Equilateral triangle solutions

The problem must be simplified considerably to permit solution in the context of this book. Suppose an equilateral triangle is subjected to some loads in the vertical direction as in Figure 7-22. A load P of 100 lb (445 N) is applied to the top joint, and that load can go in either the downward or upward direction (in the diagram, not in space ). This truss must take its reversible load with, say, a factor of safety of two against whatever event would cause it to fail. What material, size, and weight of truss element would you select to satisfy the design requirements that include building the structure for the lowest cost ... 

A planar arrangement (297) for a cluster of four Li atoms, consisting of two equilateral triangles, is found by XRD for the solid complex 298. Each Li atom is coordinated to methylene groups of both types (from n-BuLi and the metallated carbosilane) and to N and O atoms of the substituent in the carbosilane. Further characterization of the solid 298 can be made by Li and CP/MAS NMR spectroscopies, and in solution by H, Li, and Si NMR spectroscopies. The combination of both organolithium compounds in 298 is found to form a more effective reagent than each of them alone °. 

As first pointed out by Gibbs the composition of a solution containing three components may be represented by a point in an equilateral triangle whose vertices A, B and C represent the three pure components. If the side of the triangle is taken as unity, then the mole fractions Xj, Xb and Xq in the solution under consideration are given by the distances, measured along lines parallel to the sides of the triangle,... 

Whenever the miscibility of the two phases varies and is dependent on concentration, a triangular diagram is employed (Fig. 2.5). Here the three comers of the equilateral triangle stand for the pure components, the solvent S, the carrier T and the solute C. Each side of the triangle represents binary mixtures, each point within the triangle a ternary mixture. Since the sum of the perpendicular lines of any point in the triangle... 

Now we suppose that the cross-section of the tube is an equilateral triangle with side b. We place the origin at the center of the cross-section and measure the coordinate X along one of the sides of the triangle. In this case, the solution of Eq. (1.5.1) under the boundary condition (1.5.2) has the form... 

Countercurrent extraction calculations are readily made on equilateral-triangle phase equilibrium diagrams, no new principles being involved. In Fig. 11.5, we see the solution to Case 1 of Fig. 11.3h. 

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