Thick Arches Research Articles

Passive stress-strain relation for the right ventricle in diastole

Wall thicknesses and medial line radii of an in vitro canine heart are measured. These data are assumed to be characteristic of the in vivo ventricles subject to zero pressure, and in the absence of filling. The myocardium is taken to be homogeneous, isotropic, non-linearly elastic, and incompressible. The right ventricular free wall is modeled as a circular arch of constant thickness, fixed at the interventricular groove. Circumferential stress is determined from thrust, and circumferential strain from displacement, both at the crown of the midwall. Our purpose was to obtain a stress-strain relationship without inertia and ventricular filling, termed passive. The passive circumferential stress-strain relation for the right ventricle in diastole is shown to be an exponential equation with two parameters. These parameters are related to the product of material constants of the in vivo heart, and functions of right ventricular geometry in terms of the ratio of wall thickness to arch radius, and the terminal value of the central angle. Using mean values of observations, right and left ventricular passive curves are plotted over the same representative strain interval in an example from lowest diastolic pressure to the start of atrial contraction.

Design of shell shape using finite elements

A finite triangular facet element for the analysis of doubly curved thin shells is presented, the principal feature of which is a particularly simple resolution process. A simple iterative design procedure is developed, the optimality criteria of which are the elimination of bending and the minimization of the surface integral of the membrane stresses. The procedure is used to obtain numerical predictions of the optimal shapes for constant thickness arches and shells that are in good agreement with those expected. Finally, the procedure is extended to provide an optimal shape for a uniform thickness arch dam and an iterative procedure used to provide an optimal thickness variation.

Non-linear vibration of a moderately thick shallow clamped arch

Large amplitude flexural vibrations of a moderately thick arch have been studied. The material of the arch has been assumed to be homogeneous, isotropic and linearly elastic. Governing equations have been derived by the variational method. Values of the period for different amplitudes, for arches with built-in ends, have been computed by numerical integration. Phenomena like dynamic buckling, transition from a slightly curved beam to a shallow arch, etc., have been discussed. Results computed for the limiting case of a thin beam are in good agreement with the existing results.

Finite extensional deformation of a rigid plastic arch

The exact, nonlinear extensional theory of a rigid perfectly plastic arch is used to determine the complete load-deflection behavior of a clamped semicircular arch under the action of a vertical upward point load at the crown. A rate formulation of the problem is discussed. Solution of the rate problem at the yield-point state provides the basis for the construction of exact solutions for thin and for thick arches. Numerical results are presented in graphical form. These results consist of load-deflection curves for three thin arches and one thick arch. The plots together with formulas presented herein show that the slope of the load-deflection curve at the yield-point state is nonzero and positive for upward loading. This result deviates from the zero slope predicted by the usual methods of limit analysis in which geometry changes are neglected.

The safety of masonry arches

The paper describes the application of limit principles, derived from the plastic analysis of steel structures, to the masonry arch. Most voussoir arches have low stresses, and the lines of thrust lie well within the masonry, so that conventional factors of safety on stress have little relevance. However, a “geometrical” factor of safety may be defined by consideration of the arch of minimum thickness, of the same shape as the real arch, which would just contain a proper line of thrust. If the real profile of the arch is then discarded, and the calculations referred to an arch having the profile of the ideal line of thrust, it is shown that a simple analysis may be made of the effect of travelling point loads. The ideas are applied to the analysis of two actual bridges: (a) the stone arch between the western towers of Lincoln Cathedral, and (b) the Ponte Mosca in Turin. The paper is concerned only with the action of the masonry, and not with the design of the abutments to resist the thrust of the arch. However, the effect of geometry changes due to yielding of the abutments is discussed.

Stresses in thick arches with elastically fixed ends weakened by a row of round openings

1. Stresses {ei226-1 for arch I are compressive. For the extrados the stresses reach their maximum at the key section 0-0 (8.35q), and for the intrados at section 3–3 at the support (9q). 2. For the arch II with no pressure in the openings (model M-2), there are tension stresses {ei226-2 at the intrados, reaching their maximum value at the key section 0-o (3q) for a given external pressure. At the extrados the maximum compressive stress for the key section is 5.3q. 3. A considerable stress concentration occurs around openings. The compressive stresses at the edges with no pressure inside the openings reach 12.8q for arch I and 9.8q for arch II. The maximum tension stresses at the opening edge are 3q for the arch I and 2.5q for the arch II. It should be noted that the stress concentration decreases rapidly; the tension zone spreads for about 1.4r from the edge of the opening. 4. The comparison of experimental data for stress distribution around round openings with the corresponding stresses determined according to an approximate solution for a bent bar with a small round hole [4] indicates that the relative influence of one opening on the other for a given location is negligible. 5. There are compressive stresses in the rock foundation close to the arch I supports and their maximum value amounts to 4.8q. At the base of the arch II the compressive stresses reach 3.5q. 6. The presence of a uniformly distributed pressure in the opening modifies the arch II stress state close to the openings only, decreasing the compressive stresses at the edges and increasing the tension stresses to 3.5q.

Arch Dam Layout Facilitated By Use of Computer

Computer application is used to simplify the layout of a variable thickness arch dam of double curvature. With prescribed, though flexible, relationships given for the angles subtended, thickness variation, and crown to abutment overhang, a computer program determines the centers and radii of the intrados and extrados arcs and cross-sectional dimensions. By this means, a rapid evaluation of the many factors affecting dam geometry can be made.

Closure of “Cravitz on Analysis of Thick Arch Dams”

Closure of “Cravitz on Analysis of Thick Arch Dams”

Analysis of Thick Arch Dams, Including Abutment Yield

Analysis of Thick Arch Dams, Including Abutment Yield

Discussion of “Nelidov on Analysis of Thick Arch Dams”

Discussion of “Nelidov on Analysis of Thick Arch Dams”

Discussion of “Cain on Stresses in Thick Arches of Dams”

Discussion of “Cain on Stresses in Thick Arches of Dams”

Stresses in Thick Arches of Dams

Stresses in Thick Arches of Dams

Closure to “Jakobsen on Stresses in Thick Arches of Dams”

Closure to “Jakobsen on Stresses in Thick Arches of Dams”