CN110258287B - Design method for hogging moment area of steel-concrete combined continuous beam - Google Patents
Design method for hogging moment area of steel-concrete combined continuous beam Download PDFInfo
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- E—FIXED CONSTRUCTIONS
- E01—CONSTRUCTION OF ROADS, RAILWAYS, OR BRIDGES
- E01D—CONSTRUCTION OF BRIDGES, ELEVATED ROADWAYS OR VIADUCTS; ASSEMBLY OF BRIDGES
- E01D2/00—Bridges characterised by the cross-section of their bearing spanning structure
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Abstract
The invention discloses a design method for a hogging moment area of a steel-concrete combined continuous beam, which comprises the following steps of firstly calculating a general section inertia moment I and a fulcrum hogging moment area section inertia moment I' of a combined beam according to the section size of the combined beam and the thickness of bottom plate concrete in the hogging moment area; establishing a continuous beam calculation model with the full-bridge section inertia moment I, and calculating the maximum mid-span positive bending moment M under the action of constant loadmaxMaximum hogging moment M of fulcrummin(ii) a Solving an equation F (lambda) =0, and calculating to obtain lambda; and calculating the length L 'of the slab concrete section in the hogging moment zone of the composite beam according to the L' = lambda L, and finishing the design of the hogging moment zone. The hogging moment area length of the steel-concrete combined continuous beam deduced based on the structural mechanics method is used as the hogging moment area bottom plate concrete section length, the hogging moment area design of the steel-concrete combined continuous beam can be completed quickly, the design method overcomes the defects of large subjective randomness and repeated trial calculation in engineering design, and has a series of advantages of clear mechanical concept, strong universality and the like.
Description
Technical Field
The invention relates to a bridge engineering technology, in particular to a design method for a hogging moment area of a steel-concrete combined continuous beam.
Background
Steel concrete composite structures are bridges of another important structural form following steel structures and concrete structures. The bridge has the advantages of the two, and provides a new choice for solving special bridges with ultrahigh, large span, heavy load and complex structures.
The bridge deck slab in the fulcrum hogging moment area of the steel-concrete combined continuous beam is inevitably in a tension state, so that concrete is easy to crack, and the working performance and the service life of the steel-concrete combined continuous beam are further influenced. In the current engineering, a double-recombination technology is widely adopted to improve the stress performance of the hogging moment area of the steel-concrete combined continuous beam. The double recombination effect means that the upper flange and the lower flange are combined by concrete and steel beams to form a combined structure bridge with a common stress on the whole section, the concrete of the lower flange is generally arranged in the range of a hogging moment area of a middle pivot, as shown in figures 1.1-1.3, figure 1.1 is a vertical arrangement diagram of a steel-concrete combined continuous beam adopting a double recombination technology, and figures 1.2 and 1.3 are structural schematic diagrams of a cross-middle section and a pier top section respectively.
The concrete is poured on the bottom plate of the hogging moment area of the steel-concrete combined continuous beam, so that the cracking of the bridge deck in the hogging moment area can be effectively avoided, and the buckling of the bottom steel plate can be prevented. However, how to determine the length of the bottom plate concrete segment in the hogging moment area does not have a method which can be used at present, so that the main effect is large. In engineering design, a finite element model of the steel-concrete combined continuous beam is generally established, and the design of the hogging moment area is completed by repeatedly trial calculation and continuously adjusting the cross section. The trial calculation is not only complicated, but also has strong subjective randomness and no universality for different projects.
Disclosure of Invention
The invention aims to provide a more scientific and simple design method for a hogging moment area of a steel-concrete combined continuous beam.
In order to achieve the purpose, the invention can adopt the following technical scheme:
the invention relates to a design method for a hogging moment area of a steel-concrete combined continuous beam, which comprises the following specific steps of:
firstly, calculating a general section inertia moment I and a fulcrum hogging moment zone section inertia moment I' of the steel-concrete combined continuous beam according to the section size of the steel-concrete combined continuous beam and the thickness of the bottom plate concrete in the simulated hogging moment zone, and setting:
μ=I/ I’ (1)；
secondly, establishing a continuous beam calculation model with the full-bridge section moment of inertia I, and calculating the maximum mid-span positive bending moment M under the action of constant load (mainly comprising dead weight and secondary load) based on a structural mechanics methodmaxMaximum hogging moment M of fulcrumminSetting:
m=Mmin/Mmax (2)；
thirdly, solving the equation F (lambda) =0, calculating to obtain lambda,
wherein the content of the first and second substances,
；
fourthly, calculating the length L 'of the hogging moment zone bottom plate concrete segment of the steel-concrete combined continuous beam according to the condition that L' = lambda L, and finishing the design of the hogging moment zone bottom plate concrete segment; wherein L is the span length of the single hole of the steel-concrete combined continuous beam.
The thickness of the bottom plate concrete in the hogging moment area of the steel-concrete combined continuous beam is 20-80 cm.
The value of the root λ of the equation F (λ) =0 is in the range of 0 to 1 (excluding 0 and 1).
The hogging moment area length of the steel-concrete combined continuous beam deduced based on the structural mechanics method is used as the hogging moment area bottom plate concrete section length, and the hogging moment area design of the steel-concrete combined continuous beam can be completed quickly.
Compared with the existing design method, the method has the advantages that:
1. the design derivation process is based on a structural mechanics method, and the concept is clear;
2. repeated trial calculation and section adjustment are not needed, and the practicability is high;
3. the universality is strong for different steel-concrete combined continuous beams.
In conclusion, the design method for the hogging moment area of the steel-concrete combined continuous beam, provided by the invention, can overcome the defects of large subjective randomness and repeated trial calculation and section adjustment in engineering design, and has a series of advantages of clear mechanical concept, strong universality and the like.
Drawings
Fig. 1.1 is a schematic diagram of a prior steel-concrete combined continuous beam adopting a double combining technology.
Fig. 1.2-1.3 are schematic cross-sectional views of a mid-span cross section and a fulcrum cross section of the steel-concrete combined continuous beam adopting a double-recombination technology respectively.
2.1-2.4 are schematic diagrams of a 2xL two-span steel-concrete combined continuous bridge.
Fig. 3.1 is a load diagram of a 2 × L two-span steel-concrete composite continuous beam bridge.
Figure 3.2 is a graphical representation of the bending moment of 1/2 across a steel concrete composite continuous beam.
FIG. 4.1 is a load diagram of a 2XL two-span reinforced concrete combined continuous beam in the embodiment of the invention.
FIG. 4.2 is a bending moment diagram of a 2XL two-span reinforced concrete combined continuous beam in the embodiment of the invention.
FIG. 4.3 is a graphical representation of the section stiffness of a 2 × L two-span steel-concrete composite continuous beam in the embodiment of the invention.
Fig. 5.1 and 5.2 are a load graph and a bending moment graph of the 3 x 50m steel-concrete combined continuous beam in the embodiment of the invention.
Detailed Description
The following detailed description of the design method of the present invention will be made with reference to the accompanying drawings and specific examples, but the present invention is not limited to the following examples. The design method provided by the invention has applicability to multi-span steel-concrete combined continuous beams and steel-concrete combined continuous beams with different spans.
Firstly, the principle of the design method of the invention is deduced and explained with the attached drawings.
For highway bridges, the proportion of dead load to total load is more than 70%, so the bending moment of the steel-concrete combined continuous beam is basically determined by the dead load uniformly distributed along the bridge span.
For a 2xL two-span steel-concrete combined continuous beam bridge, uniformly distributed constant loads q act on the bridge, as shown in figure 2.1, the span-middle general section, the fulcrum section 1 (the concrete bridge deck is not cracked) and the fulcrum section 2 (the concrete bridge deck is cracked and quits working) of the bridge are respectively shown in figures 2.2-2.3.
Calculating to obtain the inertia moment I of the general section and the inertia moment I' of the fulcrum hogging moment section (fulcrum section 2), and setting
μ=I/ I’；
Adopting a structural mechanics method to establish a calculation model without considering the cracking of the bridge deck slab in the hogging moment area of the steel-concrete combined continuous beam, wherein the total section inertia moment of the steel-concrete combined continuous beam adopts a general section inertia moment I as shown in figures 3.1 and 3.2 (wherein
Is the centroid of the figure). Based on a hyperstatic structure displacement method, the maximum mid-span positive bending moment M can be quickly obtainedmaxMaximum hogging moment M of fulcrummin. Wherein L 'is the length of the hogging moment zone, and the lambda = L'/L.
As shown in fig. 4.1 to 4.3, it is easy to know from the knowledge of structural mechanics that the bending moment diagram curve abce is a quadratic parabola. To simplify the calculation, the area of the triangle cd 'e' is used instead of the area of the quadratic parabola cde, and the difference between the areas is about 9%. Trial calculations show that this approximation only affects the final calculation by around 1%.
As can be seen from the reference "area method of bending moment diagram for calculating structural displacement" and its application (grand wen university schooled. 2002), the sum of the static moment of 1/2 bending moment diagram on the a support divided by the corresponding section stiffness is equal to 0, that is, the following is satisfied:
wherein E isModulus of elasticity, SabcIs the area of the bending moment diagram of the arcuate portion of abc, Scd’e’The area of the cd 'e' triangle part bending moment diagram.
According to the structural mechanics diagram multiplication, the above formula is:
further simplification results in:
mixing mu = I/I', M = Mmin/Mmaxλ = L'/L substituting the above formula, one can obtain:
order function
Where μ and m are both known numbers and λ is the number to be solved.
By solving the equation F (λ) =0, λ can be calculated.
And setting the length of the bottom plate concrete section in the hogging moment area of the steel-concrete combined continuous beam to be equal to the length of the hogging moment area, so as to determine the length L' = lambda L of the bottom plate concrete section in the hogging moment area of the steel-concrete combined continuous beam.
Secondly, the following describes the specific design method of the present invention in detail with reference to a specific example.
The method is adopted for designing the hogging moment area for a certain 3 x 50m steel-concrete combined continuous beam.
Firstly, the section size of the steel-concrete combined continuous beam and the thickness of the bottom plate concrete in the hogging moment area are determined. The thickness of the bottom plate concrete in the hogging moment area is 20-80 cm generally, and the thickness of the bottom plate concrete in the hogging moment area is determined to be 50cm in the design.
The bending moment of inertia I =0.8666m of the midspan general section is calculated by adopting a conversion section method4And bending moment of inertia I' =0.6591 m of hogging moment section4(the bending moment of inertia of the section of the composite beam is generally calculated by adopting a conversion section method, so the calculation methods of I and I 'are conventional methods in the industry), wherein the bending moment of inertia of the section of the fulcrum hogging moment of inertia I' is obtained by considering the cracking of the concrete bridge deck and considering the section moment of inertia of the box chamber of the bottom plate concrete:
μ=I/ I’=1.31
and secondly, establishing a calculation model of the steel-concrete combined continuous beam, wherein the inertia moments of the sections of the full bridge are uniformly I, as shown in fig. 5.1 and 5.2. Wherein the self-weight load q1=131.9kN/m, and the secondary load q1=58.6 kN/m. Calculating to obtain the maximum mid-span positive bending moment M under the action of a common constant load q = q1+ q2=190.5 kN/M based on a structural mechanics methodmax=38097kN M and maximum hogging moment M of fulcrummin=47614kN · m, yielding:
m=Mmin/Mmax=1.25
and thirdly, bringing the values of mu and m into formula (3) to obtain:
wherein, L is the span of the steel-concrete combined continuous beam, namely L =50m, L 'is the length of the hogging moment zone, and λ = L'/L.
Solving the equation F (λ) =0, and λ =0.24 is calculated.
And fourthly, setting the length of the hogging moment zone bottom plate concrete section of the steel-concrete combined continuous beam to be L ', and finishing the design of the hogging moment zone bottom plate concrete section according to the condition that L' = lambda L =0.24 multiplied by 50=12.0 m.
In order to compare the calculation results of the method, a rod system finite element model of the embodiment is established by adopting universal finite element software Midas/civil 2019, and the length of the bottom plate concrete section in the hogging moment region is finally determined to be 11.0m through repeated trial calculation, which is more consistent with the result obtained by the method.
From the calculation process and the result, the length of the floor concrete section in the hogging moment area of the steel-concrete combined continuous beam is calculated and determined by the method, the whole process is completed only by manual calculation, a complex bridge finite element model is not required to be established by calculation software, the thickness of the floor concrete is not required to be repeatedly calculated and adjusted, and the method has the advantages of clear mechanical concept, simplicity and convenience in operation, strong practicability and the like.
Claims (3)
1. A design method for a hogging moment area of a steel-concrete combined continuous beam is characterized by comprising the following steps of: comprises the following steps:
step one, calculating a mid-span section inertia moment I and a fulcrum hogging moment zone section inertia moment I' of the steel-concrete combined continuous beam according to the section size of the steel-concrete combined continuous beam and the thickness of the bottom plate concrete in the simulated hogging moment zone, and setting:
μ=I/ I’ (1)；
secondly, establishing a continuous beam calculation model with the full-bridge section inertia moment I, and calculating the maximum mid-span positive bending moment M under the action of constant load based on a structural mechanics methodmaxMaximum hogging moment M of fulcrumminSetting:
m=Mmin/Mmax (2)；
thirdly, solving the equation F (lambda) =0, calculating to obtain lambda,
wherein the content of the first and second substances,
(3)；
fourthly, calculating the length L 'of the hogging moment zone bottom plate concrete segment of the steel-concrete combined continuous beam according to the condition that L' = lambda L, and finishing the design of the hogging moment zone bottom plate concrete segment; wherein L is the span length of the single hole of the steel-concrete combined continuous beam.
2. The design method for the hogging moment area of the steel-concrete composite continuous beam as claimed in claim 1, wherein: the thickness of the bottom plate concrete in the hogging moment area of the steel-concrete combined continuous beam is 20-80 cm.
3. The design method for the hogging moment area of the steel-concrete composite continuous beam as claimed in claim 1, wherein: the value range of the root lambda of the equation F (lambda) =0 is 0-1.
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| CN204570445U (en) * | 2015-03-17 | 2015-08-19 | 广西交通科学研究院 | Bottom flange arranges two combination continuous beams of concrete filled steel tube |
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