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 TR) for the entire MCBS.

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International Journal of Civil Engineering and Technology (IJCIET)
Volume 7, Issue 3, May–June 2016, pp. 173–181, Article ID: IJCIET_07_03_017
Available online at
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=7&IType=3
Journal Impact Factor (2016): 9.7820 (Calculated by GISI) www.jifactor.com
ISSN Print: 0976-6308 and ISSN Online: 0976-6316
© IAEME Publication
FORECASTING THE TECHNICAL
RESOURCE OF THE MECHANICAL AND
CIVIL BUILDING STRUCTURE
Nikolay 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 TR) 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 (TR) 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 TR), Cyclical
Reliability Criterion (CRC), Crash Function, Microfractures, Kinetic Diagram
of the Fatigue Destruction KDFD, CAD system
Cite this Article: Nikolay 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),
2016, pp. 173–181.
http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=7&IType=3

2. Nikolay Ivanov Petrov and Ventsislav Panev Dimitrov
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1. INTRODUCTION
A major factor in determining the efficiency of Mechanical and Civil Building
Structure (MCBS) is their bridge resist the impact of cyclical loads (CL). Given the
increase in the number of promotion cyclical loads in the process of technical
operations of metal and building structures, damage accumulation occurs
accumulation of damage in the form of surfaces (strips) from sliding and
accumulating dislocations of microbeads (crystal structures, domains, etc.). Liquid
Time occurs aging of these structures, as well as reducing their corrosion resistance,
which eventually leads to a dice-arrangement, the present and development of micro
and makrofractures.
The number of cyclical loads (CL) in the process of accumulation of failures and
rejections N lean divided by the mechanical characteristics of the material and level of
action your voltages in it. In this respect, CL are divided into levels (initial), after the
construction of the structure and of the operational (arising in the process of technical
use and aging). They in turn are divided into deterministic and random [1-10].
As an example of simple deterministic loads are considered the weight of the
metal or building structures, tensile or compressive mounting tensions in establishing,
cycles of filling and emptying of pressure vessels - tanks, gas cylinders, and others.
As random effects are considered MCBS loads caused by strong winds, hurricanes,
sea waves, seismic waves from earthquakes, thermal and electrical damage to the
structure and others.
2. GENERATION AND ACCUMULATION OF
МICROFRACTURES
For a description of the process of generation and accumulation of microfractures
(cracks) using different criteria. The strength at which the limit state of the material
occurs when an point of body tension reaches a certain value refers to the stage of the
emergence of crack [1, 7]. The criterion takes into account the efficiency of the metal
in the presence of a crack in it is the criterion of the stage of development of the crack
and draws based on the mechanics of destruction.
As examples may be given several types of construction metal structure built by
means of a CAD system, in this case, TopSolid'Design – fig. 1 [11, 12, 13].
Presumably believe that their beams or, most often in their console elements intended
to establish the buildings used to have cracks.
The border state of equilibrium is reached, if the micro fracture had the
opportunity to spread. The size of the crack in this case can be sustainable and
unsustainable. At steady state element is in mechanical equilibrium and crack in it is
still at a constant external load. The growth of a crack in MCBS with length l (δ
width) with a small length Δl [mm] is necessary increase in external load F[N] with a
small final value ΔF - Figure 2. However, if the external situation remains constant, it
reduces energy to spread the crack in the material [1, 2, 3, 7].
An stable condition for sustainable energy of destruction is fulfilled
inequality [7]:

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Figure 1 Typical examples of metal building structures [11, 12, 13]
0
dl
dF

(1)
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 lcr. In the next moment crack can
spread even with decreasing load. In this case, the inequality [7]:
0
dl
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 lcr. 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. Nikolay Ivanov Petrov and Ventsislav Panev Dimitrov
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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 (TE) 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 TRBP (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

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repairs represent a time for "technical" (training) of the various subsystems of the
MCBS. The requested resource TRBR between MR (i-in number) of Fig. 3 and
technical resource by the end of the exploitation TREE of the MCBS shall be
determined in accordance with the literature [6, 8]:

Topt
RORBR dttPT
0
)(
(3)

PMPT
ROREE dttPT
0
)(
(4)
where:
- PRO (t) - the probability of reliable operation of MCBS in the interval between
the repairing;
- Topt - optimal time for performing MR2 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 N per CL. In
the mechanics of destruction of MCBS (mechanics of cracks resistance) as a basic
parameter using the ratio of intensity of tensions KSI (mechanical stress). Under KSI 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 σH i.e.
),(. BlfK HSI  (5)
The process of destruction of the elements of the MCBS is referred to as fatigue [1].
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
VF from MCBS defined as [4, 10]:
dN
dl
VF 
(6)
where:
- l - the length of the crack;
- N - the number of elements of the CL in the MCBS.
The graphical representation of the dependence of the rate of growth of fatigue VF
parameters of the destruction of the elements of MCBS (primarily the maximum value
of the ratio of intensity of tensions KSImax) is called kinetic diagram of the fatigue
destruction KDFD. KDFD type, built in a logarithmic scale (on the abscissa axis
lgKSImax , ordinate lgVF) 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
middle and end part of KDFD (area B and area C).

6. Nikolay Ivanov Petrov and Ventsislav Panev Dimitrov
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Figure 4 Kinetic Diagram of the Fatigue Destruction KDFD for destruction of the elements
of MCBS [14]:
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 AND END 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 TREE to end of technical
exploitation of MCBS, according to (4). After point Kfc 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 VF:
m
F KC
dN
dl
V ).(
(7)
where:
C and m - experimental constants of the material they are made of the elements of
the MCBS;
ΔK - breadth ratio of intensity of tensions KSI in MCBS, which is defined by [5]:
minmax KKK 
(8)
where:
Kmax, Kmin are the maximum and minimum values of KSI at the tips of the cracks.

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Adopt the following Axiom about the reliability of the MCBS: Value Kmax, Kmin
comply with the rules in force in the course of the CL maximum σmax and minimal σmin
mechanical stress in the material it is made of MCBS. The authors of the accepted
axiom is in accordance with the equations [10]
lK maxmax  (9)
lK minmin  (10)
where:
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 = 1.12) [1];
The calculation of the critical number of load cycles Ncr 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 l0 to its stay critical lcr.
From (9) and (10) is determined magnitude of the coefficient of the strain
intensity ΔK in the MCBS using (8):
llK ..)(. minmaxmin   (11)
where:
minmax  
Performed separation of variables dN and dl in both parts of the equation (7) to
give the equation:
dl
KC
dN m
)(
1


(12)
From the resulting new equation (12) is engaging expression of ΔK of (11)
wherein follows:
dl
lC
dN mmmm 2/2/
.)(
1
 

(13)
Performed integration of both sides of the equation (13) in the range 0, Nkr for CL
of MCBS and l0, lcr length of the crack being tested. It integral equation:
 

lcr
l
mmmm
Ncr
l
dl
C
dN
0
2/2/
.
0 .)(
1

(14)
Enter the conditional mathematical notation for under integral argument x = (- m)
/2. Hence the conversion of (14) in a tabular integral, which is solved by the use of
[9]. The decision of the (14) defines the function of crash MCBS in terms of number
of Ncr. from CL that it can endure without destroying its individual elements:
mmm
mm
cr
cr
Cm
ll
N
)()12/( 2/
)12/(
0
1)2/(
.
 



(15)
where:
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;

8. Nikolay Ivanov Petrov and Ventsislav Panev Dimitrov
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lcr – the critical crack length;
l0 - original length of the crack.
4. CYCLICAL RELIABILITY CRITERION (CRC) FOR
TECHNICAL RESOURCE (TR) OF MECHANICAL AND CIVIL
BUILDING 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 0 ÷ Ncr follows a
formula for reliable operation Pro of MCBS displayed in the works of Petrov [8]:
dN
NN
tP
Ncr
N
cr
N
ro  




 

0
2
2
)(
exp
2
1
)(
 (16)
where:
χN - the mean square deviation of the current value of N number of CL from value
of Ncr.
Given that technical resource TREE to end technical exploitation aggregate MCBS
consisting of a number of units is determined by formula (4) having an analog
function types:

RBRiT
roREE dttPT
0
)(
(17)
where:
i = 1, 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) - TCRC
for the Mean time between failures (technical resource TR) from MCBS of
Petrov – Dimitrov, TREE≡TCRC:
dN
NN
T
Ncr
N
cr
T
N
CRC
RBRi
 




 

0
2
0 2
)(
exp
2
1
 (18)
5. CONCLUSION
5.1 Displayed depending on the function of crash for Mechanical and Civil Building
Structure (MCBS) in terms of the critical number Ncr 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.
5.4. Formulated a fundamental dependence manifested criteria of parametric
reliability defined by the presence of microfractures - as Cyclical Reliability

9. Forecasting the Technical Resource of the Mechanical and Civil Building Structure
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Criterion (CRC) of Petrov-Dimitrov for Technical Resource (TR) of Mechanical
and Civil Building Structure (MCBS).
5.5. 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.
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