There is a diversity of opinions as to the amount of allowable stress in a plate-girder, but all agree in this, that, on account of the great difference between the dead and live load, or more properly between minimum and maximum stresses, and the suddenness with which they change from one to the other proportionally as the spans decrease, the allowable stress should be much lower than in structures of longer spans.

*Shocks on Railway Bridges. Mr. J. W. Cloud, Proc. Am. Inst, of Mining Engineers, 1881.

Laundhart's formula gives the allowable stresses conformably to the long series of . experiment (of W*�hler), and is the one that is being more and more used by engineers, but not without some room for doubt as to whether it is applicable to all kinds of stresses under all circumstances. The following is that well-known formula for stresses in the same direction: *  p - u (1+ t - u/u minimum stress/maximum stress) in which t is the stress which by a single application produces rupture, which, according to W*�hler, can be accomplished by somewhat less stress than t if repeated a sufficient number of times; u is the stress per square inch after an indefinite number of repetitions of which the bar still returns to its original unstrained condition, and consequently its value becomes greater the less the number of repetitions to be endured is; p is the stress per square inch, which, after the greatest number of repetitions possible, is still just capable of sustaining the load. Wohler found for a certain axle-iron that:

* Compare Weyrauch's Structure of Iron and Steel Transl. by Prof. DuBois, chap. ii.

t=56,900 lbs. u=31,200 by flexure and t=46,800 " u=31,200 by tension. and for a certain kind of steel, that:

t=104,400 lbs. u=51,300 by tension.

From these figures we can give the Laundhardt formula, the following shape to be used both for iron and steel.

min. x.

a=cl (1+-----)------------(14)

max.

In which a is the allowable stress per square inch, and c is equal to u divided by the factor of safety, and is:

Further to obtain the actual allowable stress for the compressed flanges, the amount given by the above formula, whenever the unsupported distance is more than 12 times its width, must be reduced by Rankine's formula, deduced from Fair-barn's experiment, viz.: in which k is the actual allowable stress per square inch, and b the width of the flange, and l the unsupported length: a the allowable stress already found.

In all the allowable stresses above given, it is supposed that iron has an elastic limit of not less than 26,000 lbs., and an ultimate strength of not less than 50,000 lbs-per square inch when tested in ordinary test pieces, and that steel has corresponding values of not less than 36,000 lbs. and 60,000 lbs.

Returning now to our 50 ft. girder, we find that the ratio of the dead load stress to the total stress as already found, or (min/max),is about=1/5 throughout. Consequently a - 8,000 (l+1/5)=9,600 lbs. for tension.

a=7,000(1+1/5)=8400 lbs. for compression.

Hence we obtain the following sections:

Top Flange

At a 68,500/8,400 = 8.2 square inches. b 124,800/8,400 = 14.8 " "

c 161,900/8,400 = 19.3 " "

d 186, 400/8,400=22.2 " "

e 188,000/8,400=22.4 " "

Bottom Flange

At a 68,500/9,600= 7.1 square inches.

b124,800/9,600= 13.0 " "

C 161,900/9,600=16.9 " "

d 186,400/9,600=19.4 square inches.

e 188,000/9,600=19.6 " ".

It now remains to find the sizes of angles and plates to give these required sections. It is important, in making up flange areas, to keep in mind that there must always exist a certain relation be-tween the sectional areas of flange angles and plates. No normal stress can exist in flange plates without first passing through the angles which alone form connection with the web. Plate-girders are unlike rolled beams, in which every part is connected molecule to molecule, but have stresses transmitted only through rivets which are distributed only at certain distances apart. Consequently the flange angles are at every point more or less subjected to stress from the plates in addition to their own. This additional stress will evidently increase with the amount of plates on the back. It is a good practice, therefore, to make the girder so deep that the flanges do not require a large number of plates to be packed one upon another, and then to choose angles as heavy as possible, consistent with the total flange area required.

Everybody who does any designing in iron should be provided with "Book of Shapes," issued by almost every iron company in the country. Carnegie's book is especially to be recommended for the purpose. In order to give the girder the greatest amount of moment of resistence, it is usual to use angles with unequal legs, with the longer legs in the horizontal position. It is important that the top flange of a plate-girder should always have a plate running from one end to the other, even when angles may be found which alone are sufficient to make up the required section. The addition of such a plate evidently requires more work of punching and riveting, but it gives great lateral stiffness to the flange, and also helps to distribute the stress more uniformly than with angles alone, while at the same time it furnishes a cover to the small channel which is left between the angles where water can stand, as the web is not usually flush with their backs.

In making up the bottom flange section, rivet holes must be deducted to obtain the net section, and in so doing the diameter of the rivet hole should be taken at least as 1/8 inch larger, although the diameter of holes are usually made 1/16 inch larger than that of rivets. This latter provides to a certain extent for the damage done to the strength of the metal in the process of either punching or drilling. On the other hand, for the top flange, the gross sectional area may be taken without regard to the rivet holes, when the riveting is well done, i.e., every rivet completely filling up its hole.

Thus we obtain the following sections: For top:

For bottom flange, supposing we use ⅞ inch diameter rivets:

Net sectional area in the middle=20.1 square inches.

It is a fact worthy of notice that the majority of plate-girders of iron as well as of steel, though of equal top and bottom flanges, fail by tension,* a fact which has been observed in the results of experiments made some years ago by the Dutch Government to determine the comparative strength of iron and steel riveted girders. This is evidently due to the considerably diminished effective section of the bottom hinge for tension by rivet holes, and the weakening of the metal still further by punching or drilling. Rolled I beams usually fail by compression when their webs are strong enough.

In Plate II is to be seen the disposition of metals in flanges as well as in the whole girder. In order that the rough edges of the web plate may not project beyond the backs of the flange angles, the depth of the girder back to back of the latter is made ¬ inch (⅛ inch may, however, do just as well,) more than the width of the web plate, so that the additional flange plate may have a flat surface to be riveted on.

* See Charles Bender's Principles of Economy in Designs of Metallic Bridges, p. 13.

In the figure, all dimensions are given exact, but each piece should be ordered a little longer than is actually necessary, to provide for cutting and milling works in the shop. Thus, for pieces whose lengths are less than 10 feet, allowance of « inch, and for more than 10 feet, ¾ to 1 inch, according to the length, should be given.

Those flange plates which but partly cover the flange should be run sufficiently beyond the point, where, according to the calculation we have made, the sectional area of that plate is necessary to form the required section, to catch the number of rivets on the flange necessary to transmit the amount of stress which the plate is required to sustain.