Fig. 131
The centre of gravity of the joists supporting the platform can be taken with that of the platform itself, providing that the weights of each are added together and the centre of gravity of the platform only lowered to half the depth of the joists. The trussed girders supporting the platform may be treated as rectangular surfaces.
The centre of gravity of the guys, sleepers, and jib will be at a point in the centre of their length.
The centre of gravity of the engine may be somewhat difficult to find, but it will be sufficient to treat it as a cylinder. The centre of gravity of a cylinder is the middle of its axis.
Loads may be of various forms, but the centre of gravity will be found on a line drawn downwards through the load immediately under the supporting chain. In actual practice no load, the centre of gravity of which, considered separately, falls within the base of the scaffold which supports it, will cause instability. The greatest effect it can have is to bring the centre of gravity of the entire mass nearly to the edge of the base, so that a comparatively light load acting from without may cause loss of equilibrium.
It has been so far assumed that, owing to the use of braces, ties, struts, &c., the scaffolds considered have been rigid bodies, and where this is so the principles given hold good. In practice, however, owing to the lack of, or only partial use of, the members just mentioned, scaffolds are often more or less flexible bodies. Where this is the case, the lack of rigidity greatly increases the danger of collapse, as the timbers, through yielding by flexure to the loads that act upon them, allow such an alteration of the shape of the scaffold that the centre of gravity may be carried outside the base. Even where this does not occur, the racking movement allowed is dangerous, as the connections are strained and become loose, creating an element of risk that the otherwise careful scaffolder cannot altogether remove. For the scaffolder the lesson to be learned is—that, whether the force he is dealing with arises from the wind, loads, or a combination of both, he must triangulate—TRIANGULATE.
It will be necessary to know the weight of material in working out these problems. These have been given in the Appendix.
CHAPTER IX
THE STRENGTH OF A SCAFFOLD
The strength of a scaffold equals the resistance that its members and their connections can offer to the strains that act upon it. The timbers used may fail in various ways.