When the length of the rafter is greater than 24 feet it should be divided into three parts, as shown in Fig. 10, and purlins placed at each of the joints. The stresses in Fig. 10 are indicated by the lines of the diagram Fig. 11. By means of this diagram, and the explanation given for Fig. 9, the action of the various pieces in supporting the loads should be readily understood. For greater spans three pairs of struts may be used, as in Fig. 12, and this truss is also sometimes built with 10 panels, but it is not an economical type of truss for spans exceeding 65 feet.

The names given to Figs. 10 and 12 are those most commonly used to designate these types; they should not be confounded with the "queen-rod" truss, which has a horizontal top chord.

## 7. Analysis Of The Queen-Rod Truss

If we have two equal loads, W1, W2, Fig. 13, to be supported at equal distances between the walls, we can support them in the manner shown in Fig. 14, and as long as the loads remain equal the frame will be stable; but should one load become greater than the other the heavier load would push the frame over, as shown by the dotted lines.

Fig. 10. - Queen Truss.

Fie. 11.

As in actual roof construction a part of the load, such as the snow and wind, is variable, one side of the roof often being loaded when the other is not, a truss of the shape shown in Fig. 14 cannot be used. To adapt this type of truss to the actual conditions of roof construction we must build it in the manner shown in Fig. 15- In this case we will assume that the point A is loaded and the point B unloaded. The load at A will then be supported by the rafter D and by the brace or strut C. The vertical component of the stress in C will be taken up by the rod E and transferred to the point B, where it will be resolved into a horizontal stress to be resisted by H and an oblique stress to be resisted by F, the horizontal components of the stresses in D, C and F being resisted by the tie-beam. The action of the pieces will be the same if both points are loaded, provided the load at A is greater than that at B.

Fig. 13.

Fig. 14.

In practice the greater load may be at A at one time and at B at another time, so that it is necessary to use two sets of braces and two rods, as shown by the dotted lines.

The braces C and C1 are called "counter braces," because their purpose is to counteract the effects of unequal loading-; in roof trusses they are generally brought into use only by the snow or wind.

Fig.. 15.

Fig. 16.

Trusses of this type are often seen without counter braces, as in Fig. 16. When built in this way an unbalanced load at A would tend to distort the truss, as shown by the dotted lines.

When the dead loads, by which is meant those produced by the weight of the construction, are symmetrical and the tie-beam supports a ceiling, the weight on the rod R, the rigidity of the joints, and the transverse strength of the tie-beam are generally sufficient to resist the tendency of the wind pressure to push the joint B out of position. When such a truss is placed longitudinally of the roof, and the truss and loads are symmetrical, then the loads at A and B will always be the same and the counter braces will not be required.

When such trusses are placed across the roof, and there is no ceiling to be supported, counter braces should always be used, as otherwise a severe wind pressure or an uneven distribution of snow may cause the truss to fail. The greater the inclination of the rafter the greater will also be the effect of the wind, and hence the greater need of counter braces..

Fig. 17.

Fig. 18. Queen Rod Trusses.

Counter braces are also required in such trusses when they are subject to a moving load as in the case of bridges or when supporting floors.

When the length of the rafters exceeds 12 feet they should be braced as shown in Fig. 17. These braces will also assist considerably in preventing distortion under wind pressure, but in severe cases they are not sufficient.

In the trusses shown in Figs. 15 and 16 it obviously makes no difference with the strains in the rafters and tie-beam whether the loads are applied at A and B or are suspended directly underneath by means of rods, as shown in Fig. 18, the only difference in the two cases being in the strain in the rods.

Trusses of the shape shown in Figs. 17 and 18 are the modernized types of the old "Queen-post truss," in which all the members were of wood.

Fig. 19.

Fig. 19 shows a combination of a queen-rod and king-rod truss, sometimes used where it is desired to keep the centre of the attic free from obstructions.

In building this truss it will be more economical to form the lower portion of the rafters of two timbers as shown, than to make them of one size for the full length. This construction also allows of making a good joint at B. There is the same tendency to distortion under wind pressure in this truss as in the queen-rod truss, Fig. 16, but owing to the prolongation of the rafter to the ridge, the resistance to distortion is very much greater than in the queen-rod truss, so that for spans not exceeding 42 feet it will be perfectly safe to omit counter braces.