Fig. 11-32. Common Sections and Their Centroldal Moments of Inertia. For boxes and tubes, we find the I for the section by subtracting the inner I from the outer I. For a very thin annulus, / = Jt r31

For calculations of / with respect to an axis other than the neutral axis, we use the parallel axis theorem.

I (any parallel axis) = I (neutral axis) +Ad2 (11-47)

where A is the cross-sectional area, and d is the distance between the two parallel axes. The parallel axis theorem allows us to find the area moment of inertia for complex sections, such as the I-beam in Fig. 11-33. Note that the area moment of inertia increases for a reference axis other than the neutral axis.

The value for bending stress, <rb, is given in Eq. (11-48) for a point on a symmetric cross-section at a distance, c, from the neutral axis. Use of Eq. (11-48) assumes that

0 0

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