By American Institute Of Steel Construction (Aisc), Structural Steel Educational Council

This six-part guide helps the 2005 AISC Seismic Provisions. It comprises sections on basic layout concerns; layout of structures using R = three (braced and second frames); layout of braced-frame structures using R > three; layout of second body structures using R > three; and layout of different platforms using R > three.

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This results in a rapid expansion along the c axis accompanied by a contraction normal to it (see Fig. 3). In 1958 Sheard [9] applied an anisotropic continuum model to calculate the Griineisen parameters (52) The thermal expansion and elasticity of an ideal Table II. 0 Fig. 3. Thermal linear expansion of zinc showing rapid expansion along c axis and contraction along a axis below 200 K. at low and high temperatures from the pressure dependence of the elastic constants. Assuming that at long wavelengths for each of the three acoustic branches in cubic crystals pSf = c, (53) (S, is the velocity of sound and c, is the elastic constant) and v, (54) kS, = where the application of cyclic boundary conditions requires that kL = (55) 0, ±I, ±2, ...

In solids which have noncubic symmetry. 3 (46) j= 1 where sii are the elastic compliances [8]. This equation gives a linear relation between components of the expansion tensor and the heat capacity. JOO TEMPERATURE,K Fig. 2. Coefficient of expansion of germanium showing negative values between 16 and 40 K. tensor so that f3 Cv =- v 3 6 I I i=1 j=1 Si/li (47) where sii(j = 4, 5, 6) = 0, as in cubic, hexagonal, orthorhombic, and some tetragonal crystals. 633, should be isotropic. In this case ot 1 = ot 3 and s 11 + s 12 = s 13 + s 33 (see Table II).

0 .. "Thermal Vacancies and Thermal Expansion," in AlP Conf Proc. No. 3-Thermal Expansion, American Institute of Physics, New York, 169~82, 1972. 15. Anderson. 0. , '"Equation for Thermal Expansivity in Planetary Interiors," J. Geophys. Res .. 72, 3661~8, 1967. 16. Rosenfield, A. , and Averbach, B. , "Effect of Stress on the Expansion Coefficient," J. Appl. , 27, 154~6, 1956. 17. Fahmy, A. , and Ragai-Ellozy, A. , "A Discrete Element Method for the Calculation of the Thermal Expansion Coefficients of Unidirectional Fiber Composites,'' in AlP Conf Proc.