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Nonlinear analysis of buckling and postbuckling behavior of circular arches

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Zusammenfassung

Unter Vernachlässigung der Schubverzerrung und der Dehnbarkeit der elastischen Linie werden die kritischen Werte der auf einen schlanken Zweigelenkkreisbogenträger niederwärts wirkenden Gipfeleinzellast auf der Basis der nichtlinearen Eulerschen Theorie berechnet. Der Zustand des Bogenträgers im Augenblick der seitlichen Schwenkung sowie dessen Verhalten vor und nach der Knickung, werden für vier verschiedene Massverhältnisse des Bogens untersucht. Die bisherigen Näherungslösungen werden mit den berechneten Ergebnissen verglichen.

A bar on top of a letter indicates that the entity pertains to the right half of the arch.

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Abbreviations

E :

modulus of elasticity

H :

horizontal component of the internal forceR acting on a cross section of the arch rib (see figure 1)

I :

moment of inertia of the crosssectional area

L :

span (distance between supports)

M :

internal bending couple

N :

thrust

P :

downward vertical point load at the crown of the arch

Q :

shearing force

R :

internal resultant forceR 2=H 2+V 2=N 2+Q 2

V :

vertical component ofR

a :

radius of the centroidal circle of the arch rib

k :

(R/E I)1/2=(H/E I cos μ)1/2

m :

[a 2 k 2/(1+a 2 k 2sin2 ϕ 0)]

p :

P a 2 /E I; as a subscript,p indicates the crown of the arch

s :

length along the centroidal curve measured from the left support

s :

length along the centroidal curve measured from the right support

u :

displacement component, tangential to the undeformed arch

w :

displacement component, normal to the undeformed arch, positive inward

x, y :

rectangular coordinates of a point of the deformed left half of the centroidal curve

α:

half the subtending angle of the arch

θ:

angle of inclination of the tangent to the deformed left half of the centroidal curve

μ:

angle betweenH andR

ϕ:

half the angle betweenR and the tangent to the deformed arch

References

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  2. N. C. Lind,Elastic Buckling of Symmetrical Arches, University of Illinois Eng. Experiment Station Techn., Report No. 3 (1962).

  3. D. A. DaDeppo andR. Schmidt,Sidesway Buckling of Deep Circular Arches under a Concentrated Load, to be published in the J. appl. Mech., Trans. ASME.

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Authors and Affiliations

  1. Dept. of Civil Engineering, University of Arizona, Tucson, Arizona, USA

    Donald A. DaDeppo

  2. Dept. of Engineering Sci., University of Detroit, Detroit, Michigan, USA

    Robert Schmidt

Authors
  1. Donald A. DaDeppo
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  2. Robert Schmidt
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DaDeppo, D.A., Schmidt, R. Nonlinear analysis of buckling and postbuckling behavior of circular arches. Journal of Applied Mathematics and Physics (ZAMP) 20, 847–857 (1969). https://doi.org/10.1007/BF01592295

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  • DOI: https://doi.org/10.1007/BF01592295

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