New or Improved Form of Girders and Rail-road Rails.
Year: 1889

page_text: COMPLETE SPECIFICATION.
A New or Improved Form of Girders and Rail-road Rails.
I, ROBERT HENRY COUSINS a Civil Engineer, residing at the City of McKinney,
County of Collin, State of Texas, United States of America, do hereby declare the
nature of this invention and in what manner the same is to be performed, to be
particularly described and ascertained in and by the following statement :-
The object of my invention or improvement is to obtain the greatest transverse
strength of beans, girders and rail-road rails, with the least amount of material,
whereby the transverse strength is more effectively increased than by any other
method at present known. The usual and only known method used by constructors
of beams, girders and rail-road rails to compute their strength and conversely that by
which they are constructed to have a given transverse strength is that known as the
"Common theory of flexure" which theory assumes the existence of a neutral line
or fulcrum that passes through the center of gravity of the section of the beam
and girder, with respect to which the Moment of Resistance of the Section must
be computed. The stress or strain in the bottom and top fibers of the beam and
girder is assumed to be an empirical quantity, called the "Modulus of Rupture." All
of which assumptions of the "Common theory of flexure" are erroneous and assumes
the existence of "Mechanical Conditions" that are physically impossible. I have
discovered that the fulcrum, or axis around which the load breaks the beam, girder
and rail-road rail, and with respect to which the Moment of Resistance of their
transverse sections must be computed, is a line in the top or compressed side of
the beam and girder; and that there is a neutral line, or line of no strain within
the section and parallel to the above described axis; the compression and tensile
strain increases uniformly from this neutral line towards the top and bottom of the
transverse section, respectively, and at the instant of rupture becomes the crushing
and tensile strength of the material composing the beam, girder, and rail-road-rail.
The position of the above described neutral line is determined from the condition
that the Moment of Compressive Resistance shall be equal to the Moment of Tensile
Resistance, both to be computed with respect to the above described fulcrum.
Now every flanged beam, girder and rail-road rail may be conceived to be cut
from, or constructed by the removal of certain portions of a rectangular beam,
whose depth and breadth is the depth and breadth of the flanged beam, girder and
rail-road rail, respectively. The Moment of Compressive Resistance of the rectangular
beam may be graphically represented by two pyramids with rectangular bases, placed
base to base as represented in Figure 1; the sum of the heights, or altidudes of these
pyramids is the depth of the neutral line below the fulcrum or axis. The apex a of
one pyramid represents the Moment of Resistance of the material of the rectangular
beam at the fulcrum and the apex n of the other that of the material at the neutral
line, from which it is evident that the Moment of Compressive Resistance of the
compressed area of the section increases, respectively, from the fulcrum and neutral
line and that at one half of the distance between these lines it becomes a maximum
The height or
or greatest, and is represented by the bases of these pyramids.
altitude of each pyramid is one half the distance between the fulcrum and the
neutral line, and the base of each is one half this. height by the breadth of the
rectangular beam. The volume of these two pyramids multiplied by the crushing
strength is one half the required Moment of Resistance of the rectangular section.
From this graphic representation of the Moment of Compressive Resistance, it is
evident that the material at and near one half the depth between the neutral line
and the fulcrum, is the most effective in resisting the transverse load, and there-
fore should not be removed from the rectangular section in order to construct the
flanged beam, girder and rail-road rail, of any desired shape of transverse section,
as has been the practice.

page_text: In order to illustrate this process and its application, let a bdx, Figure 2 represent
a rectangular section from which it is required to be formed a beam with flanges
at the top and bottom; nl represents the neutral line, a x the axis, or fulcrum
and cs a line at one half the distance between a x and n 1, the shaded or hatched
portions of the Figure represents the material that is the least effective and that that
should be removed to form the required section; tho Moment of Resistance of the
section that is not shaded, above the line n l, must be equal to one half the required
Moment of Resistance of the section. In order to preserve the required equilibrium
between the moments of compressive and tensile resistance, sufficient metal must
be removed from the tension or extended area immediately below the neutral line,
where it is the least effective, to cause the moment of tensile resistance of the
remainder to be equal to the other half of the required Moment of Resistance of
the section. The above described method of constructing beams, girders and rail-
road rails of maximum strength and minimum amount of material, is applicable to
beams, girders and rail-road rails when made of wood, Cast-iron, Wrought-iron, steel
and other metals. The converse method is equally true that in building up a beam,
girder and rail-road rail composed of web and flanges, only such material should be
placed in them as is shown by the foregoing process of construction to be the
most effective.
I will state that I am aware that beams and girders of a similar shape have
been used in the construction of fire-proof floors, having an intermediate flange
placed anywhere on the vertical web "as may be necessary for construction purposes,'
thus serving the purpose of a mere bracket, the function being entirely different
from that described in my improvement.
Having now particularly described and ascertained the nature of my said
Invention, and in what manner the same is to be performed I declare that what I
claim is this;
1. The use, in the construction of beams, girders and rail-road rails composed of
a vertical web and a flange or flanges of a mass of the metal in a flange or flanges,
projecting from the web at and near one half the distance between the axis and
the neutral line, for the purpose and substantially as described in the foregoing
specifications.
Dated May 12 1889
ROBERT HENRY COUSINS.