In practice, it will be best to consider the scaffold as a regular body, comprised as to height within the top and bottom ledgers. The extra length of standards in this connection can safely be ignored.
If a body rests on a hard surface, it will stand or fall according as to whether a vertical line, drawn from the centre of gravity, falls within or without its base. The base of a body is within a line drawn round the points of support.
It will therefore be seen that so long as the scaffold is not acted upon by any other force it will remain in equilibrium. But a scaffold is erected to carry weights, and the effect of these weights upon the stability must now be considered. The effect of a load upon the scaffold is to alter the position of its centre of gravity.
Fig. 128
Considering the scaffold and its load as two separate bodies, the point or centre of gravity about which the two combined weights would act is found as follows:—
Let A and B, [fig. 128], represent two heavy bodies. Join the centre of A to centre of gravity of B; divide this line into as many parts as there are units of weights in A and B together. Then mark off from A the number of units there are in B, and the point thus found is the point about which the combined weights act, i.e. the required centre of gravity of the bodies.
The scaffold may, however, have several loads to carry, one or more of which may be materials slung on the hoist.
To find the Centre of Gravity of a number of Bodies.—Find the centre of gravity of two of the bodies A and B (fig. 129). From the point thus found, take a line to the centre of gravity of a third, C. Divide the line into as many parts as there are units of weight in all three bodies. Then from the centre of gravity of A and B divide off a number of units of distance equal to the number of units of weight in C. The point thus found is the required centre of gravity. This process is continued until all the bodies have been considered, care being taken that all the units of weight in the bodies which have been considered are added to the units of weight in the body under consideration when dividing the line in which the centre of gravity is found. The final centre of gravity found is the centre of gravity of the entire mass. If the vertical line taken from it falls within the base, the scaffold is in equilibrium and therefore stable.
