The usual EXTERNAL FORM of a ROOF has two surfaces, which generally rise from opposite walls, with the same inclination; and, as the walls are most commonly built parallel to each other, the section of the roof made by a plane perpendicular to the horizon, and to one of the walls, is an isosceles triangle; the base being the extension from the one wall head to the other. This extension is called the span of the roof.

TO FRAME TIMBERS, so that their external surfaces shall keep this position, is the business of trussing; and the ingenuity of the carpenter is displayed in making the strongest roof with a given quantity of timbers.

All beams, or pieces of timber, from their weight, when supported at the two ends only, acquire a concavity on the upper side; and this concavity is the greater as the distance between the props is the greater. It is, therefore, a grand object to prevent this bending as much as possible. The curvature will take place whether the position of beams be horizontal or inclined; but the same beam will have less curvature, as the angle, to which it is inclined to the horizon, is greater. For, it is evident that, when a beam is laid level, and supported at its extremities, its curvature will be greater than when inclined at any angle, however small; and, again, if it stand perpendicular to the horizon, its curvature will be nothing; that is to say, its curvature will be nothing when the angle of inclination is the greatest.

The curvature which timber obtains by bending is called sagging. To prevent timber from sagging, as much as is possible, it must be supported at a certain number of intermediate points or places, besides the two extreme points or places. Now these supports must themselves be supported from some base or other; but, if the resting points or places is upon the surface or surfaces of other timbers, the greatest care must be taken that they do not fall between the extremities of the supporting timbers intended to support the other. That is to say, the lower end of every piece of timber, used as a prop, must rest upon some fixed point; or, otherwise, the propping piece of timber must be so disposed that the pressing forces at each end must be equal to each other.

These are the general principles upon which the strength of roofs depend.