CN112231791B - Preferred method for simply supported corrugated web-steel bottom plate combined box girder top plate thickness - Google Patents
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Abstract
The application discloses a preferred method for simply supporting the thickness of a corrugated web-steel bottom plate combined box girder top plate, which comprises the steps of firstly considering the corrugated steel web fold effect to obtain the vertical deformation potential energy of the combined box girder, further obtaining an elasticity control differential equation and boundary conditions of vertical bending of the structure by using an energy transformation method, and finely analyzing the mechanical properties of the combined box girder top plate (RC plate) and the steel bottom plate based on the elasticity control differential equation and boundary conditions. Furthermore, the thickness of the top plate (RC plate) of the structure is reasonably optimized according to the mechanical characteristics and the material properties of the combined box girder. The method has the advantages that the mechanical characteristics of the combined box girder are accurately analyzed, and the effectiveness of the method is further proved by finite element numerical simulation, so that the optimized corrugated web-steel bottom plate combined box girder is lighter, various structural diseases of a PC box girder bridge are avoided, and the spanning capacity of the PC box girder bridge is obviously increased. The method has clear mechanical concept and good application value, and provides a certain theoretical and technical support for the design of the combined structure.
Description
Technical Field
The invention relates to the technical field of structural engineering, in particular to a preferred method for simply supported corrugated web-steel bottom plate combined box girder top plate thickness.
Background
The defects of the mechanical and material properties of the Prestressed Concrete (PC) box girder bridge in operation all over the world in recent decades are gradually revealed, and the defects are mainly represented by the defects of the structural rigidity degradation of the bridge, the cracking of the girder body, the excessive downwarping of the midspan and the like, and the defects seriously affect the operation safety and the durability of the PC box girder bridge. Based on this, in 1975, french CB (CampenonBemard) company first proposed the idea of replacing the traditional PC box girder web with corrugated steel web, and finally built the first corrugated steel web PC composite box girder bridge in the world-the cogniac bridge in 1986. Compared with PC box girders, the dead weight of the box girder bridge is generally reduced by about 25%, the problem of light weight of a bridge structure is solved, and deformation of a concrete top plate and a concrete bottom plate due to creep, drying shrinkage, temperature effect and other factors is not restrained due to the corrugated steel web wrinkling effect, so that the prestress efficiency in a concrete slab is improved, and more than 70 seats exist in the corrugated steel web PC box girder bridge built and constructed in China nowadays.
In recent years, the recognition of bridge specialists in China on the combined box girder is new, and the traditional corrugated steel web combined box girder lower wing plate (RC plate) is replaced by a flat steel plate, so that a novel corrugated web-steel bottom plate combined structure is formed. Compared with the traditional PC box girder bridge, the dead weight of the novel combined box girder is reduced by nearly 50%, and the novel combined box girder has good anti-seismic performance, and effectively solves the problems of cracking or crushing of lower wing plates of the traditional combined box girder. Especially, the construction progress of the novel combined box girder is improved, and the mechanical and material properties of the structure are further optimized. The novel combined box girder has the advantages of light dead weight, stable stress performance, large spanning capacity and the like, and has the characteristics of large area of high intensity earthquake areas, wide distribution of collapsible loess and soft soil areas and the like in China, so that the novel combined box girder is more suitable for building the combined girder bridge. In recent years, the bridge is applied to Gansu province (Tai) to Zhongzhong (Chuan) high speed and the engineering of the interchange of the entrance and exit highways of Zhongchuan airports. However, based on the mechanical characteristics of the novel combined box girder, the thickness of the top plate of the combined structure can be further optimized, so that the structure is lighter, and the mechanical property of the structure is more excellent. Therefore, the research and the invention of the preferred method for simply supported corrugated web-steel bottom plate combined box girder top plate thickness have more theoretical significance and engineering practical value.
Disclosure of Invention
The technical problems to be solved are as follows: aiming at the problems, the invention provides a preferred method for simply supporting the thickness of the top plate of the corrugated web-steel bottom plate combined box girder, which comprehensively considers the mechanical characteristics and the material properties of the corrugated web-steel bottom plate combined box girder, and realizes that the novel combined structure is in a good operation and stress state through reasonable selection of the thickness of the top plate.
The technical scheme is as follows:
the preferred method for simply supporting the thickness of the corrugated web plate-steel bottom plate combined box girder top plate comprises the following steps:
based on the energy variation method, first a differential equation for w (z) is derived
W in (6) (z) is a sixth order derivative of w (z); w (w) (4) And (z) is a fourth order derivative of w (z).
Further, the following equation is obtained
Finally, the positive stress of the top plate is obtained
σ sa2 ＝-Eh 1 θ'+E(M 0 -h 1 ω s2 )U' (9)
Wherein:
z, y, x are the axial, vertical and transverse coordinates, respectively, through the centroid of the cross section of the composite box girder; w (z) is the vertical deflection of the combined box girder; θ (z) is the vertical rotation angle of the cross section of the box girder, and θ' (z) is the first derivative thereof; η is the solution coefficient of the eigenvalue with respect to w (z); ch is a hyperbolic cosine function; sh is a hyperbolic sine function; i is the moment of inertia of the combined box girder about the x axis; i 1 Is the top plate related x-axis moment of inertia; i 2 The moment of inertia is related to the x-axis of the bottom plate of the box girder; i G Inducing a moment of inertia about the x-axis for the upper and lower strakes for the shear effect; q y Is combined intoUniformly distributing force on the box girder; omega s2 The function of uneven distribution of upper wing plates of the combined box girder is obtained; u (z) is a longitudinal warping displacement difference function of the wing plate of the combined box girder caused by shearing effect, and U' (z) is a first derivative thereof; h is a 1 The height of the upper wing plate from the neutral axis; m is M 0 The shear warp stress self-balancing coefficient of the top and bottom plates of the combined box girder; e, E; g is Young's modulus and shear elasticity of the top plate of the combined box girder; g s Correcting the shear modulus for the corrugated steel web; a is that s The effective shearing area of the corrugated steel web is; c 1 ；c 2 ；c 3 ；c 4 ；c 5 ；c 6 The method is a constant coefficient and can be solved according to the related boundary conditions of the combined box girder.
As a preferable technical scheme of the invention, the normal stress of the simply supported boundary condition combined box girder top plate is solved according to the equation (9), the material properties of the top plate and the bottom plate are combined, and compared with the mechanical property of the steel bottom plate, the thickness t of the corrugated web-steel bottom plate combined box girder top plate is optimized 2 。
Based on the thickness t of the top plate of the combined box girder 2 By reasonable selection of the steel plate, the dead weight of the structure is further lightened, and the mechanical property of the corrugated web-steel bottom plate combined box girder is further improved.
As a preferable embodiment of the present invention, the b 1 ；b 2 Is half of the length of the cantilever plate and the upper wing plate of the combined box girder.
As a preferable embodiment of the present invention, the t 1 ；t 2 For the thickness (t) of the cantilever plate and the upper wing plate of the combined box girder 1 ＝t 2 )。
As a preferable embodiment of the present invention, the t 3 ；t w Is the thickness of the steel bottom plate and the corrugated steel web of the combined box girder.
As a preferable technical scheme of the invention, h is the height of the combined box girder.
The beneficial effects are that: compared with the prior art, the preferred method for simply supporting the thickness of the corrugated web-steel bottom plate combined box girder top plate has the following technical effects:
1. according to the method, the corrugated steel web wrinkling effect is considered, the vertical deformation potential energy of the corrugated web-steel bottom plate combined box girder is firstly obtained, then a novel combined box girder vertical bending elasticity control differential equation and boundary conditions are deduced by using an energy transformation method, and a refined analysis method for the mechanical properties of the simply supported combined box girder is obtained based on the novel combined box girder vertical bending elasticity control differential equation;
2. finally, the mechanical property analysis of the novel combined box girder top plate (RC plate) and the steel bottom plate and the material property thereof are taken as criteria, and the thickness (t 2 )。
3. Because the method has accurate mechanical analysis, the dead weight of the optimized novel combined box girder is further reduced, and the mechanical property of the novel combined box girder is more excellent.
4. The method has the advantages of firm mechanical foundation, clear concept and good application value, and is a beneficial supplement to the design theory of the existing corrugated web-steel bottom plate combined box girder.
5. The method comprehensively considers the mechanical characteristics and the material properties of the corrugated web plate-steel bottom plate combined box girder, and realizes that the novel combined structure is in a good operation and stress state through reasonable selection of the thickness of the top plate.
6. The method has the advantages that the mechanical characteristics of the combined box girder are accurately analyzed, and the effectiveness of the method is further proved by finite element numerical simulation, so that the optimized corrugated web-steel bottom plate combined box girder is lighter, various structural diseases of a PC box girder bridge are avoided, and the spanning capacity of the PC box girder bridge is obviously increased.
7. The method has clear mechanical concept and good application value, and provides a certain theoretical and technical support for the design of the combined structure.
Description of the drawings:
FIG. 1 is a cross section and a coordinate system diagram of a corrugated web-steel floor composite box girder in an embodiment of the present invention.
FIG. 2 is a diagram of boundary conditions and a coordinate system according to an embodiment of the present invention.
Figure 3 shows the form of the assembled box girder web corrugation in an example of the present invention.
FIG. 4 is a graph showing the stress values of the roof of the composite girder of the present invention.
FIG. 5 is a graph showing the stress values of the steel bottom plate of the composite box girder according to the present invention.
Detailed Description
The above-described aspects are further described below in conjunction with specific embodiments. It should be understood that these examples are illustrative of the invention and are not intended to limit the scope of the invention. The implementation conditions employed in the examples may be further adjusted according to the conditions of the specific construction and design units, and the implementation conditions not specified are generally those in routine experiments.
Example 1:
1. derivation of vertical bending differential equation and boundary condition of corrugated web-steel bottom plate combined box girder
1.1 mechanical parameter setting and structural deformation energy
For the corrugated web-steel bottom plate combined box girder shown in fig. 1, if the structural span is L, when the box structure is in a vertical symmetrical bending state, the vertical deflection of the combined box girder is w (z), the vertical corner of the section is theta (z), and the top plate b 1 A partial longitudinal displacement of u 1 (z), roof b 2 A partial longitudinal displacement of u 2 (z) and the longitudinal displacement of the bottom plate is u 3 (z). Namely, the wing plate displacement is the warp displacement of the combined box girder caused by the shearing force hysteresis effect and the uniform displacement M of the supposedly rigid section of the horizontal section 0 U (z), where U (z) is the maximum longitudinal displacement difference function of the wing plate caused by shearing effect, and y 1 ；y 2 The distance between the upper wing plate and the lower wing plate and the neutral axis can be expressed as:
top board b 1 Section (cantilever plate)
u 1 (z)＝M 0 U(z)-y 1 ω s1 U(z) (1)
Omega in s1 Is a non-uniform distribution function of the cantilever plates of the combined box girder. And is also provided withb 2 ≤|x|≤(b 1 +b 2 )。
Top board b 2 Section (Upper wing plate)
u 2 (z)＝M 0 U(z)-y 1 ω s2 U(z) (2)
Omega in s2 Is a novel uneven distribution function of the upper wing plate of the combined box girder. And is also provided with0≤x≤b 2 。
Lower wing plate (baseboard)
u 3 (z)＝M 0 U(z)-y 2 ω s2 U(z) (3)
The magnitude of the shear modulus of the corrugated steel web in the analysis is related to the geometry of the corrugations (as in FIG. 3), and thus the shear modulus G of the corrugated steel web s The correction formula is:
wherein: e (E) s ,υ s The elastic modulus and poisson ratio of the corrugated steel web material are as follows; and L is 1 ,L 2 ,L 3 Is the length of the corrugated steel web plate section, the length of the inclined plate section and the projection of the inclined plate section on the horizontal plane, as shown in figure 3.
Then, shearing warp stress
Top board b 1 The partial shear effect causes positive and shear stresses (cantilever plates)
Top board b 2 The partial shear effect causes positive and shear stresses (upper wing plate)
The shearing effect of the lower wing plate causes positive stress and shearing stress (bottom plate)
Self-balancing condition for introducing shearing hysteresis and warp stress
Wherein: a is that 1 ,A 2 ,A 3 The areas of the cantilever plate, the upper wing plate and the bottom plate of the combined box girder are respectively.
Based on this, it is possible to obtain:
wherein alpha is Es The conversion coefficient of the section of the steel bottom plate.
Then, taking into account the influence of elementary beam theory, i.e. -Ey 1 θ' (z) and-Ey 2 θ' (z), the total stress of the wing plates of the combined box girder is:
top board b 1 Section (cantilever plate)
σ sa1 (z)＝-Ey 1 θ'(z)+EM 0 U'(z)-Ey 1 ω s1 U'(z) (8)
Top board b 2 Section (Upper wing plate)
σ sa2 (z)＝-Ey 1 θ'(z)+EM 0 U'(z)-Ey 1 ω s2 U'(z) (9)
Lower wing plate (baseboard)
σ sa3 (z)＝-Ey 2 θ'(z)+EM 0 U'(z)-Ey 2 ω s2 U'(z) (10)
(1) Deformation potential energy of top plate and bottom plate
(2) Combined box girder shear strain energy
(3) Load potential energy of combined box girder
V＝V 1 +V T +V p (14)
Wherein: m is M z (z) generating a vertical rotational angle θ (z) for the beam segment ends about the x-axis bending moment; m is M j (z) bending moment about the x-axis generated by shear hysteresis effect of the top and bottom plates of the combined box girder; q (z), Q y (z) is the vertical shearing force of the beam section end and the vertical distribution force on the combined box beam; e, G is Young's modulus and shear modulus of elasticity of the roof material; a is that 1 ,A 2 ,A 3 For combining the box girder cantilever plate, the upper wing plate and the bottom plate area, and a=a 1 +A 2 +A 3 ；E s The elastic modulus of the corrugated steel web and steel bottom plate material is that of the corrugated steel web and steel bottom plate material; g s Correcting the shear modulus for the corrugated steel web; a is that s The effective shearing area of the corrugated steel web is; y is 1 ；y 2 The distance between the top plate and the bottom plate and the neutral axis is set; i is the moment of inertia of the composite box girder about the x-axis.
1.2 differential equation and boundary Condition for controlling corrugated web-Steel floor composite Box girder
From the variational principle δv=0, the combined box girder control differential equation and boundary conditions can be derived:
EIθ”(z)+EI 1 U”(z)+G s A s (w'(z)-θ(z))＝0 (15)
EI 1 θ”(z)+EI 2 U”(z)-GI G U(z) (16)
G s A s (w”(z)-θ'(z))+q y (z)＝0 (17)
wherein U "(z) is the second order derivative of U (z); θ "(z) is the second order derivative of θ (z); w "(z) is the second order derivative of w (z).
2. Solution of novel combination box control differential equation
From equations (15), (16) and (17), it is possible to obtain:
w in (6) (z) is a sixth order derivative of w (z); w (w) (4) And (z) is a fourth order derivative of w (z).
Equation (21) eigensolution form:
r 1,2 ＝±η；r 3,4,5,6 ＝0
then, the solution of equation (21) is
Also, θ (z) can be solved by equations (18) and (22)
From equations (16) and (23), U (z) can be solved as
3. Novel natural boundary condition of combined box girder
According to differential equation (18-20), the common boundary conditions of the novel combined box girder can be simplified as
(1) Simply supported novel combined box girder displacement and mechanical boundary condition
A. Uniform load
B. Concentrated load
For the simply supported novel combined box girder, if the stress of the span is concentrated force, the distance between the left and right adjacent boundaries of the concentrated force is L 1 And L 2 . As shown in FIG. 2, wherein l is the span length, w, of the composite box girder 1 (z 1 )，θ 1 (z 1 )，U 1 (z 1 ) Is z 1 A coordinate system; w (w) 2 (z 2 )，θ 2 (z 2 )，U 2 (z 2 ) Is z 2 And (5) a coordinate system. Then the k-point must also introduce the following continuous boundary conditions
4. Thickness (t) of corrugated web-steel bottom plate combined box girder top plate 2 ) Optimization
The invention comprehensively considers factors such as the folding effect, the shearing deformation and the shearing hysteresis effect of the combined box girder, and introduces the shearing hysteresis warp stress self-balancing condition. Then, carrying out refined analysis on the mechanical properties of the top plate and the bottom plate of the combined box girder, and optimizing the thickness (t 2 ). And the dead weight of the optimized novel combined box girder is further reduced, and the mechanical property is further reducedThe performance is more excellent. Therefore, the invention has more theoretical and engineering practical significance and has guiding effect on the design of the corrugated web-steel bottom plate combined box girder.
Note that: b 1 ；b 2 The lengths of the cantilever plate and the upper wing plate of the combined box girder are half of those of the cantilever plate and the upper wing plate of the combined box girder respectively; t is t 1 ；t 2 For the thickness (t) of the cantilever plate and the upper wing plate of the combined box girder 1 ＝t 2 )；t 3 ；t w The thickness of the steel bottom plate and the corrugated steel web of the combined box girder is the thickness; h is the height of the combined box girder.
Practical application and effect verification:
5 groups of corrugated web-steel bottom plate combined box girders are selected at present to concentrate force P k (z) =15×9800N, the material parameters and the geometric parameters of which are respectively: (1) The corrugated steel web and the steel bottom plate of the combined box girder are both made of high-quality Q390 type steel, the elastic modulus is 206Gpa, the Poisson ratio is 0.26, and the thickness of the corrugated steel web is t w =1.5 cm, beam height h=2.5m, and box beam top plate adopts C50 concrete, thickness is: first group t 1 ＝t 2 =0.3m (actual bridge), second group t 1 ＝t 2 =0.25m; third group t 1 ＝t 2 =0.2m; fourth group t 1 ＝t 2 =0.15m; fifth group t 1 ＝t 2 =0.1m. And the wing plate has a length b 1 ＝2.5m；b 2 =3m, steel bottom plate thickness t 3 =2cm. The web corrugation is as in FIG. 3, where L 1 ＝L 2 ＝43cm，L 3 The corrugated steel web and the upper and lower wing plates are connected by embedded connecting keys =37 cm. (2) The material and the section size of the novel combined box girder are the same as those of the combined box girder except the thickness of the top plate. Then according to the deduction formula, the mechanical property of the wing plate of the simple combined box is finely analyzed, and the thickness t of the top plate of the combined box girder is optimized based on the material properties and the mechanical characteristics of the top plate and the bottom plate 1 ；t 2 。
Table 1 simply supported corrugated web-steel floor composite box girder roof stress (L) 1 ＝L 2 ＝15m)
Table 2 simply supported corrugated web-steel floor composite box girder floor stress (L 1 ＝L 2 ＝15m)
Figure 4 combined box girder top plate stress value (t 1 ＝t 2 =0.3m), the combined box girder steel floor stress value (t 1 ＝t 2 ＝0.3m)。
Tables 1 and 2 and fig. 4 and 5 show that the top plate and the bottom plate of the corrugated web-steel bottom plate combined box girder are affected by shear hysteresis effect, and the normal stress distribution is uneven, so that the maximum stress action point (the intersection of the wing plate and the web) is more reasonable as an analysis basis;
according to the design specification, the strength design value of the C50 concrete is 22.4Mpa, the tensile strength design value and the compressive strength design value of the Q390 type steel are both 295Mpa, and the ratio of the tensile strength design value to the compressive strength design value is 13.17; the ratio of the stress values of the bottom plate to the top plate of the above 5 groups is respectively: 27.70;23.08;18.47;13.85;9.23. therefore, the mechanical properties of the fourth group of combined box girders are superior to those of the RC top plate and the steel bottom plate, namely the mechanical and material properties of the RC top plate and the steel bottom plate are fully utilized, but the combined box girders are considered to be provided with reinforcing steel bars, reserved protective layers and the like, and the third group of combined box girders are considered comprehensively to be the preferred items in the design, namely t 1 ＝t 2 ＝0.2m。
Based on actual conditions, the thickness of the top plate of the corrugated web-steel bottom plate combined box girder bridge is generally t 1 ＝t 2 =0.3m, then the present patent chooses that the bridge weight will be reduced by about 27% compared to it, which clearly shows the superiority of the present method. Therefore, the invention has important theoretical and engineering practical significance. And 5 groups of novel combined box girders are selected, and the finite element simulation further proves the effectiveness of the method.
The foregoing embodiments are merely illustrative of the technical concept and features of the present invention, and are not intended to limit the scope of the invention. All equivalent changes or modifications made according to the spirit of the main technical proposal of the invention should be covered in the protection scope of the invention.
Claims (2)
1. The preferred method for simply supporting the thickness of the corrugated web plate-steel bottom plate combined box girder top plate is characterized by comprising the following steps: based on the energy variation method, first a differential equation for w (z) is derived
Wherein: w (w) (6) (z) is a sixth order derivative of w (z); w (w) (4) (z) is the fourth order derivative of w (z);
further, the following equation is obtained
Finally, the positive stress of the top plate is obtained
σ sa2 ＝-Eh 1 θ'(z)+E(M 0 -h 1 ω s2 )U'(z) (9)
Wherein:
z, y, x are the axial, vertical and transverse coordinates, respectively, through the centroid of the cross section of the composite box girder; w (z) is the vertical deflection of the combined box girder; θ (z) is the vertical rotation angle of the cross section of the box girder, and θ' (z) is the first derivative thereof; η is the solution coefficient of the eigenvalue with respect to w (z); ch is a hyperbolic cosine function; sh is a hyperbolic sine function; i is the moment of inertia of the combined box girder about the x axis;I 1 is the top plate related x-axis moment of inertia; i 2 The moment of inertia is related to the x-axis of the bottom plate of the box girder; i G Inducing a moment of inertia about the x-axis for the upper and lower strakes for the shear effect; q y Uniformly distributing force on the combined box girder; omega s2 The function of uneven distribution of upper wing plates of the combined box girder is obtained; u (z) is a longitudinal warping displacement difference function of the wing plate of the combined box girder caused by shearing effect, and U' (z) is a first derivative thereof; h is a 1 The height of the upper wing plate from the neutral axis; m is M 0 The shear warp stress self-balancing coefficient of the top and bottom plates of the combined box girder; e, E; g is Young's modulus and shear elasticity of the top plate of the combined box girder; g s Correcting the shear modulus for the corrugated steel web; a is that s The effective shearing area of the corrugated steel web is; c 1 ；c 2 ；c 3 ；c 4 ；c 5 ；c 6 And solving according to the relevant boundary conditions of the combined box girder as a constant coefficient.
2. The preferred method of simply supported corrugated web-steel bottom plate combined box girder top plate thickness according to claim 1, wherein: solving the normal stress of the simply supported boundary condition combined box girder top plate according to the formula (9), combining the material properties of the top plate and the bottom plate, comparing the material properties with the mechanical properties of the steel bottom plate, and further optimizing the thickness t of the corrugated web plate-steel bottom plate combined box girder top plate 2 Based on the thickness t of the top plate of the simply supported corrugated web-steel bottom plate combined box girder 2 Is a reasonable choice of (c).
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| KR101869458B1 (en) * | 2017-07-27 | 2018-06-20 | 김태균 | Composite box girder using steel beam and construction method therefor |
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| RU2001800C1 (en) * | 1990-05-07 | 1993-10-30 | Грузинский технический университет | Frameless locomotive bogie |
| CN105046027A (en) * | 2015-09-01 | 2015-11-11 | 盐城工学院 | Optimized design method for section of multi-rib type T-shaped beam bridge |
| CN105243236A (en) * | 2015-11-05 | 2016-01-13 | 盐城工学院 | Box girder bridge section design optimization method |
| KR101869458B1 (en) * | 2017-07-27 | 2018-06-20 | 김태균 | Composite box girder using steel beam and construction method therefor |
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| CN112231791A (en) | 2021-01-15 |
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