3. Two 10"-15.3 lb channels are welded together as shown in the figure. Find the moment of area of the upper channel about the horizontal centroidal axis x. of the entire section. Use Table 6-6.2 on page 199 of your textbook for the properties of channels. + 6-8 Centroids of Composite Figures The centroid of the composite figure is determined by applying the following expustions which were developed in Section 3 In these equations the elemental areas become the areas of the geo- metrical shapes into which the entire area has been divided. A similar process may be applied to lines. The given line may be divided into finite segments whose centroids are known, and the following equations may be used: (6-3.2) Before these equations are applied to illustrative problems, it will be convenient to summarize the location of centroids for com- mon geometrical shapes (determined in preceding problems) given in Table 6-6.1. Size Units In addition to the geometric shapes shown in Table 6-6.1, other sections commonly used are rolled structural sections such as angles and channels. The areas and the location of the centroids of such sections are listed in handbooks. A few typical sections and their values are shown in Table 6-6.2. If any of these sections are given Table 6-6.2. Properties of Angles and Channels 5x3x angle = ax | A = Zay Area 9 sq in. in. 3.75 1,75 0.75 9.00 2.17 DUE 5.75 1.68 13.00 2,65 4.47 6.03 6x4xl angle 6x6x angle La=Xkx| Lj = Ely 8x6x1 angle 10"-15.3 lb channel 12"-20.7 lb channel i F 0,64 0,70 1.17 Web thick- 1.65 ness / (in.) 1.68 0 0 0.240 0.280 199 Table 6-6.1. Centroids for Common Geometric Shapes Shape Rectangle Any triangle Somicirce Quarter circle Circular sector -X Segment of arc Semicircular arc Ares under spandrel y=zx BAL (20) Area or length Ind mini 3 7 1 ra 2 2m bh X + 1911 0 or 0.424 2 r sin a a r sin a 2/1/2 34 3e or 0,424 4r or 0,424 0 0 #+1