# FORECASTING THE TECHNICAL RESOURCE OF THE MECHANICAL AND CIVIL BUILDING STRUCTURE

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1 International Journal of Civil Engineering and Technology (IJCIET) Volume 7, Issue 3, May June 26, pp. 73 8, Article ID: IJCIET_7_3_7 Available online at Journal Impact Factor (26): (Calculated by GISI) ISS Print: and ISS Online: IAEME Publication FORECASTIG THE TECHICAL RESOURCE OF THE MECHAICAL AD CIVIL BUILDIG STRUCTURE ikolay Ivanov Petrov Department MEMETE, Faculty of Engineering and Pedagogy of Sliven Technical University of Sofia, Bulgaria, European Union Ventsislav Panev Dimitrov Department MEMETE, Faculty of Engineering and Pedagogy of Sliven Technical University of Sofia, Bulgaria, European Union ABSTRACT On the basis of the Axiom about the Reliability of the Mechanical and Civil Building Structure (MCBS) is displayed according to the function of the crash of the MCBS in terms of the critical number of cyclic stresses loads, until the destruction of the individual elements. Created and analyzed a mathematical model of kinetic diagram of the fatigue destruction KDFD, through a system of differential equations. Theoretically investigated is the current reliability of the components of the MCBS, built by means of CAD system TopSolid'Design until a mean time between failures (Technical Resource T R ) for the entire MCBS. Catastrophic increase stemming cracks and microfractures, is examined in the prerequisite MCBS consist of an unlimited number of functional elements. Formulated a fundamental dependence manifested criteria of parametric reliability defined by the presence of microfractures - as Cyclical Reliability Criterion (CRC) of Petrov - Dimitrov for Technical Resource (T R ) of Mechanical and Civil Building Structure (MCBS). The criterion takes into account the efficiency of the MCBS in the presence of a crack and is based on the mechanics of destruction at the stage of development of the crack. Key words: Mean time between failures (technical resource T R ), Cyclical Reliability Criterion (CRC), Crash Function, Microfractures, Kinetic Diagram of the Fatigue Destruction KDFD, CAD system Cite this Article: ikolay Ivanov Petrov and Ventsislav Panev Dimitrov, Forecasting the Technical Resource of the Mechanical and Civil Building Structure, International Journal of Civil Engineering and Technology, 7(3), 26, pp

3 Forecasting the Technical Resource of the Mechanical and Civil Building Structure Figure Typical examples of metal building structures [, 2, 3] df () In an unsustainable situation when the load becomes critical disturbing condition for mechanical equilibrium and crack starts moving constantly. The starting point of this condition is called critical (disastrous) state of the element of MCBS, as a result of the presence of a crack with a critical length l cr. In the next moment crack can spread even with decreasing load. In this case, the inequality [7]: df (2) In practice is unacceptable passage of crack in a fragile situation. (2) This leads to complete exhaustion of the bearing capacity of the structure, i.e. catastrophic destruction. Crack resistant limit of the material in a device, system or structure is referred to as a continuous whole set of values of the coefficient of the intensity of the voltage across the range of the length of the crack l. In this sense, the process of destruction of the MCBS in which there is the presence of cracks is a two stage. The first stage is characterized by stable growth of the crack until it reaches a critical value l cr. The second stage is associated with steeply increase the length of the microfracture l and reach demolition of MCBS. The ratio of the length of these stages is determined by the properties of the structural material

4 ikolay Ivanov Petrov and Ventsislav Panev Dimitrov Figure 2 Consoles Cracks: a) stable condition, b) development According to the European Union standards, the maintenance of working capacity of subsystems (elements) of the MCBS in their technical operations (То) shall be presented as a process, formed by their removal from the order status (reach and replacing them with spare subsystems. The process of Technical Element (T E ) can be seen as the removal of technical resource elements of MCBS and performing several recovery process through repairs (ТR) and major repairs (MR). This process is shown in Fig. 3: Figure 3 Model of repair cycles (MR and TR) ranging T RBP (Resource between Repairs) between two MR of MCBS. The total number of refunds shall be equal to the number of subsystems in the MCBS. The statistical characteristics of the overall process may be determined, if known the statistical characteristics of the intervals of time, making the process of exploitation and recovery [8]. Time intervals between events current and major 76

5 Forecasting the Technical Resource of the Mechanical and Civil Building Structure repairs represent a time for "technical" (training) of the various subsystems of the MCBS. The requested resource T RBR between MR (i-in number) of Fig. 3 and technical resource by the end of the exploitation T REE of the MCBS shall be determined in accordance with the literature [6, 8]: T RBR Topt P RO ( t) dt (3) T PMP TREE PRO( t) dt (4) - P RO (t) - the probability of reliable operation of MCBS in the interval between the repairing; - T opt - optimal time for performing MR 2 of the construction. Therefore, a description of the cumulative process of the current reliability of MCBS is necessary to create a mathematical model of exit from the operational condition of the individual subsystems (elements) in a relevant number per CL. In the mechanics of destruction of MCBS (mechanics of cracks resistance) as a basic parameter using the ratio of intensity of tensions K SI (mechanical stress). Under K SI is understood relative increase of the maximum mechanical stress at the tips of cracks. This ratio takes into account the size and shape on elements of MCBS the length of cracks l and the value of the nominal voltages σ H i.e. K SI. f ( l, B) H The process of destruction of the elements of the MCBS is referred to as fatigue []. The regularities and increased fatigue of material with the appropriate for fatigue cracks. It was therefore examined the rate of increase of the fatigue of the elements of V F from MCBS defined as [4, ]: V F d (6) - l - the length of the crack; - - the number of elements of the CL in the MCBS. The graphical representation of the dependence of the rate of growth of fatigue V F parameters of the destruction of the elements of MCBS (primarily the maximum value of the ratio of intensity of tensions K SImax ) is called kinetic diagram of the fatigue destruction KDFD. KDFD type, built in a logarithmic scale (on the abscissa axis lgk SImax, ordinate lgv F ) is shown in Figure 4. It is necessary to note that the process of development of cracks in the individual elements of the MCBS, it is possible to terminate by carrying out mechanical operations with them (drilling, milling, heat treatment, etc.) [7]. this is of course subject to other research. This study is dedicated to creating a mathematical model of mide and end part of KDFD (area B and area C). (5) 77

6 ikolay Ivanov Petrov and Ventsislav Panev Dimitrov Figure 4 Kinetic Diagram of the Fatigue Destruction KDFD for destruction of the elements of MCBS [4]: A - Area of generation of fatigue (F); B - zone of growth of the F; C - area of the approaching destruction of the material elements of MCBS I Area below the fatigue, II - Area of limited endurance, III - Zone fatigue destruction 3. MATHEMATICAL MODEL OF MIDDLE AD ED PART OF KDFD The full mathematical description of KDUR is a system of differential equations (linear and nonlinear). Solving this system of equations is pointless, because the interest of reliability point of view MCBS is the average and end of KDFD, zones B and C. After zone B began conducting a series of repairs (see figure 3) the elements of the structure. The purpose of these series of repairs is to increase the reliability of the elements of MCBS, according to (3) and technical resources T REE to end of technical exploitation of MCBS, according to (4). After point K fc representing the cyclical toughness load (end zone C), occurs demolition of MCBS and end of technical operation (or replace with a new culling structure). For a mathematical model of zones B and C are offered the following equation KDFD for speed of growth of the fatigue of the material V F : m V F C.(K) d (7) C and m - experimental constants of the material they are made of the elements of the MCBS; ΔK - breadth ratio of intensity of tensions K SI in MCBS, which is defined by [5]: K K max K min K max, K min are the maximum and minimum values of K SI at the tips of the cracks. (8) 78

7 Forecasting the Technical Resource of the Mechanical and Civil Building Structure Adopt the following Axiom about the reliability of the MCBS: Value K max, K min comply with the rules in force in the course of the CL maximum σ max and minimal σ min mechanical stress in the material it is made of MCBS. The authors of the accepted axiom is in accordance with the equations [] K l max max K min min l () ψ - coefficient depending on the geometry defects in the structure of the elements (for steel sheets which are made from elements of the MCBS, given that the cracks are in the edges should value of ψ =.2) []; The calculation of the critical number of load cycles cr of the structure in case of fatigue cracks spreading is done by integrating the equation (7) within the degradation of crack: from the starting value l to its stay critical l cr. From (9) and () is determined magnitude of the coefficient of the strain intensity ΔK in the MCBS using (8): K l( ).. l min max min. max min Performed separation of variables d and in both parts of the equation (7) to give the equation: d C( K) m (2) From the resulting new equation (2) is engaging expression of ΔK of () wherein follows: d m/ 2 m m m / 2 C ( ). l (3) Performed integration of both sides of the equation (3) in the range, kr for CL of MCBS and l, l cr length of the crack being tested. It integral equation:. d m / 2 m m C ( ). cr lcr l l m / 2 Enter the conditional mathematical notation for under integral argument x = (- m) /2. Hence the conversion of (4) in a tabular integral, which is solved by the use of [9]. The decision of the (4) defines the function of crash MCBS in terms of number of cr. from CL that it can endure without destroying its individual elements: cr. ( m / 2) cr l ( m/ 2 ) C ( m / 2) l m / 2 m ( ) m Δσ - reduced value of amplitude of mechanical tension in the place of crack under variable loading and execution of the axiom of the reliability of the MCBS; (9) () (4) (5) 79

8 ikolay Ivanov Petrov and Ventsislav Panev Dimitrov l cr the critical crack length; l - original length of the crack. 4. CYCLICAL RELIABILITY CRITERIO (CRC) FOR TECHICAL RESOURCE (T R ) OF MECHAICAL AD CIVIL BUILDIG STRUCTURE (MCBS). For creation of such a criterion, it is necessary to examine the theoretical reliability of current elements of the MCBS and to draw up a formula for a technical resource to the end for all MCBS. To this end, it should be borne in mind that an MCBS can consist of unlimited large number of functional elements. Under the assumption of normal distribution of the number of CL operating in the range of cr follows a formula for reliable operation P ro of MCBS displayed in the works of Petrov [8]: P ro ( t) 2 cr ( exp 2 cr ) 2 d χ - the mean square deviation of the current value of number of CL from value of cr. Given that technical resource T REE to end technical exploitation aggregate MCBS consisting of a number of units is determined by formula (4) having an analog function types: T RBRi TREE Pro( t) dt (7) i =, k - the number of running repairs in the process of technical operation of Mechanical and Civil Building Structure (MCBS), it will follow the fundamental formula, which the authors define as Cyclical Reliability Criterion (CRC) - T CRC for the Mean time between failures (technical resource T R ) from MCBS of Petrov Dimitrov, T REE T CRC : T CRC 2 T RBRi cr ( exp 2 cr ) 2 d 5. COCLUSIO 5. Displayed depending on the function of crash for Mechanical and Civil Building Structure (MCBS) in terms of the critical number cr of cyclic stresses loads, until the destruction of the individual elements, based on the axiom of reliability of MCBS 5.2 Created and analyzed a mathematical model of kinetic diagram of the fatigue destruction KDFD, through a system of differential equations. 5.3 Conducted a study on the theoretically investigated is the current reliability of the components of the MCBS, to achieve technical resource for the entire MCBS, following a catastrophic increase in due to cracks, prerequisite MSK consist of unlimited large number of functional elements Formulated a fundamental dependence manifested criteria of parametric reliability defined by the presence of microfractures - as Cyclical Reliability (6) (8) 8

9 Forecasting the Technical Resource of the Mechanical and Civil Building Structure Criterion (CRC) of Petrov-Dimitrov for Technical Resource (T R ) of Mechanical and Civil Building Structure (MCBS) It has been shown that the displayed criterion into account the performance of MCBS in the presence of a crack and expresses the basis of mechanics of destruction at the stage of development of the crack. REFERECES [] Балевски, А. Металознание. С.,Техника, 988. [2] Арзамасов, Б. Конструкционные материалы. М, 99. [3] Стаевски, К, Т. Авжиева. Материалознание и технология на материалите. УИ, Св. Климент Охридски, 24. [4] Табакова, Б. Якост, разрушаване и компютърен инженерен анализ. Курс от лекции. ТУ София. 26. [5] E ISO Надеждност в техниката. Основни термини и определения. София, 987. [6] Петров, Н. Изследване на операциите при осигуряване на надеждността на ТИС. АИ,,Марин Дринов, БАН, София, 24. [7] Димитрова, В., Б. Табакова, В. Димитров. Експериментално изследване на поведението на пукнатини по МКЕ, при високоскоростно фрезоване с палцови едноканални фрези, чрез модул SIMILATIOXpress на CAD система SOLID WorkS. [8] Петров, Н. Надеждностни изследвания на рискови технически системи. Тракийски университет, Второ издание, ИК,Учков, 27. [9] Каменаров, Г. Висша математика. Изд.,Техника, София, 994. [] Smith, Ch. The Science of Engineering Materials. Prentice-Hall, 986. [] Dimitrov V.,V.Dimitrova, S. Deckova, B.Mitev, Design Of A Metal Canopy With HPL Panels, International Journal of Innovative Science, Engineering & Technology (IJISET), Vol. 3 Issue 3, March, ISS , 26 [2] Dimitrov V., M.Ivanova, R.Yankov,.ikolov, Approach for Automated Design of Metal Pergola covered with Aluminum Composite Panels by using CAD/CAM Software TopSolid.v.6.5, International Journal of Scientific & Engineering Research, Volume 7, Issue 4, April, 26, ISS [3] Dimitrov V., Kr. Kalev, O.Petrov, A. Madgarova, Algorithm for automation engineering in the design of complex structural steel construction, The First Announcement of The International Conference Greener and Safer Energetic and Ballistic Systems (GSEBS) Bucharest, Romania, May 26-27, 26 [4] V. Dimitrov and V. Dimitrova, Optimization of Machining Conditions For High-Speed Milling with Single Flute End Mill Cutters of Elements From Aluminium Sheets, Hpl Panels and Aluminium Composite Panels, International Journal of Civil Engineering and Technology, 5(), 24, pp. 9. [5] Dimitar Tenev Panayotov, Ventsislav Panev Dimitrov and Krasimir Gochev Kalev, Comparative Analysis of The Processes For Machining of Mold Element with Using Topsolid'cam and Esprit, International Journal of Civil Engineering and Technology, 7(2), 25, pp

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