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In January 1988, I proposed a solution requiring replacement of the original chords with glued laminated timber members in very long lengths, to bridge areas of high stress Although it was presented with reservations, this solution was immediately accepted by the two departments of transportation The glued laminated timber replacement chord solution provided the Cornish-Windsor Bridge with an HS15-44 capacity without the addition of retro tted laminated timber arches This alternative required the installation of architectural grade, prefabricated, structural glued laminated timber chords and oor beams in areas of high tensile stress in the bridge6 Structural glued laminated timber, commonly referred to as glulam, was introduced into the United States in 1936 from Germany In glued laminated timber products, higher design values are obtained by providing clear, dense laminations in areas of high stress Strength-reducing defects such as large knots are removed.



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Kong (1981 h), Application of strong fluctuation random medinm theory to scattering from vegetation-like half-space, IEEE lhms Geosci Remote Sen~, 19,.

Tsang. L. . .1. A. Kong. and R. W. Npwt.on (1982), Application of st.rong fiuct.nation random mcdinlll theory t.o scat.t.ering of ('lectronmgnet.ic waves from a ha\l~space of dielE'cl.ric mixture. JEEE Tm.n". Antenna." P'IOl'flqat., 30. 292~:302.





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Veysoglu, M. E. (1994), Direct and inverse scattering models for random media and rough surfaces, Ph.D. thesis, Massachusetts Institute of Technology. Wang, H., J. Pulliainen, and M. Hallikainen (1998), Correlation functions and correlation lengths for dry snow, .1. Eleetmmag. Waves and Appl., 12, 1337-1347. Wang, H., .J. Pulliainen, and M. Hallikainen (2000a). Extinction behaviour of dry snow at microwave range up to 90 GHz by using strong fluctuation theory, P1'Ogres8 in Electrornag. Res., 25, 39-50. Wang, H., J. Pulliainen, and M. Hallikainen (2000b), Microwave emission model for dry snow by using radiative transfer and strong fluctuation theory, Progress in Electromag. Res., 29,39-55. Yueh, H. Y., R. T. Shin, and.1. A. Kong (1990), Scattering from randomly oriented scatterers with strong permittivity fluctuations, .1. EII~etrornag. Waves and Appl., 4, 983-1004.

Scattering of Electromagnetic Waves: Advanced Topics. Leung Tsang, Jin Au Kong. Copyright 2001 John Wiley & Sons, Inc. ISBNs: 0-471-38801-7 (Hardback); 0-471-22427-8 (Electronic)

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Transition Operator Multiple Scattering Equations Approximations of Multiple Scattering Equations Configurational Average of Multiple Scattering Equations Effective Field Approximation (EFA, Foldy's Approximation) Quasi-crystalline Approximation (QCA) Coherent Potential (CP) Quasi-crystalline Approximation with Coherent Potential (QCA-CP) Low-Frequency Solutions QCA-CP for Multiple Species of Particles Ward's Identity and Energy Conservation Derivation of Radiative Transfer Equation from Ladder Approximation References and Additional Readings

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Natural growth characteristics such knots, wane, and checks normally found in all timber materials are considered to be defects because of their strength-reducing capabilities7 In the production of structural glued laminated timber, laminations are glued together with waterproof glue The surface appearance of structural glued laminated timber does not have to be the slick-planed nish often seen in architectural applications A crosssanded nish approximating a rough sawn appearance can be furnished7 For the Cornish-Windsor Bridge, the use of prefabricated glued laminated timber offered ve advantages: 1 Because glued laminated timber consists of a number of pieces of laminate glued together, it can be fabricated in longer lengths than solid materials 2 It can usually be fabricated and shipped within 8 to 10 weeks This period is less than the total time required for ordering, cutting, and drying large solid timber materials 3.

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In this chapter, we study the multiple scattering theory for discrete scatterers. We establish the Foldy-Lax multiple scattering equations rigorously. Configurational averages are taken leading to a hierarchy of equations. However, to solve the equations, approximations need to be made. We study two approximations: the effective field approximation and the quasi-crystalline approximation. The coherent potential is then introduced to impose selfconsistent approximations. Energy conservation is expressed in terms of the integrated optical relation. It is shown that if (i) the quasi-crystalline approximation with coherent potential applied to the first moment equation and (ii) the correlated ladder approximation is applied to the second moment equation, then the integrated optical relation is obeyed. In Section 5, we show the derivation of the radiative transfer equation from the ladder approximation for isotropic point scatterers.

Consider the case of a single discrete scatterer centered at the origin. The permittivity is Ep(r). Then the equation that governs the Green's function is \7 x \7 x Gs(r, r') - w 2 JLEp(r)G s(r, r') = 115(r - r') The equation that governs the free-space dyadic Green's function is \7 x \7 x Go(r, r') - k2 Go(r, r') = 115(r - r') We can rewrite (5.1.1) as \7 x \7 x Gs(r, r') - k2 G,,(r, 1") = 115(1' - r') where (5.1.2) (5.1.1)

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