Engineering Transactions, 28, 3, pp. 487-500, 1980

Solution of the Differential Equations Governing the Equilibrium of a Skew-Curved Beam

D.E. Panayotounakos
Athens National Technical University, Athens

P.S. Theocaris
Athens National Technical University, Athens

The present paper deals with the closed form solution of the differential equations, with variable coefficients, governing the equilibrium of a skew or planar-curved beam. This problem is associated with a system or twelve coupled linear differential equations of first order, the closed form solution of which was achieved through tow analytical methods.
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A. E. H. LOVE, A treatise on the mathematical theory of elasticity, Forth edition, Dover Publ., New York 1944.

G. B. BIEZENO and R. GRAMMEL, Technishe Dynamik, Springer-Verlag, Berlin 1939.

P. M. GERY and J. A. CALGARO, Les matrices-transfert dans le calcul de structures, Editions Eyrolles Paris 1973.

J. T. ODEN, Mechanics of elastic structures, McGraw-Hill Book Compauy, New York 1967.

R. DABROWSKI, Wolbkrafttorsion von gekrummten Kastenträgern mit nichtverformbarem Profil, Der Stahlbau, 34, 135, 1965.

E. D. PANAYOTOUNAKOS, Statical investigation of skew-curved beams, Technika Cronika, Athens, 295, 1949.

F. BARON and J. P. MICHALOS, Laterally loaded plane structures and Structures curved space, Tran. ASCE, 117, 279-311, 1952.

J. P. MICHALOS, Numerical analysis of frames with curved girders, Trans. ASCE, 121, 521-543, 1956.

H. H. FICKEL, Analysis of curved girders, J. of the Str. Div. ASCE, 85, 113-141, 1959,

J.J. TUMA and M. N. REDDY, Analysis of laterally-loaded continuous curved beams, J. of the Str. Div., ASCE, 93, 495-513, 1967.

A. ABDUL-BAKI and A. SHUKAIR, Continuous helicoidal girders, J. of the Str. Div., ASCE, 99, 2183-2203, 1973.

F.Y. YQUNG and A. S. SCORDELLIS, An analytical and experimental study of helicoidal girders, J. of the Str. Div., ASCE, 84, 1-29, 1958.

B. VELTUNI, Analysis of continuous circular beams, J. Am. Con. Inst., 22, 217-228, 1950.

M. C. YOUNG, Flexibility influence functions for curved beams, J. of the Str. Div. ASCE 95, 1407-1429 1969.

D. C. MORRIS, Curved beam stiffnes coefficients, J. of the Str. Div. ASCE, 94 1165-1174. 1968.

D. E. PANAYOTOUNAKOS and P.S. THEOCARIS, Flexibility matrix for skew-ourved beams, Int. J. of Sol. and Str. (accepted for publication).

V. R. BERGMAN, Helicoidal straircases of reinforced concrete, J. Am. Con. Inst., 28, 403-412, 1956.

P. McMANUS, C.A. NASIR and C. G. CULVER, Horizontally curved Girders-State-of-the-Art, J. of the Str. Div. ASCE. 95- 853-870 1969.

K. WASHIZU, Some considerations on a naturally curved and twisted slender beam, J. of Math. and Phys., 43, 111-116, 1964.

M. BUIX, Les fonctions generalisees ou distributions, Masson et Cie Paris 1963.