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.
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
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
Baikov V, Sigalov E (1981) Reinforced concrete structures. MIR Publishers, Moscow
Bozdogan KB, Ozturk D (2010) Vibration analysis of asymmetric-plan frame buildings using transfer matrix method. Math Comput Appl Int J 15:279–288
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
Chopra AK (2016) Dynamics of structures theory and applications to earthquake engineering. Pearson, Carmel
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)
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
Hassan MT, Hadima SA (2015) Analysis of nonuniform beams on elastic foundations by using recursive differentiation method. Eng Mech 22(2):83–94
Heidebrecht AC, Stafford Smith B (1973) Approximate analysis of tall wall-frame structures. J Struct Anal ASCE 99(2):199–221
Hoenderkamp JCD (2001) Elastic analysis of asymmetric tall building structures. Struct Des Tall Spec 10(4):245–261
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
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
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
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
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
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
Potzta G, Kollár L (2003) Analysis of building structures by replacement sandwich beams. Int J Solids Struct 40(3):535–553
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
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
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
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
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
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
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
Zalka K (2001b) Global structural analysis of buildings. E FN Spon, London
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
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40996-019-00235-5