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Assume
a very simple numerical case. The weight of the concrete wall and its line of
action are very readily determined with accuracy. The base of the concrete wall
has been made of the height, or 7.2 feet. The batter of the outer face is at
the rate of 1 in 5, or is 3.6 feet in the total height of the wall, leaving 3.6
feet as the thickness at the top. The area of the cross-section = -} (3.6 +
7.2) 18 = 97.2 square feet. On the intersection of this line of pressure with
the base is evidently at a distance from the intersection of the line of
vertical pressure, equal to: That point is therefore 5.18 feet from the rear of
the wall, or 2.02 feet from the toe. This point represents the center of
pressure of the pressure on the subsoil. The pressure is most intense at the
toe of the wall, and is there assumed to be twice as intense as the average
pressure. It is also assumed that the pressure diminishes toward the rear,
until, at a distance back from the center of pressure equal to twice the
distance from the center of pressure to the toe, the pressure is zero. The
average pressure would equal 14,640 - 6.06 = 2,415 pounds per square foot. The
maximum pressure at the toe would therefore equal twice this average pressure,
or 4,830 pounds per square foot, or about 34 pounds per square inch. This unit pressure
is so far within that allowable for stone concrete cutting, that there is no
danger of the crushing of the concrete cutting at the toe. The pressure on the
subsoil, which is less than 2- tons per square foot, is less than that usually
allowable on good subsoil. There is therefore but little danger that the
subsoil will be crushed and that they will tip over bodily on account of the
failure of the subsoil. Since the line of pressure is likewise two feet back of
the toe of the wall, there is no danger that the concrete wall will tip over
around its toe. The accuracy with which these calculations have been carried
out should basis that this concrete cutting weighs 140 pounds per cubic foot; a
section of this concrete wall one foot long will weigh 13,608 pounds. To find
the line of application of the weight, we must find the center of gravity of
the trapezoid, and for this purpose we may divide the trapezoid into a
rectangle and a right-angled triangle. The rectangle has an area of 64.8 square
feet, and its center of gravity is 18 feet from the rear face. The center of
gravity of the trapezoid is then found numerically as follows: (64.8) < 1.8=
116.64 which is the distance of the center of gravity of the trapezoid from the
rear face of the wall. The pressure of the earth on the rear wall, as stated
above, is very uncertain; a value for it has already been computed (in the
example in section 225) as 5,400 pounds. This value is probably excessive,
except under the most unfavorable conditions. The point of application of the
resultant of this pressure, as well as the direction of that resultant, is also
uncertain, and has been the subject of much theoretical controversy. If the
soil were merely a liquid which had no internal friction, there would be no
uncertainty. In this case, the point of application of the pressure would be at
one-third the height of the concrete wall from the base, and its direction
would be perpendicular to the rear face of the wall. This is the most
unfavorable condition for stability which could be assumed; and on this account,
calculations are sometimes made on this basis, with the knowledge that if the concrete
wall is stable under these most unfavorable conditions, it will certainly be
stable no matter what the real conditions may be. On this basis we have the
resultant pressure against the rear of the concrete wall as indicated by the
arrow. The resultant pressure on the base of the concrete wall is therefore a
line the direction of which is indicated by the diagonal of a parallelogram
whose two sides are parallel to the two forces, the sides being proportional to
those forces. The amount of this pressure equals the square root of the sum of
the squares of 5,400 and 13,608, or 14,640 pounds. The

161`

**Are You in Hancock ****New Hampshire****? Do You
Need Concrete Cutting?**

**We Are Your Local
Concrete Cutter**

**Call 603-622-4441**

**We Service Hancock NH
and all surrounding Cities & Towns**