CN103268402B - Fast evaluation method for PSC (prestressed concrete) continuous T-girder bridge load capacity based on crack height - Google Patents

Abstract

The invention discloses a method for quickly evaluating the bearing capacity of a PSC continuous T-girder bridge based on the crack height. This method uses the calculation formula of bending moment-crack height at the mid-span section of the corresponding main girder on the girder bridge to obtain the measured bending moment at the mid-span section when cracks appear, and quickly calculates the bearing capacity of the girder bridge according to each bending moment value. assessment. The method of the present invention can also be used in the standard system method, that is, by using the method of the present invention to quickly evaluate the bearing capacity of the PSC continuous T-girder bridge to judge whether it is necessary to carry out the load test, so that the purpose of the load test is more clear.

Description

Rapid assessment method for bearing capacity of PSC continuous T-girder bridge based on crack height

technical field

The invention relates to a method for quickly evaluating the bearing capacity of a PSC continuous T-beam bridge based on crack height.

Background technique

When evaluating the load-carrying capacity of PSC continuous T-girder bridges using the normative system method in the "Regulations for Testing and Evaluating Bearing Capacity of Highway Bridges", the sum of the expert scores of various indicators in the appearance survey is used to judge whether it is necessary to carry out load tests on the bridge. It is not only greatly affected by subjective factors but also has a long cycle.

In addition, the main purpose of the load test in the normative system method is: when the bearing capacity of the bridge cannot be clearly determined through the calculation analysis, by applying the static load to the bridge, determine the structure of the bridge structure under the test load. Response, and based on this, determine the checking coefficient Z ₂ to re-check and evaluate the bearing capacity or directly determine whether the bearing capacity of the bridge meets the requirements. However, the traffic needs to be interrupted during the load test, which cannot be carried out on a large scale. The cost is high, the test period is long, and it is not suitable for the heavy task of bridge maintenance. This feature limits the wide application of the load test. For bridges, on-site inspection personnel cannot quickly judge the operation status of bridges, so there is an urgent need for a method that can quickly evaluate the operation status of bridges.

Contents of the invention

One of the purposes of the present invention is to provide a method for quickly assessing the bearing capacity of a PSC continuous T-girder bridge based on the crack height, by quickly assessing the bearing capacity of the beam bridge to be assessed with cracks to quickly and accurately determine whether the bridge needs to be loaded test.

For this reason, the PSC continuous T-beam bridge bearing capacity evaluation method based on the crack height provided by the invention is:

Firstly, investigate the main girders of the PSC continuous T-girder bridge to be evaluated, and determine the key section on the girder bridge to be evaluated. There are cracks in the area; the mid-span section area of the main girder is: along the bridge direction, the area 0.5m before and after the mid-span section of the main girder;

After that, the measured bending moment of each key section of the girder bridge to be evaluated is obtained respectively, and the bearing capacity of the corresponding main girder is evaluated according to the measured bending moment of each key section. The bearing capacity of the girder bridge to be evaluated is the bearing capacity of each main girder Worst case:

When the key section is the mid-span mid-span cross-section, and the mid-span mid-girder span is less than or equal to 23 meters, the calculation formula of the measured bending moment _y1 is:

y ₁ =-6688.8x ₁ ⁵ +17498x ₁ ⁴ -8968.5x ₁ ³ -2115.4x ₁ ² +2151.4x ₁ +3917.8 (Formula 1);

x ₁ ' is the average measured crack height of the mid-span mid-span section area of the mid-span, in meters; h ₁ is the beam height of the mid-span mid-beam, in meters; L ₁ is the span of the mid-span mid-beam, The unit is meter;

y ₁ ≤ 6218kN·m, indicating that the bearing capacity of the mid-span and mid-girder is in the range that meets the requirements of the standard _; interval; y ₁ ≥ 9069kN·m, indicating that the bearing capacity of the mid-span mid-girder exceeds the standard value of resistance;

When the key section is the mid-span section of the mid-span side beam, and the span of the mid-span side beam is less than or equal to 23 meters, the calculation _formula for the measured bending moment y2 is:

y ₂ =-1496.9x ₂ ⁵ +2933.5x ₂ ⁴ +2680.8x ₂ ³ -2583.9x ₂ ² +237.44x ₂ +4655.8 (Formula 2);

x ₂ ' is the average measured crack height in the mid-span area of the mid-span side beam, in meters; h ₂ is the beam height of the mid-span side beam, in meters; L ₂ is the span of the mid-span side beam, The unit is meter;

y ₂ ≤ 6854kN·m, indicating that the bearing capacity of the mid-span side beam is in the range that meets the requirements of the standard _; interval; y ₂ ≥ 10040kN·m, indicating that the bearing capacity of the mid-span side beam exceeds the standard value of resistance;

When the key section is the mid-span section of the side-span mid-girder, and the span of the side-span mid-girder is less than or equal to 23 meters, the calculation _formula of the measured bending moment y3 is:

y ₃ =-5948.5x ₃ ⁵ +14489x ₃ ⁴ -4906.3x ₃ ³ -3808.1x ₃ ² +2123.5x ₃ +4174.2 (Formula 3);

x ₃ ' is the average measured crack height in the mid-span area of the side-span mid-span, in meters, h ₃ is the beam height of the side-span mid-span, in meters, L ₃ is the span of the side-span mid-beam, The unit is meter;

y ₃ ≤ 6508kN·m, indicating that the bearing capacity of the side span middle beam is in the range that meets the requirements of the standard bearing capacity _; interval; y ₃ ≥ 9455kN m, indicating that the bearing capacity of the side span center beam exceeds the standard value of resistance;

When the key section is the mid-span section of the side-span side-beam, and the span of the side-span side-beam is less than or equal to 23 meters, the calculation _formula of the measured bending moment y4 is:

y ₄ =681.54x ₄ ⁴ +1361.8x ₄ ³ +147.95x ₄ ² +236.02x ₄ +4687.9 (Formula 4);

x ₄ ' is the average measured crack height in the mid-span area of the side-span and side-beam, in meters; h ₄ is the beam height of the side-span side-beam, in meters; L ₄ is the span of the side-span side-beam, The unit is meter;

y ₄ ≤ 7441kN·m, indicating that the load-bearing capacity of the side-span and side-beam is within the range that meets the requirements of the standard _; interval; y ₄ ≥ 10840kN·m, indicating that the bearing capacity of the side-span side beam exceeds the standard value of resistance;

When the key section is the mid-span mid-span cross-section of the mid-span mid-beam, and the span of the mid-span mid-beam is greater than 23 meters and less than or equal to 27 meters, the calculation formula for the measured bending moment _y5 is:

y ₅ =-3020x ₅ ⁵ +7523.1x ₅ ⁴ -680.55x ₅ ³ -4144.9x ₅ ² +1754.6x ₅ +5370.2 (Formula 5);

x ₅ ' is the average measured crack height of the mid-span mid-span section area of the mid-span, in meters; h ₅ is the beam height of the mid-span mid-beam, in meters; L ₅ is the span of the mid-span mid-beam, The unit is meter;

y ₅ ≤ 8130kN·m, indicating that the bearing capacity of the mid-span and mid-girder is in the range that meets the requirements of the standard _; interval; y ₅ ≥ 11840kN·m, indicating that the bearing capacity of the mid-span mid-beam exceeds the standard value of resistance;

When the key section is the mid-span section of the mid-span side beam, and the span of the mid-span side beam is greater than 23 meters and less than or equal to 27 meters, the calculation formula for the measured bending moment _y6 is:

y ₆ =-515.62x ₆ ⁵ +917.38x ₆ ⁴ +2538.5x ₆ ³ -939.01x ₆ ² -232.68x ₆ +6127.5 (Formula 6);

x ₆ ' is the average measured crack height in the mid-span area of the mid-span side beam, in meters; h ₆ is the beam height of the mid-span side beam, in meters; L ₆ is the span of the mid-span side beam, The unit is meter;

y ₆ ≤ 9200kN·m, indicating that the bearing capacity of the mid-span side girder is in the range that meets the requirements of the specification _; interval; y ₆ ≥ 13450kN m, indicating that the bearing capacity of the mid-span side beam exceeds the standard value of resistance;

When the key section is the mid-span section of the side-span mid-girder, and the span of the side-span mid-girder is greater than 23 m and less than or equal to 27 m, the calculation formula for the measured bending moment y ₇ is:

y ₇ =158.68x ₇ ⁴ +1352.4x ₇ ³ +890.62x ₇ ² +197.65x ₇ +5513.7 (Formula 7);

x ₇ ' is the average measured crack height in the mid-span section area of the side-span mid-span, in meters; h ₇ is the beam height of the side-span mid-span, in meters; L ₇ is the span of the side-span mid-beam, The unit is meter;

y ₇ ≤ 9119kN·m, indicating that the bearing capacity of the side span middle beam is in the range that meets the requirements of the standard bearing capacity _; interval; y ₇ ≥ 13030kN·m, indicating that the bearing capacity of the side span center beam exceeds the standard value of resistance;

When the key section is the mid-span section of the side-span side-beam, and the span of the side-span side-beam is greater than 23 meters and less than or equal to 27 meters, the calculation formula of the measured bending moment _y8 is:

y ₈ =294.27x ₈ ⁴ +1251.2x ₈ ³ +944.52x ₈ ² +260.14x ₈ +6324.1 (Formula 8);

x ₈ ' is the average measured crack height in the mid-span area of the side-span and side-beam, in meters; h ₈ is the beam height of the side-span side-beam, in meters; L ₈ is the span of the side-span side-beam, The unit is meter;

y ₈ ≤ 10200kN·m, indicating that the bearing capacity of the side-span side beam is in the range that meets the requirements of the standard bearing capacity; 10200kN·m<y ₈ <14730kN·m, indicating that the bearing capacity of the side-span side beam exceeds the standard bearing capacity interval; y ₈ ≥ 14730kN·m, indicating that the bearing capacity of the side span side beam exceeds the standard value of resistance;

When the key section is the mid-span mid-span cross-section, and the span of the mid-span mid-beam is greater than ₂₇ meters and less than or equal to 32 meters, the calculation formula for the measured bending moment y9 is:

y ₉ =-308.38x ₉ ⁴ +1400.9x ₉ ³ +1399x ₉ ² -92.468x ₉ +7100.2 (Formula 9);

x ₉ ' is the average measured crack height of the mid-span mid-span section area of the mid-span, in meters; h ₉ is the beam height of the mid-span mid-beam, in meters; L ₉ is the span of the mid-span mid-beam, The unit is meter;

y ₉ ≤ 11310kN·m, indicating that the bearing capacity of the mid-span and mid-girder is in the range that meets the requirements of the specification; 11310kN m<y ₉ <15980kN·m, indicating that the load-bearing capacity of the mid-span and mid-girder exceeds the allowable load capacity of the specification interval; y ₉ ≥ 15980kN·m, indicating that the bearing capacity of the mid-span mid-beam exceeds the standard value of resistance;

When the key section is the mid-span section of the mid-span side beam, and the span of the mid-span side beam is greater than 27 meters and less than or equal to 32 meters, the calculation formula for the measured bending moment y ₁₀ is:

y ₁₀ =133.95x ₁₀ ⁴ +700.16x ₁₀ ³ +985.32x ₁₀ ² +909.5x ₁₀ +7887 (Formula 10);

x ₁₀ ' is the average measured crack height in the mid-span area of the mid-span side beam, in meters; h ₁₀ is the beam height of the mid-span side beam, in meters; L ₁₀ is the span of the mid-span side beam, The unit is meter;

y ₁₀ ≤ 12540kN·m, indicating that the bearing capacity of the mid-span side beam is in the range that meets the requirements of the standard _; interval; y ₁₀ ≥ 17970kN·m, indicating that the bearing capacity of the mid-span side beam exceeds the standard value of resistance;

When the key section is the mid-span section of the side-span mid-girder, and the span of the side-span mid-girder is greater than 27 meters and less than or equal to 32 meters, the calculation formula for the measured bending moment _y11 is:

y ₁₁ =22.524x ₁₁ ⁴ +605.02x ₁₁ ³ +1376.5x ₁₁ ² +1117.8x ₁₁ +7594 (Formula 11);

x ₁₁ ' is the average measured crack height in the mid-span area of the side-span mid-span, in meters; h ₁₁ is the girder height of the side-span mid-span, in meters; L ₁₁ is the span of the side-span mid-beam, The unit is meter;

y ₁₁ ≤ 12090kN·m, indicating that the bearing capacity of the side-span center beam is in the range that meets the requirements of the standard; 12090kN·m<y ₁₁ <16420kN·m, indicating that the bearing capacity of the side-span center beam exceeds the allowable bearing capacity of the code interval; y ₁₁ ≥ 16420kN·m, indicating that the bearing capacity of the side span middle beam exceeds the standard value of resistance;

When the key section is the mid-span section of the side beam, and the span of the side beam is greater than 27 meters and less than or equal to 32 meters, the calculation formula for the measured bending moment _y12 is:

y ₁₂ =177.53x ₁₂ ⁴ +905.03x ₁₂ ³ +1077x ₁₂ ² +821.84x ₁₂ +8418.4 (Formula 12);

x ₁₂ ' is the average measured crack height in the mid-span area of the side-span and side-beam, in meters; h ₁₂ is the beam height of the side-span side-beam, in meters; L ₁₂ is the span of the side-span side-beam, The unit is meter;

y ₁₂ ≤ _13670kN ·m, indicating that the bearing capacity of the side span and side beam is in the range that meets the requirements of the standard bearing capacity; interval; y ₁₂ ≥18360kN·m, indicating that the bearing capacity of the side-span side beam exceeds the standard value of resistance;

When the key section is the mid-span mid-span cross-section, and the span of the mid-span mid-beam is greater than 32 meters and less than or equal to 37 meters, the calculation formula for the measured bending moment _y13 is:

y ₁₃ =-9603.4x ₁₃ ⁴ +42500x ₁₃ ³ -57382x ₁₃ ² +28854x ₁₃ +6185.6 (Formula 13);

x ₁₃ ' is the average measured crack height of the mid-span mid-span section area of the mid-span, in meters; h ₁₃ is the beam height of the mid-span mid-beam, in meters; L ₁₃ is the span of the mid-span mid-beam, The unit is meter;

y ₁₃ ≤ _15230kN ·m, indicating that the bearing capacity of the mid-span and mid-girder is in the range that meets the requirements of the normative bearing capacity; interval; y ₁₃ ≥ 20540kN m, indicating that the bearing capacity of the mid-span mid-beam exceeds the standard value of resistance;

When the key section is the mid-span section of the mid-span side beam, and the span of the mid-span side beam is greater than 32 meters and less than or equal to 37 meters, the calculation formula for the measured bending moment y ₁₄ is:

y ₁₄ = -9783.4x ₁₄ ⁴ +43453x ₁₄ ³ -57759x ₁₄ ² +27578x ₁₄ +8205 (14);

x ₁₄ ' is the average measured crack height in the mid-span area of the mid-span side beam, in meters; h ₁₄ is the beam height of the mid-span side beam, in meters; L ₁₄ is the span of the mid-span side beam, The unit is meter;

y ₁₄ ≤ _17170kN ·m, indicating that the bearing capacity of the mid-span side beam is in the range that meets the requirements of the standard; interval; y ₁₄ ≥ 22970kN m, indicating that the bearing capacity of the mid-span side beam exceeds the standard value of resistance;

When the key section is the mid-span section of the side-span mid-girder, and the span of the side-span mid-girder is greater than 32 m and less than or equal to 37 m, the calculation formula for the measured bending moment y ₁₅ is:

y ₁₅ =-7751.2x ₁₅ ⁴ +32067x ₁₅ ³ -36970x ₁₅ ² +14085x ₁₅ +10270 (Formula 15);

x ₁₅ ' is the average measured crack height in the mid-span area of the side-span mid-span, in meters; h ₁₅ is the girder height of the side-span mid-span, in meters; L ₁₅ is the span of the side-span mid-beam, The unit is meter;

y ₁₅ ≤ _16580kN ·m, indicating that the bearing capacity of the side-span center beam is in the range that meets the requirements of the standard bearing capacity; interval; y ₁₅ ≥ 21920kN·m, indicating that the bearing capacity of the side-span mid-beam exceeds the standard resistance value;

When the key section is the mid-span section of the side-span side-beam, and the span of the side-span side-beam is greater than 32 meters and less than or equal to 37 meters, the calculation formula for the measured bending moment _y16 is:

y ₁₆ =28.478x ₁₆ ⁴ +1302.7x ₁₆ ³ +1246x ₁₆ ² +266.87x ₁₆ +11535 (Formula 16);

x ₁₆ ' is the average measured crack height in the mid-span area of the side-span and side-beam, in meters; h ₁₆ is the beam height of the side-span side-beam, in meters; L ₁₆ is the span of the side-span side-beam, The unit is meter;

y _{16 ≤18520kN} ·m, indicating that the bearing capacity of the side span and side beam is in the range that meets the requirements of the standard bearing capacity; interval; y ₁₆ ≥ 24360kN·m, indicating that the bearing capacity of the side-span side beam exceeds the standard value of resistance;

When the key section is the mid-span mid-span section of the mid-span mid-girder, and the mid-span mid-girder span is greater than 37 meters and less than or equal to 43 meters, the calculation formula for the measured bending moment y ₁₇ is:

y ₁₇ =3784.9x ₁₇ ⁴ -5963.4x ₁₇ ³ +1915.7x ₁₇ ² +2896.2x ₁₇ +13985 (Formula 17);

x ₁₇ ' is the average measured crack height in the mid-span mid-span section area of the mid-span, in meters; h ₁₇ is the girder height of the mid-span mid-beam, in meters; L ₁₇ is the span of the mid-span mid-beam, The unit is meter;

y ₁₇ ≤ 21540kN·m, indicating that the bearing capacity of the mid-span and mid-girder is in the range that meets the requirements of _the normative bearing capacity; interval; y ₁₇ ≥ 28320kN m, indicating that the bearing capacity of the mid-span mid-beam exceeds the standard value of resistance;

When the key section is the mid-span section of the mid-span side beam, and the span of the mid-span side beam is greater than 37 meters and less than or equal to 43 meters, the calculation formula for the measured bending moment _y18 is:

y ₁₈ =-5138.9x ₁₈ ⁴ +24887x ₁₈ ³ -34330x ₁₈ ² +18848x ₁₈ +11015 (Formula 18);

x ₁₈ ' is the average measured crack height in the mid-span area of the mid-span side beam, in meters; h ₁₈ is the beam height of the mid-span side beam, in meters; L ₁₈ is the span of the mid-span side beam, The unit is meter;

y ₁₈ ≤ 22670kN·m, indicating that the bearing capacity of the mid-span side beam is in the range that meets the requirements of _the standard bearing capacity; interval; y ₁₈ ≥ 29030kN m, indicating that the bearing capacity of the mid-span side beam exceeds the standard value of resistance;

When the key section is the mid-span section of the side-span mid-girder, and the span of the side-span mid-girder is greater than 37 meters and less than or equal to 43 meters, the calculation formula for the measured bending moment _y19 is:

y ₁₉ =5610.8x ₁₉ ⁴ -7450.6x ₁₉ ³ +294.82x ₁₉ ² +4681.2x ₁₉ +15584 (Formula 19);

x ₁₉ ' is the average measured crack height in the mid-span section area of the side-span mid-span, in meters; h ₁₉ is the girder height of the side-span mid-span, in meters; L ₁₉ is the span of the side-span mid-beam, The unit is meter;

y ₁₉ ≤ 23190kN·m, indicating that the bearing capacity of the side-span center beam is in the range that meets the requirements of the standard; 23190kN·m<y ₁₉ <29910kN·m, indicating that the bearing capacity of the side-span center beam exceeds the allowable bearing capacity of the code interval; y ₁₉ ≥ 29910kN·m, indicating that the bearing capacity of the side span middle beam exceeds the standard value of resistance;

When the key section is the mid-span section of the side-span side-beam, and the span of the side-span side-beam is greater than 37 meters and less than or equal to 43 meters, the calculation formula for the measured bending moment y ₂₀ is:

y ₂₀ =1582.8x ₂₀ ⁴ +183.39x ₂₀ ³ -2031.3x ₂₀ ² +2638.1x ₂₀ +16507 (Formula 20);

x ₂₀ ' is the average measured crack height in the mid-span area of the side-span and side-beam, in meters; h ₂₀ is the beam height of the side-span side-beam, in meters; L ₂₀ is the span of the side-span side-beam, The unit is meter;

y ₂₀ ≤ 24580kN·m, indicating that the bearing capacity of the side-span side beam is in the range that meets the requirements of _the standard bearing capacity; interval; y ₂₀ ≥ 31740kN·m, indicating that the bearing capacity of the side-span side beam exceeds the standard value of resistance.

By adopting the method of the invention, the bearing capacity of the PSC continuous T-beam bridge can be rapidly evaluated. In addition, the method of the present invention can also be used in the standard system method, by utilizing the method of the present invention to quickly assess the bearing capacity of the PSC continuous T-girder bridge to judge whether it is necessary to carry out the load test: if the bearing capacity of the girder bridge to be assessed is at The interval that meets the requirements of the standard bearing capacity indicates that the beam bridge structure is in normal operating condition, and no load test is required. If the bearing capacity of the girder bridge to be evaluated exceeds the allowable range of the standard bearing capacity, a load test is required at this time to determine the Whether the bearing capacity of the bridge meets the requirements of the code, whether it is necessary to restrict or close the traffic; if the bearing capacity of the girder bridge to be assessed exceeds the resistance standard

If the standard value is not met, the traffic should be closed immediately, that is, no load test is required. This makes the purpose of the load test more specific.

Description of drawings

FIG. 1 is a reference schematic diagram of the pushing process of (Formula 01) in the specific implementation manner.

detailed description

One of the most common lesions in PSC continuous T-bridges are cracks. 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;

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.

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.

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.

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.

Based on the reliability and importance of the crack height value to the bridge bearing capacity assessment, the present invention proposes a quick assessment method for the bearing capacity of the PSC continuous T bridge based on the measured crack height.

The following is the derivation process of formulas (1) to (20) in the method of the present invention provided by the inventor.

Step 1. Establish an analysis model of a mid-span section of the bridge (such as a PSC continuous T-girder bridge with a span of 20m and a girder height of 1.5m in the general drawing) according to the corresponding design parameters of the PSC continuous T-girder bridge on the general drawing, and carry out Non-linear whole-process analysis of the section, the bending moment, curvature and centroid strain of the mid-span section under various loads are obtained; the constitutive relation used when establishing the mid-span section analysis model of the bridge is "Specification for the Design of Concrete Structures GB50010- 2010 [S]", that is, the constitutive that reflects the real situation of the bridge material, to ensure that the calculated crack parameters used in the principle derivation process of the whole method correspond to the measured crack parameters; When evaluating the bearing capacity of the bridge, the actual constitutive structure of the material is used when comparing the measured crack parameters with the calculated crack parameters in the derivation process of the method principle; when conducting the section nonlinear analysis of the whole process, the loads applied step by step are f ₁ , f ₂ ,f ₃ ,...,f _a ,...,f _A ; where f ₁ =0, the curvature of section A at load f _a+1 = the curvature of section A at load f _a +0.005 times the curvature of section A Limit curvature, when the load f _A is applied, the curvature of section A is the limit curvature of section A.

Step 2, calculate the crack height in the mid-span section under each level of load respectively, where the crack height in the mid-span section 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 (Formula 01)

(Formula 01):

ε _c is the centroid strain of the mid-span section under this level of load;

γ is the influence coefficient of concrete plasticity in tension zone;

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 is the modulus of elasticity of concrete, which is determined according to the strength grade of concrete used in the bridge;

φ is the curvature of the mid-span section under this level of load;

_yc is the vertical distance from the centroid axis of the mid-span section before cracking to the bottom surface of the beam;

Afterwards, the crack height in the mid-span section under each level of load is obtained, thus, combined with the bending moment of the mid-span section under the corresponding load in step 1, the bending moment-crack height of the mid-span section under each level of load can be obtained;

In step 3, the calculation formula of the measured bending moment of the mid-span section (key section) can be obtained by using the bending moment-crack height under various load levels to perform fitting formula processing.

The above steps 1 to 3 can be realized by using section nonlinear whole process analysis software.

The derivation of (Formula 1) to (Formula 4) uses the Psc continuous T-girder bridge with a span of 20m and a beam height of 1.5m in the general figure. The formula for calculating the measured bending moment of the section is:

y=-6688.8x ⁵ +17498x ⁴ -8968.5x ³ -2115.4x ² +2151.4x+3917.8 (Formula 21), where x is the crack height of the mid-span mid-span section of the bridge, and y is the bridge mid-span The measured bending moment of the mid-span section of the mid-girder;

Based on the fact that the span at the same structural position in the PSC continuous T-girder bridge and the load effect of the similar main girder mid-span section are similar, through the conversion between the main girder span, the beam height at the section and the crack height, the conversion The resulting crack height Substituting (Equation 11) into (Equation 1) to calculate the bending moment of the mid-span section of the main girder that is similar to the span and structure of the Psc continuous T-girder bridge with a span of 20 m and a girder height of 1.5 m.

Through the structural finite element analysis software, the basic combination value γ ₀ S _ud of the structural effect and the resistance design value R _d can be obtained, which are 6128KN.m and 9069KN.m respectively.

Using (Formula 1) to compare the bending moment value with the basic combined value of the effect γ ₀ S _ud =6128KN.m and the resistance design value R _d =9069KN.m to evaluate the bearing capacity of the main beam.

In the same way:

Among them, the derivation of (Formula 5) to (Formula 8) uses the Psc continuous T-girder bridge with a span of 25m and a beam height of 1.7m in the general figure;

The derivation of (Formula 9) to (Formula 12) uses the Psc continuous T-girder bridge with a span of 30m and a beam height of 2.0m in the general figure;

The derivation of (Formula 13) to (Formula 16) uses the Psc continuous T-girder bridge with a span of 35m and a beam height of 2.3m in the general figure;

The derivation of (Formula 17) to (Formula 20) uses the Psc continuous T-girder bridge with a span of 40m and a beam height of 2.5m in the general figure.

The following is the derivation process about (Formula 01) given by the inventor:

Referring to Figure 1, in the mid-span section of a girder of a girder bridge, it is assumed that:

Before the main beam cracks, the distance between the centroid axis of the mid-span section and the bottom surface of the beam is y _c ,

The distance between the neutral axis of the mid-span section and the bottom surface of the beam is y _n ;

The centroid axis of the main beam coincides with the neutral axis before cracking, that is, y _c =y _n ;

Under a certain level of cracking load:

The crack height is y′ _cr ;

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;

The distance from the highest point of the crack to the centroid axis ± Δ' _cr , that is, y' _cr = y _c ± Δ'_cr;

According to the assumption of the flat section: ε _y = ε _c -φ(yy _c ), y represents a certain height of the mid-span section, the value range of y is the height range of the mid-span section, and ε _y represents the mid-span section height y the strain at

Therefore: y=(ε _c -ε _y )/φ+y _c (Formula 02)

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 02):

y' _cr =(ε _c -γf _tk /E _c )/φ+y _c .

It should be noted that the measured crack height and crack height in this application refer to the vertical distance that the crack extends upward from the bottom of the beam section; The average of the measured heights of all or several fractures with relatively large heights.

Example:

Take the 3×20m continuous T-beam as an example, the span of a single hole is 20m, C50 concrete is used, the ordinary steel bar is HRB335, the standard value of the tensile strength of the prestressed steel bar is fpk=1860Mpa, the bridge deck is 12m wide, and there are four prefabricated small box girders in the transverse direction. The load class is road class I. The substructure is a gravity pier, and the abutment is a mortar block stone U-shaped abutment; the minimum thickness of the bridge deck concrete cushion is 6cm, the maximum thickness is 15cm, the thickness of the asphalt concrete pavement is 2cm, and the beam height is 1.5m.

An investigation into the development of cracks occurred in the mid-span region of the bridge's mid-span center girder. The scope of the surveyed section area can be selected as the range of 0.5m near the mid-span section, and the average of the 2 to 5 maximum fracture heights in this area is calculated, and the average fracture velocity is 121cm.

Using (Formula 1) to calculate the measured bending moment of the mid-span section of the mid-span mid-span of the girder bridge is 7655KN.m; 6218KN.m<7695KN.m<9069KN.m.

That is, the measured bending moment of the mid-span mid-span section of the girder bridge exceeds the design value R _d of the resistance. Under the current vehicle load, the bridge bearing capacity has exceeded the design value R _d of the resistance, and the prestressed steel bars yield, which must be limited immediately. traffic, otherwise a vicious accident may occur.

According to the method in "Highway Bridge Bearing Capacity Inspection and Evaluation Regulations", the load test is carried out to further evaluate the bearing capacity of the girder bridge. The load test evaluation conclusions are as follows:

(1) Under the test load of grade I highway, the average values of strain and deflection calibration coefficients are 1.05 and 0.94.

(2) For grade I highway, γ ₀ S _ud exceeds R _d by 23.6%.

(3) The overall evaluation result of the bridge is a Class III bridge. The bearing capacity of the bridge has exceeded the requirements of the code and needs to be repaired and strengthened in time.

It can be seen that the conclusion of the rapid evaluation method of this application is basically consistent with the evaluation conclusion of the load test.

Claims (1)

1. the PSC continuous T beam bridge bearing capacity rapid method for assessment of fracture height is based on, it is characterised in that method includes following Step：

First, evaluation PSC each girders of continuous T beam bridge are treated to be investigated, it is determined that the crucial section on beam bridge to be evaluated, wherein, Crucial section is the investigated girder spaning middle section of beam bridge to be evaluated, and there is crack in the girder spaning middle section region；The girder Spaning middle section region is：Along bridge to the region of 0.5m before and after the girder spaning middle section；

Afterwards, the actual measurement moment of flexure in each crucial section of beam bridge to be evaluated is asked for respectively, and according to the actual measurement moment of flexure pair in each crucial section The bearing capacity of corresponding girder is evaluated, and the bearing capacity of beam bridge to be evaluated is the worst feelings of bearing capacity in each girder Condition：

When crucial section is middle span centre girder span middle section, and when span centre girder span footpath is less than or equal to 23 meters in this, its actual measurement moment of flexure y₁Meter Calculating formula is：

y₁=-6688.8x₁ ⁵+17498x₁ ⁴-8968.5x₁ ³-2115.4x₁ ²+2151.4x₁+3917.8 （Formula 1）；

x₁' it is the actual average fracture height in span centre girder span middle section region in this, unit is rice；h₁For The deck-molding of span centre beam in this, unit is rice；L₁It is span centre girder span footpath in this, unit is rice；

y₁≤ 6218kNm, illustrates the interval of the bearing capacity in the requirement of specification bearing capacity is met of span centre beam in this； 6218kNm ＜ y₁<9069kNm, illustrates the interval that the bearing capacity of span centre beam in this is allowed beyond specification bearing capacity；y₁ >=9069kNm, illustrates that the bearing capacity of span centre beam in this has exceeded the standard value of drag；

Across the side bar spaning middle section in crucial section is, and when across side bar across footpath is less than or equal to 23 meters in this, its actual measurement moment of flexure y₂Meter Calculating formula is：

y₂=-1496.9x₂ ⁵+2933.5x₂ ⁴+2680.8x₂ ³-2583.9x₂ ²+237.44x₂+4655.8 （Formula 2）；

x₂' it is the actual average fracture height in across side bar spaning middle section region in this, unit is rice；h₂For Across the deck-molding of side bar in this, unit is rice；L₂It is across side bar across footpath in this, unit is rice；

y₂≤ 6854kNm, illustrates that the bearing capacity in this across side bar is in the interval that meets the requirement of specification bearing capacity； 6854kNm ＜ y₂<10040kNm, illustrates the interval allowed beyond specification bearing capacity across the bearing capacity of side bar in this；y₂ >=10040kNm, illustrates that the bearing capacity in this across side bar has exceeded the standard value of drag；

When crucial section be end bay central sill spaning middle section, and the end bay central sill across footpath be less than or equal to 23 meters when, its actual measurement moment of flexure y₃Meter Calculating formula is：

y₃=-5948.5x₃ ⁵+14489x₃ ⁴-4906.3x₃ ³-3808.1x₃ ²+2123.5x₃+4174.2 （Formula 3）；

x₃' it is the actual average fracture height in the end bay central sill spaning middle section region, unit is rice, h₃For The deck-molding of the end bay central sill, unit is rice, L₃It is the end bay central sill across footpath, unit is rice；

y₃≤ 6508kNm, illustrates that the bearing capacity of the end bay central sill is in the interval for meeting the requirement of specification bearing capacity； 6508kNm ＜ y₃<9455kNm, illustrates the interval that the bearing capacity of the end bay central sill is allowed beyond specification bearing capacity；y₃ >=9455kNm, illustrates that the bearing capacity of the end bay central sill has exceeded the standard value of drag；

When crucial section be end bay side bar spaning middle section, and the end bay side bar across footpath be less than or equal to 23 meters when, its actual measurement moment of flexure y₄Meter Calculating formula is：

y₄=681.54x₄ ⁴+1361.8x₄ ³+147.95x₄ ²+236.02x₄+4687.9 （Formula 4）；

x₄' it is the actual average fracture height in the end bay side bar spaning middle section region, unit is rice；h₄For The deck-molding of the end bay side bar, unit is rice；L₄It is the end bay side bar across footpath, unit is rice；

y₄≤ 7441kNm, illustrates that the bearing capacity of the end bay side bar is in the interval for meeting the requirement of specification bearing capacity； 7441kNm ＜ y₄<10840kNm, illustrates the interval that the bearing capacity of the end bay side bar is allowed beyond specification bearing capacity；y₄ >=10840kNm, illustrates that the bearing capacity of the end bay side bar has exceeded the standard value of drag；

When crucial section is middle span centre girder span middle section, and when span centre girder span footpath is less than or equal to 27 meters more than 23 meters in this, in fact Lateral bending square y₅Computing formula is：

y₅=-3020x₅ ⁵+7523.1x₅ ⁴-680.55x₅ ³-4144.9x₅ ²+1754.6x₅+5370.2 （Formula 5）；

x₅' it is the actual average fracture height in span centre girder span middle section region in this, unit is rice；h₅ It is the deck-molding of span centre beam in this, unit is rice；L₅It is span centre girder span footpath in this, unit is rice；

y₅≤ 8130kNm, illustrates the interval of the bearing capacity in the requirement of specification bearing capacity is met of span centre beam in this； 8130kNm ＜ y₅<11840kNm, illustrates the interval that the bearing capacity of span centre beam in this is allowed beyond specification bearing capacity；y₅ >=11840kNm, illustrates that the bearing capacity of span centre beam in this has exceeded the standard value of drag；

Across the side bar spaning middle section in crucial section is, and when across side bar across footpath is less than or equal to 27 meters more than 23 meters in this, in fact Lateral bending square y₆Computing formula is：

y₆=-515.62x₆ ⁵+917.38x₆ ⁴+2538.5x₆ ³-939.01x₆ ²-232.68x₆+6127.5 （Formula 6）；

x₆' it is the actual average fracture height in across side bar spaning middle section region in this, unit is rice；h₆ It is the deck-molding in this across side bar, unit is rice；L₆It is across side bar across footpath in this, unit is rice；

y₆≤ 9200kNm, illustrates that the bearing capacity in this across side bar is in the interval that meets the requirement of specification bearing capacity； 9200kNm ＜ y₆<13450kNm, illustrates the interval allowed beyond specification bearing capacity across the bearing capacity of side bar in this；y₆ >=13450kNm, illustrates that the bearing capacity in this across side bar has exceeded the standard value of drag；

When crucial section be end bay central sill spaning middle section, and the end bay central sill across footpath more than 23 meters less than or equal to 27 meters when, in fact Lateral bending square y₇Computing formula is：

y₇=158.68x₇ ⁴+1352.4x₇ ³+890.62x₇ ²+197.65x₇+5513.7 （Formula 7）；

x₇' it is the actual average fracture height in the end bay central sill spaning middle section region, unit is rice；h₇ It is the deck-molding of the end bay central sill, unit is rice；L₇It is the end bay central sill across footpath, unit is rice；

y₇≤ 9119kNm, illustrates that the bearing capacity of the end bay central sill is in the interval for meeting the requirement of specification bearing capacity； 9119kNm ＜ y₇<13030kNm, illustrates the interval that the bearing capacity of the end bay central sill is allowed beyond specification bearing capacity；y₇ >=13030kNm, illustrates that the bearing capacity of the end bay central sill has exceeded the standard value of drag；

When crucial section be end bay side bar spaning middle section, and the end bay side bar across footpath more than 23 meters less than or equal to 27 meters when, in fact Lateral bending square y₈Computing formula is：

y₈=294.27x₈ ⁴+1251.2x₈ ³+944.52x₈ ²+260.14x₈+6324.1 （Formula 8）；

x₈' it is the actual average fracture height in the end bay side bar spaning middle section region, unit is rice；h₈For The deck-molding of the end bay side bar, unit is rice；L₈It is the end bay side bar across footpath, unit is rice；

y₈≤ 10200kNm, illustrates that the bearing capacity of the end bay side bar is in the interval for meeting the requirement of specification bearing capacity； 10200kNm ＜ y₈<14730kNm, illustrates the interval that the bearing capacity of the end bay side bar is allowed beyond specification bearing capacity； y₈>=14730kNm, illustrates that the bearing capacity of the end bay side bar has exceeded the standard value of drag；

When crucial section is middle span centre girder span middle section, and when span centre girder span footpath is less than or equal to 32 meters more than 27 meters in this, in fact Lateral bending square y₉Computing formula is：

y₉=-308.38x₉ ⁴+1400.9x₉ ³+1399x₉ ²-92.468x₉+7100.2 （Formula 9）；

x₉' it is the actual average fracture height in span centre girder span middle section region in this, unit is rice；h₉For The deck-molding of span centre beam in this, unit is rice；L₉It is span centre girder span footpath in this, unit is rice；

y₉≤ 11310kNm, illustrates the interval of the bearing capacity in the requirement of specification bearing capacity is met of span centre beam in this； 11310kNm ＜ y₉<15980kNm, illustrates the interval that the bearing capacity of span centre beam in this is allowed beyond specification bearing capacity； y₉>=15980kNm, illustrates that the bearing capacity of span centre beam in this has exceeded the standard value of drag；

Across the side bar spaning middle section in crucial section is, and when across side bar across footpath is less than or equal to 32 meters more than 27 meters in this, in fact Lateral bending square y₁₀Computing formula is：

y₁₀=133.95x₁₀ ⁴+700.16x₁₀ ³+985.32x₁₀ ²+909.5x₁₀+7887 （Formula 10）；

x₁₀' it is the actual average fracture height in across side bar spaning middle section region in this, unit is rice；h₁₀ It is the deck-molding in this across side bar, unit is rice；L₁₀It is across side bar across footpath in this, unit is rice；

y₁₀≤ 12540kNm, illustrates that the bearing capacity in this across side bar is in the interval that meets the requirement of specification bearing capacity； 12540kNm ＜ y₁₀<17970kNm, illustrates the interval allowed beyond specification bearing capacity across the bearing capacity of side bar in this； y₁₀>=17970kNm, illustrates that the bearing capacity in this across side bar has exceeded the standard value of drag and leads to；

When crucial section be end bay central sill spaning middle section, and the end bay central sill across footpath more than 27 meters less than or equal to 32 meters when, in fact Lateral bending square y₁₁Computing formula is：

y₁₁=22.524x₁₁ ⁴+605.02x₁₁ ³+1376.5x₁₁ ²+1117.8x₁₁+7594 （Formula 11）；

x₁₁' it is the actual average fracture height in the end bay central sill spaning middle section region, unit is rice；h₁₁ It is the deck-molding of the end bay central sill, unit is rice；L₁₁It is the end bay central sill across footpath, unit is rice；

y₁₁≤ 12090kNm, illustrates that the bearing capacity of the end bay central sill is in the interval for meeting the requirement of specification bearing capacity； 12090kNm ＜ y₁₁<16420kNm, illustrates the interval that the bearing capacity of the end bay central sill is allowed beyond specification bearing capacity； y₁₁>=16420kNm, illustrates that the bearing capacity of the end bay central sill has exceeded the standard value of drag；

When crucial section is end bay side bar spaning middle section, and the side bar across footpath more than 27 meters less than or equal to 32 meters when, lateral bending in fact Square y₁₂Computing formula is：

y₁₂=177.53x₁₂ ⁴+905.03x₁₂ ³+1077x₁₂ ²+821.84x₁₂+8418.4 （Formula 12）；

x₁₂' it is the actual average fracture height in the end bay side bar spaning middle section region, unit is rice；h₁₂ It is the deck-molding of the end bay side bar, unit is rice；L₁₂It is the end bay side bar across footpath, unit is rice；

y₁₂≤ 13670kNm, illustrates that the bearing capacity of the end bay side bar is in the interval for meeting the requirement of specification bearing capacity； 13670kNm ＜ y₁₂<18360kNm, illustrates the interval that the bearing capacity of the end bay side bar is allowed beyond specification bearing capacity； y₁₂>=18360kNm, illustrates that the bearing capacity of the end bay side bar has exceeded the standard value of drag；

When crucial section is middle span centre girder span middle section, and when span centre girder span footpath is less than or equal to 37 meters more than 32 meters in this, in fact Lateral bending square y₁₃Computing formula is：

y₁₃=-9603.4x₁₃ ⁴+42500x₁₃ ³-57382x₁₃ ²+28854x₁₃+6185.6 （Formula 13）；

x₁₃' it is the actual average fracture height in span centre girder span middle section region in this, unit is rice； h₁₃It is the deck-molding of span centre beam in this, unit is rice；L₁₃It is span centre girder span footpath in this, unit is rice；

y₁₃≤ 15230kNm, illustrates the interval of the bearing capacity in the requirement of specification bearing capacity is met of span centre beam in this； 15230kNm ＜ y₁₃<20540kNm, illustrates the interval that the bearing capacity of span centre beam in this is allowed beyond specification bearing capacity； y₁₃>=20540kNm, illustrates that the bearing capacity of span centre beam in this has exceeded the standard value of drag；

Across the side bar spaning middle section in crucial section is, and when across side bar across footpath is less than or equal to 37 meters more than 32 meters in this, in fact Lateral bending square y₁₄Computing formula is：

y₁₄=-9783.4x₁₄ ⁴+43453x₁₄ ³-57759x₁₄ ²+27578x₁₄+8205 （14）；

x₁₄' it is the actual average fracture height in across side bar spaning middle section region in this, unit is rice； h₁₄It is the deck-molding in this across side bar, unit is rice；L₁₄It is across side bar across footpath in this, unit is rice；

y₁₄≤ 17170kNm, illustrates that the bearing capacity in this across side bar is in the interval that meets the requirement of specification bearing capacity； 17170kNm ＜ y₁₄<22970kNm, illustrates the interval allowed beyond specification bearing capacity across the bearing capacity of side bar in this； y₁₄>=22970kNm, illustrates that the bearing capacity in this across side bar has exceeded the standard value of drag；

When crucial section be end bay central sill spaning middle section, and the end bay central sill across footpath more than 32 meters less than or equal to 37 meters when, in fact Lateral bending square y₁₅Computing formula is：

y₁₅=-7751.2x₁₅ ⁴+32067x₁₅ ³-36970x₁₅ ²+14085x₁₅+10270 （Formula 15）；

x₁₅' it is the actual average fracture height in the end bay central sill spaning middle section region, unit is rice； h₁₅It is the deck-molding of the end bay central sill, unit is rice；L₁₅It is the end bay central sill across footpath, unit is rice；

y₁₅≤ 16580kNm, illustrates that the bearing capacity of the end bay central sill is in the interval for meeting the requirement of specification bearing capacity； 16580kNm ＜ y₁₅<21920kNm, illustrates the interval that the bearing capacity of the end bay central sill is allowed beyond specification bearing capacity； y₁₅>=21920kNm, illustrates that the bearing capacity of the end bay central sill has exceeded the standard value of drag；

When crucial section be end bay side bar spaning middle section, and the end bay side bar across footpath more than 32 meters less than or equal to 37 meters when, in fact Lateral bending square y₁₆Computing formula is：

y₁₆=28.478x₁₆ ⁴+1302.7x₁₆ ³+1246x₁₆ ²+266.87x₁₆+11535 （Formula 16）；

x₁₆' it is the actual average fracture height in the end bay side bar spaning middle section region, unit is rice； h₁₆It is the deck-molding of the end bay side bar, unit is rice；L₁₆It is the end bay side bar across footpath, unit is rice；

y₁₆≤ 18520kNm, illustrates that the bearing capacity of the end bay side bar is in the interval for meeting the requirement of specification bearing capacity； 18520kNm ＜ y₁₆<24360kNm, illustrates the interval that the bearing capacity of the end bay side bar is allowed beyond specification bearing capacity； y₁₆>=24360kNm, illustrates that the bearing capacity of the end bay side bar has exceeded the standard value of drag；

When crucial section be middle span centre girder span middle section, and in this span centre girder span footpath be more than 37 meters be less than or equal to 43 meters when, its Actual measurement moment of flexure y₁₇Computing formula is：

y₁₇=3784.9x₁₇ ⁴-5963.4x₁₇ ³+1915.7x₁₇ ²+2896.2x₁₇+13985 （Formula 17）；

x₁₇' it is the actual average fracture height in span centre girder span middle section region in this, unit is rice； h₁₇It is the deck-molding of span centre beam in this, unit is rice；L₁₇It is span centre girder span footpath in this, unit is rice；

y₁₇≤ 21540kNm, illustrates the interval of the bearing capacity in the requirement of specification bearing capacity is met of span centre beam in this； 21540kNm ＜ y₁₇<28320kNm, illustrates the interval that the bearing capacity of span centre beam in this is allowed beyond specification bearing capacity； y₁₇>=28320kNm, illustrates that the bearing capacity of span centre beam in this has exceeded the standard value of drag；

Across the side bar spaning middle section in crucial section is, and in this across side bar across footpath be more than 37 meters be less than or equal to 43 meters when, its Actual measurement moment of flexure y₁₈Computing formula is：

y₁₈=-5138.9x₁₈ ⁴+24887x₁₈ ³-34330x₁₈ ²+18848x₁₈+11015 （Formula 18）；

x₁₈' it is the actual average fracture height in across side bar spaning middle section region in this, unit is rice； h₁₈It is the deck-molding in this across side bar, unit is rice；L₁₈It is across side bar across footpath in this, unit is rice；

y₁₈≤ 22670kNm, illustrates that the bearing capacity in this across side bar is in the interval that meets the requirement of specification bearing capacity； 22670kNm ＜ y₁₈<29030kNm, illustrates the interval allowed beyond specification bearing capacity across the bearing capacity of side bar in this； y₁₈>=29030kNm, illustrates that the bearing capacity in this across side bar has exceeded the standard value of drag；

When crucial section be end bay central sill spaning middle section, and the end bay central sill across footpath be more than 37 meters be less than or equal to 43 meters when, its Actual measurement moment of flexure y₁₉Computing formula is：

y₁₉=5610.8x₁₉ ⁴-7450.6x₁₉ ³+294.82x₁₉ ²+4681.2x₁₉+15584 （Formula 19）；

x₁₉' it is the actual average fracture height in the end bay central sill spaning middle section region, unit is rice； h₁₉For the deck-molding units of the end bay central sill are rice；L₁₉It is the end bay central sill across footpath, unit is rice；

y₁₉≤ 23190kNm, illustrates that the bearing capacity of the end bay central sill is in the interval for meeting the requirement of specification bearing capacity； 23190kNm ＜ y₁₉<29910kNm, illustrates the interval that the bearing capacity of the end bay central sill is allowed beyond specification bearing capacity； y₁₉>=29910kNm, illustrates that the bearing capacity of the end bay central sill has exceeded the standard value of drag；

When crucial section be end bay side bar spaning middle section, and the end bay side bar across footpath be more than 37 meters be less than or equal to 43 meters when, its Actual measurement moment of flexure y₂₀Computing formula is：

y₂₀=1582.8x₂₀ ⁴+183.39x₂₀ ³-2031.3x₂₀ ²+2638.1x₂₀+16507 （Formula 20）；

x₂₀' it is the actual average fracture height in the end bay side bar spaning middle section region, unit is rice； h₂₀It is the deck-molding of the end bay side bar, unit is rice；L₂₀It is the end bay side bar across footpath, unit is rice；

y₂₀≤ 24580kNm, illustrates that the bearing capacity of the end bay side bar is in the interval for meeting the requirement of specification bearing capacity； 24580kNm ＜ y₂₀<31740kNm, illustrates the interval that the bearing capacity of the end bay side bar is allowed beyond specification bearing capacity； y₂₀>=31740kNm, illustrates that the bearing capacity of the end bay side bar has exceeded the standard value of drag.