CN111307614B - Method for measuring bending and shearing rigidity of continuous beam in sections - Google Patents
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Abstract
The invention discloses a method for measuring bending and shearing rigidity of continuous beams in sections, which utilizes the relationship between vertical displacement and corners under the action of known load and bending and shearing rigidity of structural sections and the static balance relationship and obtains the bending and shearing rigidity of each section of a beam body of the continuous beam by reversely deducing the vertical displacement and the corner value tested by a displacement and inclination angle sensor arranged on a key section. The method can realize the identification of the bending rigidity and the shearing rigidity of the continuous beam section only by knowing the vertical displacement and the corner test value under the action of the load, and has the advantages of strong practicability, simplicity and practicability; in addition, the method adopts an analytic method, does not need to establish a complex finite element model, does not need to know information such as the size of the section of the structure, composition materials and the like, and has wider applicability; in addition, the full-rank equation set is established, and the final measurement result is reliable as long as the vertical displacement and corner measurement precision is guaranteed.
Description
Technical Field
The invention belongs to the technical field of civil engineering, and particularly relates to a method for measuring bending resistance and shear stiffness of a continuous beam in sections.
Background
By the end of 2018, highway bridges in China exceed 80 thousands of seats, wherein the medium and small bridges account for more than 80%, and most of the medium and small bridges are girder bridges which are widely applied as main force bridge type continuous girder bridges. According to statistics, the overhaul or reconstruction age limit of the bridge in China is 30 years, the bridge proportion of bridges aged for 30 years or more in China is higher and higher in the future, and the aging of the bridge is accelerated. If the bridges are not possible to be completely dismantled and rebuilt, the bridges are unrealistic, and most of the bridges are in sub-health working states, so that the measurement and control of the bearing capacity evaluation indexes are very important.
As a beam structure, bending moment and shearing force are mainly borne, and bending rigidity and shearing rigidity are correspondingly important evaluation indexes. The bending stiffness is the product of the modulus of elasticity E and the moment of inertia I of the section of the constituent material of the structure, which is reflected by the ability of the structure to resist deformation. The shear stiffness calculation formula is GA/r (where G is the shear modulus, a is the cross-sectional area, r is the cross-sectional shear correction factor, and r is 6/5 for the rectangular cross-section and 10/9 for the solid circular cross-section), which is an important parameter for reflecting the shear deformation properties of the structure. For a typical beam structure, the shear induced deformation is less than 5% of the bend induced deformation, so the effect of shear deformation can be ignored. However, for deep beams (simple single span beams with span-to-height ratio less than 2 and continuous beams with span-to-height ratio less than 2.5), the influence of shear deformation on the deformation of the member is large and not negligible, and it is necessary to measure the shear stiffness by a proper method.
In addition, for a concrete continuous beam bridge, the distribution of bending and shearing stiffness after construction is unknown due to the anisotropy of materials, construction difference and the like, which brings difficulties to the work of damage identification and bearing capacity evaluation of the structure. At present, aiming at the measurement or identification method of the real bending resistance and the shear stiffness of the beam bridge, a system identification method is effectively adopted, namely a mathematical optimization algorithm is adopted, and the difference value between a structural response calculated value (generally obtained by calculation by a finite element method) and an actually measured value under the load action reaches an acceptable range by continuously adjusting calculation parameters. In practical use, the method has the problems of complexity, high difficulty, easy distortion of the recognition result and the like, so that the method is not widely used.
Disclosure of Invention
In view of the above, it is necessary to provide a method for measuring bending and shearing stiffness of continuous beam segments, so as to use the displacement and corner test data under known load to establish the intrinsic relationship between displacement and corner and bending and shearing stiffness of the beam body, thereby obtaining the bending and shearing stiffness.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
the method for measuring the bending rigidity and the shearing rigidity of the continuous beam sections comprises the following steps:
in the first step, a concentrated force is applied in each span, and the 1# span-centered concentrated force is set as p1And the 2# midspan concentration force is p2；
And secondly, segmenting the continuous beam on the concerned section, specifically, dividing each span into two equal parts, wherein the 1# span is divided into a 1 st section and a 2 nd section, the 2# span is divided into a 3 rd section and a 4 th section, the 3 rd section is adjacent to the 2 nd section, the bending rigidity and the shearing rigidity of each section of beam body in the segment are both set to be a certain value, and the bending rigidity of the 1 st section to the 4 th section of beam body are respectively (EI)r1、
The shear stiffness of the beam bodies of the 1 st section to the 4 th section is (GA/r)r1、
In k2、k3、k4Respectively the inverse number, j, of the bending rigidity ratio of the 2 nd to 4 th sections of beam bodies to the 1 st section of beam body2、j3、j4Respectively are the reciprocal of the shear stiffness ratio of the 2 nd to 4 th sections of beam bodies to the 1 st section of beam body;
thirdly, arranging displacement and inclination sensors at the beam section subsection and the three fulcrum sections, respectively testing the vertical displacement of the beam and the rotation angle of the beam rotating around the horizontal axis, and setting the vertical displacement value to be omega respectively0、ω1、ω2、ω3、ω4The test angle value is theta0、θ1、θ2、θ3、θ4(ii) a Increasing a vertical displacement test section in a certain section of the beam body, setting the distance between the section and a 0# table as h, and setting the test vertical displacement value as omegah；
Fourthly, the vertical displacement value omega of the test is measured0～ω4And omegahTesting the angle of rotation theta0～θ4Applied concentration force value p1And p2And 1# span 2l1And 2# span 2l2The distance h (between the increased vertical displacement test section and the 0# table)l1≤h≤2l1) Substituting into the following system of equations:
based on the above equation set, r is obtained0(0# table support reaction force), r1(1# pier reaction force), r2(2# counter-force of the stage), (EI)r1、(GA/r)r1、k2、k3、k4、j2、j3、j4The bending rigidity of the beam bodies from the 1 st section to the 4 th section is (EI)r1、
The shear stiffness of the 1 st to 4 th sections of the beam body is (GA/r)r1、
Further, in the third step, the increase of the segmentation of the vertical displacement test section satisfies the following condition: the subsection is divided into two small subsections by the increased vertical displacement test section, the bending rigidity between the two small subsections is the same as much as possible, and the bending rigidity of the two small subsections is close to the bending rigidity value of the subsection; the shear stiffness of the two small segments is the same as much as possible and is close to the shear stiffness value of the segment.
Further, in the third step, the displacement testing precision of each testing section is not lower than 0.01mm, and the minimum rotation angle testing precision is not lower than 0.001 degrees.
The determination method provided by the invention firstly segments the continuous beam, tests the vertical displacement and the corner of the beam body at the segments and the increased sections under the action of the known load, and then obtains the bending rigidity and the shearing rigidity value of each beam segment of the continuous beam by utilizing the basic mechanics principle and reverse-deducing based on the displacement and corner test values under the action of the known load, thereby realizing the identification of the bending rigidity and the shearing rigidity of the segments of the continuous beam.
Therefore, compared with the prior art, the invention has the following beneficial effects:
1. the method can realize the identification of the bending rigidity and the shearing rigidity of the continuous beam only by obtaining the vertical displacement and corner test values under the known load action, has simple and convenient operation, and has the advantages of strong operability, strong practicability and simplicity and feasibility.
2. The determination method provided by the invention has wider applicability, which is mainly shown in that: firstly, the method adopts an analytic method, and does not need to establish a finite element model for repeated iteration, so that the current state information of the bridge does not need to be known; and secondly, no requirements are made on the geometrical shape of the cross section, structural composition materials and the like in the inference process of the method, so that the method is applicable to continuous beam structures with unknown materials and geometrical information of the cross section.
3. The identification result of the measuring method provided by the invention has stronger credibility, which not only shows that the measuring method of the invention adopts the vertical displacement and corner measuring value of the beam structure under the action of static load, but also has less influence on the measuring process by other factors; the full-rank equation set for solving the bending rigidity and the shearing rigidity of the continuous beam is also shown in the invention, and the final measurement result is reliable as long as the vertical displacement and corner measurement precision is ensured.
Drawings
FIG. 1 is a schematic view of a method for measuring bending and shearing stiffness of a continuous beam section.
FIG. 2 is a schematic view (unit: cm) of a nondestructive continuous beam structure.
FIG. 3 is a non-destructive continuous beam finite element numerical model diagram.
FIG. 4 is a schematic view of a damaged continuous beam structure (damaged condition 3) (unit: cm).
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Referring to fig. 1, the method for measuring bending and shearing stiffness of a continuous beam segment according to the present invention includes the following steps:
in the first step, a concentrated force is applied in each span, and the 1# span-centered concentrated force is set as p1And the 2# midspan concentration force is p2。
And secondly, segmenting the continuous beam on the concerned section, specifically, dividing each span into two equal parts, wherein the 1# span is divided into a 1 st section and a 2 nd section, the 2# span is divided into a 3 rd section and a 4 th section, the 3 rd section is adjacent to the 2 nd section, the bending rigidity and the shearing rigidity of each section of beam body in the segment are both set to be a certain value, and the bending rigidity of the 1 st section to the 4 th section of beam body are respectively (EI)r1、
The shear stiffness of the beam bodies of the 1 st section to the 4 th section is (GA/r)r1、
In k2、k3、k4Respectively the inverse number, j, of the bending rigidity ratio of the 2 nd to 4 th sections of beam bodies to the 1 st section of beam body2、j3、j4The reciprocal of the shear stiffness ratio of the 2 nd to 4 th sections of beam bodies to the 1 st section of beam body.
Thirdly, arranging displacement and inclination sensors at the beam section subsection and the three fulcrum sections, respectively testing the vertical displacement of the beam and the rotation angle of the beam rotating around the horizontal axis, and setting the vertical displacement value to be omega respectively0、ω1、ω2、ω3、ω4The test angle value is theta0、θ1、θ2、θ3、θ4(ii) a Increasing a vertical displacement test section in a certain section of the beam body, setting the distance between the section and a 0# platform as h, and setting the test vertical displacement value as omegah. In the step, the displacement testing precision of each testing section is not less than 0.01mm, and the minimum corner testing precision is not less than 0.001 degrees, namely, the vertical displacement and corner testing precision of each testing section is as high as possible. In addition, in this step, adding sections of the vertical displacement test section satisfies the following condition: the segmentationThe increased vertical displacement test section is divided into two small sections, and the bending rigidity between the two small sections is the same as much as possible and is close to the bending rigidity value of the section; the shear stiffness of the two small segments is the same as much as possible and is close to the shear stiffness value of the segment.
Fourthly, the vertical displacement value omega of the test is measured0～ω4And ωhTesting the angle of rotation theta0～θ4Applied concentration force value p1And p2And 1# span 2l1And 2# span 2l2Increased vertical displacement test section distance h (l) from 0# stage1≤h≤2l1) Substituting into the following system of equations:
based on the above equation set, r is obtained0(0# stage reaction force), r1(1# pier reaction force), r2(2# counter-force of the stage), (EI)r1、(GA/r)r1、k2、k3、k4、j2、j3、j4The bending rigidity of the beam bodies from the 1 st section to the 4 th section is (EI)r1、
The shear stiffness of the 1 st to 4 th sections of the beam body is (GA/r)r1、
Of the above steps, the fourth step is a key step of the present invention, and the derivation process of the formula involved in the fourth step will be described in detail based on fig. 1.
In FIG. 1, it is known thatThe parameters are as follows: 1# span 2l1And 2# span 2l2Increased vertical displacement test section distance h (l) from 0# stage1≤h≤2l1) 1# midspan application of load p12# midspan application of load p20# table fulcrum section test vertical displacement value omega0And a value of the angle of rotation theta0And 1# cross-midspan section test vertical displacement value omega1And a value of the angle of rotation theta1And 1# pier fulcrum section test vertical displacement value omega2And a value of the angle of rotation theta2And 2# cross-midspan section test vertical displacement value omega3And a value of the angle of rotation theta3And 2# table fulcrum section test vertical displacement value omega4And a value of the angle of rotation theta4Increasing the vertical displacement value omega of the test of the sectionhThe unknown variables are: flexural rigidity (EI) of the 1 st section of the Beamr1And shear stiffness (GA/r)r1The inverse k of the bending rigidity ratio of the beam bodies from the 2 nd section to the 4 th section to the beam body from the 1 st section2、k3、k4And the reciprocal j of the shear stiffness ratio of the 2 nd to 4 th sections of beam bodies to the 1 st section of beam body2、j3、j4And the 0# table support reaction force r to be calculated in the process 01# pier supporting reaction force r1And 2# table support reaction force r2。
To solve the above unknown variables, a pulse function s (x) is used, the function expression being:
S(x)＝＜x-a>n (1)
in the formula, the < > symbol is mecolline bracket, x is unknown variable, a is any constant, and n is exponential. When the variables take different values, the pulse function has different forms, which are as follows:
when n is more than or equal to 0,
when n is less than 0, the number of the N-type metal oxide films is less than 0,
due to the special form and definition of the pulse function, the solution of an integral constant can be avoided during calculus operation, and the workload of calculation is simplified. The pulse function calculus form is summarized as follows:
the bending stiffness for the continuous beam shown in fig. 1 is expressed as a pulse function:
according to the Timoshenko beam theory, the basic differential equation system of the beam considering the influence of shear deformation is as follows:
wherein y is the deflection of the beam,
is the angle of the beam, C (x) is the shear stiffness of the beam, B (x) is the bending stiffness of the beam, and q (x) and m (x) are functions of the load density acting on the beam.
Referring to fig. 1, the load density function acting on the beam can be expressed as a pulse function:
q(x)＝p1<x-l1>-1+p2<x-2l1-l2>-1-r0<x-0>-1-r1<x-2l1>-1-r2<x-2l1-2l2>-1 (10)
m(x)＝0 (11)
substituting formula (10) for formula (8), and integrating formula (8) to obtain:
substituting formula (12) for formula (9), and integrating x to obtain:
integrating equation (13) yields the angle of rotation equation for the beam member:
equation (14) is substituted for equation (12) and x is integrated to obtain the equation for the line of deflection for the continuous beam:
substituting the measured rotation angle value and the vertical displacement value of the span center, the pivot point and the increased test section of the continuous beam into the formula (14) and the formula (15) respectively can list the following equation sets:
from fig. 1, the bending moment equation m (x) of the beam can be expressed as an impulse function:
M(x)＝p1<x-l1>1+p2<x-2l1-l2>1-r0<x-0>1-r1<x-2l1>1-r2<x-2l1-2l2>1 (17)
according to the static balance relationship, the following formula holds:
the united type (16) and the formula (18) can obtain:
as can be known from the formula (19), the conditional number of the equation set is 11, which is exactly equal to the number (11) of the unknown variables, so that the bending resistance and the shear stiffness of each section of the continuous beam can be obtained by reverse deducing the actually measured vertical displacement value and the angle value through the equation set. It is worth to be noted that the formula (19) is based on an assumption in the derivation process, that is, the bending rigidity between two small sections of the beam body divided by the increased vertical displacement test section is as same as possible and is close to the bending rigidity value of the section; the shear stiffness is also as same as possible and all approaches the shear stiffness value of the segment. Therefore, it is desirable to rationally select an increased vertical displacement test section when using the present invention. In addition, in order to ensure that the equation can be uniquely solved, only 1 vertical displacement test section needs to be added for 2-span continuous beams, but 2 vertical displacement test sections need to be added for 3-span continuous beams. Through analysis, the relation of i being equal to n-1 is required to be satisfied between the number i of the vertical displacement test sections to be increased and the span number n of the continuous beam.
Further, for a continuous beam having a span-to-height ratio of more than 2.5, since the shear deformation thereof is minute, the identified shear stiffness is easily distorted under the influence of vertical displacement and rotation angle measurement errors, so that only the bending stiffness thereof can be used to identify the result at this time. For a continuous beam (deep beam) with the span-height ratio less than or equal to 2.5, the bending rigidity and the shearing rigidity identification results can be used, and the smaller the span-height ratio is, the more accurate the shearing rigidity identification result is.
The method of the present invention is described in detail below with the results of finite element numerical analysis, taking the undamaged continuous beam and the damaged continuous beam as examples.
Example 1 non-destructive continuous Beam
The span combination of a certain concrete continuous beam is 2 multiplied by 5m, the concrete strength grade is C50, the beam height is 2.5m, and the beam width is 1 m. If the beam is not damaged, that is, the bending rigidity and the shearing rigidity are not reduced, the structural schematic diagram is shown in figure 2, and the finite element numerical model is shown in figure 3. According to the finite element calculation results, when no damage occurs, the vertical displacement and the angle of rotation of the structure in the structural state of fig. 2 are shown in table 1.
TABLE 1 non-destructive calculation of vertical displacement and angle values for continuous beams
Note: the vertical displacement value is negative downwards; the rotation angle value is positive clockwise and negative counterclockwise.
Substituting the values in table 1 into the system of equations of the present invention (equation (19)), we solve:
therefore, the bending and shear stiffness of each section of the continuous beam identified by the vertical displacement and the corner are shown in table 2, and for comparison, the bending stiffness and the shear stiffness in the finite element model are simultaneously listed in table 2.
TABLE 2 bending and shearing stiffness values of each section of continuous beam
Note: in the table EcFor concrete modulus of elasticity, C50 concrete, E, is used in this examplec＝3.45×104MPa；I0Moment of inertia of hair section, I in this example0＝1.302083m4(ii) a G in the tablecFor concrete shear modulus, this example Gc＝1.4375×104MPa; a is the cross-sectional area, and in this example A is 2.5m2(ii) a ③ for the rectangular cross section of the present embodiment, the shear correction factor r is 6/5.
As can be seen from table 2, the absolute value of the maximum difference between the flexural rigidity of the beam identified by the measurement method provided by the present invention, i.e., the vertical displacement value and the test angle value, and the flexural rigidity of the finite element model is 0.36%, and the absolute value of the maximum difference between the shear rigidity of the beam identified by the measurement method provided by the present invention and the shear rigidity of the finite element model is 0.43%. Therefore, the determination method provided by the invention has high identification precision under the condition of ensuring the test precision.
Example 2 damaged continuous Beam
The general engineering is the same as that of example 1, only different damages are artificially set, the details of the damage working conditions are shown in table 3, and the schematic structural diagram of the continuous beam under the damage working condition 3 is shown in fig. 4.
TABLE 3 Damage condition setting table for damaged beam member
According to the finite element calculation results, the vertical displacement values and the test turning angle values of the beam structure under various damage conditions in table 3 are shown in table 4.
TABLE 4 calculation of vertical displacement and angle values for damaged continuous beam structures
Note: the vertical displacement value is negative downwards; the value of the angle is positive clockwise and negative counterclockwise.
Substituting the values in Table 4 into the equation set (equation (19)) of the present invention, and solving to obtain (EI) under each damage conditionr1、(GA/r)r1、k2～k4And j2～j4The results are shown in Table 5.
TABLE 5 bending and shearing rigidity values of each section of beam body of continuous beam reversely pushed by vertical displacement and corner under each damage condition
Therefore, the bending stiffness and the shearing stiffness of each section of the continuous beam identified according to the corner under each damage condition are respectively shown in tables 6 to 8, and for comparison, the bending stiffness and the shearing stiffness in the finite element model are simultaneously listed in the tables.
TABLE 6 flexural rigidity and shear rigidity of each beam section of the damaged continuous beam (damaged condition 1)
Note: in the table EcFor concrete modulus of elasticity, C50 concrete, E, is used in this examplec＝3.45×104MPa；I0Moment of inertia of hair section, I in this example0＝1.302083m4(ii) a G in the tablecFor concrete shear modulus, this example Gc＝1.4375×104MPa; a is the cross-sectional area, and in this example A is 2.5m2(ii) a ③ for the rectangular section of the embodiment, the shear correction factor r is 6/5; fourthly, the damage working condition is that the bending rigidity damage of the 1 st section of the beam body is 5 percent, and the shearing rigidity damage is 15 percent.
TABLE 7 flexural rigidity and shear rigidity of each beam section of the damaged continuous beam (damaged condition 2)
Note: in the table EcFor concrete modulus of elasticity, C50 concrete, E, is used in this examplec＝3.45×104MPa；I0Moment of inertia of hair section, I in this example0＝1.302083m4(ii) a ② in the table GcFor concrete shear modulus, this example Gc＝1.4375×104MPa; a is the cross-sectional area, and in this example A is 2.5m2(ii) a ③ for the rectangular section of the embodiment, the shear correction factor r is 6/5; fourthly, the shear stiffness of the 1 st section of beam body is damaged by 10 percent, and the shear stiffness of the 4 th section of beam body is damaged by 20 percent.
TABLE 8 flexural and shear stiffness values of each section of the beam body of the damaged continuous beam (damaged condition 3)
Note: in the table EcFor concrete modulus of elasticity, C50 concrete, E, is used in this examplec＝3.45×104MPa；I0Moment of inertia of hair section, I in this example0＝1.302083m4(ii) a G in the tablecFor concrete shear modulus, this example Gc＝1.4375×104MPa; a is a cross-sectional area, in this example, 2.5m2(ii) a ③ for the rectangular section of the embodiment, the shear correction factor r is 6/5; fourthly, the bending rigidity of the 1 st section of beam body is damaged by 5 percent, the shearing rigidity of the 2 nd section of beam body is damaged by 20 percent, and the shearing rigidity of the 3 rd section of beam body is damaged by 25 percent.
As can be seen from tables 6 to 8, the measurement method provided by the present invention still has very high accuracy in identifying the sectional flexural rigidity and the shear rigidity of the damaged continuous beam, wherein the absolute value of the identification error of the maximum flexural rigidity does not exceed 0.36%, and the absolute value of the identification error of the maximum shear rigidity does not exceed 7.8%, which can meet the engineering accuracy requirement. Therefore, under the condition of ensuring the vertical displacement and corner testing precision, the method can be adopted to identify the bending resistance and the shearing rigidity of the continuous beam section.
According to the invention, the applied load can be changed at will according to the actual situation (i.e. any load form can be applied, such as uniform force, trapezoidal load, bending moment, etc.), the number of the beam segments can also be increased, but the identification of the bending resistance and the shear rigidity of the continuous beam segments can be carried out based on the method of the invention, and the continuous beam segments comprise multi-span (not limited to 2-span) continuous beams. The invention is only one of the common cases and any variation on the method according to the invention is within the scope of protection of the invention.
Claims (3)
1. The method for measuring the bending rigidity and the shearing rigidity of the continuous beam sections is characterized by comprising the following steps of:
in the first step, a concentrated force is applied in each span, and the 1# span-centered concentrated force is set as p1And the 2# midspan concentration force is p2；
And secondly, segmenting the continuous beam on the concerned section, specifically, dividing each span into two equal parts, wherein the 1# span is divided into a 1 st section and a 2 nd section, the 2# span is divided into a 3 rd section and a 4 th section, the 3 rd section is adjacent to the 2 nd section, the bending rigidity and the shearing rigidity of each section of beam body in the segment are both set to be a certain value, and the bending rigidity of the 1 st section to the 4 th section of beam body are respectively (EI)r1、
The shear stiffness of the beam bodies of the 1 st section to the 4 th section is (GA/r)r1、
Wherein k is2、k3、k4Respectively the inverse number, j, of the bending rigidity ratio of the 2 nd to 4 th sections of beam bodies to the 1 st section of beam body2、j3、j4Respectively are the reciprocal of the shear stiffness ratio of the 2 nd to 4 th sections of beam bodies to the 1 st section of beam body;
thirdly, arranging displacement and inclination sensors at the beam section subsection and the three fulcrum sections, respectively testing the vertical displacement of the beam and the rotation angle of the beam rotating around the horizontal axis, and setting the vertical displacement value to be omega respectively0、ω1、ω2、ω3、ω4The test angle value is theta0、θ1、θ2、θ3、θ4(ii) a Increasing a vertical displacement test section in a certain section of the beam body, setting the distance between the section and a 0# platform as h, and setting the test vertical displacement value as omegah；
Fourthly, the vertical displacement value omega of the test is measured0～ω4And ωhTesting the angle of rotation theta0～θ4Applied concentration force value p1And p2And 1# span 2l1And 2# span 2l2The distance h, l between the increased vertical displacement test section and the 0# table1≤h≤2l1Substituting into the following system of equations:
based on the above equation set, r is obtained00# stage support reaction force, r1Support reaction force r of 1# pier22# counter-force (EI)r1、(GA/r)r1、k2、k3、k4、j2、j3、j4The bending rigidity of the beam bodies from the 1 st section to the 4 th section is (EI)r1、
The shear stiffness of the 1 st to 4 th sections of the beam body is (GA/r)r1、
2. The method for determining flexural and shear stiffness of a continuous beam segment according to claim 1, wherein in the third step, the addition of the segment of the vertical displacement test section satisfies the following conditions: the subsection is divided into two small subsections by the increased vertical displacement test section, the bending rigidity between the two small subsections is the same as much as possible, and the bending rigidity of the two small subsections is close to the bending rigidity value of the subsection; the shear stiffness of the two small segments is the same as much as possible and is close to the shear stiffness value of the segment.
3. The method of claim 1, wherein the measurement accuracy of displacement of each test section is not less than 0.01mm, and the measurement accuracy of rotation angle is not less than 0.001 °.
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| CN111879626B (en) * | 2020-07-31 | 2022-05-31 | 广西交科集团有限公司 | Method for testing actual rigidity static force of bridge rubber support |
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