These timbers are subject to loads nearly uniformly distributed, and their dimensions may be obtained by Rule XXX., equation (35.), Art. 140. In this equation, U= cfl (Art. 152). Substituting this value for U, and r l for s, equation (35.) becomes -

bd3 = fcl3/1.6 Fr;

and putting for r the rate of deflection, .04, we have -

bd3 = fcl3/0.064 F' (106.)

a formula convenient for roof-timbers.

Example. - In a roof where the roofing is to be supported on white-pine roof-beams 10 feet long, placed 2 1/2 feet from centres, and where the load per foot superficial is to be 40 pounds, including wind and snow: what should be the dimensions of the roof-beams? By equation (106.) -

bd3 = 40x2 1/2x103/0.064x2900 = 538.8.

Now if d, the breadth, be fixed, say, at 3, then -

d = 538.8/3 = 1796; d = 5.64 nearly.

The roof-beams, therefore, require to be 3 x 5 2/3, or, say, 3x6. All pieces of timber subject to cross-strains will sustain safely much greater strains when extended in one piece over two, three, or more distances between bearings; therefore, roof-beams, jack-rafters, and purlins should, if possible, be made in as long lengths as practicable; the roof-beams and purlins laid on, not framed into, the principal rafters, and extended over at least two spaces, the joints alternating on the trusses; and likewise the jack-rafters laid on the purlins in long lengths.

231. - Five Examples of Roofs: are shown at Figs. 85, 86, 87, 88, and 89. In Fig. 85, a is an iron suspension-rod, b, b are braces. In Fig. 86, a, a, and b are iron rods, and d, d, c, c are braces. In Fig. 87, a, b are iron rods, d, d braces, and c the straining beam. In Fig. 88, a, a, b, b are iron rods, e, e, d, d are braces, and c is a straining beam. In Fig. 89, purlins are located at PP, etc.; the inclined beam that lies upon them is the jack-rafter; the post at the ridge is the kingpost, the others are queen-posts. In this design the tie-beam is increased in height along the middle by a strengthening piece (Art. 163), for the purpose of sustaining additional weight placed in the room formed in the truss (Art. 216).

Fig. 85.

Fig. 86.

Fig. 87.

##### Truss With Built-Rib

Fig. 90 shows a method of constructing a truss having a built-rib in the place of principal rafters. The proper form for the curve is that of the parabola (Art. 560). This curve, when as flat as is described in the figure, approximates so close-ly to that of the circle that the latter may be used in its stead. The height, a b, is just half of a c, the curve to pass through the middle of the rib. The rib is composed of two series of abutting pieces, bolted together. These pieces should be as long as the dimensions of the timber will admit, in order that there may be but few joints. The suspending pieces are in halves, notched and bolted to the tie-beam and rib, and a purlin is framed upon the upper end of each. A truss of this construction needs, for ordinary roofs, no diagonal braces between the suspending pieces, but if extra strength is required the braces may be added. The best place for the suspending pieces is at the joints of the rib. A rib of this kind will be sufficiently strong if the area of its section contain about one fourth more timber than is required for that of a rafter for a roof of the same size. The proportion of the depth to the thickness should be about as 10 to 7.

Fig. 88.