Some closed-form bending formulas for elastically restrained Euler-Bernoulli beams under point and uniformly distributed loads

• Autorzy: Yıldırım V.

Identyfikatory

DOI

10.17512/jamcm.2018.3.09

• Języki publikacji: EN

Abstrakty

EN

The transfer matrix method based on the Euler-Bernoulli beam theory is employed in order to originally achieve some exact analytical formulas for elastically supported beams under a point force together with uniformly distributed force and uniformly distributed couple moments. Those closed-form formulas can be used in a variety of engineering applications especially at the pre-design stage to get an insight into the response of the structure. Contrary to the classical boundary conditions, it is also observed that the Euler-Bernoulli solutions of a beam with elastic supports are sensitive to the ratio of length to thickness (L/h).

Słowa kluczowe

EN

Euler-Bernoulli beam; elastic support; transfer matrix method; initial value problem; bending

PL

belka Eulera-Bernoulliego; teoria Eulera-Bernoulliego; metoda macierzy transferu

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2018
• Tom: Vol. 17, nr 3
• Strony: 97--109
• Opis fizyczny: Bibliogr. 9 poz., rys., tab.

Twórcy

autor

Yıldırım V.

• Department of Mechanical Engineering, University of Çukurova Adana, Turkey

Bibliografia

• [1] Wang, C. (1995). Timoshenko beam-bending solutions in terms of Euler-Bernoulli solutions. Journal of Engineering Mechanics, 121(6), 763-765.
• [2] Young, W.C. & Budynas, R.G. (2002). Roark’s Formulas for Stress and Strain, Seventh Edition, McGraw-Hill, New York, ISBN 0-07-072542-X.
• [3] Mohammadi, R. (2014). Sextic B-spline collocation method for solving Euler-Bernoulli beam models. Applied Mathematics and Computation, 241, 151-166.
• [4] Zamorska, I. (2014). Solution of differential equation for the Euler-Bernoulli beam. Journal of Applied Mathematics and Computational Mechanics, 13(4), 157-162.
• [5] Ghannadiasl, A, & Golmogany, M.Z. (2017). Analysis of Euler-Bernoulli Beams with arbitrary boundary conditions on Winkler foundation using a B-spline collocation method. Engng. Trans., 65(3), 423-445.
• [6] İnan, M. (1968). The Method of Initial Values and the Carry-over Matrix in Elastomechanics. ODTÜ Publication, Ankara, No: 20.
• [7] Arici, M., & Granata, M.F. (2011). Generalized curved beam on elastic foundation solved by transfer matrix method. Structural Engineering & Mechanics, 40(2), 279-295.
• [8] Wimmer, H., & Nachbagauer, K. (2018). Exact transfer- and stiffness matrix for the composite beam-column with Refined Zigzag kinematics. Composite Structures, 189, 700-706.
• [9] Yıldırım, V. (2018). Several stress resultant and deflection formulas for Euler-Bernoulli beams under concentrated and generalized power/sinusoidal distributed loads. International Journal of Engineering & Applied Sciences (IJEAS), 10(2), 35-63. DOI: 10.24107/ijeas.430666

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).