assessment of the bearing capacity of the entire bridge.

发明内容Contents of the invention

本发明的目的之一在于提供一种基于裂缝高度的梁桥的主梁实际弯矩推算方法，以快速而准确地求取混凝土梁桥的主梁横截面弯矩。One of the objectives of the present invention is to provide a method for calculating the actual bending moment of the main girder of a girder bridge based on the crack height, so as to quickly and accurately obtain the bending moment of the main girder cross section of the concrete girder bridge.

为此，本发明提供的梁桥的主梁实际弯矩推算方法，该方法是对混凝土梁桥的主梁横截面弯矩进行计算，特征是以该横截面区域的平均实测裂缝高度为依据，从该横截面的弯矩-裂缝高度图中读取该横截面的弯矩；所述该横截面区域为：顺桥向，该横截面前后0.5m的区域；所述该横截面的弯矩-裂缝高度图按下述方法作取：For this reason, the girder actual bending moment calculation method of the girder bridge provided by the invention, this method is to calculate the girder cross-section bending moment of the concrete girder bridge, and the feature is based on the average measured crack height of the cross-sectional area, Read the bending moment of the cross-section from the bending moment-crack height diagram of the cross-section; the cross-sectional area is: along the bridge direction, the area of 0.5m before and after the cross-section; the bending moment of the cross-section - The fracture height map is obtained by the following method:

设所述该横截面为A截面：Let the cross-section be A section:

步骤1，根据桥梁设计参数建立桥梁的A截面分析模型，并进行截面非线性全过程分析，得到各级荷载下的A截面的弯矩、曲率和形心应变；Step 1. Establish the A-section analysis model of the bridge according to the bridge design parameters, and conduct a nonlinear whole-process analysis of the section to obtain the bending moment, curvature and centroid strain of the A-section under various loads;

步骤2，分别求取每级荷载下A截面中的裂缝高度，其中一级荷载下A截面中的裂缝高度为y′_cr，且：Step 2, calculate the crack height in section A under each level of load respectively, where the crack height in section A under one level of load is y′_cr , and:

y'_cr＝(ε_c-γf_tk/E_c)/φ+y_c（式1）y'_cr ＝(ε_c -γf_tk /E_c )/φ+y_c (Formula 1)

（式1）中：ε_c为该级荷载下A截面的形心应变；γ为受拉区混凝土塑性影响系数；f_tk为桥梁所用混凝土轴心抗拉标准值；E_c为桥梁所用混凝土弹性模量；φ为级荷载下A截面的曲率；y_c为开裂前A截面的形心轴距离梁底面的垂直距离；(Formula 1): ε_c is the centroid strain of section A under the load of this level; γ is the concrete plasticity influence coefficient in the tension zone; f_tk is the axial tensile standard value of the concrete used for the bridge; E_c is the elasticity of the concrete used for the bridge Modulus; φ is the curvature of section A under stage load;_yc is the vertical distance between the centroid axis of section A and the bottom surface of the beam before cracking;

之后，得到每级荷载下的A截面中的裂缝高度；Afterwards, the crack height in section A under each level of load is obtained;

从而，结合步骤1中的相应荷载下的A截面的弯矩可得到每级荷载下A截面的弯矩-裂缝高度；Therefore, combined with the bending moment of section A under the corresponding load in step 1, the bending moment-crack height of section A under each load can be obtained;

步骤3，以各级荷载下的弯矩-裂缝高度作图，得到该横截面的弯矩-裂缝高度图。In step 3, the bending moment-crack height diagram of the cross section is obtained by drawing the bending moment-crack height under various loads.

上述步骤1中在进行截面非线性全过程分析时，逐级施加荷载为f₁,f₂,f₃,...,f_a,...,f_A；其中f₁=0，荷载f_a+1时A截面的曲率=荷载f_a时A截面的曲率+1/200是A截面的极限曲率，荷载f_A时A截面的曲率为A截面的极限曲率。In the above step 1, when conducting the whole process of section nonlinear analysis, the loads are applied step by step as f₁ , f₂ , f₃ ,...,f_a ,...,f_A ; where f₁ =0, the load f The curvature of section A at_a+1 = the curvature of section A at load f_a + 1/200 is the limit curvature of section A, and the curvature of section A at load f_A is the limit curvature of section A.

本发明的另一目的在于提供一种梁桥承载能力评定方法，该方法是对现有规范体系法所做的改进，通过引入更多客观因素以确保桥梁技术状况调查结果的客观性，以更加客观的确定桥梁是否需要进行荷载试验，从而降低桥梁技术状况调查中人为主观因素的影响，明确荷载试验的使用条件。该方法是利用规范体系法对梁桥承载能力进行评定，特征是：利用公式γ₀S≤R(f_d,ξ_cα_dc,ξ_sα_ds)Z₁Z₃(1-ξ_e)判断被评定梁桥是否需要进行荷载试验，其中：Another object of the present invention is to provide a kind of girder bridge load-carrying capacity evaluation method, this method is the improvement done to existing code system method, by introducing more objective factors to ensure the objectivity of bridge technical condition investigation result, with more Objectively determine whether the bridge needs to carry out the load test, so as to reduce the influence of human subjective factors in the technical condition investigation of the bridge, and clarify the use conditions of the load test. This method is to use the standard system method to evaluate the bearing capacity of beam bridges, and the characteristics are: use the formula γ₀ S≤R(f_d ,ξ_c α_dc ,ξ_s α_ds )Z₁ Z₃ (1-ξ_e ) to judge Whether the assessed girder bridge needs to be subjected to load test, where:

γ₀：结构的重要性系数；S：荷载效应函数；R(·)：抗力效应函数；f_d：材料强度设计值；a_dc：构件混凝土几何参数值；a_ds：构件钢筋几何参数值；Z₁：承载能力检算系数；ξ_e：承载能力恶化系数；ξ_c：配筋混凝土结构的截面折减系数；ξ_s：钢筋的截面折减系数；γ₀ : Importance coefficient of structure; S: Load effect function; R(·): Resistance effect function; f_d : Design value of material strength; a_dc :_Geometric parameter value of member concrete; Z₁ : bearing capacity checking coefficient; ξ_e : bearing capacity deterioration coefficient; ξ_c : section reduction coefficient of reinforced concrete structure; ξ_s : section reduction coefficient of steel bars;

检算系数Z₃取值为：The value of the checking coefficient Z₃ is:

当被评价桥梁没有裂缝时，检算系数Z₃为1；When the evaluated bridge has no cracks, the checking coefficient Z3 is₁ ;

当被评价桥梁有裂缝时，检算系数Z₃计算方法如下：When the evaluated bridge has cracks, the calculation method_of the checking coefficient Z3 is as follows:

首先，分别利用上述梁桥的主梁弯矩推算方法求取待评价桥梁各关键截面的实测弯矩，其中关键截面n的实测弯矩为M_实n，n＝1,2,3,…,N；N为待评价桥梁上关键截面的总个数；所述关键截面为待评价桥梁的被调查主梁跨中截面，并且该被调查主梁跨中截面区域有裂缝；所述主梁跨中截面区域为：顺桥向，该主梁跨中截面前后0.5m的区域；First, use the main girder bending moment calculation method of the above girder bridge to obtain the measured bending moment of each key section of the bridge to be evaluated, where the measured bending moment of the key section n is Mactual_n , n=1,2,3,..., N; N is the total number of key sections on the bridge to be evaluated; the key section is the investigated main beam mid-span section of the bridge to be evaluated, and the investigated main beam span mid-section area has cracks; the main beam span The mid-section area is: along the bridge direction, the area 0.5m before and after the mid-section of the main girder span;

接着，分别利用有限元分析计算各关键截面的理论弯矩，其中关键截面n的理论弯矩为M_理n；Then, use finite element analysis to calculate the theoretical bending moment of each critical section respectively, wherein the theoretical bending moment of critical section n is M_{theoretical n} ;

然后，求取待评价桥梁的承载力修正系数ξ：Then, calculate the bearing capacity correction factor ξ of the bridge to be evaluated:

$\mathrm{\ξ}=\frac{{\mathrm{\ξ}}_1+{\mathrm{\ξ}}_2+\·\·\·+{\mathrm{\ξ}}_n+\·\·\·+{\mathrm{\ξ}}_N}{n}$(式2)，其中：$\mathrm{\ξ}=\frac{{\mathrm{\ξ}}_1+{\mathrm{\ξ}}_2+\·\·\·+{\mathrm{\ξ}}_{\mathrm{no}}+\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;+{\mathrm{\ξ}}_N}{\mathrm{no}}$ (Formula 2), where:

当ξ≤0.5时，Z₃=1.30；When ξ≤0.5, Z₃ =1.30;

当0.5＜ξ＜0.6时，Z₃＝1.8-ξ；When 0.5<ξ<0.6, Z₃ =1.8-ξ;

当ξ＝0.6时，Z₃=1.20；When ξ=0.6, Z₃ =1.20;

当0.6＜ξ＜0.7时，Z₃＝1.5-0.5ξ；When 0.6<ξ<0.7, Z₃ =1.5-0.5ξ;

当ξ＝0.7时，Z₃=1.15；When ξ=0.7, Z₃ =1.15;

当0.7＜ξ＜0.8时，Z₃＝1.05-0.5ξ；When 0.7<ξ<0.8, Z₃ =1.05-0.5ξ;

当ξ＝0.8时，Z₃=1.05；When ξ=0.8, Z₃ =1.05;

当0.8＜ξ＜0.9时，Z₃＝1.45-0.5ξWhen 0.8<ξ<0.9, Z₃ =1.45-0.5ξ

当ξ＝0.9时，Z₃=1.00；When ξ=0.9, Z₃ =1.00;

当0.9＜ξ＜1.0时，Z₃＝1.45-0.5ξ；When 0.9<ξ<1.0, Z₃ =1.45-0.5ξ;

当ξ＝1.0时，Z₃=0.95；When ξ=1.0, Z₃ =0.95;

当1.0＜ξ＜1.1时，Z₃＝1.95-ξ；When 1.0<ξ<1.1, Z₃ =1.95-ξ;

当ξ＝1.1时，Z₃=0.85；When ξ=1.1, Z₃ =0.85;

当1.1＜ξ＜1.2时，Z₃＝1.95-ξ；When 1.1<ξ<1.2, Z₃ =1.95-ξ;

当ξ＝1.2时，Z₃=0.75；When ξ=1.2, Z₃ =0.75;

当1.2＜ξ＜1.3时，Z₃＝1.95-ξ；When 1.2<ξ<1.3, Z₃ =1.95-ξ;

当ξ＝1.3时，Z₃=0.65；When ξ=1.3, Z₃ =0.65;

当1.3＜ξ＜1.4时，Z₃＝1.3-0.5ξ；When 1.3<ξ<1.4, Z₃ =1.3-0.5ξ;

当ξ＝1.4时，Z₃=0.60；When ξ=1.4, Z₃ =0.60;

当1.4＜ξ＜1.5时，Z₃＝1.3-0.5ξ；When 1.4<ξ<1.5, Z₃ =1.3-0.5ξ;

当ξ≥1.5时，Z₃=0.55；When ξ≥1.5, Z₃ =0.55;

利用公式γ₀S≤R(f_d,ξ_cα_dc,ξ_sα_ds)Z₁Z₃(1-ξ_e)判断是否需要进行荷载试验时：When using the formula γ₀ S≤R(f_d ,ξ_c α_dc ,ξ_s α_ds )Z₁ Z₃ (1-ξ_e ) to determine whether a load test is required:

当γ₀S≤R(f_d,ξ_cα_dc,ξ_sα_ds)Z₁Z₃(1-ξ_e)时，无需进行荷载试验；When γ₀ S≤R(f_d ,ξ_c α_dc ,ξ_s α_ds )Z₁ Z₃ (1-ξ_e ), no load test is required;

当γ₀S＞R(f_d,ξ_cα_dc,ξ_sα_ds)Z₁Z₃(1-ξ_e)时，需进行荷载试验。When γ₀ S＞R(f_d ,ξ_c α_dc ,ξ_s α_ds )Z₁ Z₃ (1-ξ_e ), a load test is required.

本发明的梁桥承载能力评定方法是采用本发明公开的弯矩推算方法计算待评定桥梁上关键截面处弯矩值后，利用基于裂缝特征得到的修正系数Z₃来对梁桥的承载能力进行快速评定，对于通过本发明方法评定未通过的桥梁，可以选择使用荷载试验进一步进行承载能力评定。采用本发明的桥梁弯矩计算方法可以快速计算其相应截面的弯矩，从而减少荷载试验的次数，或更加准确地评定桥梁承载能力。The girder bridge bearing capacity evaluation method of the present invention is to use the correction coefficient Z3 obtained based_on crack characteristics to calculate the bearing capacity of the girder bridge after calculating the bending moment value at the key section of the bridge to be evaluated using the bending moment calculation method disclosed in the present invention. Quick assessment, for the bridges that fail to pass the assessment by the method of the present invention, the load test can be selected to further carry out the bearing capacity assessment. The bridge bending moment calculation method of the invention can quickly calculate the bending moment of its corresponding section, thereby reducing the number of load tests or evaluating the bearing capacity of the bridge more accurately.

附图说明Description of drawings

图1为本发明的方法中公式1的推导过程参考示意图；Fig. 1 is the reference schematic diagram of the derivation process of formula 1 in the method of the present invention;

图2为实施例的弯矩-裂缝高度图，该图中显示的各直线由上自下分别表示抗力标准值R_k、抗力设计值R_d和效应的基本组合值γ₀S_ud；Fig. 2 is the bending moment-crack height diagram of the embodiment, and the straight lines shown in the diagram respectively represent the standard value of resistance R_k , the design value of resistance R_d and the basic combination value γ₀ S_ud of the effect from top to bottom;

图3是跨径为10米、梁高为0.45米的RC简支空心板桥边板跨中截面弯矩-裂缝高度图；Figure 3 is the bending moment-crack height diagram of the mid-span section of the RC simply supported hollow slab bridge with a span of 10 meters and a beam height of 0.45 meters;

图4是跨径为10米、梁高为0.45米的RC简支空心板桥中板跨中截面弯矩-裂缝高度图；Figure 4 is the bending moment-crack height diagram of the mid-span mid-span section of an RC simply supported hollow slab bridge with a span of 10 meters and a beam height of 0.45 meters;

图5是跨径为10米、梁高为0.9米的RC简支T梁桥边梁跨中截面弯矩-裂缝高度图；Figure 5 is the bending moment-crack height diagram of the side girder mid-span section of an RC simply supported T-beam bridge with a span of 10 meters and a beam height of 0.9 meters;

图6是跨径为13米、梁高为1.1米的RC简支T梁桥中梁跨中截面弯矩-裂缝高度图；Figure 6 is the bending moment-crack height diagram of the mid-span section of the RC simply supported T-beam bridge with a span of 13 meters and a beam height of 1.1 meters;

图7是跨径为25米、梁高为1.7米的PSC简支T梁桥边梁跨中截面弯矩-裂缝高度图；Fig. 7 is the bending moment-crack height diagram of the side girder mid-span section of a PSC simply supported T-beam bridge with a span of 25 meters and a beam height of 1.7 meters;

图8是跨径为40米、梁高为2.5米的PSC简支T梁桥中梁跨中截面弯矩-裂缝高度图；Fig. 8 is a bending moment-crack height diagram of the mid-span mid-span section of a PSC simply supported T-beam bridge with a span of 40 meters and a beam height of 2.5 meters;

图9是跨径为30米、梁高为2米的PSC连续T梁桥边跨边梁跨中截面弯矩-裂缝高度图；Fig. 9 is the bending moment-crack height diagram of the mid-span side-span side-span of a PSC continuous T-girder bridge with a span of 30 meters and a beam height of 2 meters;

图10是跨径为30米、梁高为2米的PSC连续T梁桥中跨边梁跨中截面弯矩-裂缝高度图；Fig. 10 is the bending moment-crack height diagram of the mid-span edge girder mid-span section of a PSC continuous T-girder bridge with a span of 30 meters and a girder height of 2 meters;

图11是跨径为35米、梁高为2.3米的PSC连续T梁桥边跨边梁跨中截面弯矩-裂缝高度图；Figure 11 is the bending moment-crack height diagram of the mid-span side-span side-span of a PSC continuous T-girder bridge with a span of 35 meters and a beam height of 2.3 meters;

图12是跨径为35米、梁高为2.3米的PSC连续T梁桥中跨中梁跨中截面弯矩-裂缝高度图；Figure 12 is the bending moment-crack height diagram of the mid-span mid-span mid-span of a PSC continuous T-girder bridge with a span of 35 meters and a beam height of 2.3 meters;

图13是跨径为20米、梁高为1.5米的PSC连续箱梁桥边跨边梁跨中截面弯矩-裂缝高度图；Fig. 13 is the bending moment-crack height diagram of the side-span and side-span mid-span of a PSC continuous box girder bridge with a span of 20 meters and a beam height of 1.5 meters;

图14是跨径为30米、梁高为2.0米的PSC连续箱梁桥边跨中梁跨中截面弯矩-裂缝高度图；Fig. 14 is the bending moment-crack height diagram of the side-span mid-span section of a PSC continuous box girder bridge with a span of 30 meters and a girder height of 2.0 meters;

图15是跨径为35米、梁高为2.3米的PSC连续箱梁桥边跨边梁跨中截面弯矩-裂缝高度图；Figure 15 is the bending moment-crack height diagram of the mid-span side-span and side-span mid-span of a PSC continuous box girder bridge with a span of 35 meters and a beam height of 2.3 meters;

图16是跨径为40米、梁高为2.5米的PSC连续箱梁桥边跨边梁跨中截面弯矩-裂缝高度图。Figure 16 is the bending moment-crack height diagram of the side-span side-girder mid-span section of a PSC continuous box girder bridge with a span of 40 m and a girder height of 2.5 m.

具体实施方式detailed description

混凝土梁桥中最常见的病害之一就是裂缝。基于以下两点，裂缝和结构的承载能力之间具有对应关系：（1）混凝土结构的破坏过程实质上就是裂缝产生、扩展和失稳的过程；（2）按照设计规范进行结构设计时，主要是从挠度、应力、裂缝宽度这三方面进行验算的；One of the most common defects in concrete girder bridges is cracking. Based on the following two points, there is a corresponding relationship between cracks and the bearing capacity of structures: (1) The failure process of concrete structures is essentially the process of crack generation, expansion and instability; (2) When designing structures according to design specifications, the main It is checked from the three aspects of deflection, stress and crack width;

在荷载试验法中，将挠度、应力、裂缝状况作为桥梁承载能力评定的几个主要指标，因此可以选择裂缝作为截面承载能力的间接反映指标。In the load test method, the deflection, stress, and crack condition are used as several main indicators for evaluating the bearing capacity of bridges, so cracks can be selected as an indirect indicator of the bearing capacity of the section.

并且在桥梁外观检查中，裂缝总是作为重点关注对象，裂缝是一个主要的检查指标，所以许多学者已经运用多种方法对裂缝的开展状况和结构的承载能力之间的关系做过研究。但养护规范及评定标准只是给出了裂缝宽度的限值，而对开裂高度、开裂位置、开裂范围等详细信息未加明确说明。And in the visual inspection of bridges, cracks are always the focus of attention, and cracks are a major inspection index, so many scholars have used various methods to study the relationship between crack development and structural bearing capacity. However, the maintenance specifications and evaluation standards only give the limit value of the crack width, but do not clearly explain the detailed information such as the crack height, crack position, and crack range.

裂缝参数有如下几种：（1）最大高度、平均高度、累计高度；（2）最大宽度、平均宽度、累计宽度；（3）最大/最小间距、平均间距；（4）开裂范围。其中裂缝宽度和间距参数影响因素众多，很难建立理论模型，且与荷载/承载能力不是单调函数关系，故难以利用；开裂范围削弱了关键截面的影响，不予利用。这样，还剩下三个与裂缝高度相关的参数。裂缝最大高度忠实记录了结构曾经受到的最大弯矩，是反映荷载/承载能力的最佳参数。Crack parameters are as follows: (1) maximum height, average height, cumulative height; (2) maximum width, average width, cumulative width; (3) maximum/minimum spacing, average spacing; (4) cracking range. Among them, there are many factors affecting the crack width and spacing parameters, it is difficult to establish a theoretical model, and the relationship between the load and bearing capacity is not a monotone function, so it is difficult to use; the crack range weakens the influence of the key section, so it is not used. This leaves three parameters related to fracture height. The maximum crack height faithfully records the maximum bending moment ever experienced by the structure, and is the best parameter to reflect the load/bearing capacity.

有文献记载根据简化方法，推导截面在承载能力极限状态下的裂缝高度。由于非线性材料本构、混凝土开裂的影响，简化方法精度十分有限；更重要的是，简化方法不能给出对评估至关重要的裂缝高度与承载能力（弯矩）的全过程关系曲线。It is documented that according to the simplified method, the crack height of the section under the limit state of bearing capacity is deduced. Due to the influence of nonlinear material constitutive and concrete cracking, the accuracy of the simplified method is very limited; more importantly, the simplified method cannot give the whole-process relationship curve between crack height and bearing capacity (bending moment), which is crucial for evaluation.

结合背景技术中的介绍，桥梁技术状况调查和荷载试验评估中均没有充分利用桥梁检测成果。如果能深入挖掘将一般检测和定期检查得到的裂缝信息应用到桥梁承载能力评定中，这不仅能够提高评定效果，而且也符合我国现行规范的整体评定体系，并没有增加太多额外的工作量，能适应任务繁重的桥梁养护工作。Combined with the introduction in the background technology, bridge detection results are not fully utilized in bridge technical condition investigation and load test evaluation. If we can dig deeper and apply the crack information obtained from general inspection and regular inspection to the evaluation of bridge bearing capacity, this will not only improve the evaluation effect, but also conform to the overall evaluation system of the current code in our country, without adding too much extra workload. It can adapt to heavy bridge maintenance work.

本发明基于裂缝高度值对桥梁承载能力评定的可靠性和重要性，提出一种根据实测裂缝高度值计算混凝土梁桥的主梁截面弯矩的计算方法，该方法是对混凝土梁桥的主梁的某一横截面弯矩进行计算，具体是以该横截面区域的平均实测裂缝高度为依据，从该横截面的弯矩-裂缝高度图中读取该横截面的弯矩；其中的该横截面区域为：顺桥向，该横截面前后0.5m的区域；也就是是以该横截面为中心，顺桥向，其前后或左右0.5m内的区域；所用到的横截面的弯矩-裂缝高度图按下述方法作取：The present invention is based on the reliability and importance of the crack height value to the evaluation of the bridge bearing capacity, and proposes a calculation method for calculating the main girder section bending moment of a concrete girder bridge according to the measured crack height value. Calculate the bending moment of a certain cross-section, specifically based on the average measured crack height of the cross-section area, and read the bending moment of the cross-section from the bending moment-crack height diagram of the cross-section; The section area is: along the bridge direction, the area within 0.5m before and after the cross section; that is, the area within 0.5m of the front, back or left and right of the cross section centered on the bridge direction; the bending moment of the cross section used is - The fracture height map is obtained by the following method:

步骤1，根据桥梁图纸上的设计参数建立桥梁的A截面分析模型，并进行截面非线性全过程分析，得到各级荷载下的A截面的弯矩、曲率和形心应变；在建立桥梁的A截面分析模型时采用的本构关系为《混凝土结构设计规范GB50010—2010[S]》中的实际本构，即反映桥梁材料真实情况的本构，以保证整个方法原理推导过程中采用的计算裂缝参数与实测裂缝参数相对应；进而保证：采用本发明的方法对桥梁的承载能力进行评定时，实测裂缝参数与方法原理推导过程中的计算裂缝参数对比时采用材料的实际本构；需要进一步限定的是，该步骤1中在进行截面非线性全过程分析时，逐级施加荷载为f₁,f₂,f₃,...,f_a,...,f_A；其中f₁=0，荷载f_a+1时A截面的曲率=荷载f_a时A截面的曲率+1/200是A截面的极限曲率，荷载f_A时A截面的曲率为A截面的极限曲率。Step 1. Establish the A-section analysis model of the bridge according to the design parameters on the bridge drawings, and conduct a nonlinear analysis of the whole process of the section to obtain the bending moment, curvature and centroid strain of the A-section under various loads; The constitutive relationship used in the section analysis model is the actual constitutive in the "Code for Design of Concrete Structures GB50010-2010[S]", that is, the constitutive that reflects the real situation of bridge materials, so as to ensure that the calculated cracks used in the derivation of the whole method principle Parameters correspond to actual measured crack parameters; and then ensure that: when adopting the method of the present invention to evaluate the bearing capacity of the bridge, the actual constitutive of the material is adopted when the actual measured crack parameters are compared with the calculated crack parameters in the method principle derivation process; need to be further limited What is more interesting is that in step 1, when conducting the whole process of section nonlinear analysis, the loads are applied step by step as f₁ , f₂ , f₃ ,...,f_a ,...,f_A ; where f₁ =0 , the curvature of the A section when the load f_a+1 = the curvature of the A section when the load f a + 1/200 is the limit curvature of the A section, and the curvature of the A section when the load f_A is the limit curvature of the A section.

步骤2，分别求取每级荷载下A截面中的裂缝高度，其中某一级荷载下（如荷载f_a下）A截面中的裂缝高度为y′_cr，且：Step 2, calculate the crack height in section A under each level of load respectively, where the crack height in section A under a certain level of load (such as under load f_a ) is y′_cr , and:

y'_cr＝(ε_c-γf_tk/E_c)/φ+y_c（式1）y'_cr ＝(ε_c -γf_tk /E_c )/φ+y_c (Formula 1)

（式1）中：(Formula 1):

ε_c为该级荷载下A截面的形心应变；_εc is the centroid strain of section A under this level of load;

γ为受拉区混凝土塑性影响系数；γ is the influence coefficient of concrete plasticity in tension zone;

f_tk为混凝土轴心抗拉标准值，根据桥梁所用的混凝土强度等级确定；f_tk is the concrete axial tensile standard value, which is determined according to the strength grade of concrete used in the bridge;

E_c为混凝土弹性模量，根据该桥梁所用的混凝土强度等级确定；E_c is the modulus of elasticity of concrete, which is determined according to the strength grade of concrete used in the bridge;

φ为该级荷载下A截面的曲率；φ is the curvature of section A under this level of load;

y_c为开裂前A截面的形心轴距离梁底面的垂直距离；_yc is the vertical distance from the centroid axis of section A to the bottom surface of the beam before cracking;

之后，得到每级荷载下的A截面中的裂缝高度，从而得到每级荷载下的弯矩-裂缝高度；Afterwards, the crack height in section A under each level of load is obtained, so as to obtain the bending moment-crack height under each level of load;

步骤3，以各级荷载下的弯矩-裂缝高度作图，得到相应的实测裂缝所在横桥向截面的弯矩-裂缝高度图，Step 3, using the bending moment-crack height diagram under various loads to obtain the corresponding bending moment-crack height diagram of the transverse section where the crack is located,

上述步骤1至步骤3可借用截面非线性全过程分析软件实现。The above steps 1 to 3 can be realized by using section nonlinear whole process analysis software.

以下是发明人给出的关于（式1）的推导过程：The following is the derivation process about (Formula 1) given by the inventor:

参考图1，在桥梁的某一横桥向截面如跨中截面中，设：Referring to Fig. 1, in a certain transverse section of the bridge such as the mid-span section, it is assumed that:

桥梁开裂前，跨中截面的形心轴距离梁底面的距离为y_c，Before the bridge cracks, the distance between the centroid axis of the mid-span section and the bottom surface of the beam is y_c ,

跨中截面的中性轴距离梁底面的距离为y_n；The distance between the neutral axis of the mid-span section and the bottom surface of the beam is y_n ;

桥梁开裂前形心轴与中性轴重合，即y_c=y_n；The centroid axis coincides with the neutral axis before the bridge cracks, that is, y_c =y_n ;

在某级开裂荷载作用下：Under a certain level of cracking load:

裂缝高度为y′_cr；The crack height is y′_cr ;

中性轴从距离梁底面y_n的位置移至距离梁底面y′_n的位置；The neutral axis moves from a position y_n from the bottom of the beam to a position y′_n from the bottom of the beam;

裂缝最高点距离形心轴±Δ'_cr的距离，即y'_cr=y_c±Δ'_cr；The distance from the highest point of the crack to the centroid axis ± Δ'_cr , that is, y'_cr = y_c ± Δ'_cr;

根据平截面假定有：ε_y＝ε_c-φ(y-y_c)，y表示跨中截面上的某一高度，ε_y表示跨中截面高度y处的应变，According to the plane section assumption: ε_y = ε_c - φ(yy_c ), y represents a certain height on the mid-span section, ε_y represents the strain at the height y of the mid-span section,

故：y＝(ε_c-ε_y)/φ+y_c（式11）Therefore: y=(ε_c -ε_y )/φ+y_c (Formula 11)

根据几何关系和材料力学，对裂缝的开裂高度有：y＝y'_cr，ε_y＝γf_tk/E_c，代入（式11）可得：According to the geometric relationship and material mechanics, the cracking height of the crack is: y=y'_cr , ε_y =γf_tk /E_c , which can be substituted into (Formula 11):

y'_cr＝(ε_c-γf_tk/E_c)/φ+y_c。y'_cr =(ε_c -γf_tk /E_c )/φ+y_c .

需要说明的是，本发明中的实测裂缝高度和裂缝高度为裂缝自梁截面底部向上延伸的垂直距离；横截面区域（主梁跨中截面区域）的平均实测裂缝高度指的是该横截面区域内所有裂缝实测高度的平均值。It should be noted that the measured crack height and crack height in the present invention are the vertical distance that the crack extends upward from the bottom of the beam section; The average of the measured heights of all fractures in the

本发明充分利用桥梁检查的裂缝信息，结合截面非线性全过程破坏的机理支持，提出一种梁桥承载能力快速评定方法，并嵌入《公路桥梁承载能力检测评定规程》中的规范体系法中，尤其适用于简支梁桥、悬臂梁桥、连续梁桥等桥型。The present invention makes full use of the crack information of the bridge inspection, combined with the mechanism support of the non-linear whole-process failure of the cross-section, proposes a rapid evaluation method for the bearing capacity of beam bridges, and embeds it into the standard system method in the "Highway Bridge Bearing Capacity Inspection and Evaluation Regulations", It is especially suitable for bridge types such as simply supported girder bridges, cantilever girder bridges, and continuous girder bridges.

本发明的混凝土梁桥承载能力评定方法是利用检算系数Z₃对混凝土梁桥承载能力进行评定，即采用Z₁Z₃代替《公路桥梁承载能力检测评定规程》中公式（7.3.1）中的Z₁，对于不满足评定要求的桥梁需要按照《公路桥梁承载能力检测评定规程》规定的要求进行荷载试验。The method for evaluating the bearing capacity of concrete beam bridges of the present invention is to evaluate the bearing capacity of concrete beam bridges by using the checking coefficient Z₃ , that is, to use Z₁ Z₃ to replace the formula (7.3. Z₁ , for bridges that do not meet the assessment requirements, load tests shall be carried out according to the requirements stipulated in the "Regulations for Testing and Assessment of Bearing Capacity of Highway Bridges".

其中：in:

当待评价桥梁没有裂缝时，检算系数Z₃为1；When the bridge to be evaluated has no cracks, the checking coefficient Z3 is₁ ;

当待评价桥梁有裂缝时，检算系数Z₃计算方法如下：When the bridge to be evaluated has cracks, the calculation method_of the checking coefficient Z3 is as follows:

首先，分别利用上述混凝土梁桥的主梁弯矩计算方法求取待评价桥梁各关键截面的实测弯矩，其中关键截面n的实测弯矩为M_实n，n＝1,2,3,…,N；N为待评价桥梁上关键截面的总个数；通过调查桥梁的边梁、中梁以及其他梁的跨中截面选取关键截面。First, use the main girder bending moment calculation method of the concrete girder bridge mentioned above to obtain the measured bending moment of each key section of the bridge to be evaluated, where the measured bending moment of the key section n is Mactual_n , n=1,2,3,… , N; N is the total number of key sections on the bridge to be evaluated; the key sections are selected by investigating the side beams, middle beams and mid-span sections of other beams of the bridge.

接着，分别利用有限元分析计算得到各关键截面的理论弯矩，其中关键截面n的理论弯矩为M_理n；Then, the theoretical bending moment of each critical section is calculated by finite element analysis, wherein the theoretical bending moment of the critical section n is M_{theoretical n} ;

然后，求取待评价桥梁的承载力修正系数ξ：Then, calculate the bearing capacity correction factor ξ of the bridge to be evaluated:

$\mathrm{\&xi;}=\frac{{\mathrm{\&xi;}}_1+{\mathrm{\&xi;}}_2+\&CenterDot;\&CenterDot;\&CenterDot;+{\mathrm{\&xi;}}_n+\&CenterDot;\&CenterDot;\&CenterDot;+{\mathrm{\&xi;}}_N}{n}$(式2)$\mathrm{\&xi;}=\frac{{\mathrm{\&xi;}}_1+{\mathrm{\&xi;}}_2+\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;+{\mathrm{\&xi;}}_{\mathrm{no}}+\&Center\; Dot;\&Center\; Dot;\&Center\; Dot;+{\mathrm{\&xi;}}_N}{\mathrm{no}}$ (Formula 2)

其中：in:

当ξ≤0.5时，Z₃=1.30；When ξ≤0.5, Z₃ =1.30;

当0.5＜ξ＜0.6时，Z₃＝1.8-ξ；When 0.5<ξ<0.6, Z₃ =1.8-ξ;

当ξ＝0.6时，Z₃=1.20；When ξ=0.6, Z₃ =1.20;

当0.6＜ξ＜0.7时，Z₃＝1.5-0.5ξ；When 0.6<ξ<0.7, Z₃ =1.5-0.5ξ;

当ξ＝0.7时，Z₃=1.15；When ξ=0.7, Z₃ =1.15;

当0.7＜ξ＜0.8时，Z₃＝1.05-0.5ξ；When 0.7<ξ<0.8, Z₃ =1.05-0.5ξ;

当ξ＝0.8时，Z₃=1.05；When ξ=0.8, Z₃ =1.05;

当0.8＜ξ＜0.9时，Z₃＝1.45-0.5ξWhen 0.8<ξ<0.9, Z₃ =1.45-0.5ξ

当ξ＝0.9时，Z₃=1.00；When ξ=0.9, Z₃ =1.00;

当0.9＜ξ＜1.0时，Z₃＝1.45-0.5ξ；When 0.9<ξ<1.0, Z₃ =1.45-0.5ξ;

当ξ＝1.0时，Z₃=0.95；When ξ=1.0, Z₃ =0.95;

当1.0＜ξ＜1.1时，Z₃＝1.95-ξ；When 1.0<ξ<1.1, Z₃ =1.95-ξ;

当ξ＝1.1时，Z₃=0.85；When ξ=1.1, Z₃ =0.85;

当1.1＜ξ＜1.2时，Z₃＝1.95-ξ；When 1.1<ξ<1.2, Z₃ =1.95-ξ;

当ξ＝1.2时，Z₃=0.75；When ξ=1.2, Z₃ =0.75;

当1.2＜ξ＜1.3时，Z₃＝1.95-ξ；When 1.2<ξ<1.3, Z₃ =1.95-ξ;

当ξ＝1.3时，Z₃=0.65；When ξ=1.3, Z₃ =0.65;

当1.3＜ξ＜1.4时，Z₃＝1.3-0.5ξ；When 1.3<ξ<1.4, Z₃ =1.3-0.5ξ;

当ξ＝1.4时，Z₃=0.60；When ξ=1.4, Z₃ =0.60;

当1.4＜ξ＜1.5时，Z₃＝1.3-0.5ξ；When 1.4<ξ<1.5, Z₃ =1.3-0.5ξ;

当ξ≥1.5时，Z₃=0.55；When ξ≥1.5, Z₃ =0.55;

利用公式γ₀S≤R(f_d,ξ_cα_dc,ξ_sα_ds)Z₁Z₃(1-ξ_e)判断是否需要进行荷载试验时：When using the formula γ₀ S≤R(f_d ,ξ_c α_dc ,ξ_s α_ds )Z₁ Z₃ (1-ξ_e ) to determine whether a load test is required:

当γ₀S≤R(f_d,ξ_cα_dc,ξ_sα_ds)Z₁Z₃(1-ξ_e)时，无需进行荷载试验；When γ₀ S≤R(f_d ,ξ_c α_dc ,ξ_s α_ds )Z₁ Z₃ (1-ξ_e ), no load test is required;

当γ₀S＞R(f_d,ξ_cα_dc,ξ_sα_ds)Z₁Z₃(1-ξ_e)时，需进行荷载试验。When γ₀ S＞R(f_d ,ξ_c α_dc ,ξ_s α_ds )Z₁ Z₃ (1-ξ_e ), a load test is required.

ξ与Z₃之间的上述取值关系的理论依据和分析说明是：校验系数Z₃=1/ξ，实际应用中，为稳妥起见Z₃的取值为上述取值。The theoretical basis and analysis of the above value relationship between ξ and Z₃ are: the calibration coefficient Z₃ =1/ξ, in practical applications, the value of Z₃ is the above value for the sake of safety.

利用公式γ₀S≤R(f_d,ξ_cα_dc,ξ_sα_ds)Z₁Z₃(1-ξ_e)判断是否需要进行荷载试验的理论依据是：通过桥梁技术状况调查得到的检算系数Z₁和基于裂缝特征得到的修正系数Z₃的综合评定，即利用公式γ₀S≤R(f_d,ξ_cα_dc,ξ_sα_ds)Z₁Z₃(1-ξ_e)判断是否需要进行荷载试验时考虑了桥梁实际的受力情况，较与利用公式γ₀S≤R(f_d,ξ_cα_dc,ξ_sα_ds)Z₁(1-ξ_e)判断梁桥是否需要进行荷载的结果更为客观、可靠。Using the formula γ₀ S≤R(f_d ,ξ_c α_dc ,ξ_s α_ds )Z₁ Z₃ (1-ξ_e ) to judge whether the load test is necessary is based on: Comprehensive evaluation of the calculation coefficient Z₁ and the correction coefficient Z₃ based on the fracture characteristics, that is, using the formula γ₀ S≤R(f_d ,ξ_c α_dc ,ξ_s α_ds )Z₁ Z₃ (1-ξ_e ) When judging whether it is necessary to carry out the load test, the actual stress situation of the bridge is considered. Compared with using the formula γ₀ S≤R(f_d ,ξ_c α_dc ,ξ_s α_ds )Z₁ (1-ξ_e ) to judge the beam bridge The result of whether loading is required is more objective and reliable.

发明人利用本申请的弯矩-裂缝高度图作取方法得到了通用图中各梁桥上各主梁跨中截面的弯矩-裂缝高度图，其中部分图如下：The inventor has obtained the bending moment-crack height diagram of the mid-span section of each girder bridge on each girder bridge in the general figure by using the method for obtaining the bending moment-crack height diagram of the present application, wherein some diagrams are as follows:

跨径为10米、梁高为0.45米的RC简支空心板桥边板跨中截面弯矩-裂缝高度图，如图3所示；The bending moment-crack height diagram of the mid-span mid-span section of the RC simply supported hollow slab bridge with a span of 10 meters and a beam height of 0.45 meters is shown in Figure 3;

跨径为10米、梁高为0.45米的RC简支空心板桥中板跨中截面弯矩-裂缝高度图，如图4所示；The bending moment-crack height diagram of the mid-span mid-span section of an RC simply supported hollow slab bridge with a span of 10 m and a beam height of 0.45 m is shown in Figure 4;

跨径为10米、梁高为0.9米的RC简支T梁桥边梁跨中截面弯矩-裂缝高度图，如图5所示；The bending moment-crack height diagram of the side girder mid-span section of an RC simply supported T-beam bridge with a span of 10 m and a girder height of 0.9 m is shown in Figure 5;

跨径为13米、梁高为1.1米的RC简支T梁桥中梁跨中截面弯矩-裂缝高度图，如图6所示；The bending moment-crack height diagram of the mid-span section of the RC simply supported T-girder bridge with a span of 13 meters and a beam height of 1.1 meters is shown in Figure 6;

跨径为25米、梁高为1.7米的PSC简支T梁桥边梁跨中截面弯矩-裂缝高度图，如图7所示；The bending moment-crack height diagram of the side girder mid-span section of a PSC simply supported T-beam bridge with a span of 25 meters and a beam height of 1.7 meters is shown in Figure 7;

跨径为40米、梁高为2.5米的PSC简支T梁桥中梁跨中截面弯矩-裂缝高度图，如图8所示；The bending moment-crack height diagram of the mid-span section of the PSC simply supported T-girder bridge with a span of 40 meters and a beam height of 2.5 meters is shown in Figure 8;

跨径为30米、梁高为2米的PSC连续T梁桥边跨边梁跨中截面弯矩-裂缝高度图，如图9所示；The bending moment-crack height diagram of the mid-span side-span and side-span mid-span of a PSC continuous T-girder bridge with a span of 30 meters and a beam height of 2 meters is shown in Figure 9;

跨径为30米、梁高为2米的PSC连续T梁桥中跨边梁跨中截面弯矩-裂缝高度图，如图10所示；The mid-span side beam mid-span bending moment-crack height diagram of a PSC continuous T-girder bridge with a span of 30 meters and a beam height of 2 meters is shown in Figure 10;

跨径为35米、梁高为2.3米的PSC连续T梁桥边跨边梁跨中截面弯矩-裂缝高度图，如图11所示；The bending moment-crack height diagram of the mid-span side span side girder of a PSC continuous T-girder bridge with a span of 35 m and a girder height of 2.3 m is shown in Figure 11;

跨径为35米、梁高为2.3米的PSC连续T梁桥中跨中梁跨中截面弯矩-裂缝高度图，如图12所示；The bending moment-crack height diagram of the mid-span mid-span mid-span of a PSC continuous T-girder bridge with a span of 35 m and a girder height of 2.3 m is shown in Figure 12;

跨径为20米、梁高为1.5米的PSC连续箱梁桥边跨边梁跨中截面弯矩-裂缝高度图，如图13所示；The bending moment-crack height diagram of the mid-span side span side girder of a PSC continuous box girder bridge with a span of 20 m and a girder height of 1.5 m is shown in Figure 13;

跨径为30米、梁高为2.0米的PSC连续箱梁桥边跨中梁跨中截面弯矩-裂缝高度图，如图14所示；The bending moment-crack height diagram of the mid-span mid-span side span of a PSC continuous box girder bridge with a span of 30 m and a girder height of 2.0 m is shown in Figure 14;

跨径为35米、梁高为2.3米的PSC连续箱梁桥边跨边梁跨中截面弯矩-裂缝高度图，如图15所示；The bending moment-crack height diagram of the mid-span side span side girder of a PSC continuous box girder bridge with a span of 35 m and a girder height of 2.3 m is shown in Figure 15;

跨径为40米、梁高为2.5米的PSC连续箱梁桥边跨边梁跨中截面弯矩-裂缝高度图，如图16所示；The bending moment-crack height diagram of the mid-span side span side girder of a PSC continuous box girder bridge with a span of 40 m and a girder height of 2.5 m is shown in Figure 16;

图3至图16中横坐标为裂缝高度，单位为米，纵坐标为弯矩，单位为KN·m。In Fig. 3 to Fig. 16, the abscissa is the crack height, the unit is meter, and the ordinate is the bending moment, the unit is KN·m.

实施例：Example:

该实施例的桥梁为：3×20m连续小箱梁，单孔跨径为20m，采用C50混凝土，普通钢筋采用HRB335，预应力钢筋抗拉强度标准值f_pk=1860Mpa，桥面宽12m，横向四片预制小箱梁，梁高1.5m。荷载等级为公路Ⅰ级。The bridge in this embodiment is: 3×20m continuous small box girder, single hole span is 20m, C50 concrete is used, common steel bar is HRB335, standard value of prestressed steel bar tensile strength f_pk =1860Mpa, bridge deck width is 12m, horizontal Four prefabricated small box girders with a beam height of 1.5m. The load class is road class I.

采用《公路桥梁承载能力检测评定规程》中的规范体系法对该实施例的桥梁的承载能力进行评定：The standard system method in the "Highway Bridge Bearing Capacity Inspection and Evaluation Regulations" is adopted to evaluate the bearing capacity of the bridge of this embodiment:

步骤1，通过桥梁技术状况调查可得检算系数Z₁=0.9；Step 1, the checking coefficient Z₁ =0.9 can be obtained through bridge technical condition investigation;

步骤2，利用公式γ₀S≤R(f_d,ξ_cα_dc,ξ_sα_ds)Z₁Z₃(1-ξ_e)判断该桥梁是否需要进行荷载试验：Step 2, use the formula γ₀ S≤R(f_d ,ξ_c α_dc ,ξ_s α_ds )Z₁ Z₃ (1-ξ_e ) to judge whether the bridge needs to be subjected to load test:

（1）该梁桥的中梁跨中截面处实测弯矩M_实的计算：(1) Calculation of the measured bending moment M at_the mid-span section of the girder bridge:

对裂缝的开展进行调查，在中跨中梁的跨中区域出现裂缝。裂缝平均高度是根据所调查截面区域最大裂缝高度的平均值。所调查截面区域范围可选为跨中截面附近0.5m的范围，计算此区域内2～5条最大裂缝高度的平均值。调查的平均实测裂缝高度为47cm；Investigating the development of cracks, cracks appeared in the mid-span region of the mid-span mid-sill. The average fracture height is based on the average of the maximum fracture heights in the surveyed cross-sectional area. The scope of the surveyed section area can be selected as the range of 0.5m near the mid-span section, and the average height of the 2 to 5 largest cracks in this area is calculated. The average measured crack height of the investigation is 47cm;

利用本发明的方法可得该实施例的梁桥的中跨中梁的跨中弯矩-裂缝高度图如图2所示。The mid-span bending moment-crack height diagram of the mid-span mid-girder of the girder bridge of this embodiment can be obtained by using the method of the present invention, as shown in FIG. 2 .

通过图2得到该梁桥中梁跨中截面的实测弯矩M_实=4010KN·m；Through Fig. 2, the measured bending moment M of the mid-span section of the girder bridge_is obtained = 4010KN m;

（2）由该实施例的桥梁设计参数，建立结构有限元分析模型，由结构有限元分析软件，得到中梁跨中截面理论弯矩。M_理＝3337KN.m(2) Based on the design parameters of the bridge in this embodiment, a structural finite element analysis model is established, and the theoretical bending moment of the mid-span section of the middle girder is obtained by the structural finite element analysis software. M =_3337KN.m

（3）承载力修正系数ξ为1.202，Z₃=0.748。(3) The bearing capacity correction factor ξ is 1.202, Z₃ =0.748.

该实施例的梁桥的结构重要性系数γ₀=1.0，根据规范《公路桥梁技术状况评定标准》、《公路桥梁承载能力检测评定规程》和《公路桥涵养护规范》的要求进行检查，得到承载能力恶化系数ξ_e、配筋混凝土结构的截面折减系数ξ_c、钢筋的截面折减系数ξ_s；The structural importance coefficient of the girder bridge of this embodiment γ₀ =1.0 is checked according to the requirements of the specification "Technical Status Evaluation Standard for Highway Bridges", "Regulations for Testing and Evaluation of Highway Bridge Bearing Capacity" and "Code for Maintenance of Highway Bridges and Culverts" to obtain the bearing capacity Capacity deterioration coefficient ξ_e , section reduction coefficient ξ_c of reinforced concrete structures, and section reduction coefficient ξ_s of steel bars;

通过结构有限元分析软件可以得到桥梁中跨中梁的效应的基本组合值γ₀S_ud和抗力设计值R_d，分别为3337KN·m和5780KN·m。The basic combination value γ₀ S_ud and the resistance design value R_d of the effect of the mid-span and mid-girder of the bridge can be obtained through the structural finite element analysis software, which are 3337KN·m and 5780KN·m respectively.

将承载能力检算系数Z₁Z₃=0.9×0.748=0.6732带入可以得到承载能力状况。验算结果如下：Bring the carrying capacity checking coefficient Z₁ Z₃ =0.9×0.748=0.6732 into it to get the carrying capacity status. The results of the calculation are as follows:

3337≤5780×0.9×0.748=3901.53337≤5780×0.9×0.748=3901.5

结构的效应要小于它的抗力，因此承载能力满足要求，无需进行荷载试验。The effect of the structure is smaller than its resistance, so the load-carrying capacity is sufficient and no load test is required.

对该实施例的梁桥的第二次调查：Second investigation of the girder bridge of this example:

由于超重车的增多，中跨中梁桥梁裂缝进一步开展，第二次调查结果和中梁跨中截面的实测弯矩如表1所示：Due to the increase of overweight vehicles, the cracks in the mid-span and mid-span bridges have been further developed. The results of the second investigation and the measured bending moments of the mid-span section of the mid-span are shown in Table 1:

表1Table 1

此次调查的承载力修正系数ξ为1.998，Z₃=0.55。The bearing capacity correction factor ξ of this investigation is 1.998, Z₃ =0.55.

采用公式γ₀S≤R(f_d,ξ_cα_dc,ξ_sα_ds)Z₁Z₃(1-ξ_e)判断该梁桥是否需要进行荷载试验，验算结果如下：Use the formula γ₀ S≤R(f_d ,ξ_c α_dc ,ξ_s α_ds )Z₁ Z₃ (1-ξ_e ) to judge whether the girder bridge needs to be subjected to a load test. The checking results are as follows:

3337＞5780×0.9×0.55=2861.13337>5780×0.9×0.55=2861.1

承载能力不满足设计要求，此时需要进行荷载试验。If the bearing capacity does not meet the design requirements, a load test is required at this time.

按《公路桥梁承载能力检测评定规程》中进行荷载试验的评定结论如下：The evaluation conclusions of the load test carried out according to the "Highway Bridge Bearing Capacity Inspection and Evaluation Regulations" are as follows:

（1）在公路Ⅰ级试验荷载作用下，应变、挠度检算系数平均值为0.94、0.90。(1) Under the test load of grade I highway, the average values of strain and deflection check coefficients are 0.94 and 0.90.

（2）公路Ⅰ级时，Z₃＝0.45；(2) For Class I roads, Z₃ =0.45;

（3）桥梁总体评定结果为三类桥，需要及时予以维修加固。(3) The overall evaluation result of the bridge is a Class III bridge, which needs to be repaired and strengthened in time.

该实施例中Z₁Z₃和Z₂误差10%，Z₁ Z₃ and Z₂ error 10% in this embodiment,

说明利用公式γ₀S≤R(f_d,ξ_cα_dc,ξ_sα_ds)Z₁Z₃(1-ξ_e)对梁桥的承载能力进行初步判定是可靠的。It shows that it is reliable to use the formula γ₀ S≤R(f_d ,ξ_c α_dc ,ξ_s α_ds )Z₁ Z₃ (1-ξ_e ) to determine the bearing capacity of girder bridges.

Claims (2)

1. beam bridge Bearing Capacity Evaluation method, is characterized in that, the method utilizes standard system method to evaluate beam bridge load-bearing capacity, and feature is: utilize formula γ₀s≤R (f_d, ξ_cα_dc, ξ_sα_ds) Z₁z₃(1-ξ_e) judge that assessed beam bridge is the need of carrying out loading test, wherein:

γ₀: the important coefficient of structure;

S: load effect function;

R (): drag effect function;

F_d: design value for strength of material;

A_dc: concrete members geometric parameter values;

A_ds: member reinforcing steel bar geometric parameter values;

Z₁: load-bearing capacity checking coefficient;

ξ_e: load-bearing capacity deterioration coefficient;

ξ_c: the cross section reduction coefficient of armored concrete structure;

ξ_s: the cross section reduction coefficient of reinforcing bar;

Checking coefficient Z₃value is:

When being evaluated bridge and thering is no crack, checking coefficient Z₃be 1;

When being evaluated bridge and having crack, checking coefficient Z₃computing method are as follows:

First, utilize the girder moment of flexure projectional technique of beam bridge to ask for the actual measurement moment of flexure in each crucial cross section of bridge to be evaluated respectively, wherein the actual measurement moment of flexure of crucial cross section n is M_{real n}, n=1,2,3 ..., N; N is total number in crucial cross section on bridge to be evaluated; Described crucial cross section be bridge to be evaluated by investigation girder spaning middle section, and this is investigated girder spaning middle section region and is had crack; Described girder spaning middle section region is: along bridge to, the region of 0.5m before and after this girder spaning middle section;

The actual moment of flexure projectional technique of girder of described beam bridge calculates the girder xsect moment of flexure of concrete beam bridge, with the actual average fracture height of this transverse cross-sectional area for foundation, reads the moment of flexure of this xsect from the moment of flexure-fracture height figure of this xsect; This transverse cross-sectional area described is: along bridge to, the region of 0.5m before and after this xsect; Moment of flexure-fracture height the figure of this xsect described gets as follows:

If this xsect is A cross section:

Step 1, sets up the A cross-section analysis model of bridge, and carries out cross section Nonlinear Full Range Analysis according to Bridge Design parameter, obtain the strain of the moment of flexure in the A cross section under load at different levels, curvature and the centre of form;

Step 2, ask for the fracture height in A cross section under every grade of load respectively, the fracture height wherein under one-level load in A cross section is y '_cr, and:

Y'_cr=(ε_c-γ f_tk/ E_c)/φ+y_c(formula 1)

In (formula 1): ε_cfor the centre of form in A cross section under this grade of load strains; γ is plastlcity coefficient of reinforced concrete member in tensile zone; f_tkfor bridge characteristic value of concrete tensile strength used; E_cfor bridge modulus of elasticity of concrete used; φ is the curvature in A cross section under grade load; y_cfor the centre of form wheelbase in front A cross section of ftractureing is from the vertical range of soffit;

Afterwards, the fracture height in the A cross section under every grade of load is obtained;

Thus the moment of flexure in the A cross section under the corresponding load in integrating step 1 can obtain the moment of flexure-fracture height in A cross section under every grade of load;

Step 3, with the moment of flexure under load at different levels-fracture height mapping, obtains the moment of flexure-fracture height figure of this xsect;

Then, utilize the theoretical moment of flexure in each crucial cross section of finite element analysis computation respectively, wherein the theoretical moment of flexure of crucial cross section n is M_{reason n};

Then, the capacity correct coefficient ξ of bridge to be evaluated is asked for:

$\mathrm{\&xi;}=\frac{{\mathrm{\&xi;}}_1+{\mathrm{\&xi;}}_2+...+{\mathrm{\&xi;}}_n+...+{\mathrm{\&xi;}}_N}{n}$(formula 2), wherein:

When ξ≤0.5, Z₃=1.30;

As 0.5 < ξ < 0.6, Z₃=1.8-ξ;

When ξ=0.6, Z₃=1.20;

As 0.6 < ξ < 0.7, Z₃=1.5-0.5 ξ;

When ξ=0.7, Z₃=1.15;

As 0.7 < ξ < 0.8, Z₃=1.05-0.5 ξ;

When ξ=0.8, Z₃=1.05;

As 0.8 < ξ < 0.9, Z₃=1.45-0.5 ξ

When ξ=0.9, Z₃=1.00;

As 0.9 < ξ < 1.0, Z₃=1.45-0.5 ξ;

When ξ=1.0, Z₃=0.95;

As 1.0 < ξ < 1.1, Z₃=1.95-ξ;

When ξ=1.1, Z₃=0.85;

As 1.1 < ξ < 1.2, Z₃=1.95-ξ;

When ξ=1.2, Z₃=0.75;

As 1.2 < ξ < 1.3, Z₃=1.95-ξ;

When ξ=1.3, Z₃=0.65;

As 1.3 < ξ < 1.4, Z₃=1.3-0.5 ξ;

When ξ=1.4, Z₃=0.60;

As 1.4 < ξ < 1.5, Z₃=1.3-0.5 ξ;

When ξ>=1.5, Z₃=0.55;

Utilize formula γ₀s≤R (f_d, ξ_cα_dc, ξ_sα_ds) Z₁z₃(1-ξ_e) when judging whether to need to carry out loading test:

Work as γ₀s≤R (f_d, ξ_cα_dc, ξ_sα_ds) Z₁z₃(1-ξ_e) time, without the need to carrying out loading test;

Work as γ₀s > R (f_d, ξ_cα_dc, ξ_sα_ds) Z₁z₃(1-ξ_e) time, need loading test be carried out.

2. beam bridge Bearing Capacity Evaluation method as claimed in claim 1, it is characterized in that, in described step 1 when carrying out cross section Nonlinear Full Range Analysis, load application is f step by step₁, f₂, f₃..., f_a..., f_a; Wherein f₁=0, load f_a+1time A cross section curvature=load f_atime A cross section curvature+1/200 be the limit curvature in A cross section, load f_atime A cross section curvature be the limit curvature in A cross section.