Skip to main content
Log in

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

  • Research Paper
  • Published:
Iranian Journal of Science and Technology, Transactions of Civil Engineering Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Ahmad J, Bajwa S, Siddique I (2015) Solving the Klein–Gordon equations via differential transform method. J Sci Arts 15(1):33–38

    MathSciNet  Google Scholar 

  • 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 35:125–132

    Google Scholar 

  • Baikov V, Sigalov E (1981) Reinforced concrete structures. MIR Publishers, Moscow

    Google Scholar 

  • Bozdogan KB, Ozturk D (2010) Vibration analysis of asymmetric-plan frame buildings using transfer matrix method. Math Comput Appl Int J 15:279–288

    MATH  Google Scholar 

  • 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 46:245–267

    Article  Google Scholar 

  • Chopra AK (2016) Dynamics of structures theory and applications to earthquake engineering. Pearson, Carmel

    Google Scholar 

  • 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 

  • ETABS (2017) Structural software for analysis and design. Evaluation version. Computers and Structures

  • Gulkan P, Akkar S (2002) A simple replacement for the drift spectrum. Eng Struct 24(11):1477–1484

    Article  Google Scholar 

  • Hassan MT, Hadima SA (2015) Analysis of nonuniform beams on elastic foundations by using recursive differentiation method. Eng Mech 22(2):83–94

    Google Scholar 

  • Heidebrecht AC, Stafford Smith B (1973) Approximate analysis of tall wall-frame structures. J Struct Anal ASCE 99(2):199–221

    Google Scholar 

  • Hoenderkamp JCD (2001) Elastic analysis of asymmetric tall building structures. Struct Des Tall Spec 10(4):245–261

    Article  Google Scholar 

  • Hosseini M, Imagh-e-Naiini MR (1999) A quick method for estimating the lateral stiffness of building systems. Struct Des Tall Build 8:247–260

    Article  Google Scholar 

  • 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):401–418

    Article  Google Scholar 

  • 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):915–934

    Article  MathSciNet  Google Scholar 

  • Kuang JS, Ng SC (2009) Lateral shear-St. Venant torsion coupled vibration of asymmetric-plan frame structures. Struct Des Tall Spec 18(6):647–656

    Article  Google Scholar 

  • 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 37:5123–5141

    Article  Google Scholar 

  • Piccardo G, Tubino F, Luongo A (2015) A shear–shear torsional beam model for nonlinear aeroelastic analysis of tower buildings. Z Angew Math Phys 66:1895–1913

    Article  MathSciNet  Google Scholar 

  • Potzta G, Kollár L (2003) Analysis of building structures by replacement sandwich beams. Int J Solids Struct 40(3):535–553

    Article  Google Scholar 

  • Rafezy B, Zare A, Howson WP (2007) Coupled lateral-torsional vibration of asymmetric, three-dimensional frame structures. Int J Solids Struct 44(1):128–144

    Article  Google Scholar 

  • 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 233–243

  • Rajasekaran S (2009) Structural dynamics of earthquake engineering: theory and application using mathematica and matlab. CRC Press, Boca Raton

    Book  Google Scholar 

  • 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, Alaska

  • 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):553–568

    Article  Google Scholar 

  • Saffari H, Mohammadnejad M (2015) On the application weak form to free vibration analysis of tall structures. Asian J Civ Eng 16(7):977–999

    Google Scholar 

  • SAP2000 (2018) Structural software for analysis and design. Evaluation version. Computers and Structures

  • Taranath BS (2010) Reinforced concrete design of tall buildings. CRC Press, Florida

    Google Scholar 

  • 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):321–330

    Google Scholar 

  • Wong KKF (2013) Evaluation of computational tools for performing nonlinear seismic analysis of structural collapse. Structures congress 2013, ASCE 2013, pp 2106–2117

  • Zalka K (2001a) A simplified method for calculation of the natural frequencies of wall-frame buildings. Eng Struct 23:1544–1555

    Article  Google Scholar 

  • Zalka K (2001b) Global structural analysis of buildings. E FN Spon, London

    Google Scholar 

  • 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):8237–8250

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Duygu Ozturk.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ozturk, D., Bozdogan, K.B. Determination of the Dynamic Characteristics of Frame Structures with Non-uniform Shear Stiffness. Iran J Sci Technol Trans Civ Eng 44, 37–47 (2020). https://doi.org/10.1007/s40996-019-00235-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40996-019-00235-5

Keywords

Navigation