The constructive solution and calculation of elements…

THE CONSTRUCTIVE SOLUTION AND CALCULATION OF ELEMENTS OF THE UNIFIED MODULE OF THE MOBILE BRIDGE OVERCROSSING Summary. In the article the construction of a modular mobile overcrossing is offered. Calculation of its constructive elements is performed and the optimum length of one module is determined. The purpose is the development of the technique and calculation for the new construction of a mobile bridge overcrossing intended for reduction of traffic jams. Methods: The methods uses are mathematical analysis, method of finite elements, method of finite differences, and analytical method of relocation. Dependencies for determination of the optimum length of the module of bridge overcrossing are identified. The calculation of the constructive-orthotropic plate for the carriageway of the bridge overcrossing using numerical methods of finite differences and finite elements is performed; the reliability of results is confirmed with coincidence of deflection values. The solution matrix of the method of finite differences developed in this work allows calculation of arbitrary plates with a wide variety of geometrical sizes, and also for different values of flexural stiffness properties of the plate and reinforcing elements. The calculation of the spatial frame of the bridge overcrossing is performed by the precise analytical method of relocation taking into account the bend and torsion of its elements.


INTRODUCTION
In the conditions of intensive automobile traffic there are traffic jams on roads, including in twofold and threefold crossroads.
In these cases, for jam elimination, various methods of traffic regulation as well as construction of capital overcrossings of various heights and configurations are applied in the plan.
A distinctive feature of the offered bridge overpass is its mobility is the conveyance on own chassis by means of the automobile trailer or using freight vehicles. Quick assembling and disassembling at the place of its installation is made possible through the use of unified collapsible modules and modes forfixing them between each other and on the ground base. It provides immediate delivery to necessary sites with autojams, repair sites of municipal underground networks or sites with infrastructure damage caused by various emergencies [1].
We offer the construction of the mobile overcrossing, which can be quickly assembled on a crossroad during rush hours, during any public actions or emergency events. The mobile overcrossing consists of horizontal modules equipped with the wheel course and bracing jacks. In necessary cases modules are transported to the crossroad and connected among themselves by means of holders forming one construction. At the same time bracing jacks lean on the base. Mobile overcrossing is 60 A. Kadyrov, K. Balabekova, A. Ganyukov, S. Akhmediyev different from military bridge layers in having to satisfy traffic rules: passing height under them is more than 4,5 m and transport strip width in one direction not less than 3,5 m.
The mobile overcrossing has two main modules: sloping (Fig. 1a) and horizontal (Fig. 1b). The basic constructive elements of the overcrossing are: 1 -barrier; 2 -plate; 3 -support; 4wheel engine; 5 -support and the mechanism of its lifting up/down.
A patent is received for the offered construction of the mobile overcrossing. Maximum travel speed for this design is 20 km / h. The maximum mass of vehicles corresponds to the movement of passenger cars and mediumfreight vehicles (with a total loaded mass of not more than 4 tons).

METHODS
The assembled construction allows driving of a part of autotransport over the perpendicular road, and its can be used at various crossroads since its sizes are regulated by the number of modules (Fig. 2). During projection of the mobile overcrossing, at the first stage, there were two tasks: -determination of the length of one module and the number of modules in the overcrossing of fixed length with conditions of retaining the size and geometry of the road as well as minimization of the weight of the metal construction; -calculation of the main (rectilinear) module for construction and loss of equilibrium.

RESULTS
For the solution of the first task it is assumed that the weight of the module is proportional to its length x, to the quantity of supports n at one support with wheel engine q; then, the total weight G is determined as follows: , The constructive solution and calculation of elements… 61 where k is the value of weight of the overcrossing per one meter of length, N/m; L is length of the overcrossing, m; n is number of supports; q is weight of one support, N; x L is number of modules.
The weight derivatives longwise of the overcrossing are presented as follows: The critical point (minimax point) at G ' = 0 k Lnq As ' ' G is greater than zero the point kp x determines the optimum length of one module from the condition of minimization of total load of the overcrossing. For example, for the overcrossing of 30 m length with 4 supports on each module, each weighing 1,5·10 4 N, and weight 3·10 4 N for one running meter of the construction, the optimum length will be equal to the following: When calculating the bearing construction (the second task) the oriented module was chosen orthogonally, which consists of the space frame having four vertical posts at the edges, two longitudinal beams, and seven cross beams, which are completely made of metal.
On the surface of the frame the steel flooring for the carriageway with the supporting longitudinal and cross edges is placed.
In the conditions of space work of load-bearing constructions of the frame when its elements are subjected to multi-axial stress in the form of noncentral compression, bend, and torsion, compound cross sections of posts, and longitudinal and cross beams, consisting of a thin-wall pipe, framed with four equilateral angles, are constructively appointed. Geometrical lengths of frame elements are appointed taking into account the compliance with requirements of traffic organization and norms of the road automotive industry.
Load-bearing constructions of the frame for ensuring space rigidity and stability are untied by longitudinal and transversal binding constructions. The dynamic effect because of transport driving is considered by introduction of the dynamic coefficient of impact appointed by means of experimental expert method. (Kd=1,3).
For providing conditions of durability, rigidity, and stability of the bearing elements of the unified module the calculation of carriageway plate and elements of the space frame on the vertical useful load according to Euronorm requirements is made [2]. Let's present the calculation of the module in the following sequence: The rectangular plate of size The calculation for the purpose of identification of power condition of the plate is carried out using numerical methods of finite differences and finite elements as a resilient non-isotropic plate [3,4]. Boundary conditions are jamming the plate along its outline.
Calculation using the method of finite differences (MFD) was carried out based on thickness of the grid ( is determined and a check for durability of the plate is performed: The System of the Simple Algebraic Equations (SSAE), based on MFD, has the representation as follows: where w  is vector of unknown node movements; p R  is vector of the free members considering the loading acting on the plate; A is square matrix of order n. This matrix, in general, is given in table 1.   Calculation of the frame consisting of vertical posts, longitudinal and cross beams (crossbars) is performed using analytical method of movements [5][6]. The calculated scheme of the frame taking into account a double symmetry is given in Fig. 4.
where A is square matrix of the 11 th order (in general, it is given in table 2) The total number of unknown angular and linear movements of four nodes of the frame (A,B,C,D) is equal to eleven ( where ) ,.....

DISSCUSION
After calculation of unknown node movements the calculated epure is constructed by the formula:   Table 2 Matrix «А» and vector p R  Realization of durability and stability conditions of the space frame elements was made according to the theory of strength of materials [11][12][13][14][15] as the constructions working for the composite resistance (noncentral compression, bend, and torsion).
is coefficient of the longitudinal bending; c) check of stability of the whole post from the plane of action of the moment of M= where Q is transversal force, av R is 130МPа: calculated resistance for cross-section.
The solutions for equations (7,9) were obtained by means of PC with use of the standard Matcad program.

CONCLUSION
1. The construction of the mobile overcrossing is proposed, which allows solving the problem of automobile jams on roads. 2. In this work the effectiveness of calculation for the constructive-orthotropic plate of the carriageway of bridge movement is shown using numerical methods of finite differences and finite elements; reliability of results is confirmed with concurrence of deflection values. 3. The accepted concrete geometrical and physical-mechanical characteristics of load-bearing constructions and the supporting edges of steel flooring (plate) with large drift provide their durability. 4. The accepted thickness of sheet flooring, equal to 20 mm, or the corresponding load-bearing frames of the plate provide a high rigidity to the carriageway of bridge movement as per requirements of autobridge building norms. 5. The obtained matrix based on the method of finite differences in a general view (with thickness of grid ).  Table 1 allows calculation of the arbitrary plates with a wide variety of geometrical sizes in the plan using thickness as well as various values of flexural rigidities of the plate and the elements supporting it. 6. The calculation of the space frame of bridge movement is performed on the main vertical loadings (useful load) by means of analytical method of movements taking into account bending