The Sun.
London, England, 1856-01-22 00:00:00

INSTITUTION OF CIVIL ENGINEERS.

At a meeting of this society, Mr. Robert Stephenson,
M.P., president, in the chair,
The paper read was, " On the relative proportions of
the top, bottom, and middle webs of Iron Girders and
Tubes," by Mr. J. M. Heppe!, M. Inst. C.E. The object
of the paper was the investigation of the forces to be re-
sisted by the middle webs of girder,. The first part
of the inquiry had reference to the case of a plat.
of metal, subjected to the action of 'various direct
forces, some compressile and others tensile—slum'.
taneously applied to it, in different directions, and
it was shown that these might always be resolved
into two principal resultants, which were invariably
at right angles to each other, and by which the
applied forces, however numerous, might be oon_
ceived to be replaced—the condition of the plate being
absolutely the same, whether considered as subject t•
the forces originally applied, or to their two principal
resultants. The next point was the consideration of the
condition of a rectangular plate, held in equilibrium by
lateral forces, applied in couples uniformly distributed
along its sides, and it wasshown that in this case also there
were two principal resultants, one tensile and the other
campressile ; that these two were of equal tensity at right
angles to each other, and at angles of 43 deg. with the ap-
plied forces. Moreover that their intensity was exactly
equal to that of the applied lateral forces. It was shown that
the middle web of a girder exposed to a load at a given
point, was exactly in the condition of the plate last con-
sidered, and a rule for the computation of load; of its
thickness was arrived at. Other cases of the distribu-
tion of loads, both fixed and movable, avere then consi-
dered, and rules for the corresponding thickness deduced.
The effect of the horizontal strains to which the. middle
web was subject was then considered, and an investige,
tion was made of the magnitude and direction of the re-
sultants, arising from their composition with the dia-
gonal forces before considered. Finally the increase to
be made in the thickness of the middle web, beyond
that already arrived at, in order to enable it to deal
with these horizontal and diagonal strains, together, was
investigated, and a rule was deduced for its definite
determination. The results arrived at were briefly
these :—Four different cases of distribution of the load
being considered, and in the first instance the horizon-
tal forces being left out of consideration, and the thick-
nesses determined with reference to' the diagonal forces
only. These four cases were :-1. That in which the,
load was fixed and central ; 2. That in which a ion,
concentrated on a point moved along from one end ,of
the beam to the other—as the case of a concentrated
' rolling load ; 3. That in which the load was fixed
and uniformly distributed ; 4. That in which a
load uniformly distributed was drawn on from. on •
end, or that of a distributed rolling load. It was
then shown that in order to enable the middle web to
deal with the diagonal strains, its thickness should be
determined by the following methods:—ln the first case,
the fixed central load, by making it of uniform thick-
ness, and such that its horizontal section was equal in
area to the central vertical sections. In the other three
cases, the thickness of the middle web, at the extremities,
was twice that determined as above. In all of them it
diminished towards the centre, but in each case accord-
ing to a different law. In the second case—the concen-
trated rolling load—the thickness varied as the distance
from the more remote extremity. In the third case—the
distributed fixed load—the thickness varied as the distance
from the centre. In the fourth case—the distributed roll-
ing load—the thickness varied as the square of the dis-
tance from the more remote extremity. The cases of
combinations of these kinds of loads was then considered,
and it was shown that by dividing the central sec-
tion into portions, proportioned to the amount of
each kind, and thence determining the thicknesses
from the middle web for each kind, according
to its own law—the sums of the thicknesses so determined
would give those necessary for dealing with the com-
pound load. The effect of the horizontal forces was next
considered, and two cases were taken—first, that in which
the section of the beam diminished from the centre
towards the extremities, in the ratio of the rectangle of
the segments of the length—in which case the horizontal
forces were constant, or nearly so, throughout. In this
case it was shown that the thicknesses as before deter-
mined, with reference to the diagonal forces alone,
should be trebled, in order to fit them to resist the re-
sultants arising from their composition with the horizon.
tal forces ; and, as in all beams where any variation what-
ever was made in the vertical section, it did or should ap-
proximate to the above law. It was considered that this
rule should be taken as applicable to the beams or variable
section. For beams of uniform section, it was shown
that the thickness of the middle web should be such,
that the horizontal section should be three times the
vertical area. The stiffening of the sides was then
considered. It was argued that as the efficiency
of stiffening must, in some way, depend on the amount
of area, compared with the amount of support applied
to it, it might reasonably be supposed to be proportion-
ate to a line which would form a web to the rectified
periphery—a, rectangle equal to the area to be supported
—which line (borrowing a phrase from hydraulics) might
be called "its mean radius." Reasons were then ad-
duced for believing that stiffening pieces might with
safety be eo distributed as to leave the mean radius of
the included spaces equal to seventy times the thick-
nest of the plate, although in most early structures it
would be found to be much less than what would result
from such a calculation.
It was announced that the following paper would be
read at the meeting of Tuesday, January 22d, " On the
past and present Condition of the River Thames," by
Mr. H. Robinson, Assoc. Inst. C.E.