This section is from the book "Early English Furniture & Woodwork", by Herbert Cescinsky, Ernest. R. Gribble. Also available from Amazon: Early English Furniture & Woodwork.
Unsatisfactory as a flat roof is, in collecting rain and snow, as it can only be pitched to allow of a slight fall to the gutters, the points of stability to be considered are only threefold.

1. Low-pitch roof with cambered-beam.

2. Cambered-beam firred up. (Firred-beam type.)

3. Firred-beam roof with beam arch-braced to wall-posts.

4. Arch-braced tie-beam roof. Kingpost arch-beamed.

5. Arch-braced tie-beam roof. Queen-posts arch-braced.

6. High-pitched roof without ties (hypothetical).

7. High-pitched roof with tie-beam.

8. High-pitched roof with collar-beam.

9. Tie - and - collar - beam roof with braced king-post.

10. Tie-and-collar-beam roof with braced queen-posts.

11. Tie-beam roof with scissors truss instead of collar.

12. Roof with scissors-braced collar without tie-beam.
Fig. 43. The Development Of The English Timber Roof.

13. Roof with braced collar and scissors truss above.

14. Roof with tie-beam strengthened by wall-posts and braces, collar also arch-braced.

15. Root with collar-beam arch-braced to wall-posts.

16. Roof with hammer-beams. The braces of the collar are taken own to arch-braced hammer-beams.

17. Roof arch-braced to wall-posts without collar or hammer-beams.

18. Hammer-beam roof with hammer-posts and wall-posts. Both hammer-beams and collar are arch-braced.

19. Double hammer-beam roof with hammer-posts; arch-braced kingposts from collar to ridge.

20. False double-hammer-beam roof. The collar-braces are taken to the back of the upper tier of hammer-beams, which, therefore, carry no weight.

21. False single-hammer-beam roof (pendentive) (Eltham Palace type). The hammer-posts bear on the tenons only of the hammer-beams, not on the beams themselves.

22. Hammer-beam roof without wall-posts. The arch-braces are continued past the hammer-beam to the corbels and act as wall-posts.

23. Arch-braced roof with wall-posts. (The progenitor of the arch-rib of No. 24.)

24. Compound hammer-beam roof with large arch-ribs (Westminster Hall). - Fig. 44. The Development Of The English Timber Roof.
(1) The walls must be strong enough to support the dead-weight of the roof.
The beams and joists must be of such thickness that they will not sag. (3) The ends of the beams, where they are housed into the wall, or where they rest upon its top, shall be efficiently protected against rot or decay.
It is obvious that on these beam-ends the stability of the whole roof depends. With a completely framed roof, the beams arc mortised at their ends to receive the wall-plates, which are laid on the wall-head.
With roofs of large span, the liability of the principal beams to sag, and thus to pull away the ends from the supporting walls, dictates the cambered beam, that is, one with either a natural or an artificial upward curve or bend in its length, or one which is deeper in the middle than at the ends. Such a beam, fixed with its concave side downwards (i.e. with its camber upwards), resists any tendency to sag, in a very efficient manner. Examples of cambering will be noticed in the tie-beams illustrated in this chapter.
The outer covering of a flat roof, whether of lead, zinc or other material, is liable to perish by atmospheric action, or to be injured mechanically. Slates or tiles have been found to be more lasting, but their use necessitates the lean-to or the pitched roof. Tiles or slates, with their overlap, must be on a slope, otherwise the rain and snow will percolate, or be driven under the overlappings. Their use, therefore, dictates either the lean-to or the pitched roof, as a logical necessity.
Both these types of roof introduce a new principle, the necessity of resisting the downward and outward pressure, or thrust, which tends to force either the supporting walls out of perpendicular,1 or the roof itself off the walls. With the lean-to roof, the type largely used in the aisles of churches, this outward thrust is exercised on the one wall only; with the pitched-roof it is thrown on both.
 
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