Question

Please answer the following,and please note that 0.00130,0.00608,-0.000558 does not work.

Mohr's circle is a graphical method used to determine an area's principal moments of inertia and to find the orientation of the principal axes. Another advantage of using Mohr's circle is that it does not require that long equations be memorized. The method is as follows: 1. To construct Mohr's circle, begin by constructing a coordinate system with the moment of inertia, I, as the abscissa (x axis) and the product of inertia, Izy, as the ordinate (v axis). 2. Next, construct a circle centered on the I axis at the average of the moments of inertia about the x and y axes. 3. Lastly, plot a reference point A at the coordinates (Iz, Iy). This point is the graphical representation of the moments of inertia associated with the x axis; it is located on the circumference of Mohr's circle As the axes about the beam's centroid are rotated, the values of I and Izy follow the values on the circumference of Mohr's circle. The points on the circle that intersect the I axis are the minimum and maximum moments of inertia. The figure shows a fully constructed Mohr's circle xy max min io The angle in Mohr's circle between OA and the I axis is twice the angle between the x axis and the beam's major principal axis. Figure 〈 1of1 CL PartA An engineer is designing a structural beam that contains a lengthwise conduit that will be used for routing cable. As shown, the cross section of the beam has the dimensions a-0.355 m , b = 0.625 m , c-0.145 m , and d : 0.235 m . (Figure 1)The beam's centroid is located at point C(2.84x10-2 m, 1.61x102 m). The engineer wishes to determine the beam's principal moments of inertia and the orientation of the principal axes using Mohr's circle. First, find the beam's moment of inertia and product of inertia. What are the beam's moments of inertia, I and Iy, about the centroidal x and y axes, respectively? What is the beam's product of inertia about its centroid? Express your answers numerically in meters to the fourth power to three significant figures separated by commas. View Available Hint(s I.Iy. Iay-.002388,.007401,1 Submit Previous Answers X Incorrect; Try Again; 5 attempts remaining

Answer 1

As per my understanding and solution, your Ix' (moment of inertia about centroidal x axis) is wrong, So please find the solution:

Solution ivem figure, the data cse: a= 0.355 m 2 centroid x=2.24x10 2. Leh us fiud the mome about ' axis > nertia of given systenm IxT (fov section a) - Ii (or cection 'i for section 2 U) 2 3 ο.usx(О :3 s s) 2 yí 2 4 Next Next hollow section X2- X2

I. 2. 12 3 and 3 3

Cross Sectiowl Area 1.014 SX lo 4- -6.597 x10 Answos Principal momentoflnettia (L,'12)っ3 2. do 4(-S.S82.xlo' 3 4- Ii - 6.SO58xIO m <1 3 20p 거.SGSo