In case the track on the girder is curved, the centrifugal force of locomotive must be taken into consideration. If A and B represent two flanges of the girder (in case of deck girder, top flanges, and in case of through girders, bottom ones,) and c c the center lines of the track, then the centrifugal force acts radial to the curve, as indicated by the arrows, and its amount is expressed by the well-known formula:

Cent. force=(wÃ--v2)/(rÃ--32.2), in which w is the moving load on the girder, v its velocity in feet per second, and r the radius of curvature of the track in feet. We have thus to consider the girder flanges top or bottom, according as the girder is deck or through, as forming a truss lying on its side. The flange section should be increased according to the stress obtained as the chord of this lateral truss. The lateral bracing should also be proportioned to resist the maximum stress due to this force, in addition to the wind stress to be presently considered.

Fig. 16.

Wind pressure on a railway bridge is usually taken at 50 lbs. per square foot when the bridge is unloaded, and 30 lbs. when loaded. It is calculated that, at the latter pressure, all empty cars will be blown away.

In plate girders of ordinary spans (say up to 65 ft.) one system only of lateral bracing is sufficient for deck spans with the system on the top, together with cross bracings, and for through spans on the bottom.

In deck span it is hardly necessary to consider the stress in the flanges due to the wind pressure, as the latter on the girder itself is for ordinary spans quite a small amount, and when the girder is loaded the stress due to the overturning moment of the wind pressure on the train will in the top flange be almost neutralized by the stress coming from the lateral system, and in the bottom flange, where the stress is due to this moment alone, can be neglected entirely, as being a very small amount. This is in many cases true only under the supposition that the total wind pressure is carried by the top lateral system to the abutment, and that the intermediate cross bracing merely serves to keep the two girders parallel to each other, and also to carry some wind pressure on the lower half of the girder up to the lateral system ; and consequently the increase of vertical loading on the leeward side girder is only due to the overturning moment above the rails.

But in through span, the stress on the lower flange, due to the wind pressure, has sometimes to be calculated, to see if the total stress per square inch, due to the Tolling load and wind pressure, does not exceed the maximum allowable stress (i. e., the value of a when min/max = 1 in the Lauudhardt's formula. (See p. 49.) The flange stress due to the wind in this case can be easily calculated.

Fig. 17.

The stress on the flange due to the over-turning (Fig. 17.) moment of the wind pressure on the train is equal to (30Ã--10Ã--lÃ--9)/b Ã--⅛Ã--löh in which h is the effective depth of the girder. The stress coming from the lateral system is equal to and the total stress is equal to [l2 (2,700+300h+60h2)]/8hb.

Now as to the stress in the lateral bracing itself (Fig. 18), we have a traveling load due to the wind pressure on the train surface, and a dead load due to the pressure on the girder surface itself. We will, however, take both as a traveling load, as the pressure on the girder itself is after all quite a small amount.

The total wind pressure on the system of the 50 foot girder, when the train covers the entire span, consists of:

* Here we have taken twice the surface of one girder, where but 1« times is sufficient, as the leeward girder is more or less protected by the windward one.

Which gives for each point a load of 30,000/10=3,000 lbs. Consequently, we obtain the following stresses, under the supposition that the girder is in each case covered with the load from one end up to the diagonal, in which we then determine the stress. It is not, however, necessary to calculate stresses in more than one or two diagonals near the end of the girder, as the stresses in the rest are inconsiderable, * 

Stress in a 6=3,000 (8+7+6+6+5+4 +3+2+1) 1/10 sec. 39° - 50'= + 1,4000.

Stress in a o=3,000 (9+8+7+ ----------------) 1/10 sec. 39° - 50'=+ 17,600.

Stress in a o=3,000 ( Ã-- 10 Ã-- «) + 15,000.

The sign ± indicates that each stress will be tension or compression, according as the wind is blowing from one side or from the other. Taking the two facts into consideration, that while the stress is alternating in each brace, and consequently requiring a low allowable stress, it is very seldom that such a wind as we have made calculation for blows, and still more seldom that it blows at the very time when the train is passing over the bridge, we will take the allowable stress at 8,000 lbs. per square inch, and reduce it by the ordinary formula of columns.

*  After a little practice in designing girders, one finds it hardly necessary to make any calculation for these braces for ordinary spans.

If we use 3"Ã--3" angles for the brace, we have in the following formula for least radius of gyration (r2), about 0.8 inch, the length of the brace (I) being about 7 feet.

lbs. per square inch.

This gives the following sections:

For a o 16,600/6,500=2.7 sq.in.

For b a 14,000/6,000=2.1 "

For a' o 15,000/6,600=2.3. "

The lateral braces are, however, constantly subjected to stresses due to the vibration which the slight lateral motion of the passing train causes in the girder, and for which we have no means of correct determination. To provide for this we add 40% to those sections we have just obtained, making, for:

The end cross-bracing should be made strong enough to carry the entire wind pressure down to the abutment, where it is resisted by friction and anchoring. The amount of stress on the cross-brace is evidently 11,300, multiplied by the secant of the angle of inclination of the brace.

The connection of diagonals to the girder is effected by plates. The number of rivets connecting the plate with the angle should be sufficient to make their total shearing strength equal to, or greater than the full strength of the angle taken as a column, but it cannot well be less than two, on account of any possible imperfection in workmanship.

Although it is not necessary in ordinary spans, yet it is better to let the diagonals intersect as near the center line of the flange as can be done conveniently.

The intermediate cross-bracing is put in merely to give stiffness to the girder, and to help to carry the wind pressure to the lateral bracing above, and may be 3" Ã-- 3" Ã--⅜" L in our case.