1 of1 Correct The polar moment of inertia is a stiffness par

1 of1 Correct The polar moment of inertia is a stiffness parameter based on shape and is given by The integral for the moment of inertia with respect to the x axis is The differential area dA is composed of a rectangle of height dy and a width that is expressed in terms of z. The integral is evaluated afhter substituting for z in terms of y. Recall that building the it is used to predict the torsional resistance according to the cross-sectional geometry, and it is the sum of I, and I ndividual parts of the inlegral- dA, z, and y-for the moment of inertia is the key to determining the correct integral Figure 1 of2 Part B Moment of inertia about the y axis Determine the moment of inertia with respect to the y axis for the area shown (Figure 2) The dimension is a #300 In Express your answer to three significant figures and include the appropriate units View Available Hint(s) dA , Value Units G. Submi Ac

Solution

Second moment of inertia with respect to y-axis, I_yy = ?x²dA

x = ?(r²- y²)

dA = ydy

therefore,

I_yy =?(?(r²- ^y2))²*(y*dy) = ?(r²- y²)*y*dy = ?(yr²- y³)dx = (yr)²/2 - y⁴/4 + C

I_yy, (y=3m) = (3r)²/2 - 3⁴/4 = (4.5r² - 20.25) m⁴