Determine the second moments of area I_{x x} and I_{y y}of the I section shown in Fig. 15.28.
Question 15.13: Determine the second moments of area Ixx and Iyy of the I se...
Using Eq. (15.34),
I_{x x}=\frac{b d^{3}}{12} (15.34)
I_{x x}=\frac{b d^{3}}{12}-\frac{\left(b-t_{ w }\right) d_{ w }^{3}}{12}
Alternatively, using the parallel axes theorem in conjunction with Eq. (15.34),
I_{x x}=2\left[\frac{b t_{ f }^{3}}{12}+b t_{ f }\left(\frac{d_{ w }+t_{ f }}{2}\right)^{2}\right]+\frac{t_{ w } d_{ w }^{3}}{12}
The equivalence of these two expressions for I_{x x} is most easily demonstrated by a numerical example. Also, from Eq. (15.35),
I_{y y}=\frac{d b^{3}}{12} (15.35)
I_{y y}=2 \frac{t_{ f } b^{3}}{12}+\frac{d_{ w } t_{ w }^{3}}{12}
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