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In case of a circular section the section modulus is given as

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In case of a circular section, the section modulus, $(Z = \frac{I}{y})$ where I = moment of inertia

$(I=\frac{\pi}{64} d^4)$, y = distance from centroid to top or bottom edge= d/2, is given by $(\;\frac{\pi }{{32}}{d^3})$