Examples 2a. and 2b. Section is a constant 10mm thick 250 78...

Examples 2a. and 2b. Section is a constant 10mm thick 250 78 mm 30 30 130mm 10mm 52 mm 300 200 (x bar = 259 mm $I_{xx}$ ans - 24,973E6 mm$^2$) Examples 2a. and 2b. (ans b: $y$ = 49.176mm and x bar = 57.259mm $I_{xx}$ ans - 12.014 E 6 mm$^2$; $I_{yy}$ ans - 8.957 E 6 mm$^2$) Determine the position of the centroids for the shapes shown above, then determine the value of $I_{xx}$ and $I_{yy}$.

Transcript

00:01 Consider the diagram, so there are three section, this section 1, this 2 and this is 3 and this length is 80 millimeter and this is 15 millimeter, this length is 125 millimeter and this is again 15 millimeter, this is also 15 millimeter length and this is 80 millimeter, this is y direction and this is the x direction.

01:04 The area of section 1 is a1 is equal to 80 plus 15 multiplied by 15 is equal to 90 multiplied by 15 is equal to 1425 millimeter square and the area of section 2 is a2 is equal to 125 multiplied by 15 is equal to 1875 millimeter square and the area of section 3 is a3 is equal to 95 multiplied by 15 is equal to 1425 millimeter square.

02:17 In section 1, the x and y coordinate of centroid is x1 is equal to 50 plus 80 divided by 2 is equal to 47 .5 millimeter and y1 is equal to 50 divided by 2 is equal to 7 .5 millimeter and in section 2, the x and y coordinate of centroid x2 is equal to 50 divided by 2 is equal to 7 .5 millimeter and y2 is equal to 15 plus 125 divided by 2 is equal to 77 .5 millimeter and in section 3, the x and y coordinates of the centroid x3 is equal to 15 plus 80 divided by 2 is equal to 47 .5 millimeter and y3 is equal to 15 plus 125 plus 50 divided by 2 is equal to 147 .5 millimeter.

03:56 Therefore, the x and y coordinate of the centroid of the cross section x bar is equal to a1 x1 plus a2 x2 plus a3 x3 divided by a1 plus a2 plus a3 is equal to 1425 multiplied by 47 .5 plus 1875 multiplied by 7 .5 plus 1425 multiplied by 47 .5 all divided by 1425 plus 1875 plus 1425 is equal to 31 .63 millimeter and y bar is equal to a1 y1 plus a2 y2 plus a3 y3 divided by a1 plus a2 plus a3 is equal to 1425 multiplied by 7 .5 plus 1875 multiplied by 77 .5 plus 1425 multiplied by 147 .5 all divided by 1425 plus 1875 plus 1425 is equal to 77 .5 millimeter.

06:02 Therefore, the centroid of the cross section x bar y bar is equal to 31 .63 millimeter 77 .5 millimeter...

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