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sharing between individual leaves. The trunnels not only connect chords and lattice together, they also allow for load sharing within the individual chord sticks to provide continuity through joint locations. Drawings for new or existing Town lattice trusses should show the distribution of joints in all chords with the length of the chord sticks noted. Replacement chord sticks installed in a bridge should respect the original joint locations. During the rst Covered Bridge Conference held in Burlington, Vermont, in February 2003, we observed and brie y reviewed the analysis of several covered bridges as performed by universities for government agencies, and by traditional highway bridge engineers as consultants. In the rst case, the effort is academic, resulting in an educational tool used to transfer knowledge to the design community. In the second case, there are serious gaps in the understanding of how these timber structures perform by some members of the highway bridge design community. Some engineers demonstrate their lack of knowledge of timber design when they talk of shear planes in the design of trunnels. The capacity of trunnels used as the primary connector in Town lattice trusses is governed by the bearing in the trunnel perpendicular to grain. Timber elements do not fail in shear across the grain. When a load is applied perpendicular to the longitudinal axis of a timber pin, it may fail in bearing perpendicular to grain, in horizontal shear, or bending; but not in shear through its cross-section. Since bearing in the pin controls the design, increased capacity in Town lattice connections can be achieved by increasing the diameter of the pins or by



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k*2) ('ljJ*(O)'lj)(O)) }

= ('ljJ*(2'))Q(2', 2) ('lj)(2))

+ (G*(O, 1'))1(0,2; 1', 2') ('ljJ(2)) ('ljJ*(2'))

+ (G*(O, 1'))1(0,2; 1', 2')(G(2, 3))(G*(2', 3'))1(3, 4; 3', 4') ('ljJ (4)'ljJ* (4')) + Q(2', 2)(G(2, 3))(G*(2', 3'))1(3, 4; 3', 4') ('ljJ(4)'ljJ* (4'))

- Q*(2, 2')('4',*(2')) ('lj)(2)) - (G(I', 0))1(0, 2; 1', 2') ('lj)(2)) ('ljJ*(2')) - (G(I', 0))1(0, 2; 1', 2')(G(2, 3))(G*(2', 3'))1(3, 4; 3', 4') ('ljJ (4)'ljJ* (4')) (4.2.32) - (G(2, 3) )Q*(2, 2')(G* (2',3'))1(3,4; 3',4') ('lj)(4)'lj)* (4')) Integration is performed over all repeated arguments on the right-hand side of (4.2.32).





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Consider a plane electromagnetic wave of unit amplitude with polarization incident angle Crr - B ,1Ji) impinging upon a half-space medium of oi N dielectric scatterers of permittivity Es and wavenumber k s (Fig. 7.5.1). The particles occupy volumes VI, V2,'" VN, respectively. The background permittivity in the lower half-space as well as the upper half-space is E. Let E(A) and S(A) denote respectively the electric field and time-averaged Poynting's vector, respectively, and the superscript (A) is used to denote

Figure 7.5.1 Problem A: Active remote sensing with a plane electromagnetic wave of unit amplitude, polarization ti, and incident angle (7r - (JOi, li) impinging upon a half-space of

particles. Electrical field and Poynting's vector are denoted respectively by El(A) and S(A).

breaking above its resistance level. Notice the pullback to the former resistance level after the breakout, after which the price soared.

Problem A. The electric field E(A) obeys the vector wave equation,

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selecting trunnel material with a high allowable design value in bearing perpendicular to grain such as live oak, locust, or mesquite. Many highway, county, and consulting engineers, considering ways to increase the capacity of Town lattice trusses, have added steel splice plates at bottom chord joints. Connections such as these may be effective if the drilling is very accurate, the holes not more than 1/16th of an inch larger than the bolt diameter, the connection consists of two plates with the connection in double shear, and the connections are prestressed by jacking some camber into the bridge prior to drilling the holes. In actual practice, none of these conditions are met. The iron and steel dogs, found in Town lattice railroad bridges, to fasten chord sticks together, work much better because they were installed with great precision during original construction. In some cases they are adjustable and can be tightened.

\7 x \7 x E(A) (r) - k2 E(A) (r) -

Vi (r)E(A) (r) = 0

(7.5.1)

seA) =

{E(A)* x (\7 x EA) - E(A) x (\7 x E(A)*) }

(7.5.2)

L E~Vi(r) IE(A\r)1

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