Advertisement

Determination of the Dynamic Characteristics of Frame Structures with Non-uniform Shear Stiffness

  • Duygu OzturkEmail author
  • Kanat Burak Bozdogan
Research Paper
  • 4 Downloads

Abstract

Structures consisting of frames can be considered as shear structures under certain assumptions. The frame can be idealized as an equivalent shear beam in this case. In this study, the dynamic characteristics of non-uniform frames were investigated. For this purpose, the method of differential transform was used to solve the governing differential equation of the equivalent shear beam. This shear beam represented the structure of which shear stiffness varies along the height. In this study, the contribution of the axial deformation was taken into account with the help of equivalent shear stiffness. The least squares method was used in order to determine the parameter that defines the change of the shear stiffness. Thus, the dynamic characteristics were determined more realistically. Tables were prepared for use for the determination of the dynamic characteristics of frame structures with non-uniform shear stiffness. Response spectrum analysis can be easily conducted using these tables. The suitability of the approach was investigated through examples at the end part of the study. The suggested method could be used safely during the preliminary design stage. It is particularly easy to understand the structural behavior due to the usage of fewer parameters.

Keywords

Non-uniform frame Shear beam Differential transform Response spectrum analysis Axial deformation 

References

  1. Ahmad J, Bajwa S, Siddique I (2015) Solving the Klein–Gordon equations via differential transform method. J Sci Arts 15(1):33–38MathSciNetGoogle Scholar
  2. Attarnejad R, Shahba A, Jandaghi Semnani S (2010) Application of differential transform in free vibration analysis of Timoshenko beams resting on two-parameter elastic foundation. Arab J Sci Eng 35:125–132Google Scholar
  3. Baikov V, Sigalov E (1981) Reinforced concrete structures. MIR Publishers, MoscowGoogle Scholar
  4. Bozdogan KB, Ozturk D (2010) Vibration analysis of asymmetric-plan frame buildings using transfer matrix method. Math Comput Appl Int J 15:279–288zbMATHGoogle Scholar
  5. Caterino N, Cosenza E, Azmoodeh BM (2013) Approximate methods to evaluate story stiffness and interstory drift of RC buildings in the seismic area. Struct Eng Mech 46:245–267CrossRefGoogle Scholar
  6. Chopra AK (2016) Dynamics of structures theory and applications to earthquake engineering. Pearson, CarmelGoogle Scholar
  7. Ertutar Y (1987) Calculation of the lateral displacements of the structures that are under the influence of the lateral loads and have a nonlinear change of the frame shear rigidity along the height of the structure. Earthq Res Bull 57:1 (in Turkish) Google Scholar
  8. ETABS (2017) Structural software for analysis and design. Evaluation version. Computers and StructuresGoogle Scholar
  9. Gulkan P, Akkar S (2002) A simple replacement for the drift spectrum. Eng Struct 24(11):1477–1484CrossRefGoogle Scholar
  10. Hassan MT, Hadima SA (2015) Analysis of nonuniform beams on elastic foundations by using recursive differentiation method. Eng Mech 22(2):83–94Google Scholar
  11. Heidebrecht AC, Stafford Smith B (1973) Approximate analysis of tall wall-frame structures. J Struct Anal ASCE 99(2):199–221Google Scholar
  12. Hoenderkamp JCD (2001) Elastic analysis of asymmetric tall building structures. Struct Des Tall Spec 10(4):245–261CrossRefGoogle Scholar
  13. Hosseini M, Imagh-e-Naiini MR (1999) A quick method for estimating the lateral stiffness of building systems. Struct Des Tall Build 8:247–260CrossRefGoogle Scholar
  14. Kaviani P, Rahgozar R, Saffari H (2008) Approximate analysis of tall buildings using sandwich beam models with variable cross-section. Struct Des Tall Spec 17(2):401–418CrossRefGoogle Scholar
  15. Kaya MO, Ozdemir Ozgumus O (2010) Energy expressions and free vibration analysis of a rotating uniform Timoshenko beam featuring bending-torsion coupling. J Vibr Control 16(6):915–934MathSciNetCrossRefzbMATHGoogle Scholar
  16. Kuang JS, Ng SC (2009) Lateral shear-St. Venant torsion coupled vibration of asymmetric-plan frame structures. Struct Des Tall Spec 18(6):647–656CrossRefGoogle Scholar
  17. Li QS (2000) A new exact approach for determining natural frequencies and mode shapes of non-uniform shear beams with arbitrary distribution of mass or stiffness. Int J Solids Struct 37:5123–5141CrossRefzbMATHGoogle Scholar
  18. Piccardo G, Tubino F, Luongo A (2015) A shear–shear torsional beam model for nonlinear aeroelastic analysis of tower buildings. Z Angew Math Phys 66:1895–1913MathSciNetCrossRefzbMATHGoogle Scholar
  19. Potzta G, Kollár L (2003) Analysis of building structures by replacement sandwich beams. Int J Solids Struct 40(3):535–553CrossRefzbMATHGoogle Scholar
  20. Rafezy B, Zare A, Howson WP (2007) Coupled lateral-torsional vibration of asymmetric, three-dimensional frame structures. Int J Solids Struct 44(1):128–144CrossRefzbMATHGoogle Scholar
  21. Rahgozar R, Saffari H, Kaviani P (2004) Free vibration of tall buildings using Timoshenko beam with variable cross-section. In: Proceedings of SUSI VIII, Crete, Greece, pp 233–243Google Scholar
  22. Rajasekaran S (2009) Structural dynamics of earthquake engineering: theory and application using mathematica and matlab. CRC Press, Boca RatonCrossRefGoogle Scholar
  23. Rodriguez AA, Miranda E (2014) Seismic response of buildings with non-uniform stiffness modeled as cantilevered shear beams. In: Tenth U.S. national conference on earthquake engineering frontiers of earthquake engineering July 21–25, 2014 10NCEE Anchorage, AlaskaGoogle Scholar
  24. Rodriguez AA, Miranda E (2016) Assesment of effects of reductions of lateral stiffness along height on buildings modeled as elastic cantilever shear beam. J Earth Eng 22(4):553–568CrossRefGoogle Scholar
  25. Saffari H, Mohammadnejad M (2015) On the application weak form to free vibration analysis of tall structures. Asian J Civ Eng 16(7):977–999Google Scholar
  26. SAP2000 (2018) Structural software for analysis and design. Evaluation version. Computers and StructuresGoogle Scholar
  27. Taranath BS (2010) Reinforced concrete design of tall buildings. CRC Press, FloridaGoogle Scholar
  28. Tekeli H, Atimtay E, Turkmen M (2015) An approximation method for design applications related to sway in RC framed buildings. Int J Civ Eng 13(3):321–330Google Scholar
  29. Wong KKF (2013) Evaluation of computational tools for performing nonlinear seismic analysis of structural collapse. Structures congress 2013, ASCE 2013, pp 2106–2117Google Scholar
  30. Zalka K (2001a) A simplified method for calculation of the natural frequencies of wall-frame buildings. Eng Struct 23:1544–1555CrossRefGoogle Scholar
  31. Zalka K (2001b) Global structural analysis of buildings. E FN Spon, LondonGoogle Scholar
  32. Zhang H, Kang YA, Li XF (2013) Stability and vibration analysis of axially-loaded shear beam-columns carrying elastically restrained mass. Appl Math Modell 37(16–17):8237–8250MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Shiraz University 2019

Authors and Affiliations

  1. 1.Civil Engineering Department, Engineering FacultyEge UniversityIzmirTurkey
  2. 2.Civil Engineering Department, Engineering FacultyCanakkale Onsekiz Mart UniversityCanakkaleTurkey

Personalised recommendations