scholarly journals Discussion: “Nonlinear Creep Deformations of Columns of Rectangular Cross Section” (Bleich, H. H., and Dillon, Jr., O. W., 1959, ASME J. Appl. Mech., 26, pp. 517–525)

1960 ◽  
Vol 27 (2) ◽  
pp. 371-372
Author(s):  
H. G. McComb
1959 ◽  
Vol 26 (4) ◽  
pp. 517-525
Author(s):  
H. H. Bleich ◽  
O. W. Dillon

Abstract Creep deformations of columns of rectangular cross section are studied for the case of materials following the nonlinear law ϵ̇ = (1/E) σ̇ + λσk. The essential point of the paper is the following: The time rate of the curvature κ̇ of an element of a bar loaded by a constant force P and an increasing bending moment M(t) has bounds, which depend on P and on the instantaneous values of M and Ṁ, but not on the history of M. In combination with the collocation method, this permits the formulation of ordinary differential equations for upper and lower bounds on the deformations. Closed solutions for the critical time are obtained for one bound, while the other requires numerical integration. The bounds which are a function of the initial eccentricity are reasonably close and are presented in tables and graphs. By qualitative reasoning it is further shown that the location of the actual critical time with respect to the two bounds is governed by the ratio of the column load P and the nominal Euler buckling load PE of the column if it were elastic.


Water ◽  
2021 ◽  
Vol 13 (15) ◽  
pp. 2119
Author(s):  
Luís Mesquita David ◽  
Rita Fernandes de Carvalho

Designing for exceedance events consists in designing a continuous route for overland flow to deal with flows exceeding the sewer system’s capacity and to mitigate flooding risk. A review is carried out here on flood safety/hazard criteria, which generally establish thresholds for the water depth and flood velocity, or a relationship between them. The effects of the cross-section shape, roughness and slope of streets in meeting the criteria are evaluated based on equations, graphical results and one case study. An expedited method for the verification of safety criteria based solely on flow is presented, saving efforts in detailing models and increasing confidence in the results from simplified models. The method is valid for 0.1 m2/s 0.5 m2/s. The results showed that a street with a 1.8% slope, 75 m1/3s−1 and a rectangular cross-section complies with the threshold 0.3 m2/s for twice the flow of a street with the same width but with a conventional cross-section shape. The flow will be four times greater for a 15% street slope. The results also highlighted that the flood flows can vary significantly along the streets depending on the sewers’ roughness and the flow transfers between the major and minor systems, such that the effort detailing a street’s cross-section must be balanced with all of the other sources of uncertainty.


2001 ◽  
Vol 68 (6) ◽  
pp. 865-868 ◽  
Author(s):  
P. Ladeve`ze ◽  
J. G. Simmonds

The exact theory of linearly elastic beams developed by Ladeve`ze and Ladeve`ze and Simmonds is illustrated using the equations of plane stress for a fully anisotropic elastic body of rectangular shape. Explicit formulas are given for the cross-sectional material operators that appear in the special Saint-Venant solutions of Ladeve`ze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized displacement). A new definition is proposed for built-in boundary conditions in which the generalized displacement vanishes rather than pointwise displacements or geometric averages.


Soft Matter ◽  
2021 ◽  
Author(s):  
Aditya Natu ◽  
Uddipta Ghosh

Flow of polymeric liquids in narrow confinements of rectangular cross section, in the presence of electrical double layers is analyzed here. Our analysis is motivated by the fact that many...


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