The membrane forces discussed in the last two chapters are sufficient to resist many commonly encountered loading conditions. At locations where the deflection is restricted or there is a change in geometry such as cylindrical-to-spherical shell junction, the membrane theory is inadequate to maintain deflection and rotation compatibility between the shells as illustrated in Example 9-3. At these locations discontinuity forces are developed which result in bending and shear stresses in the shell. These discontinuity forces are localized over a small area of the shell and dissipate rapidly along the shell. Many structures such as missiles, Fig. 10-1, pressure vessels, and storage tanks are designed per the membrane theory and the total stress at discontinuities is determined from the membrane and bending theories. In this chapter the bending theory of cylindrical shells is developed and in Chapter 11 the bending theory of spherical and conical shells is discussed.