Compute the coordinates of the centroid (, ) of the area shown. Also compute the area moment of intertia about the az' and y' axes with origin at the centroid. y C a a b + =b. b* 2013 Michael Swanbom -a- Values for dimensions on the figure are given in the following table. Note the figure may not be to scale Variable Value 25 cm 11 cm 31 cm c с The a coordinate of the centroid is The y coordinate of the centroid is y The moment of inertia about the z' axis going through the centroid is It' The moment of inertia about the y' axis going through the centroid is I BY NC SA cm. cm. x cm4. cm4.

Give the following problem a try. If you get stuck, here is one way to work it: Essential Solution Video. For the shape below, assume the following dimensions: a = 175 mm b = 220 mm d = 300 mm t = 23 mm The centroid of this shape is located 71.762 mm to the right of point H shown in the figure. What is the moment of inertia ly about the y centroidal axis for this shape? H Answer: ly M b 2t mm4

The correct answer is 99.9 in ^4. Also why is lc = 2.9 in ^4 not being used anywhere? Moment of Inertia 9-31. Determine the moment of inertia about the centroidal x-axis of the fabricated area shown in Figure P9-31. FIGURE P9-31 For each angle A = 3.98 in.² = 2.9 in.4 4- 2 87 3" 10"

This is an exercise to illustrate the effects of mesh refinement on a 1-d rod. To estimate the self-weight elongation (8) of the tapered conical rod shown in the figure. The diameter varies linearly from Do at the bottom to aDo at the top, where 0.1 < E Young's Modulus y Unit weight (Diameter at top) 8 clongation D (Diameter at bottom) a<0.5. Solve for L= 5m, y= unit weight of steel, E= young's modulus of steel, Do=3m and a=0.3. Solve the problem at least four times using an increasing number of rod elements (nels=2, 4, 6, 8). Make appropriate assumptions about how to deal with the changing cross-sectional area and self-weight loading along the length of the rod. A plot of the dimensionless tip deflection SE/yL? vs. number of elements (nels) used in the discretization to show convergence on the exact solu- tions of