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Using Mohr’s circle, prove that the expression
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Vector Mechanics for Engineers: Statics
- It is known that for a given area Iy = 48 x 106 mm4 and Ixy = -20 x 106 mm4, where the x and y axes are rectangular centroidal axes. If the axis corresponding to the maximum product of inertia is obtained by rotating the x axis 67.5° counterclockwise about C , use Mohr’s circle to determine (a) the moment of inertia Ix of the area, (b) the principal centroidal moments of inertia.arrow_forwardThe shaded area shown is bounded by y axis and the curve y2 =(2.56−x)m2 , where x is in m. Suppose that a = 2.56 m and h = 1.6 m . Determine the moment of inertia for the shaded area about the y axis. Iy = ?arrow_forwardQ2: Determine the moments of inertia of the rectangular area about the x – axes and y – axes, polar axes z through 0, and the centroidal polar axes z through C. - y 2h 3 C --x h 36 4 4 pg.arrow_forward
- Q2: Determine the moments of inertia of the rectangular area about the x — axes and y — axes, polar axes z through 0, and the centroidal polar axes z through C. ¥ |arrow_forwardThe shaded area has the following properties: 4 = 126 x10 mm* ; 1, = 6,55 x10* mm* ; and Pay =-1.02 10° mm* Determine the moments of inertia of the area about the x' and v' axes if e=30°.arrow_forwardC |₂ 12 mm 24 mm A B O 12 mm 24 mm dmm a mm a mm dmm Determine the moment of inertia (x 1000 mm) of the rectangle area marked C with respect to the x axis. The rectangle has a thickness d = 5-mm and a distance 31-mm from the x axis.arrow_forward
- H.w1: Determine the moment of inertia of figure that show below about x-x axis. • Ans • Ixt = 62485 cm4 10 cm D=15cm 30cm 20cmarrow_forwardKnowing that the shaded area is equal to 6000 mm2 and that its moment of inertia with respect to AA′ is 18 × 106 mm4, determine its moment of inertia with respect to BB′ for d1 = 50 mm and d2 =10 mm.arrow_forward| Find the moment of inertia about the x-axis of a thin plate bounded by the parabola x y- y2, and the line x+y 0 if 8(x, y) 5x+yarrow_forward
- Four L3 × 3 × 늪 -in. angles are welded to a rolled W section as shown. Determine the moments of inertia and the radii of gyration of the combined section with respect to the centroidal x and y axes if a = 5.5 in. - L 3X3 X W 8 X 31 The moment of inertia with respect to the x axis is The radius of gyration with respect to the x axis is The moment of inertia with respect to the y axis is The radius of gyration with respect to the yaxis is 4 int. in. lin4. in.arrow_forward2. Determine the moments of inertia Ix and Iy of the shaded area, with respect to an axis passing through GH and FH respectively. 24 mm 100 mm G 36 mm 18 mm. 40 mm 42 mmarrow_forwardFour L3 × 3 × -in. angles are welded to a rolled W section as shown. Determine the moments of inertia and the radii of gyration of the combined section with respect to the centroidal x and yaxes if a = 5 in. y с W 8 X 31 L3×3× // x The moment of inertia with respect to the x axis is The radius of gyration with respect to the x axis is The moment of inertia with respect to the y axis is The radius of gyration with respect to the y axis is in 4. in. in4 in.arrow_forward
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