A treatise on masonry construction by Baker Ira O. (Ira Osborn) 1853-1925

Author:Baker, Ira O. (Ira Osborn), 1853-1925
Language: eng
Format: epub, pdf
Tags: Masonry
Publisher: New York : J. Wiley
Published: 1909-03-25T05:00:00+00:00

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I'iibl' I-MbV-bX) I'hirl* I=A7rn*-lV

Fig. 82.— Moment of Inertia op Various Cross Sections.

692. If the area of the section AB, Fig. 81, is a rectangle, S = lb, and I = Y^bP. Substituting these values in equation 1 gives

^ W 6M

^ = ^6 + 17^- (3)

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

W 6H.h Ib'^ bp'

(4)

To still further simplify the above formula, notice that Fig. 81 gives the proportion

H :W ::NCiaC, from which

H. aC = W. NC; or, changing the nomenclature,

H h = W d. Notice that the last relation can also be obtained directly by the principle of moments.

Substituting the value of H h, as above, in equation 4 gives

„ W 6Wd ,.

''-Fb + 'bir' ^')

which is a convenient form for practical application.

An examination of equation 5 shows that when d = N C = ^l, 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 suflEicient for the case in hand; but the subject is discussed more fully in the chapter on Masonry Dams (see Chapter XVII).

693. 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 occasional 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.

694. Sliding. The pressure of the wind is a force tending to sUde the foundation horizontally. This is resisted by the friction caused by the weight of the entire structure, and also by the earth around the base of the foundation; and hence there is no need, in this connection, of considering this manner of failure.

695. Spread Footings. The term footing is usually understood as meaning the bottom course or courses of masonry which extend beyond the faces of the wall. It will be used here as applying to the material—whether masonry, timber, or iron—employed to increase the area of the base of the foundation. Whatever the character of the soil, footings should extend beyond the face of the wall (1) to add to the stability of

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