Structural components designed to resist lateral loading are generally circular or rectangular in shape, but in some situations other geometrical shapes are used. Triangular and rectangular plates, plate strips, elliptical and sector shaped plates, are considered in this chapter. Recall that the bending problem of plates of any shape is solved when the vertical displacement function is derived, which satisfies the governing equation and the specified conditions at the boundaries. From the examples worked out so far, it becomes evident that a rigorous determination of the deflection for a plate with a more complicated shape is likely to be very difficult.

When solutions are not readily available, the method of images as shown in this chapter and the numerical methods to be discussed in the next chapter can be used effectively. In developing approximate formulas for the deflections of polygonal plates, the membrane analogy has proven very valuable. For the case in which the uniformity of the cross-sectional area of the plate is interrupted, as in the case of a ship deck or airplane fuselage with holes or windows, a perturbation in stress takes place. Determination of this disturbed stress distribution is discussed briefly in the last section.