CN113806942A - Method for acquiring lossy deformation of inclined frame - Google Patents
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Abstract
The invention discloses a method for acquiring lossy deformation of an inclined frame, which respectively calculates lossy interlaminar deformation SnAnd no interlayer distortion ZnThereby utilizing SnEvaluating the performance of the building structure and rejecting ZnThereby increasing the accuracy of the performance evaluation. Using gamma1n、γ2n、ν1nV and v2nBy transformation of the parameters of (1), R is obtainedn', thereby constructing RnAnd Rn‑1The function relationship between the two is calculated in turn by recursion relationship to obtain each RnAnd all parameters used in the calculation and derivation process can be obtained by looking up the table or using a horizontal displacement meter, so that the use of an inclinometer is avoided.
Description
Technical Field
The invention relates to a method for acquiring lossy deformation of a tilting frame, and belongs to the field of tilting frame analysis.
Background
In the building structure, the inclined frame with the frame columns inclined relative to the building height direction is adopted, so that the integration of the structural form and the building aesthetics can be achieved, and the complex horizontal conversion structure can be avoided. Therefore, the method has important practical value for the structural performance evaluation of the inclined frame.
Aiming at the traditional vertical frame, only the horizontal displacement between layers needs to be measured through a horizontal displacement meter, and a relatively accurate structural performance evaluation result can be provided for the vertical frame. But for the inclined frame, the horizontal displacement meter is also adopted to measure the horizontal displacement between each layer to evaluate the structural performance, and the evaluation result is often very low in accuracy. This requires a completely new parameter to replace or assist the horizontal displacement data between the layers to make an accurate assessment of the performance of the tilt frame structure.
Disclosure of Invention
The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and to provide a method for obtaining a lossy deformation of a tilt frame.
The technical scheme adopted by the invention is as follows:
a method of acquiring lossy deformation of a tilt frame, comprising the steps of:
step S1: acquiring lateral displacement D of cross beam of the n-th layer of inclined framenFrame column inclination angle alphanAnd a frame layer height hn；
Step S2: lateral beam displacement D of the inclined frame of the (n-1) th layern-1And the corner R of the beamn-1Calculating the lossless interlayer distortion Z of the n-th layer tilt frame by combining the data obtained in step S1nFurther calculating the frame column corner gamma of the two sides of the n-th layer inclined frame1nAnd gamma2n；
Step S3: gamma ray1nAnd gamma2nCombining the data obtained in the step S1, respectively calculating the vertical displacement v of the two ends of the beam of the nth layer inclined frame1nV and v2n；
Step S4, acquiring the beam length L of the inclined frame of the nth layern，ν1nV and v2nBinding of LnAnd calculating the beam corner R of the n-th layer inclined frame caused by interlayer stressn'；
Step S5: rn-1Bound to RnTo calculate the firstCrossbeam corner R of n-layer inclined framen；
Step S6: znBinding of DnAnd Dn-1To calculate the damaged interlayer deformation S of the tilting frame of the nth layern。
The invention has the beneficial effects that:
the method respectively calculates the deformation S between the damaged layersnAnd no interlayer distortion ZnThereby utilizing SnEvaluating the performance of the building structure and rejecting ZnThereby increasing the accuracy of the performance evaluation. Using gamma1n、γ2n、ν1nV and v2nBy transformation of the parameters of (1), R is obtainedn', thereby constructing RnAnd Rn-1The function relationship between the two is calculated in turn by recursion relationship to obtain each RnAnd all parameters used in the calculation and derivation process can be obtained by looking up the table or using a horizontal displacement meter, so that the use of an inclinometer is avoided.
The invention
Invention Zn＝Rn-1hn。
The invention
The invention
Invention Rn＝Rn-1+Rn'。
Invention Sn＝Dn-Dn-1-Zn。
Invention R0＝0。
Invention D0＝0。
Other features and advantages of the present invention will be disclosed in more detail in the following detailed description of the invention and the accompanying drawings.
Drawings
The invention is further described below with reference to the accompanying drawings:
FIG. 1 is a deformation analysis diagram of a building structure of prior art 1;
FIG. 2 is a deformation analysis diagram of a building structure of prior art 2;
FIG. 3 is a flow chart of a method of obtaining a lossy deformation of a tilt frame according to an embodiment of the present invention;
FIG. 4 is a diagram illustrating a process of computing a method for obtaining a lossy deformation of a tilt frame according to an embodiment of the present invention;
FIG. 5 is a first diagram illustrating a deformation index of an n-th inclined frame according to an embodiment of the present invention;
FIG. 6 is a second diagram illustrating deformation indexes of the n-th inclined frame according to the embodiment of the present invention;
FIG. 7 is a construction structure of example 1 according to an embodiment of the present invention;
FIG. 8 is a construction structure diagram of embodiment 2 of the present invention;
fig. 9 is a construction structure diagram of embodiment 3 of the present invention.
Detailed Description
The technical solutions of the embodiments of the present invention are explained and illustrated below with reference to the drawings of the embodiments of the present invention, but the following embodiments are only preferred embodiments of the present invention, and not all embodiments. Based on the embodiments in the implementation, other embodiments obtained by those skilled in the art without any creative effort belong to the protection scope of the present invention.
In the following description, the appearances of the indicating orientation or positional relationship such as the terms "inner", "outer", "upper", "lower", "left", "right", etc. are only for convenience in describing the embodiments and for simplicity in description, and do not indicate or imply that the device or element being referred to must have a particular orientation, be constructed and operated in a particular orientation, and are not to be construed as limiting the present invention.
Prior art 1:
the inclination angle alpha of the frame column of the vertical frame is 90 degrees, referring to fig. 1, the 1 st floor and the 2 nd floor of the building structure both adopt vertical frames, and the frame height of the 1 st floor vertical frame is h1The height of the frame layer of the 2 nd layer vertical frame is h2. Under the action of interlayer pressure, the vertical frames of the 1 st layer and the 2 nd layer are deformed, but because the deformation quantity of the frame columns on two sides of the same vertical frame is the same, the cross beam of the vertical frame still keeps a horizontal state.
Measuring the lateral displacement D of the beam of the vertical frame of the 1 st layer by a horizontal displacement meter1Lateral displacement D of the beam of the 2 nd-level vertical frame2Correspondingly, the relative deformation between the layers is D2-D1。
Prior art 2:
the inclination angle alpha of the frame column of the inclined frame is not 90 degrees, referring to fig. 2, the 1 st layer of the building structure adopts the inclined frame, the 2 nd layer adopts the vertical frame, and the frame layer height of the 1 st layer of the inclined frame is h1The height of the frame layer of the 2 nd layer vertical frame is h2. Under the action of interlayer pressure, the inclined frame and the vertical frame are deformed, and the lateral displacement D of the beam of the inclined frame at the 1 st layer is measured by a horizontal displacement meter1Lateral displacement D of the beam of the 2 nd-level vertical frame2Correspondingly, the relative deformation between the layers is D1-D2。
In particular, due to the different deformation of the frames at the two sides of the inclined frame, the cross beam of the corresponding inclined frame rotates relative to the horizontal plane. Thus D2-D1This is caused by the rotation of the cross beams in the tilting frame in addition to the forces between the floors. For convenience of description, the interlayer stress is paired with D2-D1The contribution amount of (D) is recorded as S, and the beam rotation pair D2-D1Is denoted as Z, and thus D1-D2Z + S. Where S is closely related to elastoplastic damage and Z is not related to structural damage.
It can be seen that, objectively, Z is 0 in prior art 1 and Z is not 0 in prior art 2. But in the past performance evaluations for the prior art 2 building structure,often default to 0, neglecting Z vs D2-D1The deviation between the calculated value and the actual value of S is caused, and the building structure performance is misestimated.
Example (b):
referring to fig. 3-6, the method for obtaining the lossy deformation of the inclined frame of the embodiment comprises the following steps:
step S1: obtaining the lateral displacement D of the beam 2 in the tilting frame of the nth layernInclination angle alpha of frame column 1nAnd a frame layer height hnWherein D isnMeasured in situ by means of a horizontal displacement meter, alphanAnd hnAre all design values, obtainable by consulting architectural drawings, DnIs defined as the horizontal transverse displacement distance of the middle point of the front and rear beams 2 after the deformation of the nth layer of inclined frames, the inclined frames account for N layers, and N belongs to [1, N ]]；
Step S2: obtaining the lateral displacement D of the beam 2 in the inclined frame of the (n-1) th layern-1And the corner R of the cross member 2n-1To calculate the lossless interlayer distortion Z of the n-th layer tilt frame by combining the data obtained in step S1nFurther calculate the corner gamma of the frame column 1 on both sides in the n-th layer inclined frame1nAnd gamma2n，γ1nIs an included angle between the connecting line of the two ends of the left frame column 1 after deformation and the left frame column 1 before deformation, gamma2nIs the included angle between the connecting line of the two ends of the frame column 1 on the right side after deformation and the frame column 1 on the right side before deformation, and is Dn-1Can likewise be measured in situ by means of a horizontal displacement meter, Dn-1Is defined as the horizontal transverse displacement distance of the midpoint of the front and rear beams 2 of the deformation of the inclined frame of the (n-1) th layer;
according to the foregoing ZnDefinition of, ZnSpecific numerical values of (1) and Rn-1Having a correlation, in particular Zn＝hntan(Rn-1). In the actual case of Rn-1Is very small, therefore Zn≈Rn-1hnThereby effectively reducing the field calculation amount;
on the basis of the above-mentioned technical scheme,
Dn、Dn-1、αnand hnAre all known constants since only R needs to be knownn-1By using the specific numerical value of (2), gamma can be calculated1nAnd gamma2n；
Step S3: gamma ray1nAnd gamma2nCombining the data obtained in the step S1, respectively calculating the vertical displacement v of the two ends of the beam 2 in the nth layer inclined frame1nV and v2n；
Corresponding to the above-mentioned gamma1nAnd gamma2nThe formula for the calculation of (a) is,
in calculating v1nV and v2nNo new variables are introduced, so γ can be directly converted1nAnd gamma2nConversion to v1nV and v2nCompleting the conversion between the angle and the displacement;
step S4, obtaining the length L of the beam 2 of the inclined frame of the nth layern，LnAlso for the architectural design values, v can be obtained by referring to architectural design drawings1nV and v2nBinding of LnCalculating the corner R of the beam 2 caused by the interlayer stress of the nth layer of inclined framen'；
In a corresponding manner, the first and second optical fibers are,
thus calculating Rn' numerical unique variables in Rn-1；
Step S5: rn-1Bound to RnTo calculate the angle R of the beam 2 of the tilting frame of the nth layern；
Corresponding to, Rn＝Rn-1+Rn'; proceeding according to the foregoing steps, R can be obtainedn'＝Rn'(Rn-1) Thereby obtainingTo obtain RnAnd Rn-1So long as R is obtained0Then R can be obtained in turn1、R2...RN(ii) a Due to Rn-1Recursion to RnL used in the processn、Dn、αn、Dn-1、hnThe angle measurement is obtained by looking up a table or a horizontal displacement meter, so that the field angle measurement is effectively avoided, an inclinometer is not required correspondingly, and compared with the prior art, the measuring instrument and the measuring step are not additionally increased; especially for the existing large amount of retained intrinsic data, data correction can be carried out according to the method process of the embodiment on the basis of not carrying out supplementary measurement, so that the waste of past measurement data is avoided;
step S6: znBinding of DnAnd Dn-1To calculate the damaged interlayer deformation S of the tilting frame of the nth layern(ii) a As can be seen from the analysis procedure of prior art 2, Sn＝Dn-Dn-1-ZnThus Sn＝Sn(Rn-1)，Zn＝Zn(Rn-1) Therefore only R needs to be knownn-1Can effectively distinguish ZnAnd SnTo Dn-Dn-1To thereby eliminate ZnThe influence of (2) can be used for more accurately evaluating the safety of the building structure.
Wherein R is0Is the corner of the cross beam 2 of the 0 th layer inclined frame, namely the rotation angle at the bottom support, so R00, corresponding to R1、R2...RNCan obtain S in turn and can also obtain S in turn1、S2...SNAnd Z1、Z2...ZN，D0Is the lateral displacement of the cross beam 2 of the inclined frame of the 0 th floor, i.e. the lateral displacement of the bottom support, so D0＝0。
In order to verify the accuracy of the method of the present embodiment, the present embodiment provides three examples, and referring to fig. 7 to 9, each example comprises three layers of inclined frames. In example 1,. alpha.1＝α2＝α3＝80°，L1＝5m，L2＝3.6m，L32.2 m. In example 2,. alpha.1＝100°，α2＝α3＝80°，L1＝5m，L2＝3.6m，L32.2 m. In example 3,. alpha.1＝α2＝α3＝80°，L1＝7m，L2＝5.6m，L34.2 m. Examples 1, 2 and 3 h1＝h2＝h3The elastic modulus of the inclined frame is 3.0 multiplied by 10 which is 4m10N/m2。
Finite element numerical models were built for the examples 1, 2, 3 based on openses. The modeling process is as follows: the method is characterized in that elastic beam column units (elastic Beam column elements) are adopted to simulate beams and frame columns of a three-layer inclined frame, each beam and frame column is equally divided into 5 units, consolidation constraint is adopted at a bottom support, namely, all degrees of freedom are constrained, and D is set1＝0.1m，D2＝0.3m，D3＝0.5m。
The method of this embodiment also sets D1＝0.1m，D2＝0.3m，D3Calculation was performed for each of examples 1, 2 and 3 at 0.5m, and the results are shown in table 1.
TABLE 1
The results and finite element numerical solutions calculated by the method of the present embodiment and the prior knowledge are shown in table 2. Specifically, the 'prior knowledge' refers to the results of the current theory on the corner of the beam, such as the results in the literature [ Liufeng. concrete structure design manual example detailed [ M ]. Beijing: chemical industry publishers, 2016.] said: in a shear-type variant of the frame structure, the beam corner value R of the invention is considered to be zero. Namely, the cross beam corners obtained by 'existing cognition' are all 0. Therefore, the data of the 'prior knowledge' item in table 2 are all zero.
TABLE 2
It can be seen that the error rates of the calculation results of the embodiment are less than 8%, and the method can be effectively applied to the calculation of the rotation angle of the cross beam 2 of the inclined frame. Meanwhile, compared with numerical simulation, the method has the advantages that the calculated amount is small, the rule of the deformation index can be visually seen, complex and accurate finite element modeling is avoided, the essential influence factors of the deformation index can be more favorably disclosed, and in all, the method is accurate, visual, concise and economical.
While the invention has been described with reference to specific embodiments thereof, it will be understood by those skilled in the art that the invention is not limited thereto, and may be embodied in many different forms without departing from the spirit and scope of the invention as set forth in the following claims. Any modification which does not depart from the functional and structural principles of the present invention is intended to be included within the scope of the claims.
Claims (9)
1. A method of acquiring a lossy deformation of a tilted frame, comprising the steps of:
step S1: acquiring lateral displacement D of cross beam of the n-th layer of inclined framenFrame column inclination angle alphanAnd a frame layer height hn；
Step S2: lateral beam displacement D of the inclined frame of the (n-1) th layern-1And the corner R of the beamn-1Calculating the lossless interlayer distortion Z of the n-th layer tilt frame by combining the data obtained in step S1nFurther calculating the frame column corner gamma of the two sides of the n-th layer inclined frame1nAnd gamma2n；
Step S3: gamma ray1nAnd gamma2nCombining the data obtained in the step S1, respectively calculating the vertical displacement v of the two ends of the beam of the nth layer inclined frame1nV and v2n；
Step S4, acquiring the beam length L of the inclined frame of the nth layern，ν1nV and v2nBinding of LnAnd calculating the beam corner R of the n-th layer inclined frame caused by interlayer stressn'；
Step S5: rn-1Bound to Rn' toCalculating the beam corner R of the nth layer of inclined framen；
Step S6: znBinding of DnAnd Dn-1To calculate the damaged interlayer deformation S of the tilting frame of the nth layern。
2. Method for obtaining a lossy deformation of a tilting frame according to claim 1,
3. method for obtaining a lossy deformation of a tilting frame according to claim 2, characterised in that Zn＝Rn-1hn。
4. Method for obtaining a lossy deformation of a tilting frame according to claim 1,
5. method for obtaining a lossy deformation of a tilting frame according to claim 1,
6. method for obtaining a lossy deformation of a tilted frame according to claim 1, wherein R isn＝Rn-1+Rn'。
7. Method for obtaining a lossy deformation of a tilted frame according to claim 1, characterised in that Sn＝Dn-Dn-1-Zn。
8. Method for obtaining a lossy deformation of a tilted frame according to claim 1, wherein R is0＝0。
9. Method for obtaining a lossy deformation of a tilted frame according to claim 1, characterized in that D0＝0。
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