A width of 21 inches is chosen above, since according to Carnegie Handbook, p. 183, a 1-inch rivet is the largest which can he used in the channel flange.
The post U,L, must be designed for a total stress of 87 000 pounds. It will be assumed that two 10-inch 20-pound channels with a radius of gyration 3.66 and an area of 5.80 square inches each will be sufficient. The length, as before, is 30.1 feet, and the unit stress is: P = 16 000 — 70 X 30.1X 12 = 0 080 pounds.
3.66 000 The required area is = 9.60 square inches. Since the total area of the two channels is 11.76 square inches, and the required area is 9.6 square inches, it is seen that they do not coincide very closely. These channels, however, will be used, since the thickness of the web is the thinnest allowed by the Spedifications, and the width of the channels is the smallest that can be used and still give sufficient room to make the connections with the end connection angles of the floor-beams.
The lower end of this post also has a diaphragm which must transfer half of the stress to the outer eha.nnel of the post. The sides of the diaphragm are the same as in the posts previously de signed; and the number of rivets required is computed in a simi lar manner and found to be as • indicated in .Fig. 18], which shows the cross-section of this post.
At the upper end the bear ing area required on one chan nel is 87 = 1.814 square inches, and the thickness required is 1.814 = 0.363 inch, a 5-inch pin being used. As the web of the channel is 0.382 inch thick, it will give sufficient bearing area without pin-plates. • At the lower end, the vertical component of is 157 500 pounds. The bearing area required on each side of the post is 157 500 2 X 24 00 3.28 square inches, and the thickness is 3. 28 — 0.66 inch. The thickness of the channel web being 0.382 inch leaves 0.660 — 0.382 = 0.278 inch as the required thickness of the pin-plate; but j inch must be used, making a total thickness of 0.382 + 0.375 = 0.757 inch. The plate will carry 0.375X 2 157 500 0.757 = 39 000 pounds, and this requires 7 2 = 6 shop rivets in single shear.
The distance, back to back of channels, will be the same as in and therefore the tie-plates and lacing bars will be the same. Fig. 182 gives a detail of the lower end of 86. The Top Chord. The top chords of small railway bridges
may be made of two channels laced on their top and bottom sides. This is not very good practice, since it leaves the tops of the channels open and lets in the rain and snow, which tends to deteriorate the joints. It is better to add a small cover-plate, even if this does give an excessive section. In case of stress such as is demanded, the chords may consist of two channels and a cover-plate. In this case it is necessary to place small pieces called flats upon the lower flanges of the channel, in order to lower the center of gravity of the section and to bring it near the center of the web. This section makes a very economical section in that it saves much riveting. On account of channels being made only up to 15 inches in depth, 'the use of this section is quite limited owing to the fact that it is not deep enough to allow the I-bar heads sufficient clearance, for the I-bar heads in bridges of even ordi nary span will exceed this amount.
The most common section is that whith consists of two side plates, four angles, and one cover-plate. Sometimes this section has flats placed upon the lower angle in order to lower the center of gravity, as ex plained above. According to (33), the sec tion should be as symmetrical as possible, and the center of gravity should lie as near the center of the web as is consistent with economy.
In case the stress is great enough to demand a heavier section than that above described, additional plates are added upon the sides of the original plates, and heavier and larger cover-plates and angles are used. Fig. 183 shows different types of chord sec tions.
Ir addition to the cover-plate being designed to withstand the total stress, close attention must be paid to (42). This clause has been inserted on account of practical considerations, since it has been found out that if plates are made much thinner than the proportions here required, they will crumple up and fail long before the allowable unit of stress as computed from the formula has been reached. In some eases--especially where the stress is light—the proportions laid down in (42) and (36) will govern the design of the section, instead of the required net area as determined by the formula for the allowable unit compressive stress.