2015-08-13
652
Bending tensile and shear stresses depend on the section geometry, not only the cross-sectional area A. The section can be characterized by the following:
moments of inertia Ixx, Iyy,
polar moment of inertia J.
The last characteristic is important for analysis of torsion deformation. The moments of inertia have units of [length4]. Polar moment of inertia is equal to sum of the other two moments. It does not depend on orientation of the axes.
The moments of inertia depend on the placement and orientation of the axes. Practical engineers use values of the moments of inertia which pass through the center of the area called the centroid (xc,yc).
For simple geometry the moment of inertia can be easy calculated. For more complicated sections, the information can be found in reference books.
The moment of inertia Ixx is higher if many elements of the area are located far from the neutral axis. The removed area of the circle decreases the moment of inertia. The decrease is small if the distance from the neutral axis to the center of the hole is small.
For a symmetrical geometry the principle axes pass through the centroid (center of area). An axis coincides with the line of symmetry.
For a composite cross-section an axis tends towards the region with most area furthest from the neutral axis.
