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- 50 mm 150 mm 150 mm 300 mm find the moment of inertia for this exercise, with the following formulas: Polar Jo= Iox + + Toy Iox - Icx + Adg² Toy = Icg + dobe ² Caculation of centroid attached below. use it to solve the question in red box asap Som Av 3com for Portion A₁ - the figure is symme about y-aris. 2=0. AL 120mm AALD Area of A₁ = 300x50 = 15000 Y₁ = y₁ y = 300 for Pation A2 Area Az = 50x300 = 15000 By Considering Centroid, from the Bottom of the section. 300+ 50 = ₁ + 3/2 = 325 Centroid (ā, y) = = [0₁ SE = 50mm A, Ya+ A₂4 0, A₁+A₂ 15000x150 +15000x325 15000 15000 (0.237.5)1. For the Isosceles triangle shown to the right, find the moments of inertia, Ix and Iy, about the centroidal axes. Hint: break into two right triangles and use parallel axis theorem. Ans: Iy = bh³/36, I, = hb³/48 y 2h/3 h/3 X b/2 b/21. Solve for the of the location of the centroid with respect to the x and y axes of the given fig. 2. Solve for the moment of inertia with respect to centroidal axes of the given figure. 200 mm Y 150 150 500 mm ww 007 ww OSL ww OSL
- 1. -200 mm 200 mm 150 mm 125 mm 60 mm 125 mm Determine the coordinates of the centroid of the shaded area. 100 mm 20 mm Yo 140 mm 20 mm 20 mm 100 mm Determine the moments of inertia of the Z-section about its centroidal x and y axes. Consider x - axis to be at the extreme bottom of the figure and y - axis at the left most of this figure. 2.Compute the coordinates of the centroid (z, 9) of the area shown. Also compute the area moment of intertia about the z' and y' axes with origin at the centroid. 2013 Michael Swanbom BY NC SA a W. k d Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value 6 mm 28 mm 7 mm 13 mm h 33 mm 5 mm w The z coordinate of the centroid is a = mm. The y coordinate of the centroid is j = 26.74 mm. The moment of inertia about the z' axis going through the centroid is I, mm*. The moment of inertia about the y' axis going through the centroid is Iy mmt.The composite shape in Question5 consists of a (1) square, (2) isoscelestriangle. The shape also has a hole in the form of (3) circle.a. Determine the x and y centroids of each shape based on the given axis.b. Determine the x and y centroids of the composite shape based on the given axis.c. Determine the first moment of area with respect to x axis of the composite shape
- (a) Find the centroidal axes (coordinates xc and xs) of the given composite area. (b) Determine ly of the composite area about its y-centroidal axis found in part (a). Enter the ly value as the answer in the Respondus answer-box. y 1 in 5 in 3 in 2 in 3 in 3 in 6 in XCompute the coordinates of the centroid (î, g) of the area shown. Also compute the area moment of intertia about the r' and y' axes with origin at the centroid. 2013 Michael Swanbom cc BY NC SA a k-d Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 14 mm 111 mm 12 mm d 45 mm h 89 mm w 22 mm The z coordinate of the centroid is a = mm. The y coordinate of the centroid is j mm. The moment of inertia about the z' axis going through the centroid is Iz mm. The moment of inertia about the y' axis going through the centroid is Iy = mm*.4. Find the centroid of the figure shown. 30° 30⁰ x X
- The composite shape in Question 5 consists of a (1) square, (2) isosceles triangle. The shape also has a hole in the form of (3) circle.a. Determine the x and y centroids of each shape based on the given axis.b. Determine the x and y centroids of the composite shape based on the given axis.c. Determine the first moment of area with respect to x axis of the composite shaped. Determine the first moment of area with respect to y axis of the composite shapee. Determine the polar moment of inertia of each shape with respect to the origin.f. Determine the polar moment of inertia of composite shape with respect to the origin.When the point O is the origin of the coordinate axis (x-y axes) in Fig. 3-1, (1) ) determine the centroid (location of the point C) of the given area. (2) with respect to the x'and y' axes (Iy). (Note that x'- y'axes pass through the centroid of the given area) determine moment of inertia with respect to the x'axis (I:) and y'axis (I,), and product of inertia (3) determine the principal axes about C and the values of the principal moments about C. 250 mm Ik = 12 bh", ly =; hb3 %3D I 30 mm 300 mm h 30 mm 1 30 mm 150 mm Fig. 3-1 Fig. 3-2 3." Locating the Centroid of an Area " Please locate the centroid of the shaded area ABC the radian is alpha=0.9273 radian and betha=0.6435 radian. the radius of the i thinks it's semi circle DAC is 300mm sorry if I'm wrong if it is not semicircle Thankyou!