CN111879626B - Method for testing actual rigidity static force of bridge rubber support - Google Patents
Method for testing actual rigidity static force of bridge rubber support Download PDFInfo
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Abstract
The invention discloses a method for testing the actual rigidity static force of a bridge rubber support. And then, applying a concentrated force on or near the midspan section of the simply supported beam, testing the vertical displacement of the beam at different positions under the concentrated force, and constructing a displacement curve of the beam by using the displacement data. And finally, deducing to obtain the rigidity value of the boundary according to the relation between the displacement curve and the internal force of the beam and combining the definition of rigidity, thereby indirectly obtaining the vertical support and the rotational rigidity of the support. Compared with the mechanical property test of the existing bridge support, the method directly obtains the actual vertical support rigidity and the rotation rigidity of the support directly related to the structural stress, and has more practical significance; the invention adopts an indirect method, does not need a large-scale compression and shearing testing machine, and has the advantages of simplicity, easy operation and reliable result; in addition, the method can also be used for the quantitative evaluation of the working performance of the damaged support, and has good application prospect.
Description
Technical Field
The invention relates to the technical field of civil engineering, in particular to a static test method for actual rigidity of a bridge rubber support.
Background
As an important component of a bridge structure, the support plays a role in transmitting the acting force of the superstructure and adapting to the structural deformation, and is an important and indispensable connecting member. The rubber support applied to the bridge mainly comprises a plate type rubber support and a basin type rubber support. The rubber support has the advantages of simple structure, less steel consumption, easy processing and manufacturing, convenient installation, low cost and the like, and is widely applied to roads and railway bridges in China since the 20 th century and the 60 th year, thereby being the most common support form.
With the construction of the traffic infrastructure in China, the total number of bridges is continuously climbing, and by the end of 2019, the total number of highway bridges in China reaches 87.83 thousands. The demand of the bridge rubber support is increased, the number of manufacturers is increased, the annual output is increased in multiples, and the exposed quality problem of rapid development is more and more prominent. From the aspect of the performance detection condition of the rubber support products in recent years, the reject ratio is still high, for example, the spot check result of the plate type rubber support of the highway bridge is published in the traffic product quality industry supervision spot check result report of the highway corrugated beam steel guardrail and the like published in recent years by the official network of the transportation department: in 2016, 2017 and 2019, the group of the supports 482 is sampled and inspected together, and the qualification rates are 73.8%, 90.7% and 89.5% respectively. In addition, under the influence of various factors such as product quality, installation and construction quality, large-tonnage large-traffic load and the like, the service life of the conventional rubber support is shorter and shorter. The data shows that 3/4 supports are damaged when the vehicle is driven for more than one year; most of the plate-type rubber supports of a highway in Qingyuan county of Guangdong are damaged and replaced after being used for 3 years; the support of a highway bridge traffic vehicle built in Jilin province in 1995 is seriously damaged in 7 years, and the vehicle starts to be replaced in 2002; according to statistics, diseases of different degrees occur in a plurality of highway bridge supports operating for no more than 10 years in Guangxi regions, the number of the sick working supports accounts for 2.5-15.7% of the total number, and even the damage rate of some bridge supports after 1 year of traffic is over 20%. In this case, how to evaluate the working performance of the product through detection means is important to find out the quality defect of the product.
At present, the detection of domestic rubber supports mainly aims at the mechanical properties of the rubber supports, including indexes such as compression elastic modulus, shear elastic modulus, ultimate compression strength and the like. The testing of these mechanical indicators is generally done in a laboratory by means of a compression shear tester. When the support is used for mechanical property tests, the accuracy of the detection result can be directly influenced by the precision of the detection equipment and the working condition of the equipment. Particularly, when the support is used for a compression elastic modulus test, the deformation of the support is different due to different thicknesses and rigidities of the upper and lower pressure-bearing plates of different testing machines, so that the accuracy of a detection result is influenced, the detection results of different testing machines are different to some extent, and even the detection error can reach 20%. In addition, although indexes such as the compression elastic modulus, the shear elastic modulus, the ultimate compressive strength and the like of the support can be obtained in a mechanical property test, the vertical support rigidity and the rotational rigidity which are directly related to the structural stress cannot be obtained, and whether the support with the mechanical property index meeting the standard requirement meets the stress requirement of an actual structure cannot be known. Finally, the method has important practical significance for testing the actual vertical support and the rotational rigidity of the support working with diseases.
The method comprises the steps of firstly placing a support to be tested at the bottoms of two ends of a beam with equal rigidity to form a simply supported beam stress system, then applying a concentrated force on or near the midspan section of the simply supported beam, testing vertical displacement of different positions of the beam under the concentrated force, constructing a displacement curve of the beam by using displacement data, and finally deducing the rigidity value of a boundary according to the relation between the displacement curve and the internal force of the beam and combining with the definition of rigidity, thereby indirectly obtaining the vertical support and the rotational rigidity of the support.
Disclosure of Invention
In order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a method for testing actual rigidity static force of a bridge rubber support comprises the following steps:
firstly, placing supports at beam bottoms at two ends of a beam, wherein the beam and the supports form a simply supported beam stress system;
secondly, applying a vertical force on or near the midspan section of the simply supported beam structure, and testing the force value by using a force transducer, wherein the force value is set as F;
thirdly, dividing the simply supported beam into two parts by taking the vertical force F as a boundary, and respectively defining the two parts as an s section and a t section; four measuring points are uniformly arranged at the beam bottoms of the s-section beam body and the t-section beam body, a displacement sensor is arranged at the beam bottom position of each measuring point and the beam bottom position of the vertical force F acting point, and the vertical displacement values of the measuring points and the beams at the acting points under the action of the vertical force F are tested through the displacement sensors; if a coordinate system is established with the vertical force F acting point as the origin of coordinates, the horizontal right direction as the x axis and the vertical downward direction as the y axis, the following data coordinate points can be formed:
Coordinate points of four measuring points of the s-section beam body are respectively as follows: (x)s1,ys1)、(xs2,ys2)、(xs3,ys3)、(xs4,ys4)，
Coordinate points of four measuring points of the t-section beam body are respectively as follows: (x)t1,yt1)、(xt2,yt2)、(xt3,yt3)、(xt4,yt4)，
Vertical force F action point position: (0, y)0)，
In the coordinate points, the horizontal coordinate represents the distance from the vertical displacement test section where the measuring point is located to the origin of the coordinate, and the vertical coordinate represents the vertical displacement value when the measuring point is tested;
fourth, fitting (0, y) with a one-dimensional cubic polynomial function0)、(xs1,ys1)、(xs2,ys2)、(xs3,ys3)、(xs4,ys4) The 5 coordinate points construct a vertical displacement curve y of the s-section beam bodys(x)，ys(x)＝s0+s1x+s2x2+s3x3To obtain s0、s1、s2And s3；
Fitting (0, y) with a one-dimensional cubic polynomial function0)、(xt1,yt1)、(xt2,yt2)、(xt3,yt3)、(xt4,yt4) The 5 coordinate points construct the vertical direction of the t-section beam bodyDisplacement curve yt(x)，yt(x)＝t0+t1x+t2x2+t3x3To obtain t0、t1、t2And t3；
Wherein s is0And t0Are constant terms, s, of two fitting functions, respectively1And t1Coefficient of first order, s, of two fitting functions, respectively2And t2Coefficient of quadratic term, s, of two fitting functions, respectively3And t3Cubic term coefficients of the two fitting functions respectively;
the fifth step is to use the above s0、s1、s2、s3、t0、t1、t2、t3And F, substituting the following formulas to respectively calculate the vertical supporting rigidity and the rotational rigidity of the support at the side of the s-section beam and the t-section beam:
vertical support stiffness of s-section beam-side support
Rotational stiffness of s-section beam-side mount
Vertical support stiffness of t-section beam-side support
Rotational stiffness of t-section beam-side mount 
In the formula, n and m are respectively the distance between the center of the support at the side of the s-section beam and the center of the support at the side of the t-section beam and the origin of coordinates.
Furthermore, in the first step, the beam that chooses for use needs to satisfy the equal condition in its bending stiffness everywhere, and should choose for use the equal cross-section girder steel of not damaged.
Further, in the second step, the magnitude of the vertical force F is such thatUnder the action of the displacement sensor, the beam can generate (0.001-0.005) l of vertical displacement at most, namely, y0L is (0.001-0.005), wherein l is the net span of the simply supported beam.
Furthermore, in the third step, the test precision of the displacement sensors is not less than 0.001mm, and the distances between two adjacent displacement sensors are equal.
Further, in the fourth step, the goodness of fit R of the univariate cubic polynomial function2It should be infinitely close to 1 and should be no less than 0.99999 at the lowest.
The support to be tested is firstly placed at the beam bottoms at the two ends of the equal-rigidity beam to form a simply supported beam stress system; then, applying a concentrated force on or near the midspan section of the simply supported beam, testing the vertical displacement of the beam at different positions under the concentrated force, and constructing a displacement curve of the beam according to the displacement data; and finally, deducing to obtain the rigidity value of the boundary according to the relation between the displacement curve and the internal force of the beam and combining the definition of rigidity, thereby indirectly obtaining the vertical support and the rotational rigidity of the support.
Compared with the prior art, the invention has the following beneficial effects:
1. compared with the mechanical property test of the existing bridge support, the method directly obtains the actual vertical support rigidity and the rotation rigidity of the support directly related to the structural stress, and has more practical significance.
2. The invention adopts an indirect method, does not need a large-scale compression-shear testing machine, and avoids the influence of the precision of the detection equipment and the working condition of the equipment on the accuracy of the detection result when the support is used for carrying out a mechanical property test; the method has the advantages of simplicity, feasibility and reliable result.
3. The method can also be used for quantitatively evaluating the working performance of the damaged support, provides a solution for researching the performance degradation and other problems of the support in various environments and after fire, and has wide application prospect.
Drawings
FIG. 1 is a schematic diagram of an actual rigidity static test method of a bridge rubber support, wherein the diagram shows a beam, a support and a displacement sensor placement position.
FIG. 2 is a finite element model diagram of a simply supported steel beam (with the same type of supports arranged on both sides) (unit: kN).
FIG. 3 is a fitting curve of vertical displacement of a t-section beam.
FIG. 4 is a fitting curve of vertical displacement of the s-section beam.
FIG. 5 is a finite element model diagram of a simply supported steel beam (with different types of supports arranged on both sides) (unit: kN).
FIG. 6 is a fitting curve of vertical displacement of a t-section beam.
FIG. 7 is a fitted curve of vertical displacement of the s-section beam.
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 testing actual rigidity of a bridge rubber bearing provided by the invention is characterized by comprising the following steps:
firstly, placing supports at beam bottoms at two ends of a beam, wherein the beam and the supports form a simply supported beam stress system; wherein, the selected beam needs to satisfy the condition that the bending rigidity is equal everywhere, and a non-damaged uniform-section steel beam is suitable to be selected.
Secondly, applying a vertical force on or near the midspan section of the simply supported beam structure, and testing the force value by using a force transducer, wherein the force value is set as F; in the invention, the vertical force F meets the condition that the beam generates (0.001-0.005) l vertical displacement at maximum under the action of the vertical force F, namely, y is enabled0L is (0.001-0.005), wherein l is the net span of the simply supported beam.
Thirdly, dividing the simply supported beam into two parts by taking the vertical force F as a boundary, and respectively defining the two parts as an s section and a t section; four measuring points are uniformly arranged at the beam bottoms of the s-section beam body and the t-section beam body, a displacement sensor is arranged at the beam bottom position of each measuring point and the action point of the vertical force F, preferably, the measuring precision of the displacement sensors is not lower than 0.001mm, the distances between two adjacent displacement sensors are equal, and the vertical displacement values of the measuring points and the beams at the action points under the action of the vertical force F are measured through the displacement sensors; if a coordinate system is established with the vertical force F acting point as the origin of coordinates, the horizontal right direction as the x axis and the vertical downward direction as the y axis, the following data coordinate points can be formed:
The coordinate points of four measuring points of the s-section beam body are respectively as follows: (x)s1,ys1)、(xs2,ys2)、(xs3,ys3)、(xs4,ys4)，
the coordinate points of the four measuring points of the t-section beam body are respectively as follows: (x)t1,yt1)、(xt2,yt2)、(xt3,yt3)、(xt4,yt4)，
Vertical force F action point position: (0, y)0)，
In the coordinate points, the abscissa represents the distance from the vertical displacement test section where the measuring point is located to the origin of the coordinate, and the vertical coordinate represents the vertical displacement value during the measuring point test.
Fourth, fitting (0, y) with a one-dimensional cubic polynomial function0)、(xs1,ys1)、(xs2,ys2)、(xs3,ys3)、(xs4,ys4) The 5 coordinate points construct a vertical displacement curve y of the s-section beam bodys(x)，ys(x)＝s0+s1x+s2x2+s3x3To obtain s0、s1、s2And s3；
Fitting (0, y) with a one-dimensional cubic polynomial function0)、(xt1,yt1)、(xt2,yt2)、(xt3,yt3)、(xt4,yt4) The 5 coordinate points construct a vertical displacement curve y of the t-section beam bodyt(x)，yt(x)＝t0+t1x+t2x2+t3x3To obtain t0、t1、t2And t3；
Wherein s is0And t0Are constant terms, s, of two fitting functions, respectively1And t1Coefficient of first order, s, of two fitting functions, respectively2And t2Coefficient of quadratic term, s, of two fitting functions, respectively3And t3Respectively of three of two fitting functionsThe term coefficient. It should be noted that, in the fourth step, the goodness of fit R of the one-dimensional cubic polynomial function2It should be infinitely close to 1 and should be no less than 0.99999 at the lowest.
The fifth step is to use the above s0、s1、s2、s3、t0、t1、t2、t3And F, substituting the following formulas to respectively calculate the vertical supporting rigidity and the rotational rigidity of the support at the side of the s-section beam and the t-section beam:
Vertical support stiffness of s-section beam-side support
Rotational stiffness of s-section beam-side mount
Vertical support stiffness of t-section beam-side support
Rotational stiffness of t-section beam-side mount
In the formula, n and m are the distances from the center of the beam side support at the s section and the t section to the origin of coordinates respectively.
Of the above steps, the fourth step and the fifth step are key steps of the present invention, and the derivation process of the formulas involved in the fourth step and the fifth step will now be described in detail based on fig. 1.
In fig. 1, an equal stiffness beam (assuming that the cross-sectional bending stiffness thereof is E) is knownbIb) The vertical displacement values of a plurality of measuring points and action points under the action of the load F near the midspan section are that the coordinates of all the points are (x)s1,ys1)、(xs2,ys2)、(xs3,ys3)、(xs4,ys4)、(0,y0)、(xt1,yt1)、(xt2,yt2)、(xt3,yt3)、(xt4,yt4) (wherein xs1Measuring the distance of the cross-section from the origin of coordinates, y, for vertical displacements1The vertical displacement test value of the corresponding section is obtained, other letters mean the same, and the like), thereby identifying the vertical support of the supports at the two ends of the beam (the support rigidity k of the support at the left side)dtRight side support stiffness kds) And rotational stiffness (left side support rotational stiffness k)rtRight side support rotational stiffness krs)。
The beam corner equation theta can be known from the approximate differential equation of the beam deformation and the differential relation among the load concentration, the shearing force and the bending momentb(x) Bending moment equation M b(x) Shear equation Qb(x) The load concentrations q (x) and the displacement equations y (x) are related as follows:
the displacement function y (x) of the beam can be selected according to the load concentration condition by the formulas (1) to (4), and the details are shown in the table 1.
TABLE 1 Displacement equation of beams under different load conditions
For the beam in fig. 1, no load is applied to the s-segment and t-segment, which belongs to case 1 in table 1, so that the displacement function can adopt a unitary cubic equation. Therefore, only any 4-point displacement value is needed to be known, the displacement function curve of the section of the beam body can be constructed, and in view of accuracy, the displacement values of 5 points are taken to fit the displacement curve.
After displacement curves of s section and t section are constructed by testing displacement values, setting a displacement curve y of s sections(x)＝s0+s1x+s2x2+s3x3T-segment displacement curve yt(x)＝t0+t1x+t2x2+t3x3. According to formula (3):
shear force of s-section beam body
Shear force of t-section beam body
From the equilibrium condition, | Qbs|+|Qbt|＝F (7)
From the formulas (5) to (7), the beam flexural rigidity can be obtained
From formula (3), pressure at s-section beam side bearing
Compression of the support at the s-section beam side support (i.e. vertical displacement here)
ωs＝ys(n)＝s0+s1n+s2n2+s3n3 (10)
The vertical supporting rigidity of the s-section beam side support is defined by rigidity
The simultaneous type (8) to (11) can be obtained by considering only the magnitude of the stiffness value and neglecting the sign thereof
By formula (2), bending moment at s-section beam side support
By formula (1), the corner of the s-section beam side support
The rotational stiffness of the s-section beam side support is known by the definition of stiffness
The simultaneous type (8), formula (13) to formula (15) can be obtained by considering only the magnitude of the stiffness value and ignoring the sign thereof
Similarly, the vertical support rigidity k of the t-section beam side support can be obtaineddtAnd a rotational stiffness krt：
The method of the present invention is described in detail below with respect to the finite element numerical analysis results, taking the same and different types of supports disposed on both sides of the beam as examples.
EXAMPLE 1 arrangement of identical types of supports on both sides of the Beam
A certain pier adopts a GYZ300 multiplied by 65 round plate type rubber support, and the rigidity of the pier is tested by adopting the method disclosed by the invention. Two supports of the type are respectively placed at the beam bottoms at the two ends of the steel beam with the equal cross section to form a simply supported beam stress system. The steel beam is made of Q355 steel, the section of the steel beam is square, the width and the height of the steel beam are both 350mm, and the plate thickness of the steel beam is both 6 mm. Theoretically, the GYZ 300X 65 circular plate type rubber support has the vertical supporting rigidity of 497326.953N/mm and the rotating rigidity of 2797464109.012N mm/rad. The support is set to have good working performance, namely the actual rigidity is the same as the theoretical calculation rigidity, and the rigidity value of the support is identified by the method under the boundary condition.
The stress model of the simply supported beam is established by a finite element method, and is shown in detail in figure 2. The span of the simply supported beam is 5m, a concentrated force of 100kN acts on the simply supported beam, and under the action of the concentrated force, a vertical displacement value obtained through calculation is shown in table 2.
TABLE 2 vertical displacement value (unit: mm) of simply supported beam under action of midspan concentration force
Firstly, establishing a coordinate system by taking a vertical force action point as a coordinate origin, taking a transverse rightward direction as an x axis and taking a vertical downward direction as a y axis; x in the table represents the distance between the vertical displacement test section and the origin of coordinates, and y represents the vertical displacement value of the corresponding section; dividing the simply supported beam into two parts by taking vertical force as a boundary, and respectively defining the two parts as an s section and a t section, wherein the s section is an x-axis positive section, and the t section is an x-axis negative section; setting the test precision of the displacement sensor to be 0.001mm, so that only 3-bit effective digits are reserved for the vertical displacement value in the table (the last 1-bit estimated data is considered to be zero); the vertical displacement at the vertical force action point is 7.337mm, 5mm is 0.001l, 7.337mm and 0.005l is 25mm, and the value of the visible vertical force is proper.
With a simple cubic polynomialFitting the last 5 data points in the table 2 by a formula function to obtain a fitting equation y of the vertical displacement of the t-section beam bodyt＝-0.000000000252667x3-0.000001729428571x2+0.000150309523809x +7.3369857142851, see fig. 3 for details. Fitting the first 5 data points in the table 2 by using a first-order cubic polynomial function to obtain a fitting equation y of the vertical displacement of the s-section beam bodys＝0.000000000252667x3-0.000001729428571x20.00015030952381x +7.33698571428565, see FIG. 4 for details.
Then, s0＝7.33698571428565、s1＝-0.00015030952381、s2＝-0.000001729428571、s3＝0.000000000252667、t0＝7.3369857142851、t1＝0.000150309523809、t2＝-0.000001729428571、t3＝-0.000000000252667。
The coefficient s in the unary cubic polynomial obtained by the fitting 0、s1、s2、s3、t0、t1、t2、t3And F are substituted into the calculation formula in the patent of the invention, and the following results can be obtained:
the vertical support rigidity of the supports on the two sides of the s section is as follows:
rotational stiffness of the support at the side of the s-section beam:
the vertical supporting rigidity of the supports on the two sides of the t section is as follows:
the rotational stiffness of the support at the side of the t-section beam is as follows:
from the above, the vertical support stiffness and the rotational stiffness of the side beam end supports at the s section side and the t section side are the same, which are consistent with the preset working condition. Wherein the relative error between the tested vertical support stiffness and the preset theoretical vertical support stiffness is
The relative error between the tested rotational rigidity and the preset theoretical rotational rigidity is
Therefore, the method can test the vertical support and the rotational stiffness of the rubber support with high precision, which has important significance for evaluating the working performance of the support.
EXAMPLE 2 arrangement of different types of Supports on both sides of the Beam
A bridge abutment adopts a GYZF150 multiplied by 30 tetrafluoro sliding plate rubber support, a pier adopts a GYZ300 multiplied by 65 round plate type rubber support, and the rigidity of the bridge abutment is tested by adopting the method. Two different types of supports are respectively placed at the beam bottoms at two ends of the steel beam with the equal cross section (the GYZF150 multiplied by 30 type supports are placed at the right end, and the GYZ300 multiplied by 65 round plate type rubber supports are placed at the left end) to form a simply supported beam stress system. The steel beam is made of Q355 steel, the section of the steel beam is square, the width and the height of the steel beam are both 350mm, and the plate thickness of the steel beam is both 6 mm. Theoretically calculating, the vertical supporting rigidity of the GYZ300 multiplied by 65 circular plate type rubber support is 497326.953N/mm, and the rotational rigidity is 2797464109.012 N.mm/rad; the vertical supporting rigidity of the GYZF 150X 30 tetrafluoro skateboard rubber support is 166995.284N/mm, and the rotational rigidity is 234837118.817N mm/rad. The support is set to have good working performance, namely the actual rigidity is the same as the theoretical calculation rigidity, and the rigidity value of the support is identified by the method under the boundary condition.
The stress model of the simply supported beam is established by a finite element method, and is shown in detail in figure 5. The span of the simply supported beam is 5m, a concentrated force of 100kN acts on the middle section of the simply supported beam, and under the action of the concentrated force, a vertical displacement value obtained through calculation is shown in table 3.
TABLE 3 vertical displacement value (unit: mm) of simply supported beam under action of centralized force on midspan section
Firstly, establishing a coordinate system by taking a vertical force action point as a coordinate origin, taking a transverse rightward direction as an x axis and taking a vertical downward direction as a y axis; x in the table represents the distance between the vertical displacement test section and the origin of coordinates, and y represents the vertical displacement value of the corresponding section; dividing the simply supported beam into two parts by taking vertical force as a boundary, and respectively defining the two parts as an s section and a t section, wherein the s section is an x-axis positive section, and the t section is an x-axis negative section; setting the test precision of the displacement sensor to be 0.001mm, so that only 3-bit effective digits are reserved for the vertical displacement value in the table (the last 1-bit estimated data is considered to be zero); the vertical displacement at the vertical force action point is 7.869mm, 5mm is 0.001l, 7.869mm and 0.005l is 25mm, and the value of the visible vertical force is proper.
Fitting the last 5 data points in the table 3 by using a unitary cubic polynomial function to obtain a fitting equation y of the vertical displacement of the t-section beam bodyt＝-0.000000000263333x3-0.000001799142857x2+0.000253547619047x +7.86892857142788, see fig. 6 for details. Fitting the first 5 data points in the table 3 by using a first-order cubic polynomial function to obtain a fitting equation y of the vertical displacement of the s-section beam body s＝0.000000000242x3-0.000001799428571x20.000046642857143x +7.86898571428564, see FIG. 7 for details.
Then, s0＝7.86898571428564、s1＝-0.000046642857143、s2＝-0.000001799428571、s3＝0.000000000242、t0＝7.86892857142788、t1＝0.000253547619047、t2＝-0.000001799142857、t3＝-0.000000000263333。
The coefficient s in the unary cubic polynomial obtained by the fitting0、s1、s2、s3、t0、t1、t2、t3And F are substituted into the calculation formula in the patent of the invention, and the following results can be obtained:
the vertical support rigidity of the support at the s-section beam side is as follows:
the rotational stiffness of the support at the side of the s-section beam is as follows:
the vertical supporting rigidity of the support at the side of the t-section beam is as follows:
the rotational stiffness of the support at the side of the t-section beam is as follows:
from the above, the vertical support stiffness and the rotational stiffness of the side beam end supports at the s section side and the t section are different, which is consistent with the preset working condition. The relative error between the vertical support rigidity tested at the s section side and the preset theoretical vertical support rigidity is
The relative error between the tested rotational rigidity and the preset theoretical rotational rigidity is
the relative error between the vertical support rigidity tested at the t section side and the preset theoretical vertical support rigidity is
The relative error between the tested rotational rigidity and the preset theoretical rotational rigidity is
Therefore, for the situation that different types of supports are arranged on two sides of the beam, the vertical support and the rotation rigidity of the supports can be tested with high precision by adopting the method provided by the invention.
Claims (5)
1. A method for testing the actual rigidity static force of a bridge rubber support is characterized by comprising the following steps:
Firstly, placing supports at beam bottoms at two ends of a beam, wherein the beam and the supports form a simply supported beam stress system;
secondly, applying a vertical force on or near the midspan section of the simply supported beam structure, and testing the force value by using a force transducer, wherein the force value is set as F;
thirdly, dividing the simply supported beam into two parts by taking the vertical force F as a boundary, and respectively defining the two parts as an s section and a t section; four measuring points are uniformly arranged at the beam bottoms of the s-section beam body and the t-section beam body, a displacement sensor is arranged at the beam bottom position of each measuring point and the beam bottom position of the vertical force F acting point, and the vertical displacement values of the measuring points and the beams at the acting points under the action of the vertical force F are tested through the displacement sensors; if a coordinate system is established with the vertical force F acting point as the origin of coordinates, the horizontal right direction as the x axis and the vertical downward direction as the y axis, the following data coordinate points can be formed:
the coordinate points of four measuring points of the s-section beam body are respectively as follows: (x)s1,ys1)、(xs2,ys2)、(xs3,ys3)、(xs4,ys4)，
the coordinate points of the four measuring points of the t-section beam body are respectively as follows: (x)t1,yt1)、(xt2,yt2)、(xt3,yt3)、(xt4,yt4)，
Vertical force F action point position: (0, y)0)，
In the coordinate points, the horizontal coordinate represents the distance from the vertical displacement test section where the measuring point is located to the origin of the coordinate, and the vertical coordinate represents the vertical displacement value when the measuring point is tested;
fourth, fitting (0, y) with a one-dimensional cubic polynomial function 0)、(xs1,ys1)、(xs2,ys2)、(xs3,ys3)、(xs4,ys4) The 5 coordinate points construct a vertical displacement curve y of the s-section beam bodys(x)，ys(x)＝s0+s1x+s2x2+s3x3To obtain s0、s1、s2And s3；
Fitting (0, y) with a one-dimensional cubic polynomial function0)、(xt1,yt1)、(xt2,yt2)、(xt3,yt3)、(xt4,yt4) The 5 coordinate points construct a vertical displacement curve y of the t-section beam bodyt(x)，yt(x)＝t0+t1x+t2x2+t3x3To obtain t0、t1、t2And t3；
Wherein s is0And t0Are constant terms, s, of two fitting functions, respectively1And t1First order coefficients, s, of two fitting functions, respectively2And t2Coefficient of quadratic term, s, of two fitting functions, respectively3And t3Cubic term coefficients of the two fitting functions respectively;
the fifth step is to use the above s0、s1、s2、s3、t0、t1、t2、t3And F, substituting the following formulas to respectively calculate the vertical supporting rigidity and the rotational rigidity of the support at the side of the s-section beam and the t-section beam:
vertical support stiffness of s-section beam-side support
Rotational stiffness of s-section beam-side bearing
Vertical support stiffness of t-section beam-side support
Rotational stiffness of t-section beam-side mount
In the formula, n and m are the distances from the center of the beam side support at the s section and the t section to the origin of coordinates respectively.
2. The method for testing the actual rigidity of the bridge rubber support according to claim 1, wherein in the first step, the selected beam needs to satisfy the condition that the bending rigidity is equal everywhere, and a non-damaged steel beam with the equal section is preferably selected.
3. The method for testing the actual rigidity of the rubber bearing of the bridge according to claim 1, wherein in the second step, the magnitude of the vertical force F meets the condition that the beam generates (0.001-0.005) l vertical displacement at maximum under the action of the vertical force F, namely, y is enabled 0(0.001-0.005) l, wherein l is the net span of the simply supported beam.
4. The method for testing the actual rigidity and the static force of the bridge rubber support according to claim 1, wherein in the third step, the testing precision of the displacement sensors is not lower than 0.001mm, and the distances between two adjacent displacement sensors are equal.
5. The method for testing the actual rigidity of the rubber bearing of the bridge according to claim 1, wherein in the fourth step, the goodness of fit R of a one-element cubic polynomial function2It should be infinitely close to 1 and should be no less than 0.99999 at the lowest.
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