Practice Question: Centroid of Fastener Group

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Solution

Equation for Centroid Along X-Axis:
\[x̄ = \frac{\sum_{i=1}^{n} A_i x_i}{\sum_{i=1}^{n} A_i}\]Equation for Centroid Along Y-Axis:

\[ȳ = \frac{\sum_{i=1}^{n} A_i y_i}{\sum_{i=1}^{n} A_i}\]Since each bolt has the same cross sectional area, consider:

\[A_i = 1\]

\[\sum_{i=1}^{4} A_i = 4\]\[x̄ = \frac{(2 \ bolts)(4 in)(1) + (2 \ bolts)(12 in)(1)}{(4)} = 8 \ in\]\[ȳ = \frac{(2 \ bolts)(3 in)(1) + (2 \ bolts)(10 in)(1)}{(4)} = 6.5 \ in\]

 

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