By A C Liebenberg; et al
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Extra info for Concrete bridges : design and construction
7 /7! 136) we conclude that Eq. 134) is equivalent to Eq. 1) with α = nπ, and thus we obtain the minimal eigenvalue given in Eq. 1). 94% error. With more terms the error diminishes rapidly. We followed Bürgermeister and Steup (1957) here in exposing the direct series representation method. The method was greatly expanded and re-interpreted by Eisenberger (1991a–d). He considered bars, columns and beams of variable properties. 139) where W is the transverse displacement, N(x) the axial force, P(x) the distributed transverse load along the member and D(x) = EI(x) is the ﬂexural rigidity.
Who were the ﬁrst investigators to tackle the inverse problems? H. Abel . . in 1823. This problem consists of ﬁnding curve Xin a vertical plane where X is assumed to be graph of an increasing function x = Φ(y) such that the falling time of a body (falling only under the inﬂuence of gravity) is a known function t(y) of the height from which the body falls. This problem reduced to an Abel integral equation has a unique solution. If Φ is multi-valued then inﬁnitely many solutions exist. G. Stokes for the ﬁrst time raised the question of the relationship between the Newtonian potential at the exterior of a closed surface containing an attracting body and the distribution of the body’s density p producing the assigned potential.
If Φ is multi-valued then inﬁnitely many solutions exist. G. Stokes for the ﬁrst time raised the question of the relationship between the Newtonian potential at the exterior of a closed surface containing an attracting body and the distribution of the body’s density p producing the assigned potential.
Concrete bridges : design and construction by A C Liebenberg; et al