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A
multitude of simple rules, formula, and tables for designing reinforced concrete
work have been proposed, some of which are sufficiently accurate and applicable
under certain conditions. But the effect of these various conditions should be
thoroughly understood. Reinforced concrete should not be designed by
"rule-of-thumb" concrete construction engineers. It is hardly too
strong a statement to say that a man is criminally careless and negligent when
he attempts to design a structure on which the safety and lives of people will
depend, without thoroughly understanding the theory on which any formula he may
use is based. The applicability of all formulae is so dependent on the quality
of the steel and of the concrete, and on many of the details of the design,
that a blind application of a formula is very unsafe. Although the greatest
pains will be taken to make the following demonstration as clear and, plain as
possible, it will be necessary to employ symbols, and to work out several
algebraic formulae on which the rules for designing will be based. The full
significance of many of the terms mentioned below may not be fully understood
until several subsequent paragraphs have been studied: Breadth of concrete
beam; Depth from compression face to center of gravity of the steel; A = Area
of the steel; p = Ratio of area of steel to area of concrete above the center
of gravity of the steel, generally referred to as percentage of reinforcement, =
Modulus of elasticity of steel; = Initial modulus of elasticity of concrete; r
= Ratio of the module; = Tensile stress per unit of area in steel; c =
Compressive stress per unit of area in concrete at the outer fiber of the concrete
beam; this may vary from zero to C'; c' = Ultimate compressive stress per unit
of area in concrete - th9 stress at which failure might be expected; Deformation
per unit of length in the steel; "11in outer fiber of concrete; in outer
fiber of concrete when crushing is imminent; = Deformation per unit of length
in outer fiber of concrete under a certain condition (described later);

q
= Ratio of deformations;

k
= Ratio of depth from compressive face to the neutral axis to the total
effective depth

x
= Distance from compressive face to center of gravity of compressive stresses;

X
= Summation of horizontal compressive stresses;

M
= Resisting moment of a section.

As
a preliminary to the theory of the use of reinforced concrete in concrete beams,
a very brief discussion will be given of the statics of an ordinary homogeneous
concrete beam. Let A B represent a concrete beam carrying a uniformly distributed
load W; then the concrete beam is subjected to transverse tributes load
stresses. Let us imagine that one-half of the concrete beam is a "free
body" in space, and is acted on by exactly the same external forces; we
shall also assume the forces C and T (acting on the exposed section), which are
just such forces as are required to keep that half of the concrete beam in
equilibrium. These forces, and their direction, are represented in the lower
diagram by arrows. The load W is represented by the series of small, equal, and
equally spaced vertical arrows pointing downward. The reaction of the abutment
against the concrete beam is an upward force shown at the left. The forces
acting on a section at the center are the equivalent of the two equal forces C
and T. The force C, acting at the top of the section, must act toward the left,
and there is therefore compression in that part of the section. Similarly, the
force T is force acting toward the right, and the fibers of the lower part of
the concrete beam are in tension. For our present purpose we may consider that
the forces C and T are in each case the resultant of the forces acting on a
very large number of "fibers." The stress in the outer fibers is of
course greatest.

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

**We Are Your Local
Concrete Cutter**

**Call 603-622-4441**

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