10.2 Section Stiffness

\includegraphics[]{./Images/sectionStiffness.png}

The section stiffnesses are the most useful results of this chapter. With them, you can compute deflections and rotations of any beam using mechanics of materials tables. Figure 10.2 of the textbook is reproduced here for convenience:
\includegraphics[]{./Images/Fig102.png}

For composite beams, the section stiffnesses are enclosed in parenthesis () to emphasize that the product cannot be broken into a modulus and a geometric property. For example, the bending stiffness (EI) cannot be separated into E and I, unless you think of E as an equivalent modulus for the section. In reality, the section has different moduli in each layer in each panel.

The first group of results are the bending stiffnesses in user coordinates, which is in the coordinate system used by you to describe the beam. Axis x is along the length of the beam. Axes y, z are perpendicular to x and perpendicular among themselves, but other than that you choose them in such a way the describing the section is easier. This usually means y, z are chosen parallel to the flanges and web of the section, respectively. See Figure 10.2 for an illustration of the (x,y,z) user c.s.

CADEC also computes the center of gravity (C.G.), the shear center (C.S.), the orientation of principal axes of bending $\eta , \zeta $, and the section stiffnesses with respect to principal axes.