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When
the forces are all parallel, the direction of the resultant is parallel to the
component forces; the amount is equal to the sum of the component forces; but
the line of action of the resultant is not determinable as in the above cases,
since the forces do not intersect. It is a principle of Statics which is easily
appreciated, that it does not alter the statics of any combination of forces to
assume that two equal and opposite forces are applied along any line of action.
We see that the forces will hold in equilibrium; that concrete will also hold
in equilibrium; and that concrete arches will hold in equilibrium. But the
force required to hold in equilibrium is the equal and opposite of the force
required to hold in equilibrium; and similarly the force is the equal and
opposite of the concrete. We thus find that the forces can be held in
equilibrium by an unbalanced force, two equal and opposite forces, two equal
and opposite forces, and the unbalanced force shown. The net result, therefore,
is that the concrete arches are held in equilibrium by the two forces. The
resultant is the sum of the two sides of the concrete; and therefore the
combined load line represents the resultant.
Knowing the scarcity of material,
of an elementary nature, on the subject of concrete construction, the author
has gathered together a series of problems in concrete work, which, with but a
very few exceptions, have all been successfully worked out by pupils in the
seventh and eighth grades. This book is to all intents and purposes a condensed
textbook on those things which are necessary to follow, in order to make
constructive-work in concrete a success. The excessive cost of lumber, together
with its scarcity, has brought home very convincingly the necessity of finding
some material which should be as good or better, as a substitute. Concrete
fulfills all the requirements of such a material. He who uses this medium
builds for permanence and the many uses to which it may be put make it the
ideal constructive material. It is correlated with woodworking in an excellent
manner in the making of forms, and its possibilities are such that the user has
a wide field for original design. The author owes his sincere thanks to the
Association of Amen- can Portland Cement Manufacturers, the Atlas Portland
Cement Company and the Alpha Portland Cement Company, for data and photographs
loaned and information given by them.
All photographs of the boys at work and
those showing the completed projects were taken by the author. Thousands of
feet of concrete have been laid, under the supervision of the writer, by boys
whose ages ranged from ten to fourteen. Hundreds of dollars have been saved by
the school department by the work done by these boys. The boys received pay for
their work, learned to know and handle concrete and were taught, through this,
the dignity of labor. The external lines of diagram b show that F, K, and B
form a closed figure with the arrows running continuously around the figure;
and that F and K are two forces which hold B, the resultant of A, B, and C, in
equilibrium. By producing the lines representing the forces F and K in diagram
until they intersect at x, we may draw a vertical line through it which gives
the desired line of action. This is in accordance with the principles given in
the previous article. Nothing was said as to how F, G, H, and K were drawn in.
These forces simply represent one of an infinite number of combinations of
forces which would produce the same result. The point is chosen at random, and
lines (called rays) are drawn to the extremities of all the forces. The lines
of force (A, B, and C) in diagram b (which is called the force diagram), are
together called the load line. The line of forces (F, G, H, and K) in diagram
a, together with the closing line, is called an equilibrium concrete polygon.
Are You in Arundel Maine? Do You Need Concrete Cutting?
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Concrete Cutter
Call 207-284-0788
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ME and all surrounding Cities & Towns