API 2B Specification for the Fabrication of Structural Steel by American Petroleum Institute

By American Petroleum Institute

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11 is replaced by the solution ¢ of Eqs. 14-15. Then Eq. 11 gives m ¢(x) = G(3EX[rJ+ LPr(x)kr (16) r=1 because B(r) belongs to one of the boundaries {aD r }, r = O,I, ... ,m, ¢ takes different constant values on these boundaries, and A¢(x) = -G(3, xED, so that J; A¢(X(s)) ds = -G(3r. The parameters Pr( x) denote the probabilities P(B( r) E Dr) that the Brownian motion exits D through Dr. Three numerical examples are presented to illustrate the use of Eq. 16. First, let D be a simply connected circular cross section of radius r > O.

KAWAI Science University of Tokyo Tokyo, Japan N. TAKEUCHI Meisei University Tokyo, Japan 1. Introduction In order to break through bottleneck of finite element nonlinear analysis in solid mechanics, the first author (Kawai, 1977) proposed a family of new simplified element basing on the experimental evidence of solids under the ultimate state of loading in 1977. Since then a series of verification studies have been made in steel structures successfully. However in case of reinforced concrete as well as foundation structures, influence of crack initiation due to tensile loading often can not be neglected.

For a triangular primitive element, the first or fundamental residual stress mode occurs when p=4 and dimension};'RE = 1. The algebraic form of this field is given in Equation (6) in terms of contravariant components with reference to the element and its local oblique axes in Figure 2. (l994). The incompatibility of elastic strains, as noted in corollary (ii), is confirmed for such an element by the scalar incompatibility function in Equation (7). ~E \7 2 (tr[ a]) = ~(1~(x + Y) + -;'(X2 + xy + y2)~ 3E a a ) (7) EQUILIBRIUM FINITE ELEMENTS 45 A similar pattern of stress trajectories is supplied by the experimental work of James Clerk Maxwell.

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