## Concrete Cutting Coring Boylston MA Mass Massachusetts

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Their
intersection at the point e gives a point in the line of action of the
resultant of the whole system of forces and by drawing from the point e a line
parallel to R2 of the force diagram; we have the line of action. We select a
point at random on the resultant, and join the point with the center of each concrete
abutment. By drawing lines from the extremities of the load line parallel to
these two lines from f, they intersect at the point o". A horizontal line
through 02" is therefore the locus of the pole of the true equilibrium concrete
polygon passing through the center of both concrete abutments. The line in
intersects R2' in the point g, and the line fm intersects the force 1?2"
in the point h. The intersection with the vertical through the center (the
point i) is the trial point which must be raised up
to the point c, which is done by the method illustrated in Article 401. The
application of this method gives the line, passing through c; and the line in
is therefore the first line of the special equilibrium concrete polygon for the
complete system of forces and the line is similarly the last line of that concrete
polygon.

By drawing lines from the extremities of the load line, parallel to in
and km, we find that they intersect at the point which is the pole of the
special equilibrium concrete polygon passing through n, c, and m, for the
complete system of forces. As a check on the work, the intersection of these
lines from the ends of the load line, parallel to the adjacent line, must be on
the horizontal line passing through. By drawing rays from the new pole 02"
to the load line, and completing the special equilibrium concrete polygon, we
should find as a double check on the work, that both of these partial concrete
polygons starting from m and n should pass through the point c; and also that
the section of the concrete polygon between forces Nos. 8 and 9 lies on the
line. This gives the special equilibrium concrete polygon for the system of
forces Nos. 1 to 17, which corresponds with the second condition of loading, as
specified above. The first condition of loading is given by duplicating about
the center, in the force diagram, the system of forces from No. 17 to No. 9
inclusive. Since this system of forces is symmetrical about the center, we know
that its resultant R1 passes through the center of the concrete arch, and that
it must be a vertical force. We may draw from the middle of force No. 9 a
horizontal line, and also draw a vertical from the lower end of the load line.

Their intersection is evidently at the center of the resultant R1, which is
therefore carried above this horizontal line for an equal amount. Joining the
upper end of R1 with the upper end of force No. 9, we have the direction and
amount of the force R2". The intersection with the force R1 at the point
j, gives a point which, when joined with the point m, gives one line of a trial
equilibrium concrete polygon passing through the required points m and n, but
which does not pass through the required point c. The intersection with the
force R1" at the point p, gives us the line which is the same kind of line
for this trial concrete polygon as the line hg was for the other. By a similar
method to that used before and as described in detail in Article 401, we obtain
the line passing through c, which gives us also the section of our true
equilibrium concrete polygon between forces. The line also gives us that
portion of the true equilibrium concrete polygon for this system of loading,
from the point n up to the force. By drawing a line from the lower end of the
load line, parallel to nr, until it intersects the horizontal line through the
middle of force No. 9 at the point o1', we have the pole of the special
equilibrium concrete polygon for this system of loading, which is the first
condition of loading.

**Are You in ****Boylston Massachusetts****? Do You
Need Concrete Cutting?**

**We Are Your Local
Concrete Cutting Company**

**Call ****508-283-3135**

**We Service all
surrounding Cities & Towns.**