Dimensions: h 1h1 h 2h2 h 3h3 d w 1w1 w 2w2 w 3w3 w 4w4 w 5w5 2.67 in 4.19 in Pr

Question

Dimensions:

h1h1

h2h2

h3h3

d

w1w1

w2w2

w3w3

w4w4

w5w5

2.67 in

4.19 in

Problem Statement:
Given the shape shown, with the dimensions given above, find:
?? the x location of the centroid of the shape,
?? the y location of the centroid of the shape,
?? the Second Moment of Area of the shape about the x axis,
?? the Second Moment of Area of the shape about the y axis
?? the Second Moment of Area of the shape about a horizontal axis passing through the centroid of the shape
?? the Second Moment of Area of the shape about a vertical axis passing through the centroid of the shape

h1h1

h2h2

h3h3

d

3.74 in 3.55 in 0.178 in 0.853 in

w1w1

w2w2

w3w3

w4w4

w5w5

2.95 in 2.54 in

2.67 in

4.19 in

6.28 in 2013 Michael Swanbom 030 BY NC SA 2 Dimensions. 3.74 in 3.55 in 0.178 in 0.853 in W1 W2 W3 W4 W5 2.95 in2.54 in 2.67 in 4.19 in 6.28 in Problem Statement: Given the shape shown, with the dimensions given above, find * the x location of the centroid of the shape, » the y location of the centroid of the shape, » the Second Moment of Area of the shape about the x axis, » the Second Moment of Area of the shape about the y axis » the Second Moment of Area of the shape about a horizontal axis passing through the centroid of the shape » the Second Moment of Area of the shape about a vertical axis passing through the centroid of the shape

Explanation / Answer

Given problem is composite figure i.e it consists many number of regular geometrical figures.

Step 1. Divide the composite figure into familiar geometric shapes like ( rectangles,triangles,circles,semicricles etc)

Step 2. Locate the centroid of individuals and it areas

Step 3. Formulate the centroid of the composite plane figure with individuals

Step 4. Locate the centroid value of the composite plane figure

Note . If there is a hole or void i.e non existing area then it may treated as negative area

For solution refer the upload document

First refer the sheet one and then tabular form sheet and remaining one

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