L,'L, = +15.0 X 1.544 = +23.15 L,'L, = -15.0 = + 9.0 X 1.544 = +13.91 L,'L, - - 9.0 The maximum chord stresses due to this load of 450 pounds per linear foot of train, occur when the train covers the entire span; and they are directly proportional to the stresses produced by the fixed load, in the same ratio as the live panel load is to the fixed panel load.
This ratio is 3 = 3.0. The chord stresses, therefore, are: Table X, Article 53, gives the stresses in the top and bottom lateral systems for wind right and wind left.
52. Overturning Ef fect of Wind on Truss. When the wind blows on the top chord, it tends to overturn the truss. As the truss is held down by its own weight, the action of the wind does not overturn it, but causes the dead-load reaction on the windward side to be less and that on the lee ward side to increase by a like The amount is ± V = 2° X where Ew = the sum of all .the wind panel loads, h = the height of the truss, and b = the distance center to center of, trusses. The effect upon the leeward truss is the same as if two ver tical loads, each equal to V and acting downward, were placed at the hips U, and U, (see Fig. 9S). The effect on the windward truss is the same as if two vertical loads, each equal to V and acting upward, were placed at the hips U,' and U,'.
The stresses in the leeward truss will now be worked out. The stresses in the windward truss are the same, but with opposite signs.
The truss is that of Article 47. Here V = 10 X ?? = 11 Fig. 99 shows the truss with the loads in the correct position, the reactions each being 11.00. V, = + 11.00, and = +11.00 11.00 = 0. The shears in the 2d, 3d, 4th, and 5th panels are also zero. As the shear in these panels is zero, the stress in the diagonals and vertical posts is zero X secant cs = zero. The stress in the hip verticals U,L, and is zero, as there are no loads at L, and The stress in the end-post is 11.00 X 1.28 = 14.08. Taking the center of moments at U the stress equation of = is: X 25 + 11.00 X 20 = 0; whence L,L, +8.8. The stress in all the lower chord members will be found to be + 8.8. By summing the horizontal forces at the section a a, noting that, as is zero, its component is also zero, there results: +L,L, -1- U,U, = 0; whence U,U, = L,L, = (+8.80) _ 8.80. This is also
the stress in all members of the top chord.
It is now seen that the overturning effect of the wind on the truss causes stresses only in the end-posts and chords. The wind on the lower chord causes no overturning effect, as it is transferred directly to the abutments.
53. Overturning Effect of Wind on Train. The wind blowing upon the train tends to overturn it, and in so doing the pressure on the leeward stringer is increased and that on the windward stringer decreased by the same amount. This difference in pressures is transferred to the floor-beam and then to the panel points (see Fig. 100), where its value is: The action of the wind in tending to overturn the train is the same as if the truss were under a live panel loading of L, the panel load L acting upward on the windward and downward on the leeward truss.
The chord stresses due to this will be proportional to the dead load stresses in the same ratio as this panel load L is to the dead panel load. For the truss of Article 47, this ratio is = 0.303, and the chord stresses caused by the overturning effect of the wind on the train (see Table VII) are: It is unnecessary to compute the shears further than one panel past the middle of the span, as only the maximum stresses are usually required.
The wind stresses from various causes are grouped together and given in Table X.
From Table X it is seen that large wind stresses occur in some of the members. Most specifications require that the stresses due to wind shall he neglected in the design unless they exceed 25 per cent of the sum of the dead-load and live-load stresses.
The subject of wind stresses does not ordinarily receive the con sideration it should have; in fact, it appears to be common practice, in the case of spans up to 200 feet, to neglect the action of the wind in all members of the bridge except the top and bottom lateral diagonals, the top struts, the portal, and the bending effect in the end-post. For the last two effects mentioned, see the next succeeding article.