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Find the y-coordinate (��̅) of the centroid of the composite area
Find coordinates (��̅, ��̅) of the centroid of the composite area.
Centroids of Composite Bodies
Find the centroid of the given area
xc1 =6.67 in xc2 =15.0 in
yc1 =3.33 in yc2 = 5.0 in
| Part | Ai(in2) | xci(in) | My(in3) | yci(in) | Mx(in3) |
| 1 | 50 | 6.67 | 333.3 | 3.33 | 166.7 |
| 2 | 100 | 15.0 | 1500.0 | 5.0 | 500.0 |
| ∑ | 150 | 1833.3 | 666.7 |
Locate the centroid of the body
| component | Volume , mm3 |  |  |
| hemisphere | 0.5*4/3*π*603= 0.4524 × 106 | -22.5 | -10.18 * 106 |
| cylinder | π*602 * 100 = 1.131 *106 | 50 | 56.55 * 106 |
| cone | -1/3*π 602 * 100 = −0.377 * 106 | 75 | -28.28 * 106 |
| ∑ | 1.206 * 106 | 18.09 *106 |
| Segment | A (in2) |  |  |  |  |
| Rectangle 1 | 17.25 | 0 | 5.75 | 0 | 99.19 |
| Rectangle 2 | 12 | 0 | 12.25 | 0 | 147 |
| Rectangle 3 | 5.25 | -4.75 | 9.75 | -24.94 | 51.19 |
| Rectangle 3 | 5.25 | 4.75 | 9.75 | 24.94 | 51.19 |
| ∑ | 39.75 | 0 | 348.57 |
| Segment | A (in2) |  |  |  |  |
| Rectangle 1 | 9 | 5.5 | 0.5 | 49.5 | 4.5 |
| Rectangle 2 | 24 | 0.5 | 12 | 12 | 298 |
| Rectangle 3 | 9 | 5.5 | 23.5 | 49.5 | 211.5 |
| 42 | 111 | 514 |
The document Centroid for Composite Bodies | Engineering Mechanics - Civil Engineering (CE) is a part of the Civil Engineering (CE) Course Engineering Mechanics.
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FAQs on Centroid for Composite Bodies - Engineering Mechanics - Civil Engineering (CE)
| 1. What is the centroid of a composite body? |  |
The centroid of a composite body is the point at which the body can be balanced perfectly in any orientation. It is the average position of all the individual centroids within the body, taking into account their respective areas or volumes.
| 2. How is the centroid of a composite body calculated? | |
To calculate the centroid of a composite body, you need to find the centroid of each individual component and then determine the weighted average of their positions based on their respective areas or volumes. This can be done using mathematical formulas or graphical methods, depending on the complexity of the body.
| 3. What are some practical applications of finding the centroid of a composite body? | |
Finding the centroid of a composite body is crucial in various engineering and design applications. It helps determine the stability and balance of structures, such as bridges, buildings, and vehicles. It is also used in manufacturing processes to ensure even distribution of materials or weight within a product.
| 4. How does the centroid of a composite body affect its stability? | |
The centroid of a composite body plays a significant role in determining its stability. If the centroid is located outside the base or support area of the body, it can cause tipping or overturning. On the other hand, if the centroid is positioned within the base or support area, the body will be more stable and less prone to tipping.
| 5. Can the centroid of a composite body be located outside the body itself? | |
No, the centroid of a composite body cannot be located outside the body itself. The centroid always falls within the boundaries of the body, as it represents the average position of all the component centroids. If the centroid is outside the body, it means there is an error in the calculations or the components have not been properly included in the analysis.
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