tailieunhanh - CRC Press - Mechanical Engineering Handbook- Mechanics Of Solids Part 4

Tham khảo tài liệu 'crc press - mechanical engineering handbook- mechanics of solids part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 1-30 Section 1 I IC Md2 I IC Ad2 Jq Jc Ad2 for a mass M for an area A for an area A where I or JO moment of inertia of M or A about any line IC or JC moment of inertia of M or A about a line through the mass center or centroid and parallel to d nearest distance between the parallel lines Note that one of the two axes in each equation must be a centroidal axis. Products of Inertia The products of inertia for areas and masses and the corresponding parallel-axis formulas are defined in similar patterns. Using notations in accordance with the preceding formulas products of inertia are Ixy J xy dA for area or J xy dM for mass Iyz J yzdA or J yz dM I 1 xz dA xz J or J xz dM Parallel-axis formulas are Ị Ix y A dxdy for area or I M d d for mass xy x y ĩ I A dd yz y z y z or I . M dd_ y z y z I I A đđ xz x z x z or I Mdd x z x z Notes The moment of inertia is always positive. The product of inertia may be positive negative or zero it is zero if x ory or both is an axis of symmetry of the area. Transformations of known moments and product of inertia to axes that are inclined to the original set of axes are possible but not covered here. These transformations are useful for determining the principal maximum and minimum moments of inertia and the principal axes when the area or body has no symmetry. The principal moments of inertia for objects of simple shape are available in many .