Then the maximum pressure per unit of area at A is Equations 1 and 2 are applicable to any symmetrical vertical section and to any horizontal cross section, and also to any system of horizontal and vertical forces. In succeeding chapters they will be employed in finding the unit pressure in masonry dams, bridge piers, arches, etc.
The value of I in the above formulas is given in Fig. 82 for the sections occurring most frequently in practice. Notice that 1 is the dimension parallel to the direction of the wind, and b the dimension perpendicular to the direction of the wind.
If the area of the section AB, Fig. 81, is a rectangle, S = lb, and I = 1'. Substituting these values in equation 1 gives The moment of the wind, M, is equal to the product of its total pressure, H, and the distance, h, of the center of pressure above the horizontal section considered; or M = H. h. H is equal to the pressure per unit of area, p, multiplied by the area of the surface exposed to the pressure of the wind. Substituting the above value of M in equation 3 gives To still further simplify the above formula, notice that Fig. 81 gives the proportion which is a convenient form for practical application.
An examination of equation 5 shows that when d = N C a 11, the maximum pressure at A is twice the average. Notice also that
under these conditions the pressure at B is zero. This is equivalent to what is known, in the theory of arches, as the principle of the middle third. It shows that as long as the center of pressure lies in the middle third, the maximum pressure is not more than twice the average pressure, and that there is no tendency to produce tension at B.
The above discussion of the distribution of the pressure on the foundation is amply sufficient for the case in hand; but the subject is discussed more fully in the chapter on Masonry Dams (see Chapter The average pressure per unit on AB has already been adjusted to the safe bearing power of the soil, and if the maximum pressure at A does not exceed the ultimate bearing power, the occa sional maximum pressure due to the wind will do no harm; but if this maximum exceeds or is dangerously near the ultimate strength of the soil, the base must be widened.