The stresses on the right half of the principal are the same as those on the left, and if the diagram be correctly drawn it will be found to close. The following table gives the stresses on one half of the truss. It is usual in principals of this class to introduce a vertical member connecting the apex with the centre of the horizontal tie G O. Theoretically there is no stress on this vertical, and it is not shown in the figure. The reason of its introduction is to keep the horizontal tie straight. Sao × 17:3=10-93 × 35 – 3-125 (8·75+175+26-25), GO Several modifications of the French truss are in common use, and by the introduction of extra counterbracing, principals of this class may be used for spans up to 150 feet. The method of calculating the stresses on such structures is similar to what has already been given; no fresh difficulties arising in the construction of the stress diagrams. 224. Saw-Tooth Truss.-An example of this form of truss is shown in fig. 190, where it will be noticed that the inclination of the rafters is different. This form of truss is extensively used in weaving sheds and other factories where a steady light is required. The shorter and steeper inclination of the roof is glazed and faces the north, thereby giving a steady light; while the longer slope is usually covered with slates or tiles; these latter being supported on wrought-iron angle laths which are spaced from 8 to 14 inches apart, according to the size of the slates or tiles. Example 12.-Determine the stresses on the truss shown in fig. 190, the span being 20 feet, and the rafters inclined at 60° and 30°. The principals are placed 11 feet apart, and the vertical load on the roof is 40 lbs. per square foot of the horizontal projection. Total load on principal = 20 × 11 × 40 lbs. = 4 tons nearly. This load is apportioned in such a manner that 0.5 ton rests at a, 1.25 tons at c, 1.5 tons at d, and 0.75 ton at b. The abutment reactions in trusses of this description may be most readily found by the aid of a polar diagram and funicular polygon as shown by the dotted lines. The vertical reactions at a and b are DO (fig. 191) 1.5 tons, and O F = 1.25 tons. These reactions may be checked analytically in the usual way. The stresses on the truss as found from the stress diagram are as follows:: Members, . TABLE LXXIV. DA EB FC BC АО AB со Stress in Tons, +1.75 +1.75 +2.5 +1.25 -0.875 -1.25 -2.125 The stress on A O may be checked by taking moments about c; thus SAO × 86 = 1.5 x 5, or SA o = 0.87 ton. The form of truss represented in fig. 192 is commonly employed at railway stations for covering island platforms. The roof is supported by two lines. of columns-one at a, and the other at a, upon which the truss is supported, so that the overhanging portions a b c and a, b, c are cantilevers He H, d B B1 F F C A, A a E O E, Fig. 192 E which are connected together by the braced girder, a c c1 a1. Determine the stresses on the truss when two loads of 1 ton each rest at the extremities b and b1, and loads of 2 tons each rest on d, c, e, c1, and d1. The vertical reactions at the points of support a and a1 are equal to 6 tons each. In fig. 193, on a vertical line set off EF = 1 ton, FG=GHHH1 = 2 tons, EO 6 tons, the vertical reaction at a. The diagram is constructed in the manner already explained. F H H1 Fig. 193. Table LXXV. gives the stresses on the left half; those on the right half being the same. Members, 225. Curved Roof Trusses. In calculating the stresses on curved trusses, the top member or bow is assumed to be made up of a series of straight lines; the portions of the curve between two adjacent apices being considered to be straight. This assumption, as has been explained in the case of bowstring girders, has little or no effect in altering the stresses on the truss. The main ties of such trusses may be arranged in one or more straight lines. In the latter case the points of intersection of the ties usually lie in the curve of a circle which must be of larger radius than that of the top member. Fig. 194 represents a simple form of curved truss of the ordinary bowstring pattern; the main tie-bar being horizontal. If the purlins rest on the apices d, e, c, f, g, it is evident that each bay, ad, de, ec, &c., will have a tendency to bend outwards from the effects of the compressive stress. It is important, therefore, that the top member of trusses loaded in this manner be made sufficiently stiff to resist this bending action. It is also advisable not to expose curved rafters of this description to so great a working stress as straight rafters, especially if the radius of the curve be small. If the purlins rest at or near the centres of the different bays, this tendency to bend is to a certain extent counterbalanced by the dead weight acting through the purlin. Under such conditions, the curved member is in a more favourable condition to resist the compressive stress than is the case with straight rafters similarly loaded. In curved roofs the wind pressure is not of equal intensity along one side, as it is in roofs with a straight slope; the slope being different at different parts of the curve, the intensity of the wind pressure per unit of area will vary as well as its direction. To calculate with exactitude the stresses arising from this. force is, therefore, a tedious operation, and for all practical purposes it will be sufficiently accurate to take the mean pressure and direction into consideration. Example 14.-Find the stresses on the truss shown in fig. 194, the span being 55 feet and the rise 8 feet 3 inches, the top member being the curve of a circle of 50 feet radius; loads of 2 tons rest at the apices d and e, 1.5 tons at c, and 1 ton each at f and g. The reactions at the abutments are most readily determined by the aid of a polar diagram and funicular polygon, as shown by the dotted lines in figs. 194 and 195. H TH, Fig. 195. FO and FO (fig. 195) represent the reactions of left and right abutments, and the fig. represents the stress diagram. The following are the stresses on the truss : TABLE LXXVI. Top Members, FA GB HD HD G1 B1 F1 A1 Stress in Tons, +88 +7.9 +7.25 +67 +65 +6.7 Stress in Tons, -0.2 +0.1 -0.5 +0.5 +0.5 −0·5 +0·2 −0·3 By taking moments about the apex c, we get SEO × 8·25=4·3 × 27·5 – 2(21·1 + 10), or SÅ 。 = 6·8 tons. This differs slightly from the stress as found by scale. Example 15.-Fig. 196 represents a circular truss 100 feet span, the versines of the two flanges being 12 feet 6 inches and |