CN102914473A - Method for recognizing cross-section bending moment and curvature relation of reinforced concrete beam - Google Patents

Abstract

The invention discloses a method for recognizing the cross-section bending moment and curvature relation of a reinforced concrete beam. The method includes: using macroscopic displacement measured by a bending member for recognizing the cross-section bending moment and curvature relation of the reinforced concrete beam, namely, using the load-displacement relation under loads at each level, combining a conjugate beam method, and recognizing the cross-section bending moment and curvature relation of the bending member by a least square method, so that analysis of nonlinear bending member mechanical properties is benefited. The method has the advantages that the cross-section bending moment and curvature relation of the bending member is recognized accurately, so that corresponding materials can be selected accurately according to engineering structure forms, and the member can be designed reasonably.

Description

A kind of method of Sectional Dimension of Reinforced Concrete Beam moment curvature relation recognition

Technical field

The present invention relates to a kind of structural test technical field, more particularly, relate to a kind of method of Sectional Dimension of Reinforced Concrete Beam moment curvature relation recognition.

Background technology

The application of reinforced concrete structure in engineering is very extensive, all uses widely this version such as industry and covil construction, road engineering, bridge, hydraulic engineering, underground works etc.Along with improving constantly of economic, scientific and technological development and social demand, the researcher begins to explore and the better steel-concrete combined structure of exploitation stress performance (such as built-in T-shaped or steel case beam etc.) and other new material members (such as the fiber reinforcement composite material-concrete structural elements etc.).The principle of work of these members is similar to reinforced concrete member, namely gives full play to the mechanical property of utilizing each combined material.The ultimate bearing capacity of determining member is to analyze the key of flexural member mechanical property with its rigidity in the different stressed stages.And that these members all have is stronger non-linear, obtains the moment of flexure (M) of member section-curvature by test

Relation curve is the effective way that addresses these problems.Generally be to obtain Constitutive relationship of metals (strain-stress relation) by test at present, then by plane cross-section assumption and Constitutive relationship of metals, pair cross-section carries out layering, obtains the cross section according to equilibrium condition

Relation.But because the discreteness of material and the finiteness of measuring error and measured data, there is certain error in the constitutive relation of acquisition; Slippage between the surface of contact of combined material and friction also can affect the strain-stress relation of layers of material reality, and these factors affect the cross section to a certain extent

The reliability of relation curve and accuracy affect mechanics property analysis and its application in engineering of member then, can not select exactly respective material and reasonably carry out member designs according to the engineering structure form.

Summary of the invention

The present invention is directed to the proposition of above problem, and a kind of method of Sectional Dimension of Reinforced Concrete Beam moment curvature relation recognition is provided.

A kind of method of Sectional Dimension of Reinforced Concrete Beam moment curvature relation recognition is characterized in that, may further comprise the steps:

S1, the two ends that will need to measure the beam l of cross section moment curvature relation are hinged on the rigid mount, choose A, B, C 3 points of bottom, beam l cross section, the place arranges displacement meter D1 at the A point, the place arranges displacement meter D2 at the B point, the place arranges displacement meter D3 at the C point, adopt two concentrated forces, three branch load modes that beam l is loaded load step by step, left load is l apart from the distance of beam l left end _b, right load is l apart from the distance of beam l right-hand member _b

S2, beam l stage loading is carried P, ask for the cross section moment M of beam l, wherein, initial load is zero, and the load of i level load level correspondence is P _i, at load P _iEffect under, the measured displacements that j is ordered is namely surveyed amount of deflection and is

(j=1,2,3), the cross section moment of flexure of beam l is formula one $M_i\left(x\right)=\left\{\begin{array}{cc}{P}_{i}x,& x\∈\[0,l_b)\\ P_i{l}_b,& x\∈\[l_b,l-2l_b\],\\ P_i(l-x),& x\∈(l-2l_b,l\]\end{array}\right.$ By displacement meter D1, displacement meter D2 and displacement meter D3 record respectively 3 displacement under the front i level load action, obtain front i level load-displacement relation curve;

S3, the cross section moment M that identifies according to front i level load-displacement relation curve are less than P _il _bThe time corresponding cross section moment M and curvature

Relation, k level load P _kEffect is lower, and beam l spaning middle section moment of flexure is

Corresponding sectional curvature is formula two

(k=1,2 ..., i);

S4, when the cross section moment of flexure of two adjacent load level correspondences

With

Between moment-curvature close when being linearity, according to the front i level moment-curvature relation of having surveyed, and the displacement of the i+1 level load of measuring, identify each corresponding under i+1 level load action sectional curvature;

S5, beam l is loaded i+1 level load P _I+1The time, ask for the cross section moment M of beam l according to formula one _I+1(x), the spaning middle section moment of flexure of beam l is

When the cross section moment M _I+1(x) less than or equal to

The time, to the moment curvature relation that calculates (k=1,2 ..., i) carry out linear interpolation, obtain sectional curvature; The moment of flexure in cross section greater than

The time, set beam l moment of flexure and exist

Between the time sectional curvature be linear change, slope is k _I+1, obtain i+1 level load P _I+1The sectional curvature of lower correspondence is formula three

Given arbitrary value k _I+1, according to formula one and formula three, determine at i+1 level load P _I+1Act on cross section moment of flexure and the sectional curvature of underbeam l, then try to achieve the amount of deflection δ (x) of beam l according to conjugate beam method, be formula four

At i+1 level load P _I+1Effect is lower, and the amount of deflection that bottom, beam l cross section is 3 is designated as δ _{1, i+1}(k _I+1), δ _{2, i+1}(k _I+1), δ _{3, i+1}(k _I+1), δ _{J, i+1}(k _I+1) (j=1,2,3) be about k _I+1Linear function, this function is designated as formula five δ _{J, i+1}(k _I+1)=a _J1k _I+1+ a _J2(j=1,2,3); Respectively will

Assignment is 0, will Assignment is 1, will

With

Bring formula three into, ask for the sectional curvature of beam l, with k _I+1Bring formula four into, ask for the coefficient a in the formula five _J1And a _J2Be formula six $\left\{\begin{array}{c}{a}_{\mathrm{<figure-callout\; id="1"\; label="j"\; filenames="HDA00002223586100021.png,HDA00002223586100031.png"\; state="\{\{state\}\}">j</figure-callout>}1}={\mathrm{\&delta;}}_{j,i+1}^{\left(1\right)}-{\mathrm{\&delta;}}_{j,i+1}^{\left(2\right)}\\ a_{\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00002223586100031.png,HDA00002223586100041.png"\; state="\{\{state\}\}">j</figure-callout>}2}={\mathrm{\&delta;}}_{j,i+1}^{\left(2\right)}\end{array}\right.$ Ask at i+1 level load P (j=1,2,3) _I+1Effect underbeam l is at the amount of deflection at j point place, formula seven ${\mathrm{\&delta;}}_{j,i+1}\left(k_{i+1}\right)=({\mathrm{\&delta;}}_{j,i+1}^{\left(1\right)}-{\mathrm{\&delta;}}_{j,i+1}^{\left(2\right)})k_{i+1}+{\mathrm{\&delta;}}_{j,i+1}^{\left(2\right)}$ (j=1,2,3）；

S6, by minimizing objective function formula eight, make δ _{J, i+1}(k _I+1) and the actual measurement amount of deflection

The most approaching, ask for k _I+1, formula eight $\min \mathrm{imize\&Delta;}\left(k_{i+1}\right)=\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{({\mathrm{\&delta;}}_{j,i+1}\left(k_{i+1}\right)-{\mathrm{\&delta;}}_{j,i+1}^{*})}^2,$ (j=1,2,3）， ${\mathrm{\&delta;}}_{1,i+1}^{*},{\mathrm{\&delta;}}_{2.i+1}^{*},{\mathrm{\&delta;}}_{3,i+1}^{*}$ For beam l at i+1 level load P _I+1A under the effect, B, the measured displacements that C is 3;

S7, utilize least square method formula nine k _I+1=(A ^TA) A ^TB, $A=\left\{\begin{array}{c}{\mathrm{\&delta;}}_{1,i+1}^{\left(1\right)}-{\mathrm{\&delta;}}_{1,i+1}^{\left(2\right)}\\ {\mathrm{\&delta;}}_{2,i+1}^{\left(1\right)}-{\mathrm{\&delta;}}_{2,i+1}^{\left(2\right)}\\ {\mathrm{\&delta;}}_{3,i+1}^{\left(1\right)}-{\mathrm{\&delta;}}_{3,i+1}^{\left(2\right)}\end{array}\right\},$ $b=\left\{\begin{array}{c}{\mathrm{\&delta;}}_{1,i+1}^{*}-{\mathrm{\&delta;}}_{1,i+1}^{\left(2\right)}\\ {\mathrm{\&delta;}}_{2,i+1}^{*}-{\mathrm{\&delta;}}_{2,i+1}^{\left(2\right)}\\ {\mathrm{\&delta;}}_{3,i+1}^{*}-{\mathrm{\&delta;}}_{3,i+1}^{\left(2\right)}\end{array}\right\},$ Ask for coefficient k _I+1

S8, according to k _I+1, and i+1 level load P _I+1The lower corresponding sectional curvature of effect is asked for corresponding spaning middle section curvature according to formula ten, and formula ten is

S9, circulation said method are asked for sectional curvature corresponding under the load of each load level, and the moment curvature relation of obtaining beam l obtains the moment curvature relation in free beam cross section

(i=1,2 ..., n)

Owing to adopt the method for Sectional Dimension of Reinforced Concrete Beam moment curvature relation recognition of the present invention, has following beneficial effect: utilize macroscopical displacement of flexural member actual measurement to identify its cross section moment-curvature relation, namely utilize the load-displacement relation under the loads at different levels, in conjunction with the conjugate beam method, by the cross section moment of flexure of least square method identification flexural member and the relation of curvature, then be of value to and analyze non-linear flexural member mechanical property, thereby can select exactly respective material according to the engineering structure form, member is carried out appropriate design.

This technology can class be pushed into the calculating of the cross section bending-curvature relationship of the non-linear flexural members such as steel-concrete composite beam.The cross section Relation has reflected the internal force of member and the relation of distortion, therefore, in the member stress whole process analysis, after this relation that obtains according to test, further calculate member load (p)-amount of deflection (δ) curve is more accurately objective.In addition, according to member

Can analyze the stiffness variation of flexural member, for reinforced concrete member, before the concrete cracking, moment M and curvature φ are substantially linear, and the cross section is the elastic working stage.Behind the test specimen cracking, curvature increases suddenly, occurs turnover on the curve.When compression steel was surrendered, curvature is accelerated growth again, and rate of curve reduces rapidly.Like this according to different phase

Curve can calculate the average bending stiffness of member.Determine that exactly load-the sag curve of member and the variation of member stress process middle section rigidity are the key of non-linear flexural member reliability application in Practical Project, determine objective and accurately that according to test figure the moment-curvature relation of member is the most important thing here.

Description of drawings

Fig. 1 is that load-displacement of the present invention is measured structural drawing;

Fig. 2 is the moment curve of beam of the present invention under the symmetrical load effect;

Fig. 3 is concrete stress of the present invention-strain constitutive relation figure;

Fig. 4 is reinforcement stresses of the present invention-strain constitutive relation figure;

Fig. 5 is this cross section moment-curvature graph of a relation that calculates by the cross section top and bottom process;

Fig. 6 is the load-displacement curve figure of 3 of the A, the B that utilize conjugate beam method to calculate and C;

Fig. 7 is that the load-displacement curve figure under 5% noise situations is considered in simulation;

Fig. 8 is by the anti-cross section moment-curvature graph of a relation that pushes away identification of load-displacement relation;

Fig. 9 is the member load-deflection relation figure that bending-curvature relationship is calculated that is obtained by test.

Embodiment

The invention provides a kind of method of Sectional Dimension of Reinforced Concrete Beam moment curvature relation recognition, below in conjunction with accompanying drawing technical scheme of the present invention is elaborated.

Fig. 1 is that load-displacement of the present invention is measured structural drawing, as shown in the figure, chooses a beam l, and the square-section of beam l is of a size of 300mm * 650mm, and span is 6m.The concrete design strength grade is C30, and the arrangement of reinforcement of compressive region and tensile region is respectively 804mm ²And 1964mm ²Protective layer thickness is 35mm.The two ends of beam l are hinged on (bearing T1 and bearing T2) on the bearing, and bearing is rigid member, sedimentation can not occur in loading procedure.Choose A, B, C 3 points of bottom, beam l cross section, the place arranges displacement meter D1 at the A point, and the place arranges displacement meter D2 at the B point, and the place arranges displacement meter D3 at the C point, adopts two concentrated forces, three branch load modes that beam l is loaded load step by step, and left load is l apart from the distance of beam l left end _b, right load is l apart from the distance of beam l right-hand member _b, the displacement of measuring every grade of load underbeam l.

To beam l hierarchical loading load P, wherein the 1st grade of load P ₁=0, namely initial load is zero; The i time loads corresponding load is P _i, the measured displacements that corresponding j is ordered is namely surveyed amount of deflection and is (j=1,2,3).At load P _iEffect is lower, and cross section Expression of Moment formula is formula one, $M_i\left(x\right)=\left\{\begin{array}{cc}{P}_{i}x,& x\&Element;\&lsqb;0,l_b)\\ P_i{l}_b,& x\&Element;\&lsqb;l_b,l-2l_b\&rsqb;,\\ P_i(l-x),& x\&Element;(l-2l_b,l\&rsqb;\end{array}\right.$ By displacement meter D1, displacement meter D2 and displacement meter D3 record respectively 3 displacement under the front i level load action, and Fig. 2 is the moment curve of beam of the present invention under the symmetrical load effect, as shown in Figure 2.By, front i level load-displacement relation curve is obtained in 3 the displacement that displacement meter D1, displacement meter D2 and displacement meter D3 record respectively under the front i level load action.

At first order load P ₁=0, namely initially not under the load condition, the moment of flexure of establishing corresponding arbitrary section is M ₁(x)=0, sectional curvature is The amount of deflection that corresponding A, B and C are 3 all is 0, i.e. δ ₁₁=0, δ ₂₁=0, δ ₃₁=0.

The cross section moment M that identifies according to front i level load-displacement relation curve is less than P _il _bThe time corresponding cross section moment M and curvature

Relation, k level load P _kEffect is lower, and beam l spaning middle section moment of flexure is

Corresponding sectional curvature is formula two

(k=1,2 ..., i).

Cross section moment of flexure when two adjacent load level correspondences

With Between moment-curvature close when being linearity, according to the front i level moment-curvature relation of having surveyed, and the displacement of the i+1 level load of measuring, identify each corresponding under i+1 level load action sectional curvature.

Beam l is loaded i+1 level load P _I+1The time, ask for the cross section moment M of beam l according to formula one _I+1(x), the spaning middle section moment of flexure of beam l is

When the cross section moment M _I+1(x) less than or equal to

The time, to the moment curvature relation that calculates

(k=1,2 ..., i) carry out linear interpolation, obtain sectional curvature; The moment of flexure in cross section greater than

The time, set beam l moment of flexure and exist

Between the time sectional curvature be linear change, slope is k _I+1, obtain i+1 level load P _I+1The sectional curvature of lower correspondence is formula three

Determine slope value k _I+1It is the key of each sectional curvature of correspondence under the identification i+1 level load action.Given arbitrary value k _I+1, according to formula one and formula three, determine at i+1 level load P _I+1Act on cross section moment of flexure and the sectional curvature of underbeam l, then try to achieve the amount of deflection δ (x) of beam l according to conjugate beam method, be formula four

At i+1 level load P _I+1Effect is lower, and the amount of deflection that bottom, beam l cross section is 3 is designated as δ _{1, i+1}(k _I+1), δ _{2, i+1}(k _I+1), δ _{3, i+1}(k _I+1), δ _{J, i+1}(k _I+1) (j=1,2,3) be about k _I+1Linear function, this function is designated as formula five δ _{J, i+1}(k _I+1)=a _J1k _I+1+ a _J2(j=1,2,3); Respectively will

Assignment is 0, will

Assignment is 1, will

With Bring formula three into, ask for the sectional curvature of beam l, with k _I+1Bring formula four into, ask for the coefficient a in the formula five _J1And a _J2Be formula six $\left\{\begin{array}{c}{a}_{\mathrm{<figure-callout\; id="1"\; label="l"\; filenames="HDA00002223586100021.png,HDA00002223586100031.png"\; state="\{\{state\}\}">l</figure-callout>}1}={\mathrm{\&delta;}}_{l,i+1}^{\left(1\right)}-{\mathrm{\&delta;}}_{l,i+1}^{\left(2\right)}\\ a_{\mathrm{<figure-callout\; id="2"\; label="l"\; filenames="HDA00002223586100031.png,HDA00002223586100041.png"\; state="\{\{state\}\}">l</figure-callout>}2}={\mathrm{\&delta;}}_{l,i+1}^{\left(2\right)}\end{array}\right.(l=\mathrm{1,2,3}),$ Ask at i+1 level load P _I+1Effect underbeam l is at the amount of deflection at j point place, formula seven ${\mathrm{\&delta;}}_{j,i+1}\left(k_{i+1}\right)=({\mathrm{\&delta;}}_{j,i+1}^{\left(1\right)}-{\mathrm{\&delta;}}_{j,i+1}^{\left(2\right)})k_{i+1}+{\mathrm{\&delta;}}_{j,i+1}^{\left(2\right)},(j=\mathrm{1,2,3}).$

Make δ _{J, i+1}(k _I+1) and the actual measurement amount of deflection

Immediate k _I+1Be the slope value that to ask for.Ask for k by minimizing target formula eight _I+1, formula eight is $\min \mathrm{imize\&Delta;}\left(k_{i+1}\right)=\underset{i=1}{\overset{3}{\mathrm{\&Sigma;}}}{({\mathrm{\&delta;}}_{j,i+1}^{*}\left(k_{i+1}\right)-{\mathrm{\&delta;}}_{j,i+1}^{*})}^2,$ (j=1,2,3),

For beam l at i+1 level load P _I+1A under the effect, B, the measured displacements that C is 3.

Utilize least square method formula nine k _I+1=(A ^TA) A ^TB asks for coefficient k _I+1, in the formula $A=\left\{\begin{array}{c}{\mathrm{\&delta;}}_{1,i+1}^{\left(1\right)}-{\mathrm{\&delta;}}_{1,i+1}^{\left(2\right)}\\ {\mathrm{\&delta;}}_{2,i+1}^{\left(1\right)}-{\mathrm{\&delta;}}_{2,i+1}^{\left(2\right)}\\ {\mathrm{\&delta;}}_{3,i+1}^{\left(1\right)}-{\mathrm{\&delta;}}_{3,i+1}^{\left(2\right)}\end{array}\right\},$ $b=\left\{\begin{array}{c}{\mathrm{\&delta;}}_{1,i+1}^{*}-{\mathrm{\&delta;}}_{1,i+1}^{\left(2\right)}\\ {\mathrm{\&delta;}}_{2,i+1}^{*}-{\mathrm{\&delta;}}_{2,i+1}^{\left(2\right)}\\ {\mathrm{\&delta;}}_{3,i+1}^{*}-{\mathrm{\&delta;}}_{3,i+1}^{\left(2\right)}\end{array}\right\}.$

According to k _I+1, and i+1 level load P _I+1The lower corresponding sectional curvature of effect is asked for corresponding spaning middle section curvature according to formula ten, and formula ten is

The circulation said method is asked for sectional curvature corresponding under the load of each load level, until curvature corresponding to n level load is all calculated, obtains the moment curvature relation of beam l, thereby obtains the moment curvature relation in free beam cross section

(i=1,2 ..., n)

Fig. 3 is concrete stress of the present invention-strain constitutive relation figure, and Fig. 4 is reinforcement stresses of the present invention-strain constitutive relation figure.Suppose still to satisfy plane cross-section assumption after the normal section distortion of free beam, the cross section is divided into 80 layers, go out the moment-curvature relation in cross section by iterative computation, see Fig. 5, Fig. 5 is this cross section moment-curvature graph of a relation that calculates by the cross section top and bottom process.Press table 1 pair free beam hierarchical loading, calculate the moment of flexure in each cross section of free beam under the loads at different levels by formula one, and determine the curvature in each cross section according to the moment-curvature among Fig. 5 relation, then calculated the amount of deflection of free beam by formula four according to conjugate beam method, thereby obtain corresponding A, B and the displacement under 3 loads at different levels of C, its displacement curve of 3 is seen Fig. 6, and Fig. 6 is the load-displacement curve figure of 3 of the A, the B that utilize conjugate beam method to calculate and C.

Table 1 hierarchical loading

Be the error of simulation actual measurement, consider 5% gaussian random noise in the displacement calculating.Fig. 7 is that the load-displacement curve figure under 5% noise situations is considered in simulation, as shown in Figure 7.The below introduces the moment-curvature relation of the load-displacement curve identification free beam normal section that how to utilize Fig. 7.

The 1st grade is loaded as initial load P ₁During=0kN: the spaning middle section moment of flexure

The 2nd grade loads P ₂During=30kN: (a) calculate the moment of flexure in each cross section by formula (1); (b) k ₂Value is

Substitution formula (3) obtains the curvature in each cross section, is the amount of deflection that formula (4) obtains free beam by conjugate beam method then, thereby obtains the displacement of 3 of A, B and C, for

(c) k ₂Value is Repeat the step of (b), obtain the corresponding displacement of 3 of A, B and C, for

(d)

When substitution formula (9) calculates the 2nd grade of loading, the slope k that curvature changes ₂=1.2487 * 10 ^-14The moment of flexure of spaning middle section when (d) calculating the 2nd grade of loading by formula (10) Corresponding curvature is

3rd level loads P ₃During=60kN: similar the 2nd grade of load finally calculates moment of flexure

Corresponding curvature

With this recursion, can calculate the moment-curvature relation of spaning middle section under all grades load action.

Fig. 8 is by the anti-cross section moment-curvature graph of a relation that pushes away identification of load-displacement relation.As shown in Figure 8, can find out that the moment-curvature relation of identification is consistent with actual relation curve basically, verify the validity of method.

By what obtain

Curve can be judged the different operating stage of member.When cross section moment of flexure during less than 60kNm, M with Substantially linear, illustrate that the cross section is in the elastic working stage.When moment of flexure reached 60kNm, rate of curve reduced suddenly, and member concrete in tension zone cracking is described.Then the crack is in the steady development state.After the cross section moment of flexure reached 360kNm, rate of curve reduced rapidly again, illustrated that the cross section compression steel begins surrender.Like this, according to the cross section

Curve is judged the different operating stage of member, then carries out the calculating of each stage component load-bearing ability and distortion.

When the cross section parameter of member was identical, its cross section moment-curvature relation was identical.Therefore utilize this cross section moment-curvature that obtains to concern to calculate below to have same cross-sectional but the load-sag curve of different another free beam of span, to verify the application of this technology in engineering.

The square-section of beam is of a size of 300mm * 650mm, and span is 7.2m.The concrete design strength grade is C30, and the arrangement of reinforcement of compressive region and tensile region is respectively 804mm ²And 1964mm ²Protective layer thickness is 35mm.Apply two concentrated forces on the member, load point is respectively 2.880m apart from two ends.The cross section parameter of this member is identical with free beam in the above-mentioned test, so the two has identical cross section

Curve.When this member is carried out stressed whole process analysis, utilize test to obtain

Curve such as Fig. 8 (identification curve), can calculate the load (p) of member-amount of deflection (δ) curve: 1) increase step by step sectional curvature

2) by having obtained

Relation obtains corresponding cross section moment M, easily knows the corresponding external load p that acts on the member according to M; 3) simultaneously according to conjugate beam method by curvature

But the amount of deflection δ of Calculation of Beam; 4) repeat load-sag curve that above-mentioned steps just can obtain member.Load-the sag curve of the member span centre that obtains can find out that shown in Fig. 9 (estimation) under 5% noise effect, it is better that estimated value and theoretical value are coincide, and can reflect more truly load-bearing capacity and the distortion of member.

Fig. 9 is the member load-deflection relation figure that bending-curvature relationship is calculated that is obtained by test.As shown in Figure 9, can find out that the cross section moment curvature by technical scheme identification of the present invention concerns that the member load-deflection relation and the actual relation curve that calculate are consistent basically, also verify the validity of technical scheme of the present invention.

To sum up, measured displacements according to the beam under the load actions at different levels, can identify the moment-curvature relation of Sectional Dimension of Reinforced Concrete Beam, this technology can be extrapolated to the calculating of the cross section bending-curvature relationship of the non-linear flexural members such as steel-concrete composite beam or FRP combination beam, has very high precision.Then use this technology to help to have the overall process force analysis of other non-linear flexural members of same cross-sectional parameter, improve member in the accuracy that different operating stage bearing capacity calculates, improve its fiduciary level in engineering is used.

The above; only be the better embodiment of the present invention; but protection scope of the present invention is not limited to this; anyly be familiar with those skilled in the art in the technical scope that the present invention discloses; be equal to replacement or change according to technical scheme of the present invention and inventive concept thereof, all should be encompassed within protection scope of the present invention.

Claims (1)

1. the method for a Sectional Dimension of Reinforced Concrete Beam moment curvature relation recognition is characterized in that, may further comprise the steps:

S1, the two ends that will need to measure the beam l of cross section moment curvature relation are hinged on the rigid mount, choose A, B, C 3 points of bottom, beam l cross section, the place arranges displacement meter D1 at the A point, the place arranges displacement meter D2 at the B point, the place arranges displacement meter D3 at the C point, adopt two concentrated forces, three branch load modes that beam l successive loading is carried, left load is l apart from the distance of beam l left end _b, right load is l apart from the distance of beam l right-hand member _b

S2, beam l stage loading is carried P, ask for the cross section moment M of beam l, wherein, initial load is zero, and the load of i level load level correspondence is P _i, at load P _iEffect under, the measured displacements that j is ordered is namely surveyed amount of deflection and is

(j=1,2,3), the cross section moment of flexure of beam l is formula one

X is the distance of left section of the cross-sectional distance beam paid close attention to, and by displacement meter D1, displacement meter D2 and displacement meter D3 record respectively 3 displacement under the front i level load action, obtain front i level load-displacement relation curve;

S3, the cross section moment M that identifies according to front i level load-displacement relation curve are less than P _il _bThe time corresponding cross section moment M and curvature

Relation, k level load P _kEffect is lower, and beam l spaning middle section moment of flexure is

Corresponding sectional curvature is formula two

(k=1,2 ..., i);

S4, when the cross section moment of flexure of two adjacent load level correspondences

With

Between moment-curvature close when being linearity, according to the front i level moment-curvature relation of having surveyed, and the displacement of the i+1 level load of measuring, identify each corresponding under i+1 level load action sectional curvature;

S5, beam l is added i+1 level load P _I+1The time, ask for the cross section moment M of beam l according to formula one _I+1(x), the spaning middle section moment of flexure of beam l is

When the cross section moment M _I+1(x) less than or equal to

The time, to the moment curvature relation that calculates

(k=1,2 ..., i) carry out linear interpolation, obtain sectional curvature; The moment of flexure in cross section greater than The time, set beam l moment of flexure and exist

Between the time sectional curvature be linear change, slope is k _I+1, obtain i+1 level load P _I+1The sectional curvature of lower correspondence is formula three

Given arbitrary value k _I+1, according to formula one and formula three, determine at i+1 level load P _I+1Act on cross section moment of flexure and the sectional curvature of underbeam l, then try to achieve the amount of deflection δ (x) of beam l according to conjugate beam method, be formula four Z is variable, the distance of left section bearing of expression place cross-sectional distance beam; R represents the end reaction of conjugate beam;

At i+1 level load P _I+1Effect is lower, and the amount of deflection that bottom, beam l cross section is 3 is designated as δ _{1, i+1}(k _I+1), δ _{2, i+1}(k _I+1), δ _{3, i+1}(k _I+1), δ _{J, i+1}(k _I+1) (j=1,2,3) be about k _I+1Linear function, this function is designated as formula five δ _{J, i+1}(k _I+1)=a _J1k _I+1+ a _J2(j=1,2,3); Respectively will

Assignment is 0, will

Assignment is 1, will

With

Bring formula three into, ask for the sectional curvature of beam l, with k _I+1Bring formula four into, ask for the coefficient a in the formula five _J1And a _J2Be formula six

(j=1,2,3) ask for the amount of deflection at j point place at i+1 level load Pi+1 effect underbeam l, formula seven (j=1,2,3);

S6, by minimizing objective function formula eight, make δ _{J, i+1}(k _I+1) and the actual measurement amount of deflection

The most approaching, ask for k _I+1, formula eight

(j=1,2,3), For beam l at i+1 level load P _I+1A under the effect, B, the measured displacements that C is 3;

S7, utilize least square method formula nine k _I+1=(A ^TA) A ^TB,

Ask for coefficient k _I+1

S8, according to k _I+1, and i+1 level load P _I+1The lower corresponding sectional curvature of effect is asked for corresponding spaning middle section curvature according to formula ten, and formula ten is

S9, circulation said method are asked for sectional curvature corresponding under the load of each load level, and the moment curvature relation of obtaining beam l obtains the moment curvature relation in free beam cross section

(i=1,2 ..., n).

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