CN115329257B - Load-displacement relation estimation method for assembled integral bidirectional multi-ribbed superposed floor system - Google Patents
Load-displacement relation estimation method for assembled integral bidirectional multi-ribbed superposed floor system Download PDFInfo
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- 238000006073 displacement reaction Methods 0.000 title claims abstract description 51
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- 230000002457 bidirectional effect Effects 0.000 title claims abstract description 27
- 238000005336 cracking Methods 0.000 claims abstract description 65
- 238000005452 bending Methods 0.000 claims abstract description 27
- 239000002131 composite material Substances 0.000 claims abstract description 16
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- E04B—GENERAL BUILDING CONSTRUCTIONS; WALLS, e.g. PARTITIONS; ROOFS; FLOORS; CEILINGS; INSULATION OR OTHER PROTECTION OF BUILDINGS
- E04B5/00—Floors; Floor construction with regard to insulation; Connections specially adapted therefor
- E04B5/16—Load-carrying floor structures wholly or partly cast or similarly formed in situ
- E04B5/17—Floor structures partly formed in situ
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Abstract
The application discloses a load-displacement relation estimation method for an assembled integral bidirectional multi-ribbed superposed floor, which comprises the following working stages before cracking: obtaining a cracking bending moment of the component, and calculating to obtain cracking deflection by a method for calculating the bending stiffness of the bidirectional plate; the method provided by the application simplifies the nonlinear stage after cracking into a section of straight line, can comparatively simplify and estimate the load-displacement relation of the assembled integral type bidirectional multi-ribbed composite floor, and obtains the deflection of the assembled integral type bidirectional multi-ribbed composite floor under the working condition, and compared with the traditional method, the method is more convenient and quicker.
Description
Technical Field
The application relates to the field of assembled buildings, in particular to a load-displacement relation estimation method for an assembled integral bidirectional multi-ribbed superposed floor system.
Background
The novel assembled integral type two-way dense rib superposed floor system is used as a novel system with the advantages of the laminated slab floor and the two-way dense rib floor system, has the advantages of the two floor systems, and effectively solves a plurality of problems of the traditional engineering application. The novel assembled integral bidirectional multi-ribbed superposed floor system consists of three main parts: the concrete slab comprises (1) a prefabricated two-way ribbed concrete bottom plate, (2) a mould box and (3) a laminated slab (upper cast-in-situ part). The precast concrete ribbed bottom plates are connected with the post-pouring lamination layer through two mechanical connecting sleeves, and the die box can be used as an internal die for increasing the hollow rate and can also be used as an internal die for casting the lamination layer in situ.
Deflection of the existing assembled integral type bidirectional multi-ribbed composite floor system applied to extreme working conditions is required to be measured by a test, the operation is relatively complicated, and the test cost is high.
Therefore, how to solve the above-mentioned drawbacks of the prior art is the subject of the present application.
Disclosure of Invention
In order to solve the problems, the application discloses a load-displacement relation estimation method for an assembled integral bidirectional multi-ribbed composite floor system.
In order to achieve the above purpose, the present application provides the following technical solutions: a load-displacement relation estimation method for an assembled integral bidirectional multi-ribbed superposed floor system comprises the following steps:
working stage before cracking:
obtaining a cracking bending moment of the component, and calculating to obtain cracking deflection by a method for calculating the bending stiffness of the bidirectional plate; working stage after cracking:
wherein, the displacement after cracking is calculated by the following formula:
w 2 ＝(q 2 -q 1 )/q 1 βw 1
the load after cracking is calculated by the following formula:
wherein,,
q 1 the surface load is the surface load when cracking;
q 2 the surface load after cracking;
q is the maximum face load to reach the ultimate bearing capacity;
a is a bending moment coefficient of the two-way plate;
beta is the ratio of rigidity after yielding to rigidity before yielding, and the novel floor system is 0.5;
la and lb are widths of the floor in the horizontal direction;
e is an elastic mould of the concrete;
h is the thickness of the floor;
mu is the Poisson's ratio of the concrete;
m x is the ultimate bending moment per unit length of the plastic strand in the x direction.
In the scheme, the cracking displacement in the working stage before cracking is calculated by the following formula:
w 1 ＝M 1 /D；
the cracking load is calculated by the following formula:
q 1 ＝M 1 /(αl 2 )
in the above scheme, the displacement after cracking comprises yield displacement and limit displacement.
In the above scheme, the load after cracking comprises yield load and limit load.
The beneficial effects of the application are as follows: the method provided by the application simplifies the nonlinear stage after cracking into a section of straight line, can comparatively simplify and estimate the load-displacement relation of the assembled integral type bidirectional multi-ribbed composite floor, and obtains the deflection of the assembled integral type bidirectional multi-ribbed composite floor under the working condition, and compared with the traditional method, the method is more convenient and quicker.
Drawings
Fig. 1 is a schematic diagram of an analytical method first-order mode f1=12.20hz in an embodiment;
fig. 2 is a schematic diagram of an analytical second-order mode f 2= 30.49Hz in the embodiment;
fig. 3 shows the analytical second-order mode f 2= 30.49Hz in the example;
fig. 4 is a schematic diagram of the analytical method third-order mode f3= 48.78Hz in the embodiment;
FIG. 5 is a schematic diagram showing the failure of the novel assembled integral two-way multi-ribbed composite floor system of the present application under the action of uniform load;
FIG. 6 is a schematic diagram of test results of (a) equivalent area and (b) ASTM equivalent area using eigenvalue determination methods in an embodiment of the present application;
FIG. 7 is a graph comparing the calculated results with the finite element modeling results in the embodiment of the present application.
Detailed Description
The present application is further illustrated in the following drawings and detailed description, which are to be understood as being merely illustrative of the application and not limiting the scope of the application.
Examples: referring to fig. 1-7, a load-displacement relationship estimation method for an assembled integral bidirectional multi-ribbed composite floor system includes the steps of:
working stage before cracking:
obtaining a cracking bending moment of the component, and calculating to obtain cracking deflection by a method for calculating the bending stiffness of the bidirectional plate; working stage after cracking:
wherein, the displacement after cracking is calculated by the following formula:
w 2 ＝(q 2 -q 1 )/q 1 βw I
the load after cracking is calculated by the following formula:
wherein,,
q 1 the surface load is the surface load when cracking;
q 2 after cracking ofSurface loading;
q is the maximum face load to reach the ultimate bearing capacity;
a is a bending moment coefficient of the two-way plate;
beta is the ratio of rigidity after yielding to rigidity before yielding, and the novel floor system is 0.5;
la and lb are widths of the floor in the horizontal direction;
e is an elastic mould of the concrete;
h is the thickness of the floor;
mu is the Poisson's ratio of the concrete;
mx is the ultimate bending moment per unit length of the plastic strand in the x-direction.
In the scheme, the cracking displacement in the working stage before cracking is calculated by the following formula:
w 1 ＝M l /D；
the cracking load is calculated by the following formula:
q 1 ＝M 1 /(αl 2 )
in the above scheme, the displacement after cracking comprises yield displacement and limit displacement.
In the above scheme, the load after cracking comprises yield load and limit load.
The following examples illustrate:
preparing test pieces with the numbers of XJB-1, XJB-2, DXB-1, DXB-3 and DXB-4;
working stage before cracking:
after the cracking bending moment of the key component, the displacement during cracking still needs to be calculated, and the calculation of the bidirectional plate resistance is adopted in this section
And calculating the bending stiffness to obtain the cracking deflection. The cracking bending moment M1 can be converted into the surface load value by a table look-up method and converted
The formula is shown in the following formula 7.1:
M 1 ＝αql 2 (71)
where l is the span of the plate, q is the face load, and α is the bending moment calculation coefficient.
The bi-directional plate can be characterized by a rectangular thin plate with equal thickness mainly comprising bending, wherein the side length and the thickness of the rectangular thin plate are respectively a, b and h, the elastic modulus and the poisson ratio of the material are respectively E and mu, the displacement corresponding to the directions of coordinate axes x, y and z of the rectangular thin plate is respectively u, v and w, and the static equilibrium equation of the thin plate under the action of the surface distribution load p is known by elastic mechanics:
wherein D is the flexural rigidity of the panel,
when the plate vibrates freely, no additional load is applied to the plate, but according to the dynamic balance principle, the inertia force generated when the thin plate vibrates can be used as the additional load, and then the balance equation can be converted into:
wherein p and m represent the density and distribution quality of the plate, respectively.
With the above, the free vibration equation of the elastic sheet is
The method is a four-order homogeneous partial differential equation, can be solved by a method of separating variables, and is set as the solution form
w(x，y，t)＝W(x，y)q(t) (7.5)
Substituted into the above transformation to obtain two partial differential equations
Where ω is the natural frequency of the sheet.
Substituting boundary conditions, the vertical displacement and bending moment of the four-side simple support plate at the boundary are 0, so that the four-side simple support plate has
When x=0 or x=a, w=0,when y=0 or y=b, w=0, ++>
The vibration mode of the thin plate W (x, y) is obtained by solving
W in the above ij (x, y) is a vibration mode, and such a vibration mode represents a bending surface having i half-waves in the x direction and j half-waves in the y direction.
When i=1, j=1,
the natural vibration frequency at this time is
As shown in fig. 1 to 4, compared with the dynamic measurement test and the finite element modal analysis result, the vibration mode and the self-vibration frequency obtained by the analytic method are larger in second order error, the errors of the first order and the third order (the sixth order in the finite element analysis and the dynamic measurement) are smaller than 5%, and the correctness of the calculation formula of the flexural rigidity of the bidirectional plate is proved from the other aspect.
Working stage after cracking: after the bi-directional plate is cracked, the rigidity of the bi-directional plate is reduced, and as the number of cracks is gradually increased, the load-deflection curve of the bi-directional plate bears a nonlinear relation. But in this chapter it is simplified to a double-fold model and therefore only the final load (the load when the longitudinal bars yield) and deflection need to be determined.
In the full-scale static load test of the novel assembled integral bidirectional multi-ribbed superposed floor system, regular X-shaped cracks are generated when the floor slab is damaged, and meanwhile, the investigation conditions of domestic and foreign documents are referred to, and in this section, a limit balance method is adopted as a basis to analyze and calculate the working stage of the floor slab after cracking.
Fig. 5 is a schematic diagram of the novel assembled integral bidirectional multi-ribbed composite floor under the action of uniform load, and the whole structure is strictly centrosymmetric, so that the damage mode is distributed along the diagonal line in an X-shape, and basically accords with the damage condition in the test.
According to the virtual work principle, virtual displacement w (x, y) at any point under the action of the limit uniform load, the work done by external force and internal force is the same, and the expression of the work done by external force under the action of load is as follows:
wherein W is e And the virtual work is done by external force.
The work done by the internal force mainly considers the work done by the bending moment of the novel assembled integral bidirectional multi-ribbed composite floor, when the damage occurs under the action of limit load, the part formed by plastic hinges is larger, other parts are still in elastic deformation, the elastic deformation can be ignored, and the deformation of the plates is mainly concentrated in the area with smaller deformation near the plastic stranded wires assuming that each small plate is similar to a steel sheet, and the expression mode is as follows:
wherein m is x And m y The ultimate bending moment of each plastic strand in the x and y directions is per unit length.
The limit uniform load of the assembled integral bidirectional multi-ribbed composite floor slab can be calculated by combining 7.18 and 7.19 as follows:
and carrying l2=0, l3=0 and the failure load in the second chapter into the formula 7.20, so that the limit uniform load is 34.03kN/m < 2 >.
To better characterize the load-displacement curve and to investigate the relationship between the parameters, this section introduced yield load and ductility in a pseudo static test to calculate cracking load, yield load and limit load. The characteristic values of the load-displacement skeleton curve mainly comprise peak displacement delta m, peak load Pm, yield displacement delta y, yield load Py, elastic displacement delta e, elastic load Pe, limit displacement delta u and limit load Pu. The yield load Py, limit load Pu and corresponding yield displacement ay and limit displacement au can be determined in two ways:
1. equivalent area method. According to the point of the excessive maximum load as a horizontal peak line and the point of the excessive maximum load as a dividing line, the areas of the shadow parts are equal, namely A1=A2, as shown in fig. 6 (a), the displacement corresponding to the intersection point of the dividing line and the peak line is yield displacement deltay, the load corresponding to the yield displacement is yield load Py, in addition, the limit displacement deltau is the displacement corresponding to the load reduced to 0.85 times of the peak load, and the limit load Pu is 0.85 times of the peak load;
2. improved equivalent area method: according to the relevant rules of the ASTM E2126-11 standard, a bilinear model is formed by making oblique lines through an origin and forming a bilinear model with a horizontal straight line, so that the area of a shadow part is equal, namely a1=a2, see fig. 6 (b), at this time, the curve is called an equivalent energy elastoplastic curve, the displacement corresponding to the turning point of the curve is yield displacement deltay, the load corresponding to the horizontal straight line is yield load Py, the displacement corresponding to the tail end of the curve is limit displacement deltau, and the load on the skeleton curve corresponding to the limit displacement is limit load Pu. The method 2 not only can fully consider the stress condition of the test piece before the peak load as in the method 1, but also can consider the stress condition after the peak load at the same time, namely, the characteristic value of the skeleton curve is obtained according to the integral stress condition of the test piece.
The test result shows that the steel bar and the concrete are deformed in a coordinated manner, so that the accurate cracking bending moment is obtained by calculating the load when the steel bar strain reaches the concrete cracking strain. Meanwhile, according to the method b in fig. 7-7, the relation among the cracking load, the yield load and the limit load is obtained through programming calculation in matlab as shown in the following table:
TABLE 7-1 Key parameter relationship Table
As can be seen from the table, although the six groups of unidirectional plate members are different in size, the ratio of ultimate load to cracking load is relatively similar, and the ratio of yield load to cracking load is regular. Because the construction of the part with the biggest bending moment in the span is similar to that of DXB-1 and DXB-3, the average value of the two is taken, the ratio of the yield load to the cracking load is 3.08, and the ratio of the yield displacement to the cracking displacement is 4.97.
Therefore, the ratio of the rigidity of the key component of the assembled integral bidirectional multi-ribbed composite floor system after cracking to the rigidity of the key component of the assembled integral bidirectional multi-ribbed composite floor system in the elastic working stage is 0.50, the bending moment during cracking can be calculated according to the relation between the cracking load and the yield load, and meanwhile the deflection during yielding can be obtained according to the conversion of the rigidity ratio.
As can be seen from the comparison result of the double-broken line model and the test in the above figure 7, the error of the two is within 15%, and the effectiveness of the double-broken line model and the test is proved. However, the method also has certain limitations in that: (1) The stress stage is divided into two stages, namely a pre-cracking stage and a post-cracking stage, so that the yield load and the limit load are contained in the latter stage; (2) The nonlinear stage after cracking is simplified into a section of straight line, but the nonlinear stage is well matched with the test result. In summary, although the theoretical design method is simplified, the theoretical calculation of the novel assembled integral type bidirectional multi-ribbed superposed floor system can be guided to a certain extent.
It should be noted that the foregoing merely illustrates the technical idea of the present application and is not intended to limit the scope of the present application, and that a person skilled in the art may make several improvements and modifications without departing from the principles of the present application, which fall within the scope of the claims of the present application.
Claims (4)
1. A load-displacement relation estimation method for an assembled integral bidirectional multi-ribbed superposed floor system is characterized by comprising the following steps of: the method comprises the following steps:
working stage before cracking:
obtaining a cracking bending moment of the component, and calculating to obtain cracking deflection by a method for calculating the bending stiffness of the bidirectional plate; working stage after cracking:
wherein, the displacement after cracking is calculated by the following formula:
w 2 ＝(q 2 -q 1 )/q 1 βw 1
the load after cracking is calculated by the following formula:
wherein,,
q 1 the surface load is the surface load when cracking;
q 2 the surface load after cracking;
q is the maximum face load to reach the ultimate bearing capacity;
beta is the ratio of the rigidity after yielding to the rigidity before yielding, and 0.5 is taken;
l a 、l b the width of the floor in the horizontal direction;
m x is the ultimate bending moment per unit length of the plastic strand in the x direction.
2. The method for estimating the load-displacement relationship of the assembled integral type two-way multi-ribbed composite floor system according to claim 1, wherein the method comprises the following steps of: the displacement at cracking is calculated by the following formula:
w 1 ＝M 1 /D；
wherein,,
m1 is a cracking bending moment;
d is the flexural rigidity of the panel;
the cracking load is calculated by the following formula:
q 1 ＝M 1 /(αl 2 )
wherein:
alpha is the bending moment coefficient of the two-way plate;
e is an elastic mould of the concrete;
h is the thickness of the floor;
mu is the Poisson's ratio of the concrete;
l is the span of the plate.
3. The method for estimating the load-displacement relationship of the assembled integral type two-way multi-ribbed composite floor system according to claim 1, wherein the method comprises the following steps of: the displacement after cracking includes yield displacement and limit displacement.
4. The method for estimating the load-displacement relationship of the assembled integral type two-way multi-ribbed composite floor system according to claim 1, wherein the method comprises the following steps of: the post-cracking load includes yield load and limit load.
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| CN114491733A (en) * | 2021-12-28 | 2022-05-13 | 中国矿业大学 | Concrete floor bearing capacity calculation method considering beam-plate interaction |
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| CN104264782A (en) * | 2014-10-29 | 2015-01-07 | 中国建筑第八工程局有限公司 | Assembling integral pre-stress framework structure and construction method thereof |
| CN112464337A (en) * | 2020-11-20 | 2021-03-09 | 西安近代化学研究所 | Method for calculating bending dynamic resistance of simply-supported reinforced concrete beam under near-field explosion |
| CN113010941A (en) * | 2021-02-25 | 2021-06-22 | 东华理工大学 | Mechanical analysis measuring and calculating method for built-in thin-wall corrugated cylinder hollow floor |
| CN114491733A (en) * | 2021-12-28 | 2022-05-13 | 中国矿业大学 | Concrete floor bearing capacity calculation method considering beam-plate interaction |
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