ABSTRACT
When making calculations for stresses and deflections for members in bending or torsion, the shape and dimensions of the cross section of the member are critical. This chapter includes methods of computing properties of pertinent geometric shapes such as circles, squares, rectangles, and triangles, along with other shapes made up of combinations of such shapes. Examples are hollow circular bars, hollow rectangles, and I-shapes, often used for beams. The primary objective of such calculations is to determine the moment of inertia of those shapes, a factor critical to the calculation of stresses and deflections of beams and shafts. A related geometric property of the cross section of a load-carrying member is the section modulus, often used for computing stress due to bending. Also, the location of the geometric centroid of the shape is a critical factor in the calculation of both stresses and deflections. Another important property of a cross section included in this chapter is the radius of gyration, required when analyzing long, slender members carrying axial compressive loads. Such members must have sufficient strength, but they also must also have sufficient rigidity to prevent excessive deformation and buckling, particularly for long, slender members.
