Engineering Transactions, 10, 4, pp. 679-711, 1962

Powłoki Walcowe Zamknięć Wodnych

R. Dąbrowski
Politechnika Gdańska
Poland

This is an analysis of the stress in the covering of steel water gates which may be treated as a circular cylindrical shell. After a brief discussion of various theories of such a shell (Sec. 1) further analysis is based on the Donnell differential equation. First, double series are used to solve the problem of a simply supported shell subjected to a hydrostatic pressure or a uniform radial load (Sec. 2). For shells of stronger curvature the convergence of the series is poor. In this case, a boundary value problem is solved, taking into consideration-the coefficient v ≠ 0. Equations for the internal forces are derived (Sec. 3).

Next, Sec. 4 contains a discussion, also by using double series, of a clamped shell considered to constitute a portion of a continuous shell. For an orthotropic shell, differential equation is derived corresponding to the Donnell equation (Sec. 5). In Sec. 6 several examples are used to illustrate the distribution of internal forces, above all, in simply supported isotropic shells and the influence of various parameters on their magnitude. Final remarks are devoted to the verification of the stresses taking into consideration the danger of buckling. They are based on the analysis known from textbooks.

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References

C. F. KOLLBRUNNER, Hydraulic Steel Gates, Proc. of Research and Construction on Steel-Engineering, 13, 1950.

S. TIMOSHENKO, Theory of Plates and Shells, McGraw-Hill, N. York 1940.

W. FLÜGGE, Statik und Dynamik der Schalen, Springer-Verlag, Berlin 1934.

K. GIRKMANN, Flächentragwerke, 3. Aufl., Springer, Wien 1954.

S. L. LEE, Bending of Partially Loaded Simply Supported Cylindrical Shells, Publ. Int. Ass, for Bridge and Structural Eng. 19, 1959, s. 155.

Am. Soc. Civ. Eng., Manuals of Engineering Practice, No 31., Design of Cylindrical Concrete Shell Roofs, N. York 1952.

U. FINSTERWALDER, Die Theorie des kreiszylindrischen Schalengewölbes System Zeiss-Dywidag, Abh. IVBH. 1, 1932, s. 127.

[in Russian]

H. SCHORER, Line Load Action 0n Thin Cylindrical Shells, Proc. Am. Soc. Civ. Eng., 61, 1935, s. 181.

Cement and Concrete Assoc., Concrete Shell Roof Construction, Proceedings of a Symposium, London 1954.

D. YITZHAKI, The Design of Prismatic and Cylindrical Shell Roofs, Haifa 1958.

L. H. DONNELL, Stability of Thin-Walled Tubes under Torsion, NACA Techn. Rep., 479, 1933.

T. KARMÁN, TSIEN HSUE SHEN, The Bending of Thin Cylindrical Shells under Axial Compression, J. Aeron. Sci., 8, 1941, s. 303.

R. S. JENKINS, Theory and Design of Cylindrical Shell Structures. Modern Build. Techn. Bull. 1, London 1947.

J. E. GIBSON, D. W. COOPER, The Design of Cylindrical Shell Roofs, Spon Ltd, London 1954.

G. GRÜNING, Die Berechnung von Kreiszylinderschalen ohne Benutzung von Randwerttafeln, Bauplanung-Bautechnik, 11, 1957, s. 297.

[in Russian]

[in Russian]

F. DISCHINGER, Die strenge Theorie der Kreiszylinderschale in ihrer Anwendung auf die Zeiss-Dywidag-Schalen, Beton und Eisen, 34, 1935, S. 257, 283.

K. MIESEL, Über die Festigkeit von Kreiszylinderschalen bei nichtachsensymmetrischer Belastung, Ing.-Arch., 1, 1930, s. 22.

AAS JAKOBSEN, Über das Randstörungsproblem an Kreiszylinderschalen, Bauingenieur, 20, 1939, s. 394.

R. OHLIG, Räumliche Tragwerke des Stahlbetonbehälterbaues, Beton- und Stahlbetonbau,

, 1953, s. 233.

N.J. HOFF, Boundary-Value Problems of the Thin-Walled Circular Cylinder, J. Appl. Mech., 76, 1954, s. 343.

H. SCHMIDT, Ein Beitrag zum Randstörungsproblem an den Binderscheiben der Kreiszylin-derschalen, Bauplanung-Bautechnik, 11, 1957, H. 1,2.

A.L. PARME, Ribless Cylindrical Shells, Proc. of the Second Symposium on Concrete Shell Roof Construction, Oslo 1958.

I. HOLLAND, An Application of Donnell's Theory of Circular Cylindrical Shells to the Analysis of Curved Edge Disturbancy, Publ. Int. Ass. for Bridge a. Structural Eng., 19, 1959, s. 65.

J. MOE, On the Theory of Cylindrical Shells. Explicit Solution and Discussion of the Accuracy of Various Shell Theories, Publ. Int. Ass. for Bridge a. Structural Erg., 13, 1953, s. 283.

N.J. HOFF, The Accuracy of Donnell's Equations, J. Appl. Mech., 77, 1955, s. 329.

[in Russian]

L. TING, S. W. YUAN, On Radial Deflections of a Cylinder of Finite Length with Various End Conditions, J. Acron. Sci., 25, 1958, S. 230.

L. S. D. MORLEY, An Improvement on Donnell's Approximation for Thin-Walled Circular Cylinder, Quart. J. Mech. a. Appl. Math., 12, 1959, 8. 89.

V. LEWE, Pilzdecken und andere trügerlose Eisenbetonplatten, W. Ernst, Berlin 1926.

H. LUNDGREN, Cylindrical Shells, Vol. 1, The Danish Technical Press, Copenhagen 1949.

A. JAKOBSEN, Die Berechnung von Kreiszylinderscholen, Springer, Berlin 1958.

W. FLÜGGE, Stresses in Shells, Springer, Berlin 19C0.

K. GIRKMANN, Dźwigary powierzchniowe, Warszawa 1957, Arkady oraz Dodatek, Arkady, Warszawa 1961.

O. OLSEN, Continuous Shells. Proc. of the Second Symposium on Concrete Shell Roof Construction, Oslo 1957.

[in Russian]

Y. C. FUNG, E. B. SECHLER, Instability of Thin Elastic Shells, Proc. First Symposium on Naval Structural Mechanics, Pergamon Press, Oxford. 1960.

[in Russian]

R. DABROWSKI, Skręcanie mostowych i hydrotechnicznych konstrukcji cienkościennych o prze- kroju zamkniętym, Gdańsk 1958.

Y.C. DAS, On the Bending of Orthotropic Cylindrical Shells, J. Aero-Space Sci., 28, 1961, s. 661.

[in Russian]

R. DABROWSKI, Die Bgrechnung der allseitig starr Rauingenieur. 37 (1962), 459.