This distinction would, however, appear to fail unless the loading of the principal is purely vertical in both classes. Where the assumptions as to wind pressure include a horizontal component, as in the case of wind pressure taken normal to the slope of the roof, other considerations present themselves, and the reactions of one or both supports, even in self-contained structures, must contribute a corresponding and opposing force.

Roof principals of the class (a) or (b) present three main features in their design, viz.: -

The upper or compressive member, usually denominated the principal rafter, either straight, curved, or polygonal, as the case may be.

The lower or tension member, denominated the main tie, or, in timber roofs, the tie beam.

The intermediate bracing of struts and ties, fulfilling similar functions to those of the web of lattice girders.

The upper or compressive member, or principal rafter, will have its scantlings determined in the first instance by the laws governing the strength of long columns or struts, the length of the column under consideration being determined in a vertical plane by the distance between the apices or points of junction of the intermediate bracings. In a longitudinal direction, however, the column will be free to deflect laterally between the points of support of the purlins, assuming the latter to offer a sufficient resistance to lateral flexure of the principal as a whole; but, as remarked further on, roof principals in course of erection or testing are, in the temporary absence of purlins or roof coverings, somewhat flexible in a plane at right angles to their elevations, owing to the smallness of their dimensions in that plane as compared with their span. Security in this respect is obtained by a properly designed system of what is called wind bracing, being an arrangement of diagonal braces from the heel or shoe of one principal to the ridge or summit of another, whereby the possibility of the overturning of a series of roof principals like a pack of cards is obviated. Where the length of roof is not great, and the roof is enclosed between stout gable walls at the ends, or is hipped, the addition of wind bracing is not so imperative.

It will be found, however, in practical design, that the scantlings of the principal rafter will be ruled by other considerations than those of columns or strut area alone, even if the compressive stresses be purely axial, in the direction of the length of the column. If, on the other hand, the column is subjected to transverse stress arising from the position of the purlin not being precisely over the junction of a brace, a condition which will frequently arise in roofs of small span, then the stresses arising from the bending moments must be considered in connection with those arising from purely compressive stress, and the area or moment of inertia of the section increased accordingly.

The construction of skylights or ventilating lanterns with standards attached to the principal rafters, examples of which will be given later on, will frequently influence the choice of section, and impose a minimum dimension in order that the bolted or riveted attachments may be properly made. Thus, for example, a tee-steel section for the principal rafter may be selected, giving a sufficiency of area for the calculated stresses, but the top table of which may be too narrow to receive the bolts required to connect a cast-iron louvre standard of the type shown in Fig. 265.

Or again, the section may not be suitable to properly arrange the details required at the connection of the rafters at the apex of the principal.

Mistakes in points of detail such as these (upon which much of the success in design depends) will be usually avoided if the student is careful to draw each detail in cross-section as well as in elevation.

The details of connection of the purlins with the principal rafter must also be considered and allowed for. Where wind bracing is adopted, the scantlings required for connection to the top table or web of the rafter must be remembered.

The sections commonly used in the construction of the principal rafter are various, and adapted to the span, distance apart of principals, load, and working stress allowed.

Thus for roofs of small span, and where precise symmetry about a central axis is not necessary, a single angle (Fig. 142) may be used. For roofs up to about 40 to 50 feet span a single tee section (Fig. 147) is commonly adopted. A section of double angles (Fig. 143) is very convenient for connection, and affords more space for bolted or riveted details in the top tables. A built-up tee section of plates and angles is convenient for larger spans, as in Fig. 146, with the addition of a vertical web plate.

A section of double channels (Fig. 150) has been used for spans of from 90 to 100 feet, while the built-up channel sections shown in Fig. 163, with flat bar lattice bracing, have been used in a roof of about 120 feet span. Roofs of still larger spans, up to 200 feet or more, have been constructed with principal rafter sections of the types shown in Fig. 151, or in Fig. 162, with additional flange plates top and bottom.

The details of the lower or shoe end of the upper rafter are variable in character, depending largely on the span of the principal, and the scantlings of the main tie. If this latter is of heavy section, the connection at the heel of the principal becomes of corresponding importance, and demands careful consideration.

For roofs of moderate span, say up to 60 feet or thereabouts, the lower end of the principal rafter terminates in, and is connected to, a shoe which forms the seating of the principal upon the wall, column, or girder, as the case may be. Formerly this shoe was of cast iron of various forms, and some defective details may be discovered in those forms of shoe in which the method of connection of the main tie involved tension upon certain portions of the cast iron. In present-day practice these cast-iron shoes have generally been superseded by shoes of a simple form in mild-steel riveted work. A few examples of shoes of this type, with their connection to the main tie, are shown in Figs. 280, 286 to 293, 298 to 302.

In roofs of large span the expansion and contraction of the structure under changes of temperature have to be provided for and in these cases the place of the ordinary shoe is frequently taken by a system of rocker plates and rollers resembling the ordinary expansion apparatus of a girder of large span, although it may be questioned whether such rollers, not easily accessible as a rule to inspection, do not frequently become rusted up to an extent which interferes with their efficiency.