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Simply supported beam live load calculation method based on Heaviside function
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A calculation method, simply supported beam technology, applied in electrical digital data processing, instruments, geometric CAD, etc., can solve the problems of low efficiency and lack of versatility of finite element calculation method
Active Publication Date: 2020-06-19
CHINA RAILWAY DESIGN GRP CO LTD
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However, for simply supported beam systems, the finite element calculation method is not efficient, and the specific calculation formula method lacks versatility
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[0120] The diagram of "Medium-Live Load" is attached Image 6 As shown in Table 1, the user can customize the live load field in the form of Table 1.
[0121] Table 1 Example of self-defined parameters of "medium-live load" live load field
[0122]
[0123] The meanings of the parameters in the table are:
[0124] Ni (i=, 0, 1, 2, ...) - cycle of the Nith group of parameters (Pi, Wi, dDi);
[0125] Pi(i=, 0, 1, 2, ...)——represents the size of the load, for concentrated loads, the unit is KN, for line loads, the unit is KN / m;
[0126] Wi(i=, 0, 1, 2,...)——represents the width of the load, for the concentrated load, its width is 0; for the line load, it is the actual width, and its unit is m;
[0127] dDi (i=, 0, 1, 2, ...) - the distance between each load, the unit is m;
[0128] From attached Im...
Embodiment 2
[0141] Railway "Medium-Live Load" (attached Image 6 ) under the action of double-hole heavy load calculation results of simply supported beam piers.
[0142] Since midas cannot extract the calculation results of double-hole heavy load, for the calculation of double-hole heavy load, the finite element software "Wolong" self-compiled by China Railway Engineering Corporation was used for calculation and comparison.
[0143] R of the simply supported beam under the action of "medium-live load" 1 ~R 4 The complete general formula of reaction force value is the same as embodiment 1.
[0144] For double-hole heavy load, the criterion max{R 2 +R3 , R 1 +R 4}Find the position X of the load starting point at this time k . Then substitute back into R 1 ~R 4 The general complete expression of R 1 ~R 4 value. Double hole heavy load is R 2 +R 3 value.
[0145] The test condition is L 1 =L 2 = 32.7m, a 1 =a 2 =a 3 =a 4 = 0.35m. attached Figure 10 It is the calculatio...
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Abstract
The invention provides a simply supported beam live load calculation method based on a Heaviside function, and relates to the field of transportation bridge engineering. The method mainly comprises the following steps: step A, constructing a live load field; step B, customizing live load by a user; step C, splitting the live load into three independent loads: a live load and a live load; step D, R1-R4 expressions represented by a Heaviside function are introduced; step E, constructing universal and complete expressions R1 to R4 of the self-defined live load; step F, determining a criterion; step G, solving an extreme value problem by adopting a bubbling method according to the criterion and solving a loading position xk of the extreme value problem; and step H, solving final reaction values R1 to R4. By the adoption of the method and system, calculation of simply supported beam live load loading can be conducted according to different types of live load types such as railways, highways, municipal administration and light rails in the transportation field, the loading result is directly obtained through one set of system, calculation does not need to be conducted according to different types, and the calculation efficiency is improved on the whole.
Description
technical field [0001] The invention relates to the technical field of bridge engineering in the transportation industry, in particular to a method for calculating live load loading of a simply supported beam based on a Heaviside function. Background technique [0002] In modern bridge structures, live loads account for a large proportion of all loads. Therefore, accurate and fast calculation of external force effects caused by live loads is a prerequisite for bridge structure design. [0003] For different industries such as railways, highways, subways, municipalities, etc., the types of train loads vary widely. In the same industry such as the railway industry, due to the different types of locomotives, live loads such as ZK, ZC, and ZH will also be derived. In the existing design methods In the process, calculation formulas or finite element calculations are usually used for different types of live loads. However, for simply supported beam systems, the finite element cal...
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