Question
Download Solution PDFFind the centroid of laminae shown in figure
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
- The centroid is the geometric center of a plane figure or lamina. It is the point at which the entire area of the lamina can be assumed to be concentrated for analysis purposes.
- In uniform materials, the centroid corresponds to the center of mass or center of gravity, assuming uniform density and thickness.
Calculations:
Taking reference as the bottom part of the flange.\(A_1=(50\times10)= 500 mm^2\)
\(y_1=20+\frac{50}{2}=45mm\)
\(A_2=(100\times20)= 2000 mm^2\)
\(y_2=\frac{20}{2}=10mm\)
\(\bar y=\frac{A_1y_1+A_2y_2}{A_1+A_2}\)
\(\bar y=\frac{500\times45 + 2000\times45}{2000+500}=\frac{42500}{2500}=17mm\)
The section is symmetric about the vertical axis passing through the center of the web.
Therefore, the centroid lies at the centerline of the web horizontally.
\(\bar x =\frac{100}{2}=50mm\)
The centroid is (50 mm, 17 mm).
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