Engineering Transactions, 12, 1, pp. 137-157, 1964

### Zginanie Łuków Falistych

S. Borkowski
Politechnika Śląska
Poland

This is a tentative determination of the flexibility factor and the stresses in a corrugated pipe bend (Fig. 1). The problem is considered from the viewpoint of the theory of orthotropic shells (structural orthotropy), The fundamental equation is the generalized equation of E. Reissner, [10]. The orthotropy functions k1 and k2 are assumed by assuming a sinusoidally corrugated middle surface according to the equations given in [14]. The middle surface of the bend is treated as a toroidal one. After ia number of simplifications the functions ki, k2 are determined by the final equations (2.6) (2.7). It is shown that the function kt has no essential influence on the phenomenon and may be disregarded so that the simplified equation has the final form (4.5). The integration of this equation leads to a set of linear Eqs. (4.2) from which the flexibility factor can be obtained as well as the coefficients bn of the series of internal forces (6.1). A certain view of the convergence of these series may be Hz gained by means of Fig. 7 in the case where Hz =0.
In conclusion a numerical example is given to illustrate the way of computation of such arcs. The end diagrams of stresses are those of Fig. 8.

Full Text: PDF

#### References

A. BANTLIN, Formänderung und Beanspruchung federnder Ausgleichröhren, Z. Ver. deut. Ing., 54 (1910), 43.

R. A. CLARK, E. REISSNER, Bending of curved tubes, Adv. Appl. Mech., 2 (1951), 93.

E. T. COPE, E. A. WERT, Load-deflection relations for large plain corrugaded and creased pipe bends, Trans. ASME (Fuels a. St. Pow.), 16, 54 (1932), 115.

L. H. DONNELL, The flexibility of corrugated pipes under longitudinal forces and bending, Trans. ASME (Appl. Mech.), 11, 54 (1932), 69.

H. FORD, C. E. TURNER, Examination of the theories for calculating the stresses in pipe bends subjected to in-plane bending, Proc. Inst. Mech. Engs, 15,171 (1957), 513.

N. GROSS, Experiments on short-radius pipe-bends bending of curved thin-walled tubes without internal pressure, Heat. Treat. Eng., 15 (1953), 73, 106, 134.

M. T. HUBER, Odkształcenie sprężyste rury cienkościennej o przekroju eliptycznym przy jej zginaniu, Arch. Mech. Stos., 1, 1 (1949). 1.

P. G. KAFKA, M. B. DUNN, Stiffness of curved circular tubes with internal pressure, J. Appl. Mech., 2, 23 (1956), 247.

T. KARMÁN, Über die Formänderung dünnwandiger Rohre insbesondere federnder Aus- gleichrohre, Z. Ver. deut. Ing., 55 (1911), 1889.

B. REISSNER, Rotationally symmetric problems in the theory of thin elastic shells, Proc. Th. U.S. Nat. Congr. Appl. Mech., (1958), 51.

E. REISSNER, On the finite bendig of pressurised tubes, J. Appl. Mech., 3, 26 (1959), 386.

E. REISSNER, On finite pure bending of cylindrical tubes, Österr. Ing.-Arch., 15 (1961), 165.

Design of Piping Systems, (praca zbiorowa), New York 1957.

[in Russian]

[in Russian]

[in Russian]

[in Russian]

[in Russian]

[in Russian]

[in Russian]

[in Russian]

[in Russian]

[in Russian]

[in Russian]

[in Russian]

[in Russian]

[in Russian]

[in Russian]

[in Russian]

[in Russian]

[in Russian]