
Chernov Yuriy Tikhonovich 
Central Scientific Research Institute for Building Structures named after V.A. Kucherenko (V.A. Kucherenko CSRIBS)
Doctor of Technical Sciences, Professor, Central Scientific Research Institute for Building Structures named after V.A. Kucherenko (V.A. Kucherenko CSRIBS), 6 2nd Institutskaya St., Moscow, 109428, Russian Federation.

Petrov Ivan Aleksandrovich 
Moscow State University of Civil Engineering (MSUCE)
postgraduate student, Department of Structural Mechanics, Moscow State University of Civil Engineering (MSUCE), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation;
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.
The algorithm of analysis of systems that have disruptable constrains is described in the article. The algorithm is based on the joint solving of two linear systems. The first linear system is the one that describes the processes before constraints get disrupted; the second linear system represents the system describing the processes in the aftermath of disruption of constrains with account for the influence of free vibrations. Free vibrations are caused by disrupted constraints. The proposed approach is more effective, if applicable to the systems that have their constraints disrupted only once. Also, the method describing disrupted constraints is considered as a special case of physical nonlinearity. Physical nonlinearity adds some fictitious load to regular loads.
Formulas of equivalent static loads, with the help of which the systems are analyzed when constraints are disrupted, are generated. No inertial force is to be derived to obtain equivalent static loads. This is important in view of their application in dynamic analyses .
Analysis of the static system in the event of disrupted constraints is based on the equations derived by the authors. The result of the analysis represents an inverse linear relation of static loading and relative stiffness of the system with disrupted constraints. This means that the lower the stiffness of the system, the higher the static loading.
DOI: 10.22227/19970935.2012.4.98  101
References
 Chernov Yu.T. Vibratsii stroitel'nykh konstruktsiy [Vibrations of Engineering Structures]. Moscow, ASV Publ., 2011, 382 p.
 Timoshenko S.P., Yang D.Kh., Univer U. Kolebaniya v inzhenernom dele [Vibrations in Engineering]. Мoscow, Mashinostroenie [Machine Building],1985, 472 p.
 Chernov Yu.T. K raschetu sistem s vyklyuchayushchimisya svyazyami [About the Analysis of Systems That Have Disruptable Constraints]. Stroitel'naya mekhanika i raschet sooruzheniy [Structural Mechanics and Analysis of Structures]. 2010, no. 4, pp. 53—57.

Petrov Ivan Aleksandrovich 
Moscow State University of Civil Engineering (MSUCE)
postgraduate student, Department of Structural Mechanics, Moscow State University of Civil Engineering (MSUCE), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation;
This email address is being protected from spambots. You need JavaScript enabled to view it
.
The objective of this article is to present the analysis of a doublespan beam that has disabled
constraints, including its analysis in the state of static equilibrium and in the event of forced
vibrations. Hereinafter, the original system is entitled System 1, while the system that has disabled
constraints is System 2.
The analysis is performed in furtherance of the following pattern. First, System 1 static analysis
and System 2 static and dynamic properties analysis is executed. Later, we calculate the deflection
and the internal force of System 2 as the consequence of disabled constraints. By comparing
the process of static equilibrium of System 2 and the process of free vibrations of System 2, we
identify that the moment of flexion in the midspan increases by 85 %, while the support moment
increases by 66 %.
The analysis of the system that has disabled constraints in the process of forced vibrations is
the same as the analysis demonstrated hereinbefore, except that the initial condition is calculated
differently. By disabling constraints, we can both reduce and increase the peak values of displacement
of the system in the process of forced vibrations.
This research proves that the proposed method can be used to calculate defl ection and the
internal force of static and dynamic systems having disabled constraints. That can be very important
in evaluation of the safety of structures after destruction of their individual elements.
DOI: 10.22227/19970935.2012.9.148  154
References
 Chernov Yu.T. K raschetu sistem s vyklyuchayushchimisya svyazyami [About the Analysis of Systems That Have Disrupting Constraints]. Stroitel’naya mekhanika i raschet sooruzheniy [Structural Mechanics and Analysis of Structures]. 2010, no. 4, pp. 53—57. Available at: http://elibrary.ru. Date of access: June 18, 2012.
 Chernov Yu.T., Petrov I.A. Opredelenie ekvivalentnykh staticheskikh sil pri raschete sistem s vyklyuchayushchimisya svyazyami [Identification of Equivalent Static Forces as part of Analysis of Systems That Have Disrupting Constraints]. Vestnik MGSU [Proceedings of Moscow State University of Civil Engineering]. 2012, no. 4, pp. 98—101. Available at: http://vestnikmgsu.ru. Date of access: June 18, 2012.
 Karpilovskiy V.S., Kriksunov E.Z., Malyarenko A.A. Vychislitel’nyy kompleks SCAD [SCAD Computer System]. Moscow, ASV Publ., 2008, 592 p.
 Timoshenko S.P., Yang D.Kh., Univer U. Kolebaniya v inzhenernom dele [Vibrations in Engineering]. Moscow, Mashinostroenie Publ., 1985, 472 p.
 Darkov A.V., Shaposhnikov N.N. Stroitel’naya mekhanika [Structural Mechanics]. Moscow, Vyssh. shk. publ., 1986, 607 p.
 Chernov Yu.T. Vibratsii stroitel’nykh konstruktsiy [Vibrations of Engineering Structures]. Moscow, ASV Publ., 2011, 382 p.
 Salvatore Mangano. Mathematica Cookbook. O’Reilly Media, 2010, 830 p.
 Perel’muter A.V., Kriksunov E.Z., Mosina N.V. Realizatsiya rascheta monolitnykh zhilykh zdaniy na progressiruyushchee (lavinoobraznoe) obrushenie v srede vychislitel’nogo kompleksa «SCAD Office» [Analysis of a Building Consisting of Castinsitu Reinforced Concrete to Resist Progressive Collapse Using «SCAD Offi ce» Computer System]. Inzhenernostroitel’nyy zhurnal [Journal of Civil Engineering]. 2009, no. 2, pp. 13—18. Available at: http://engstroy.spb.ru. Date of access: June 18, 2012.