the funicular polygon method ofthrust line analysis became a standard way of analyzing arches in the nineteenth century when the introduction of graphical methods made it more user-friendly than the mathematical methods with which the principles were developed. I use it in Chapter 8 to test the efficacy of various techniques discussed in this study. In what follows, I provide an example of how to perform a simple thrust line analysis for a barrel vault. It can be done with a pencil and paper, but I use AutoCad for greater accuracy and ease.

PART 1

STEPS FOR CONSTRUCTING THE THRUST LINE THROUGH A BARREL VAULT (FIG. 145):

1. Draw a scaled profile of the vault to be analyzed (shaded area in Drawing 1).

2. Divide the vault into an odd number of vertical sections (the more sections the more accurate the final curve) so that the middle section is centered on the crown of the vault. Number each section starting with “1” at the far left.

3. 3a. Determine the unit weight of the material used for each section in kg/m3. Calculate the mass (M) of each section in m3 and multiply it times the unit weight of the material used. The weight (W) in kg must then be translated into units of force in Newtons (N) by multiplying by 9.8 m/sec/sec. These are the force vectors, each of which is referred to by the number of its corresponding section, for example, F1, F2, F3, and so on.

4. 3b. To draw the force vectors, choose a convenient scale for the vectors so that each unit in the drawing equals a certain number of Newtons (e.g., scale above Drawing 2). Draw each calculated force vector as point load located at the center of gravity of its section. (A program such as AutoCad can calculate the center of gravity of unsymmetrical shapes automatically.)

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