Analysis of a continuous double-s pan beam that has disabled constraints

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-ɥɟɛɚɧɢɹ. ɉɪɢɜɟɞɟɧɵɮɨɪɦɭɥɵɞɥɹɨɩɪɟɞɟɥɟɧɢɹɩɟɪɟɦɟɳɟɧɢɣɢɷɤɜɢɜɚɥɟɧɬɧɵɯɫɬɚɬɢɱɟɫɤɢɯ

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1. ɑɟɪɧɨɜ ɘ.Ɍ. //

. 2010. № 4. . 53—57. : http://elibrary.ru. :

18.06.12.

2.ɑɟɪɧɨɜɘ.Ɍ., ɉɟɬɪɨɜɂ.Ⱥ.

// . 2012. № 4. . 98—101. :

http://vestnikmgsu.ru. : 18.06.12.

3. SCAD / . . , . . , . .

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4. Ɍɢɦɨɲɟɧɤɨɋ.ɉ., əɧɝȾ.ɏ., ɍɧɢɜɟɪɍ. . . : , 1985. 472 .

5. ȾɚɪɤɨɜȺ.ȼ., ɒɚɩɨɲɧɢɤɨɜɇ.ɇ. . . : . ., 1986. 607 . 6. ɑɟɪɧɨɜɘ.Ɍ. . . : - , 2011. 382 .

7. Salvatore Mangano. Mathematica Cookbook. O’Reilly Media, 2010. 830 p.

8. ɉɟɪɟɥɶɦɭɬɟɪȺ.ȼ., Ʉɪɢɤɫɭɧɨɜɗ.Ɂ., Ɇɨɫɢɧɚɇ.ȼ.

( )

«SCAD Ofﬁ ce» // - . 2009. № 2. . 13—18. : http://

engstroy.spb.ru. : 18.06.12.

ɉɨɫɬɭɩɢɥɚɜɪɟɞɚɤɰɢɸɜɢɸɥɟ 2012 ɝ.

: ɉɟɬɪɨɜɂɜɚɧ Ⱥɥɟɤɫɚɧɞɪɨɜɢɱ — ,

ɎȽȻɈɍȼɉɈ «Ɇɨɫɤɨɜɫɤɢɣɝɨɫɭɞɚɪɫɬɜɟɧɧɵɣɫɬɪɨɢɬɟɥɶɧɵɣɭɧɢɜɟɪɫɢɬɟɬ» (ɎȽȻɈɍȼɉɈ

«ɆȽɋɍ»), 129337, . , , . 26, ivpetrov87@yandex.ru.

: ɉɟɬɪɨɜɂ.Ⱥ. // . 2012. № 9. . 148—155.

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(8)

I.A. Petrov

ANALYSIS OF A CONTINUOUS DOUBLE-S PAN BEAM THAT HAS DISABLED CONSTRAINTS

The objective of this article is to present the analysis of a double-span beam that has dis-abled 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 analy-sis and System 2 static and dynamic properties analyanaly-sis is executed. Later, we calculate the deﬂ ec-tion 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 ﬂ exion in the mid-span 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 displace-ment 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.

Key words: free vibration, forced vibration, equivalent static loads, disabled constraints, pro-gressive collapse.

References

1. 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.

2. Chernov Yu.T., Petrov I.A. Opredelenie ekvivalentnykh staticheskikh sil pri raschete sistem s vyk-lyuchayushchimisya svyazyami [Identiﬁ cation of Equivalent Static Forces as part of Analysis of Systems That Have Disrupting Constraints]. Vestnik MGSU [Proceedings of Moscow State University of Civil En-gineering]. 2012, no. 4, pp. 98—101. Available at: http://vestnikmgsu.ru. Date of access: June 18, 2012.

3. Karpilovskiy V.S., Kriksunov E.Z., Malyarenko A.A. Vychislitel’nyy kompleks SCAD [SCAD Com-puter System]. Moscow, ASV Publ., 2008, 592 p.

4. Timoshenko S.P., Yang D.Kh., Univer U. Kolebaniya v inzhenernom dele [Vibrations in Engineer-ing]. Moscow, Mashinostroenie Publ., 1985, 472 p.

5. Darkov A.V., Shaposhnikov N.N. Stroitel’naya mekhanika [Structural Mechanics]. Moscow, Vyssh. shk. publ., 1986, 607 p.

6. Chernov Yu.T. Vibratsii stroitel’nykh konstruktsiy [Vibrations of Engineering Structures]. Moscow, ASV Publ., 2011, 382 p.

7. Salvatore Mangano. Mathematica Cookbook. O’Reilly Media, 2010, 830 p.

8. 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 Ofﬁ ce» [Analysis of a Building Consisting of Cast-in-situ Reinforced Concrete to Resist Progressive Collapse Using «SCAD Ofﬁ ce» Computer System]. Inzhenerno-stroitel’nyy zhurnal [Journal of Civil Engineering]. 2009, no. 2, pp. 13—18. Available at: http://engstroy.spb.ru. Date of access: June 18, 2012.

A b o u t t h e a u t h o r: Petrov Ivan Aleksandrovich —postgraduate student, Department of Structural Mechanics, Moscow State University of Civil Engineering (MGSU), 26 Yaroslavskoe shosse, Moscow, 129337, Russian Federation, ivpetrov87@yandex.ru.