Title 80 Moment of Inertia.pdf ✅

MSTC 79: Moment of Inertia 1. Moment of Inertia The moment of inertia is the amount of resistance a cross-section gives against rotation about an axis. It is also the second moment of the area. I = Ar 2 2. Choice of Differential Strip When solving values derived from the bounded area, the choice of differential strips can make the procedure much easier or much harder. A good differential strip is one in which endpoints do not both touch the curve. Consider the area bounded by the parabola and the x-axis, A vertical differential strip is feasible since its top end is on the parabola, and the bottom end is on the x- axis. A horizontal differential strip is impractical since its sides are both on the parabola. When finding moments of inertia using integration, the following integrals are used. Ix = ∫ y 2 dA Iy = ∫ x 2 dA 3. Integration Taking a differential area dA = dx dy, Ix = ∫ ∫ y 2 dx dy Iy = ∫ ∫ x 2 dx dy