Girders.-The sketch shows a very strong form for this description of firder, when rolled solid. The top ange being condensed and square is in a good form to resist compression; the bottom flange has a wider surface to rest on, and the middle rib is light; an experimental beam of this description 8 ins. deep and 11 feet long re quiring 5 tons to break it.

The top flange should have a sectional area 1 1-2 times that of the bottom. When thus proportioned:

Sec. area top flange, ins. X depth ins./ Length feet.X 5 = Breaking weight in tons.

.This is an inferior shape.

In such a beam the top flange should have an area 1 3-4 that of the bottom flange.

When thus proportioned:

Sec. area top flange ins. x depth ins./ Length feet.X4= Breaking.

weight, tons.

Beams of the above forms, made of plates and of L iron, are of equal Strength with the above; care being taken to make the bottom flange of double plates, with joint plates over the butts, allowing a little extra area in the bottom to compensate for the rivet holes, though this is not necessary if they are rivetted up by steam.

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Fig. 3.

Fig. 4.

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Fig. 5.

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Hollow Girders. - The sketch represents the form for hollow girders combining the greatest strength with the least weight, the top being in the best form for resisting compression.

The proportion of the bottom sectional area to that of the top should be as 11 to 12, or 4-5; and the sides should be well stiffened with angle iron, to keep them from buckling; the sectional area of the top and bottom may be reduced at the extremities to 1-3 of the area at the middle, without diminishing the strength of the beam.

When thus proportioned:

Section. area top, ins. X depth ins. / Length feet. X 5 = Breaking weight, tons.

An experimental beam of this form, 75 feet long between supports, 4 feet 6 inches deep, with 6 cells at the top, about 6 inches square each, with a sectional area 24 sq. ins., the sides stiffened with 1 1-2 L irons, 2 feet apart, required 86 tons to break it.

Fig. 6.

Wrought Iron Beams 58

In the plain hollow girder the top should have a sectional area 1 3-4 that of the bottom.

Thus proportioned:

Section, area top, ins. X depth ins./Length feet.X 4 = Breaking weight tons.

To find, the strength of a round girder.

Sec. area, ins. X dia. ins./Length feet.= Breaking weight, tons

To find the strength of any beam.

If the top flange is the weakest, find the compressive breaking strain in tons per square inch due to its shape, thickness, and length. (See Columns.)

If the bottom is the weakest, find the tensional breaking strain of the material in tons per square inch.

Then,

Sec. area ins. of weakest flange x breaking strain, tons per in. X depth of beam ft. .x4/ Length between supports, feet.

= Breaking weight, tons.

This rule will be found useful, either to confirm the results obtained from the previous rules, or to find the strength of any beams of irregular shape not included in them.

The mode of ascertaining the compression and tension on the top and bottom flanges of beams is sufficiently simple.

Take the case of a beam, 20 feet long, 2 feet deep, with a weight of 20 tons on the middle; the force counteracting this weight will be 10 tons on each end; the force of compression at the top in the middle of the beam, and that of tension at the bottom, taking the centra] weight as the fulcrum, will be just in proportion to the leverage; in this case, as 10 to 2, or 5 to 1. The force of 10 tons applied to the end will thus result in a force of 50 tons of compression and tension on the flanges in the middle of the beam. Or in a simple form,

Weight, tons X length, feet / Depth, feet X 4 = Strain on top and bottom flanges, tons.

The ultimate compressive strength of boiler plate iron may be taken at 16 tons per square inch, the tensile strength at 20 tons per square inch; and this is the reason why, in all wrought iron beams, the top requires to be the strongest.

But as in cast iron the compressive strength is about 48 tons, while the tensile strength is only about 7 tons per square inch, the bottom flange in cast iron girders requires to be much the strongest.

The fullest information on this subject, and the experiments in detail, will he found in Mr. Eaton Hodgkinson's experiments on the strength of cast iron beams, and in Mr. Edwin Clark's work on the Britannia and Conway tubular bridges.