To remedy the defect above mentioned, a tie (TT, Fig. 318) is added, which, by holding in the feet of the rafters, prevents them from spreading and thrusting out the walls. The strain on the tie, caused by the tendency of the rafters to settle and spread out can easily be calculated, and it will be found that a comparatively slight rod of iron will be sufficient to hold the feet of the rafters together.

In timber roofs, however, a wooden beam is generally used for the tie, and it is frequently required to act as a ceiling joist, or to carry ceiling joists, for which an iron rod would not be suitable. These wooden "tie beams," especially when loaded, have a tendency to "sag," or droop in the middle, and to draw the walls inwards. Collar-beam Roofs. - In buildings where considerable height is required internally, or in those with low walls where the tie beam would be in the way of the occupants; it is replaced by a " collar beam" (CT) placed higher up, as shown, so as to give the required space below.

Fig. 318. Couple-close Roof.

1 From Wray's Application of Theory to the Practice of Construction.

Fig. 319. Collar-beam Roof.

This is a bad construction; the lower parts (a b) of the rafters are liable to bend if the walls are not competent to take the thrust, and as they are not tied in at the feet they thrust on to the walls, tending to force them out, as shown in dotted lines.

This tendency is sometimes aggravated by using the supported rafters as Principals,2 placing them 8 to 10 feet apart, and adding purlins (P P) resting upon the collar as shown; these carry light intermediate rafters, the weight of which, with their load, increases the evils already pointed out.

The collar is generally about halfway up the rafters, and is intended to act as a strut and support them in the middle, but when the walls give way the collar becomes a tie, and tends to assist the bending of the rafters.3

This construction is therefore objectionable, except for small buildings not exceeding 18 feet span, when the distance a b is small, the rafters stout enough to prevent bending, and the walls thick in proportion to the span. When a ceiling is applied to a collar-beam roof it follows the line ba,ab. The collar beam is sometimes supported by an iron rod hanging from the ridge (11).

There are many forms of roof in which the tie beam is dispensed with for the sake of appearance, or to gain height. Several of the Gothic roofs are of this class, but the consideration of such is beyond the scope of these notes.

1 Sometimes called Top beam, Wind beam. Sc. Baulk. 2 See p. 159.

3 The weakness of the lower part of the rafters is sometimes remedied by strapping pieces under them from a to b (see Fig. 319). These pieces may be continued so as to fill the angle at a, and support the collar beam.

If a tie beam at the level of the springing be added to a collar-beam roof, as shown by the dotted line in Fig. 331, the collar becomes permanently a strut, and a very good roof is formed.

Scantlings for Collar-beam Roofs. Pitch up to 30°. If 45°, add 1" to depth of rafters.

* If the collar is required half-way up, about 1/4" must be added to both breadth and depth of rafters, and 3/4 " to depth of collars, but with unstable walls, ties are far cheaper, and may be at long intervals if sufficient width is given to the wall plates to enable them to take the thrust between the ties.

Thickness of Walls to resist Thrust of Roof.

The following solid walls are strong enough, when built in Lias lime mortar 1 to 2, to resist the thrust of roof; allowance must be made for door and window openings. Height to be taken from level of the floor below roof.

When the walls are not capable of resisting the thrust of the roof place the collar low down; but if the collar is required half-way up, the scantlings must be increased as follows: -

Rafters, add quarter inch to both breadth and depth; Collar, add three-quarter inch to depth, but it would be better to use the scantlings for walls capable of taking the thrust, and make some arrangement to prevent the walls from spreading, such as tying the wall plates together at intervals.1