Basit Mesnetli Kirişlerde Eğilme ve Kaymadan Dolayı Oluşan Sehim Denklemlerinin Bulunması

Kiriş uygulamalarının genelinde kaymadan dolayı oluşan sehimler ihmal edilir. Fakat; yüksek kayma modülüne sahip, kısa ve kalın kirişlerde kaymadan dolayı oluşan sehimin ihmal edilmesi çok büyük hatalara neden olmaktadır. Bu çalışmada her iki tarafında mesnetlenmiş orta noktasından tekil yüke maruz kompozit kirişlerdeki eğilme ve kaymadan dolayı ortaya çıkan sehim denklemleri analitik olarak elde edilmiştir. Örnek malzeme olarak kayma modülü diğer malzemelere göre yüksek olan ahşap seçilmiştir. Kaymanın etkisini incelemek için, elde edilen fonksiyonlar kullanılarak, kirişin orta noktasındaki maksimum sehimler 0, 30, 45, 60 and 90 oryantasyon açıları için elde edilmiştir. Aynı zamanda kayma etkisinin en fazla olduğu kısa kirişin orta noktasındaki eğilme gerilmeleri 0, 30, 45, 60 ve 90 oryantasyon açıları için verilmiştir. Kaymadan dolayı oluşan sehimin; kirişe uygulanan yüke, kirişin uzunluğuna ve yüksekliğine göre değiştiği tespit edilmiştir. Kayma etkisi; 45 oryantasyon açısında en küçük, 0 oryantasyon açısında ise en büyük olmaktadır.

Anahtar Kelimeler:

Kayma etkisi, Kaymadan dolayı oluşan sehim, Basit desteklenmiş kompozit kiriş, Ahşap.

Derivation of Equations for Flexure and Shear Deflections of Simply Supported Beams

Shear deflection of wood beams generally is exluded in plannning calculations. Ignoring shear deflection could cause significant errors, expecially for short and thick beams. In this study, two deflection functions due to flexure and shear of simply supported composite beam subjected to single force are obtained analytically. Wood being high shear modulus according to other material is selected for sample problem. The deflections the mid point of the beam are calculated to see the effect of shear by using the obtained functions for 0, 15, 30, 45, 60 and 90 orientation angles. Also, bending stresses at the mid point of the short beam are given for 0, 15, 30, 45, 60 and 90 orientation angles. It is shown that the magnitude of shear deflection depends on force, length and height of the beam. The shear effect is the smallest for 45 orientation angle and the biggest for 0 orientation angle.

Keywords:

Shear effect, Shear deflection, Simply supported composite beam, Wood.,

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Altenbach, H. 2000. On the determination of transverse shear stiffnesses of orthotropic plates, Zeitschrift für Angewandte Mathematik and Physik, 51 (4), 629-649.
Aydoğan, M. 1995. Stiffness-matrix formulation of beams with shear effect on elastic foundation, Journal of Structural Engineering, 121 (9), 12651270.
Biblis, E. J. 1997. Shear deflection of two species laminated wood beams, Wood Science and Technology. 1 (3), 231-238.
Esendemir, Ü. 2004. An elastic-plastic stress analysis in a polymer-matrix composite beam of arbitrary orientation supported from two ends acted upon with a force at the mid point. Journal of Reinforced Plastics and Composites, 23 (6), 613-623.
Esendemir, Ü. 2005. The effects of shear on the deflection of linearly loaded composite cantilever beam, Journal of Reinforced Plastics and Composites. 24 (11), 1159-1168.
Esendemir, Ü., Usal, M.R., Usal, M. 2006. The effects of shear on the deflection of simply supported composite beam loaded linearly, Journal of Reinforced Plastics and Composites. 25 (8), 835-846.
Evangelas, J. Biblis, 1967. Shear deflection of two species laminated wood beams, Wood Science and Technology. 1 (3), 231-238.
Faella, C., Martinelli, E., and Nigro, E. 2003. Shear connection nonlinearity and deflections of steel concrete composite beams: a simplified method, Journal of Structural Engineering. 129 (1), 12-20.
Hiroaki, K., Tohru, N. 1993. Shear deflection of anisotropic plates. JSME Internatianal Journal Series A: Mechanics and Material Engineering. 36 (1). 7379.
Jones, R. M. 1975. Mechanics of composite materials. Mcgraw-Hill, Kogakusha, Tokyo.
Kılıç, O., Aktaş, A. and Dirikolu, M.H. 2001. An investigating of the effects of shear on the deflection of an orthotropic cantilever beam by use of anisotropic elasticity theory. Composites Science and Technology. (61), 2055-2061.
Kubojima, Y., Ohtani, T., and Yoshihara, H. 2004. Effect of shear deflection on vibrational properties of compressed wood, Wood Science and Technology. 38 (3), 237-244.
Lee, S.J, Reddy, J.N. 2004. Nonlinear deflection control of laminated plates using third-order shear deformation theory, International journal of Mechanics and Materials Design, 1 (1), 33-61.
Lekhnitskii, S.G. 1968. Anisotropic Plates, Gordon and Breach Science, New York.
Lekhnitskii, S.G. 1981. Theory of Elasticity of an Anisotropic Body. Mir Publishers, Moscow.
Liu, J.Y and Rammer, D.R. 2003. Analysis of wood cantilever loaded at free end, Wood and Fiber Science. 35 (3), 334-340.
Machado, S. P., Cortinez, V.H. 2005. Non-linear model for stability of thin-walled composite beams with shear deformation, Thin-Walled Structures. (43), 1615-1645.
Nie, J. and Cai, C.S. 1998. Steel-concrete composite beams considering shear slip effects, Journal of Structural Engineering. 129 (4), 495-506.
Nie, J., Cai, C.S. 2000. Deflection of cracked rc beams under sustained loading, Journal of Structural Engineering. 126 (6), 708-716.
Onu, G. 2000. Shear effect in beam finite element on two-parameter elastic foundation, Journal of Structural Engineering. 126 (9), 1104-1107.
Pilkey, W. D., Kang, W., Schramm, U. 1995. New structural matrices for a beam element with shear deformation, Finite Elements Journal of Structural Engineering, 121 (9). In Analysis and design, 19 (1), 2544.
Schramm, U., Kitis, L., Kang, W., Pilkey, W.D. 1994. On the shear deformation coefficient in beam theory, Finite Elements in Analysis and Design. 16 (2), 141-162.
Thomas, W. H. 2002. Shear and flexural deflection equations for OSB floor decking with point load, Holz als Roh-Und Werstoff. 60 (3), 175-180.
Usal, M.R., Usal, M., Esendemir, Ü. 2008. Static and dynamic analysis of simply supported beams, Journal of Reinforced Plastics and Composites, 27 (3): 263-276.
Wang, Y.C. 1998. Deflection of steel-concrete composite beams with partial shear interaction, Journal of Structural Engineering. 124 (10), 1159-1165.