Homepage
Login
Profile
BookClubs
dmBox
Read Ebook: Instructions on Modern American Bridge Building by Tower G B N George Bates Nichols
Font size:
Background color:
Text color:
Add to tbrJar First Page Next Page Prev Page
Ebook has 181 lines and 21291 words, and 4 pages
In tensional strains, the length of the beam does not affect the strength; but in the beams submitted to compression, the length is a most important element, and in the table given above, the safety strains to which beams may be subjected, without crushing or bending, has been given for lengths, varying from 6 to 60 diameters.
PRACTICAL RULES.
Now to find the necessary sectional area for resisting any strain, we have the following general formula:
or, by substituting the working strengths for the various materials in the formula, we have for wood,
But, in practice, cast iron is seldom used except to resist compression.
As this pamphlet has to do with wooden bridges only, nothing will be said of the proper relative dimensions of cast-iron columns to sustain the strains to which they may be subjected, but a table of the strength of columns will be found further on.
Then, for the power of a beam to resist a transverse strain, we shall have,
This formula has been derived from experiments made by the most reliable authorities.
The constant, 1250, adopted for wood in the following formula, is an average constant, derived from the table, of those woods more commonly used.
Now to reduce the formula to the most convenient shape for use, we substitute the value of s, and we have
But, to reduce the load to the proper working strain, we must divide this equivalent by 4, the factor of safety, and we shall have
Let us apply the formula--
Required the safe load.
becomes, by substitution,
Required the depth. From the above formula we have
substituting
Required the breadth. Deriving b from the foregoing, we have,
substituting
For a cast iron beam or girder--Mr. Hodgkinson found from numerous carefully conducted experiments that, by arranging the material in the form of an inverted T--thus creating a small top flange as well as the larger bottom one, the resistance was increased, per unit of section, over that of a rectangular beam, in the ratio of 40 to 23.
In this beam the areas of the top and bottom flanges are inversely proportional to the power of the iron to resist compression and extension. Mr. Hodgkinson's formula for the dimensions of his girder, is
The factor of safety being 6 for cast iron beams--the formula for the working load will be,
and, to find area of lower flange, we shall have
The general proportions of his girders are as follows:
Length, 16 Height, 1 Area Top Flange, 1.0 Area Bottom Flange, 6.1
In the above formula for cast iron beams,
The web uniting the two flanges must be made solid--as any opening, by causing irregularity in cooling, would seriously affect the strength of the beam.
and the area of the top flange will be,
so that our dimensions will be as follows:
Length, 30 feet. Depth, 45 inches. Area Top Flange, 6.16 inches. Area Bottom Flange, 37 inches.
The thickness of web is usually a little greater at the bottom than at the top, and varies from 1/14 to 1/24 of the depth of the girder. The bottom rib is usually made from six to eight times as wide as it is thick, and the top rib from three to six times as wide as thick, so that, in the example above given, we could have as dimensions for the parts
Top Flange, 4 1/4 x 1 1/2 inches nearly. Bottom Flange, 6 x 2 1/2 inches nearly. Web, 1 1/2 inches thick.
The simplest bridge, consisting of a single stick, to span openings of 20 feet and under, is calculated according to the formula
The following Table was calculated by the above rule--and the dimensions altered according to the actual practice of the writer.
Span. Breadth. Depth.
Span. Bolsters. Stringers. Ties. Braces. Diameter of Bolts.
which would require an area of about 15 square inches of section to resist compression, or a piece 3x5 inches. Now, as this stick is more than 6 or 8 diameters in length, it will yield by bending--and consequently its area must be increased. The load, which a piece of wood acting as a post or strut will safely sustain, is found by the formula already given.
Now substituting 3 for b, and 5 for d, we have
which is not enough. Using 6 for b and 8 for d, we have
A F : D F :: A B : D H
This style of structure may be used up to 50 feet, but it is not employed for spans exceeding 30 feet in length. It is very customary to make the braces in pairs so as to use smaller scantling, and gain in lateral stiffness--the two pieces forming one brace by being properly blocked and bolted together. Below is given a table of dimensions for the various parts of this style of structure:
Span. Rise. Bolster. Stringer. Braces. Rod. No. Size.
Span. Rise. Stringer. Post. Rod. Rods. Feet. In Feet.
It is as well to tenon the post into the beam, and also strap it firmly with iron plates--and the end should be shod with iron to form a saddle for the rods to bear upon.
The braces A a and C c, must support all of the weight of the bridge and its load within the parallelogram B a c D--and the next set of braces, B b and D b, sustain that part of the load which comes over the centre of the bridge. Consequently the braces must increase in size from the centre towards the abutments. The rods resist the same pressure in amount as their braces--but being vertical, do not need the increase, given to the braces on account of their inclination--but increase simply with the strain upon them, from the centre to the ends of the truss.
There are many forms of small bridges differing from those enumerated, in various minor details, but sufficient has been said to give the reader a fair idea of the strains upon the different parts, and how to arrange and proportion the materials to resist them.
PRACTICAL RULES AND EXAMPLES IN WOODEN BRIDGE BUILDING.
In any case that may arise, we must determine approximately the gross weight of the bridge and its load--as a basis, and then we can proceed as follows--in case of a Howe, Pratt, or Arch Brace Truss.
Mr. G.L. Vose, in his admirable work on R.R. Construction, observes very truly that "The braces, at the end of a long span, may be nearer the vertical than those near the centre, as they have more work to do. If the end panel be made twice as high as long, and the centre panel square, the intermediates varying as their distance from the end, a good architectural effect is produced."
Now it is necessary for us to have some data from which to determine the approximate weight of the bridge, and also its load. These can be found by comparing weights of bridges in common use, as obtained from reports. In a small bridge of short span, the weight of the structure itself may be entirely neglected, because of. the very small proportion the strains caused by it bear to those due to the load;--but, in long spans, the weight becomes a very important element in the calculations for strength and safety--inasmuch as it may exceed the weight of the load.
allowing for splicing 72 square inches, " " foot blocks, 24 " " " " bolts, 24 " " " " washers, 8 " "
Add to tbrJar First Page Next Page Prev Page