Problem 3 (22 points): A diagram shown below is a cross...

Problem 3 (22 points): A diagram shown below is a cross section of a beam. With clear steps, calculate the following: i. The centroidal x-axis (3 pts) ii. The centroidal y-axis (3 pts) iii. The area moment of inertia through the centroid, Ixx (6 pts) iv. The area moment of inertia through the centroid, Iyy (6 pts) v. The radius of gyration of an area, kx (2 pts) vi. The radius of gyration of an area, ky (2 pts)

Transcript

00:01 In this question we have been given a diagram which is a cross -section of a beam.

00:05 We need to first find out what is the centroidal x -axis.

00:10 Centroidal x -axis we need to find.

00:14 So, for that what we are going to do, we will first write down the formula for this.

00:20 So, this is summation of a y over summation of a.

00:26 So, let's see what is the value of a here.

00:28 So, first of all we will draw one table to write down what is the area of each of the section.

00:34 Okay, so here i write down the section that is we have three section here, section 1, 2, 3.

00:42 Then i will write down area.

00:44 So, a is representing the area of this section.

00:47 So, for first section you can see this is the first section.

00:50 This is, let me write here first section.

00:53 This is the second section and this is the third section.

00:57 So, for the first section it is rectangular.

01:00 So, area is 400 times 50 and then we have 600 length 50 as the width and 200 as length and 75 at the width.

01:10 This is what we get and then here i will write down what is the center.

01:16 Correct and in that center i will write down the value of x as well as the value of y.

01:24 So, here i will write x value and the y value.

01:27 So, x value here it is 200, 200 and 200.

01:33 Correct, that is the center.

01:36 Similar way we calculate the value of y...

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