Could you Show that the shape factor for a rectangular section is 1.5?

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1055769

2026-05-11 16:00

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The shape factor for a rectangular section is calculated as the ratio of the moment of inertia (I) to the area (A) of the section, divided by the distance from the neutral axis to the extreme fiber (c). For a rectangular section with width ( b ) and height ( h ), the moment of inertia is ( I = \frac{b h^3}{12} ), the area is ( A = b h ), and the distance ( c = \frac{h}{2} ). Plugging these values into the shape factor formula ( \text{Shape Factor} = \frac{I}{A c} ), we find that it simplifies to ( \text{Shape Factor} = \frac{\frac{b h^3}{12}}{b h \cdot \frac{h}{2}} = \frac{1}{6} \cdot 2 = 1.5 ).

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