1. A beam and plate vertical displacement calculation method based on corners is characterized by comprising the following steps:

step S1: measuring the span length l of each span of the bridge or the plate body, the actually measured inclination angle theta of each span and the absolute value ordinate H of the span end of each span at two ends, and calculating to obtain a final positive angle alpha;

step S2: the final positive angle alpha is utilized to carry out final positive on the inclination angles theta of the m spans to obtain a final positive inclination angle theta' after final positive;

step S3: constructing a deflection-spanning curve function of the bridge or the plate body;

step S4: constructing an orthogonal polynomial basis function, and fitting the constructed cross-deflection curve function of the bridge or the plate body by using a least square method of the orthogonal polynomial basis function to obtain a preliminary deflection curve function of the whole bridge or the plate body;

step S5: and settling the preliminary deflection curve function of the whole bridge or plate body to obtain the final deflection curve function of the whole bridge or plate body.

2. The method for calculating the vertical displacement of the beam and the plate based on the rotation angle according to claim 1, wherein the final positive angle α is calculated in step S1 by taking the span length of the ith span as l_iTaking the cross end absolute value ordinate of two ends of the ith cross as H_iAnd H_i+1Taking the final positive angle of the span as alpha_i

Then there is a change in the number of,

wherein Δ h_i＝H_i-H_i+1

Then there is theta'_i＝θ_i-α_iWherein θ'_iIs the final positive inclination angle of the ith span, theta_iIs the measured inclination angle of the ith span.

3. The method for calculating the vertical displacement of the beam and the plate based on the corner according to claim 1, wherein the method for constructing the span deflection curve function of the bridge or the plate body is that K inclinometers are arranged at the ith span and are arranged atThe ith deflection curve across the upper beam is y_i(x)，y_i(x) Meet the perturbance bound conditioning of the span, y_i(x) The expression of (a) is as follows:

the x in the formula refers to an axial abscissa taking the left beam end in the span of the bridge or the plate body as an origin and the axis of the bridge or the plate body as a transverse axis of orthogonality; l is the span length of the span of the bridge or plate body,is a constructed orthogonal polynomial basis function.

4. The method for calculating the vertical displacement of the beam and the plate based on the corner according to claim 3, wherein the method for fitting the cross-deflection curve function of the constructed bridge or plate by the least square method of the orthogonal polynomial basis function comprises the steps of constructing the orthogonal polynomial basis function, and selecting a known orthogonal polynomial basis functionAndthen can obtain includingThe set of orthogonal functions in the inner set,to construct the first-term function expression of the orthogonal polynomial basis function,

wherein a and b are coefficients in the construction process, x refers to an axial abscissa taking the left beam end in the span of the bridge or the plate body as an origin and the axis of the bridge or the plate body as a transverse axis of orthogonality,

thereby obtaining K mutually orthogonal functionsSubstituting the system matrix A into the system matrix A, and finishing the expression to obtain,

substituting A into the Cramer matrix A^TAX^*＝A^Tθ', an approximate solution X of the equation is obtained^*Wherein X is^*＝(X₁，X₂，...，X_k)^T，θ’＝(θ’₁，θ’₂，...，θ’_k)^TIs the final positive inclination angle after the final correction,

mixing X^*＝(X₁，X₂，...，X_k)^TIs substituted into

And obtaining a preliminary deflection curve function of the whole bridge or plate body.

5. The method for calculating the vertical displacement of the beam and the plate based on the corner in claim 4, wherein the step five of settling the preliminary deflection curve function of the whole bridge or plate body is to,

Δh_i＝H_i-H_i+1，

then y'_i(x) As a function of the final deflection curve of the entire bridge or slabX in (2) is an axial abscissa which takes the left beam end in the span of the bridge or the plate body as an origin and the axis of the bridge or the plate body as a transverse axis of orthogonality; l is the span length of the span of the bridge or plate.

Background

With the rapid improvement of economic strength in China, the construction quantity of concrete structural plate bodies, beam bodies, steel structures and bridges is increased year by year, and the construction proportion of large and medium-sized bridges is increased year by year. However, accidents such as damage and even collapse of concrete structural plates, beams, steel structures and bridges caused by structural degradation, natural factor damage, external force, environmental mutation and other factors are increased year by year. Therefore, the health condition of the concrete structure plate, the beam body, the steel structure and the bridge needs to be monitored, and the concrete structure plate, the beam body, the steel structure and the bridge can be settled, so that the axial longitudinal plane displacement values of the concrete structure plate, the beam body, the steel structure and the bridge need to be monitored in the monitoring process of the concrete structure plate, the beam body, the steel structure and the bridge, and the axial longitudinal plane displacement values of the concrete structure plate, the beam body, the steel structure and the bridge cannot be objectively and accurately reflected due to the large calculation error of the existing axial longitudinal plane displacement value calculation processing method. Therefore, the method is improved, and a beam and plate vertical displacement calculation method based on the corner is provided.

Disclosure of Invention

In order to solve the technical problems, the invention provides the following technical scheme:

the invention relates to a beam and plate vertical displacement calculation method based on a corner, which comprises the following steps:

step S1: measuring the span length l of each span of the bridge or the plate body, the actually measured inclination angle theta of each span and the absolute value ordinate H of the span end of each span at two ends, and calculating to obtain a final positive angle alpha;

step S2: the final positive angle alpha is utilized to carry out final positive on the inclination angles theta of the m spans to obtain a final positive inclination angle theta' after final positive;

step S3: constructing a deflection-spanning curve function of the bridge or the plate body;

step S4: constructing an orthogonal polynomial basis function, and fitting the constructed cross-deflection curve function of the bridge or the plate body by using a least square method of the orthogonal polynomial basis function to obtain a preliminary deflection curve function of the whole bridge or the plate body;

step S5: and settling the preliminary deflection curve function of the whole bridge or plate body to obtain the final deflection curve function of the whole bridge or plate body.

As a preferred embodiment of the present invention, the method for calculating the final positive angle α in step S1 is to take the span length of the ith span as l_iTaking the cross end absolute value ordinate of two ends of the ith cross as H_iAnd H_i+1Taking the final positive angle of the span as alpha_i

Then there is a change in the number of,

wherein Δ h_i＝H_i-H_i+1

Then there is theta'_i＝θ_i-α_iWherein θ'_iIs the final positive inclination angle of the ith span, theta_iIs the measured inclination angle of the ith span.

As a preferred technical scheme of the invention, the method for constructing the span deflection curve function of the bridge or the plate body is that K inclinometers are arranged on the ith span, and the beam deflection curve on the ith span is y_i(x)，y_i(x) Meet the perturbance bound conditioning of the span, y_i(x) The expression of (a) is as follows:

the x in the formula refers to an axial abscissa taking the left beam end in the span of the bridge or the plate body as an origin and the axis of the bridge or the plate body as a transverse axis of orthogonality; l is the span length of the span of the bridge or plate body,is a constructed orthogonal polynomial basis function.

As a preferred technical scheme of the invention, the method for fitting the cross-deflection curve function of the constructed bridge or plate body by the least square method of the orthogonal polynomial basis function is to construct the orthogonal polynomial basis function and select the known orthogonal polynomial basis functionAndis ready to obtainIncludedThe set of orthogonal functions in the inner set,to construct the first-term function expression of the orthogonal polynomial basis function,

wherein a and b are coefficients in the construction process, x refers to an axial abscissa taking the left beam end in the span of the bridge or the plate body as an origin and the axis of the bridge or the plate body as a transverse axis of orthogonality,

thereby obtaining K mutually orthogonal functionsSubstituting the system matrix A into the system matrix A, and finishing the expression to obtain,

substituting A into A^TAX^*＝A^Tθ', an approximate solution X of the equation is obtained^*Wherein X is^*＝(X₁，X₂，...，X_k)^T，θ’＝(θ’₁，θ’₂，...，θ’_k)^TIs the final positive inclination angle after the final correction,

mixing X^*＝(X₁，X₂，...，X_k)^TIs substituted into

And obtaining a preliminary deflection curve function of the whole bridge or plate body.

As a preferred technical scheme of the invention, the method for settling the preliminary deflection curve function of the whole bridge or plate body in the step five is that,

then y'_i(x) The x in the formula refers to an axial abscissa taking the left beam end in the span of the bridge or the plate body as an origin and the axis of the bridge or the plate body as a transverse axis of positive coordinate; l is the span length of the span of the bridge or plate.

As a preferred embodiment of the present invention,

the invention has the beneficial effects that: the method for calculating the vertical displacement of the beam and the plate based on the corner comprises the steps of firstly measuring the span length l of each span of the bridge or the plate body, the actually measured inclination angle theta of each span and the absolute value vertical coordinate H of the span ends of each span, and calculating to obtain a final positive angle alpha; the inclination angles theta of the m spans are finally corrected by using the final positive angle alpha to obtain a final positive inclination angle theta'; constructing a deflection-spanning curve function of the bridge or the plate body; constructing an orthogonal polynomial basis function, and fitting the constructed cross-deflection curve function of the bridge or the plate body by using a least square method of the orthogonal polynomial basis function to obtain a preliminary deflection curve function of the whole bridge or the plate body; and settling the preliminary deflection curve function of the whole bridge or plate body to obtain the final deflection curve function of the whole bridge or plate body. Through the processes, deflection displacement values of all points of the axes of the steel structure, the concrete structure plate body and the beam body (longitudinal plane displacement values of all points in each span relative to a connecting line of two end points) are calculated, and the absolute settlement amounts of the end points of the steel structure, the concrete structure plate body and the beam body are obtained by increasing monitoring on the end points of the steel structure, the concrete structure plate body and the beam body, so that the longitudinal plane displacement values of all points are obtained, the obtained longitudinal plane displacement values are more accurate, and errors are smaller.

Drawings

The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention and not to limit the invention. In the drawings:

FIG. 1 is a flow chart of a method for calculating vertical displacement of a beam and a plate based on a corner according to the present invention.

Detailed Description

The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it will be understood that they are described herein for the purpose of illustration and explanation and not limitation.

Example (b): as shown in FIG. 1, the invention relates to a method for calculating vertical displacement of a beam and a plate based on a corner, which comprises the following steps:

step S1: measuring the span length l of each span of the bridge or the plate body, the actually measured inclination angle theta of each span and the absolute value ordinate H of the span end of each span at two ends, and calculating to obtain a final positive angle alpha;

step S2: the final positive angle alpha is utilized to carry out final positive on the inclination angles theta of the m spans to obtain a final positive inclination angle theta' after final positive;

step S3: constructing a deflection-spanning curve function of the bridge or the plate body;

step S4: constructing an orthogonal polynomial basis function, and fitting the constructed cross-deflection curve function of the bridge or the plate body by using a least square method of the orthogonal polynomial basis function to obtain a preliminary deflection curve function of the whole bridge or the plate body;

step S5: and settling the preliminary deflection curve function of the whole bridge or plate body to obtain the final deflection curve function of the whole bridge or plate body.

In step S1, the final positive angle α is calculated by taking the span length of the ith span as l_iTaking the cross end absolute value ordinate of two ends of the ith cross as H_iAnd H_i+1Taking the final positive angle of the span as alpha_i

Then there is a change in the number of,

wherein Δ h_i＝H_i-H_i+1

Then there is theta'_i＝θ_i-α_iWherein θ'_iIs the final positive inclination angle of the ith span, theta_iIs the measured inclination angle of the ith span.

4. The method for constructing the span deflection curve function of the bridge or the plate body is that K inclinometers are arranged on the ith span, and the beam deflection curve on the ith span is y_i(x)，y_i(x) Meet the perturbance bound conditioning of the span, y_i(x) The expression of (a) is as follows:

the x in the formula refers to an axial abscissa taking the left beam end in the span of the bridge or the plate body as an origin and the axis of the bridge or the plate body as a transverse axis of orthogonality; l is the span length of the span of the bridge or plate body,is a constructed orthogonal polynomial basis function.

As a preferred technical scheme of the invention, the method for fitting the cross-deflection curve function of the constructed bridge or plate body by the least square method of the orthogonal polynomial basis function is to construct the orthogonal polynomial basis function and select the known orthogonal polynomial basis functionAndthen can obtain includingThe set of orthogonal functions in the inner set,to construct the first-term function expression of the orthogonal polynomial basis function,

wherein a and b are coefficients in the construction process, x refers to an axial abscissa taking the left beam end in the span of the bridge or the plate body as an origin and the axis of the bridge or the plate body as a transverse axis of orthogonality,

thereby obtaining K mutually orthogonal functionsSubstituting the system matrix A into the system matrix A, and finishing the expression to obtain,

substituting A into A^TAX^*＝A^Tθ', an approximate solution X of the equation is obtained^*Wherein X is^*＝(X₁，X₂，...，X_k)^T，θ’＝(θ’₁，θ’₂，...，θ’_k)^TIs the final positive inclination angle after the final correction,

mixing X^*＝(X₁，X₂，...，X_k)^TIs substituted into

And obtaining a preliminary deflection curve function of the whole bridge or plate body.

The settlement finishing method for the preliminary deflection curve function of the whole bridge or plate body in the step five is that,

then y'_i(x) The x in the formula is the deflection curve function of the final whole bridge or plate body, and the left beam end in the span of the bridge or plate body is taken as the origin, and the bridge or plate body is taken as the originThe axis of the plate body is an axial abscissa of the transverse axis of the positive coordinate; l is the span length of the span of the bridge or plate.

The method for calculating the vertical displacement of the beam and the plate based on the corner comprises the steps of firstly measuring the span length l of each span of the bridge or the plate body, the actually measured inclination angle theta of each span and the absolute value vertical coordinate H of the span ends of each span, and calculating to obtain a final positive angle alpha; the inclination angles theta of the m spans are finally corrected by using the final positive angle alpha to obtain a final positive inclination angle theta'; constructing a deflection-spanning curve function of the bridge or the plate body; constructing an orthogonal polynomial basis function, and fitting the constructed cross-deflection curve function of the bridge or the plate body by using a least square method of the orthogonal polynomial basis function to obtain a preliminary deflection curve function of the whole bridge or the plate body; and settling the preliminary deflection curve function of the whole bridge or plate body to obtain the final deflection curve function of the whole bridge or plate body. Through the processes, deflection displacement values of all points of the axes of the steel structure, the concrete structure plate body and the beam body (longitudinal plane displacement values of all points in each span relative to a connecting line of two end points) are calculated, and the absolute settlement amounts of the end points of the steel structure, the concrete structure plate body and the beam body are obtained by increasing monitoring on the end points of the steel structure, the concrete structure plate body and the beam body, so that the longitudinal plane displacement values of all points are obtained, the obtained longitudinal plane displacement values are more accurate, and errors are smaller.

Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that changes may be made in the embodiments and/or equivalents thereof without departing from the spirit and scope of the invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.