10 p1 - 352 —— Chapter 10 Properties of Areas The...

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Unformatted text preview: 352 —— Chapter 10 Properties of Areas The parallel axis theorem, used to determine the moment of inertia about a parallel axis some distance removed from a centroidal axis, is derived from the following relation: " (-2 PROBLEMS 10.1 Derive the equation for the area of an ellipse with a major axis of a and a minor axis of b. 10.2 Derive the equation for the area of an equilateral triangle with an altitude of h and a base of b. 10.3 Derive the equation for the area of a semicircle. 10.4 A straight line is described by y = ax + b. Determine the area between the line and the x-axis fromx= Otox=b. 10.5 For the curve described by y = ax2 + bx + 0, determine the area between the curve and the x- axis fromx=0tox=3. nun 2.5 2.5 10.6 Determine the first moment of the area shown in Fig. P10.6 about the x—axis. Y Fig. P10.6 lbl. 10.7 Determine the first moment of the area shown in Fig. P10.6 about the y—axis. 10.8 Determine the first moment of the area shown in Fig. P10.8 about the x-axis. Fig. P10.8 10.9 Determine the first moment of the area shown in Fig. P109 about the x—axis. Fig. P10.9 10.10 Determine the first moment of the area shown in Fig. P10.9 about the y-axis. 354 —— Chapter 10 Properties of Areas 10.11 Determine the first moment of the semi-elliptical area, shown in Fig. P101 1, about the x-axis. V Fig. P10.11 10.12 Determine the location of the centroid of the semicircular area shown in Fig. P10.12. y , Fig. P10.12 ' ‘ 10.13 Determine the location of the centroid of the semi-elliptical area shown in Fig. P10.11. 10.14 Determine the location of the centroid of the spandrel area shown in Fig. P10.14. Fig. P10.14 Y Fig. P10.16 10.17 Locate the position of the centroid in the composite area shown in Fig. P10.17. Fig. P10.17 Fig. P10.18 10.20 Locate the position of the centroid in the composite area shown in Fig. P1020. Y Fig. P1020 S Statics -- 355 X ...
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10 p1 - 352 —— Chapter 10 Properties of Areas The...

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