_THE STABILITY OF A SCAFFOLD_
A scaffold, considered as a whole, is in a stable condition when,
under the forces that may act upon it, it remains in a state of rest
or equilibrium. Two forces which tend to create a loss of equilibrium
are: the pressure of wind which acts from any direction in a horizontal
plane, and the force of gravity due to the weight of the scaffold and
that of attendant loads.
=Wind Pressures.=—_The effect of wind upon a pole scaffold_:
The effect of wind acting on a single scaffold pole, erected as a
standard, can be first considered. For this purpose the pole shall be
taken as 32 feet long, 2 feet of which are below ground level. The
force of wind depends upon its velocity, and it is measured by the
pressure it exerts on a square foot of surface normal to its direction.
_If a point in a body is fixed, so that the body cannot move out of
its place, but may rotate about that point; a force which acts at any
other point, but in a direction that does not pass through the fixed
point, will produce rotation._
In applying this principle to the effect of wind on the scaffold pole,
the ground level will be the fixed point about which the standard may
rotate.
The wind acting upon the exposed surface of the pole may be likened to
a series of parallel forces that, not acting through the fixed point,
tend to produce rotation.
An advantage is gained if, instead of taking the wind as a series of
parallel forces, it is considered as a resultant force of proportionate
magnitude exerting a pressure upon the centre of the exposed surface.
In practice it will be sufficiently correct to take the centre of
surface of the pole at a point at half its height.
The tendency of a force to produce rotation about a fixed point is
termed its moment about that point. It is measured by multiplying the
units of force exerted by the units of the distance between its point
of application and the fixed point.
Example: If at the centre of surface of the pole under consideration,
that is at 15 feet above the fixed point, the resultant force of the
wind is equal to a pressure of 100 lbs., the moment about the fixed
point will be 15 by 100 = 1500.
In like manner the moment of resistance due to the weight of earth
packed round that portion of the pole below ground can be estimated.
For the pole to remain in equilibrium it will be necessary for the
moment of resistance to equal the moment of the overturning force,
assuming that the fixed point is stable.
No practical good can result by pursuing this calculation further.
It may be taken for granted that as the wind occasionally exerts a
pressure of over 50 lbs. per square foot, and a pressure of 40 lbs. per
square foot is the least for which calculations should be made, it will
always be necessary when scaffolding to any height to adopt special
measures to preserve stability.
When the ledgers are added to the standards they have some effect upon
the equilibrium of the erection, and this must now be considered.
The wind can be taken as acting from two directions, first directly
along the scaffold, and secondly across the scaffold. When at any other
angle to the structure it will have effect in both of these directions,
being greatest in the one with which it most nearly corresponds.
_When blowing along the scaffold._—The standards and ledgers form
with the ground level a series of rectangular parallelograms. The
connections between the sides of the parallelograms are not rigid. They
most nearly approach cup and ball joints, and as such, it will be wise
to regard them as entirely loose to a rotating force.
_The shape of a parallelogram with loose joints can be altered by a
force acting in the plane of its surface, and this alteration of shape
can take place without creating any strain on its joints or members._
From this it will be seen that the tyings and ledgers of the erection
may be considered as offering no resistance to a force tending to
rotate the standards about their fixed points; but by adding to
the surface upon which the force can act, the ledgers increase the
overturning moment about the fixed point.
In practice, although the scaffold may not entirely fail, any change
from regularity of structure due to wind pressure would cause the
members of the erection to offer a less effective resistance to the
other forces acting upon it. This being so, means must be taken to give
that rigidity to the standards, without which the scaffold may collapse.
_Although a parallelogram with loose joints will alter its shape
under pressure, a triangle under similar conditions cannot do so._
Advantage is taken of this fact to obtain the rigidity which is
necessary.
Taking a standard, and one of the ledgers, or the ground level as
forming two sides of a triangle, a pole, termed a brace, is fixed to
form the third side.
The triangle thus formed is a rigid figure offering resistance to any
force acting upon it in the same plane as its surface, and it will
remain rigid until the destruction of one of its joints or members. It
follows, therefore, that the standard forming one side of the triangle
becomes a sufficiently rigid body to withstand any pressure of wind
that may act upon it. The other standards in the erection, if not tied
to the brace, gain rigidity from the triangulated standard because of
their connection thereto by the ledgers.
_When the wind is blowing across the scaffold._—If the erection is
of the dependent type, the standards, putlogs, wall of building, and
ground level form a series of parallelograms which differ from those
previously noted in that a sufficiently rigid angle is formed between
the wall and ground level.
The effect of this inflexibility is to create rigidity throughout
the parallelogram, always providing that the other sides are firmly
connected at their points of juncture.
In practice this is not so; the putlogs, if tied to the ledgers,
which for this purpose is the same as being tied to the standards,
have no fixed connection to the wall of the building; but if they are
supplemented by poles tied from the standards to within the building,
they can be regarded as having, in effect, fixed joints.
If it be impossible to tie the standards within the building, the same
effect can be gained by strutting from the ground level.
This scaffold, if so treated, is sufficiently rigid to withstand any
wind force that tends to overturn the standard, either towards or from
the building.
If the erection is of the independent type, the cross section also
shows a series of parallelograms with loose joints, and so similar
conditions exist as in the first example, except that the overturning
force is acting in a different direction.
Any of the methods of gaining rigidity already given, and shown on
figs. 21 and 24, can be applied in this instance.
Guard boards, rails, face boards, &c., have no other effect than that
of increasing the surface upon which the wind can act. In consequence,
the overturning moment of the standards about their fixed point is also
greater.
Gantries form parallelograms with fixed joints with sufficient
strength—unless carried to a great height—to withstand any wind
pressure. If necessary, they can be braced in the same manner as the
pole scaffold.
Scotch derricks are so strongly built that, unless a wind force
exerting great pressure acted upon them, they could be considered safe
from destruction by that means.
The four pillars standing square to form each leg are crossed at right
angles by transoms which are bolted to the uprights. The parallelograms
thus formed have joints which allow of rotation; but the cross braces
fitted in each bay give rigidity in two ways. Besides triangulating
the frame, they offer a definite resistance to movement on the bolt by
butting against the transom, as will be seen by reference to fig. 1.
This resistance to movement is to some extent due to the resistance of
the timber to crushing.
The larger parallelograms formed by any two legs, the trussed beam and
the ground level, have joints that can only be destroyed by very great
force.
As the highest pressures noted in this country have equalled 80 lbs.
per square foot, and therefore have to be guarded against, it is wise
to triangulate the sides as shown on Frontispiece.
=The Force of Weight or Gravity.=—_The weight of a body equals
the force with which that body is drawn towards the earth’s centre._
The weight of a scaffold may thus be considered as a force acting
vertically downwards. The point at which the force acts is known as the
centre of weight or the centre of gravity.
As a first example, the effect of the forces of gravity may be
considered when acting upon an independent unloaded scaffold in its
simplest form, consisting of four standards, erected square on plan,
with ledgers and braces on each side.
This form of scaffold having regular sides, and its weight being
equally distributed throughout, may be considered as a single, evenly
disposed, rigid, rectangular body. The centre of such a body will
coincide with its geometrical centre, and may be found thus:—
Draw a diagonal from A to B and from C to
D (see fig. 127). The point of intersection will represent the
centre of gravity required.
[Illustration: FIG. 127]
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.
[Illustration: 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.
[Illustration: FIG. 129]
When boards are laid on a scaffold, they may be treated as a load. If,
however, they are evenly distributed over the entire top of a scaffold,
their comparatively light weight may be usually neglected, as, their
centre of gravity occurring immediately above the centre of gravity of
the scaffold itself, would have no other effect than to slightly raise
the centre of gravity of the structure.
=To find the Centre of Gravity of Scaffold Boards laid to form a
Platform.=—A scaffolding platform, being of a slight depth in
comparison with its length and breadth, may be treated as a surface
usually rectangular.
[Illustration: FIG. 130]
The centre of gravity of a rectangular surface is the point of
intersection of its diagonals (fig. 130).
=To find the Centre of Gravity of a Dependent Scaffold and the Effect
of Loads upon it.=—A dependent scaffold, having only one frame of
standards and ledgers, to which are attached the putlogs, cannot be
considered as an evenly disposed regular body. Nevertheless, the rule
that the scaffold will not be in equilibrium unless a line from the
centre of gravity fall within the base still holds good. In the case
under consideration, as the wall of the building to which the scaffold
is securely attached by the putlogs and ties, carries its share of
the weight of the loads and putlogs, it must be taken as forming an
integral portion of the scaffold itself.
Therefore the centre of gravity of a dependent scaffold will be the
resultant centre of gravity of the outer frame, the putlogs, and the
wall, considered as separate bodies.
The centre of gravity of the frame may be found by taking it as a
rectangular surface. If necessary, the boards may be treated in like
manner.
The system of putlogs, if they are regularly placed, may be treated as
a regular body, and the centre of gravity found by the method already
given; but in practice their weight would have no effect towards loss
of equilibrium.
The wall may also be treated in like manner if of even thickness. If
of varying thickness, the centre of gravity of each portion of even
thickness should be found.
The resultant will be found by the method already given for finding the
centre of gravity of a number of bodies.
The base of the erection in this case should include the base of the
wall.
The effect of ordinary loads upon the stability of a scaffold of this
type is practically nil. No weight that the scaffold was capable of
carrying in itself could bring the resultant centre of gravity of the
scaffold and wall outside of the base; so that unless the scaffold
failed from rupture of its members or connections, it may be considered
safe from collapse due to instability.
=To find the Centre of Gravity of a Gantry.=—This can be found by
the method given for independent pole scaffolds.
=To find the Centre of Gravity of a Scotch Derrick.=—Owing to
the unevenly distributed weights about these scaffolds, they cannot
be taken as regular bodies. It will therefore be necessary to take
each part of the erection separately, and after finding the centre of
gravity of each, to find the resultant centre of gravity of the mass by
the method already given.
To find the Centre of Gravity of each Part.—Each leg can be treated as
an evenly disposed rigid body.
The mass of brickwork that is placed at the foot of the legs may be
treated similarly.
The platform may be considered as a surface. If triangular, the centre
of gravity is found by the following method:—
Bisect the base and join the point of bisection to the opposite angle.
The centre of gravity is at a point one-third of the length of the line
measured from the side divided (fig. 131).
[Illustration: 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.