Question
Download Solution PDFSelect the correct statement regarding the 1st and 2nd moment of area of a circular lamina with radius ‘R’.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDF1st Moment of Area(Q): it measures how a shape's area is distributed in reference to an axis. Used to find out the centroid of a shape.
Q = perpendicular dist(d) x Area(A) … (unit = m3)
The axis can be chosen as per the requirement and hence, the perpendicular distance can be either positive or negative. Hence 1st moment of area can be either +ve or -ve depending on the location from the reference axis
2nd Moment of Area: It is also called the moment of inertia(I) which is the capacity of a body to resist bending or angular rotation about a certain axis.
Using the parallel axis theorem we can find the moment of inertia of any C/S using the below expression
Ix = Ixc + Ad2
Iy = Iyc + Ad2
Where
Ix and Iy = moment of inertia about any random x-axis and y-axis respectively, Ixc and Iyc = moment of inertia about the shape’s centroidal x-axis and y-axis respectively, A = area of shape, d1 = distance of reference x-axis and centroidal x-axis , d2 = distance of refrence y-axis and centroidal y-axis, Ix (circle) = ℼd4/64 (cannot be negative), Ad2 this term cannot be negative too.
Hence 2nd moment area can never be negative for circular lamia( always +ve)
Last updated on May 28, 2025
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