For the shaded area shown, find: (a) The location of the centroid (X,Y). (b) The moment of inertia about the centroidal x- axis (horizontal axis going through the centroid) Use the table shown to tabulate all information for the moments of inertia. See the useful equations on the following page. 45° 6 in 9 in 45° 6 in 8 in 10 in

For the shaded area shown, find: (a) The location of the centroid (X,Y). (b) The moment of inertia about the centroidal x- axis (horizontal axis going through the centroid) Use the table shown to tabulate all information for the moments of inertia. See the useful equations on the following page. 45° 6 in 9 in 45° 6 in 8 in 10 in

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.8P: Using integration, compute the polar moment of inertia about point O for the circular sector. Check...

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Using integration, compute the polar moment of inertia about point O for the circular sector. Check your result with Table 9.2.
For the following area, determine: a) the coordinates of the geometric center of the area taking the axes shown in the figure as a reference. Consider b = 36 cm.Adopt π = 3.14159. b) the moments of inertia about the axes that pass through the geometric center of the area. (IxCG = IyCG in cm4)
04) In the figure shown, determine the centroidal coordinates and moment of inertia about x & y-axis, if the value of b=4 in. 0.5 in L3x3x -5 in -5 in
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)
a. find the area and vertical distances from the bottom edge of the cross-section to the centoid of rectangles b. Find Iz, the area moment of inertia about the z centroidal axis for the cross-section. c. Find QH, the first moment of area about the z centroidal axis for the entire area below point H. This area has width 2c2c and height tt. Also, find QK, the first moment of area about the z centroidal axis for the entire area above point K with width b and height t. d. Determine the magnitudes of the shear stress at point H and the shear stress at point K. e. Find Qmax, the maximum first moment of area about the z centroidal axis for any point in the cross section, and τmax, the maximum horizontal shear stress magnitude in the cross section.
4. Find the Area Moment of Inertia Ix about the X-axis, if a = 7 inches, b = 14 inches h = 7 inches, and Y bar = 3.11 inches to the Centroid of the diagam from the base of the diagram. The X-axis is Ithe horizontal axis that goes through the Centroid (C) and is located 3.11 inches (Y bar) from the base of the diagram. %3D MacBook Air
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. 100 mm 20 mm 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.
For the purple region bounded by a parabola with vertex at (-1, 5) and the green line, solve y = -a(x – h)? + k for: a. Area b. Centroid c. Volume when revolved 230° about the green line (-2.1, 2.2) d. MOI and radius of gyration about the x-axis using horizontal strips. e. MOI and radius of gyration about the y-axis using vertical strips. f. MOI and radius of gyration about the z-axis (1, n)
QUESTION 1) In the section in which geometric properties are given in figure; Calculate the moments of inertia Ix, Iy, Ixy On the coordinate set placed at the center of the section (n= 3). 4em 4cm 4cm G 4cm 4cm 12cm 8cm 4cm 8em 4cm 8cm ++
For the composite area shown in the image below, if the dimensions are a = 38 mm, b = 240 mm, c = 276 mm, and b = 124 mm, determine its area moment of inertia Ī (in 106 mm²) about the centroidal horizontal X-axis (not shown) that passes through point C. Please pay attention: the numbers may change since they are randomized. Your answer must include 2 places after the decimal point. 1 a
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.