EFFECTS PRODUCED BY EARTHQUAKES UPON BUILDINGS.
The destruction of buildings is not irregular—Cracks in
buildings—Buildings in Tokio—Relation of destruction to
earthquake motion—Measurement of relative motion of parts of a
building shaken by an earthquake—Prevention of cracks—Direction
of cracks—The pitch of roofs—Relative position of openings in a
wall—The last house in a row—The swing of buildings—Principle of
relative vibrational periods.
The subject of this chapter is, from a practical point of view, one
of the most important with which a seismologist has to deal. We
cannot prevent the occurrence of earthquakes, and unless we avoid
earthquake-shaken regions, we have not the means of escaping from
them. What we can do, however, is in some degree to protect ourselves.
By studying the effects produced by earthquakes upon buildings of
different construction and variously situated, we are taught how to
avoid or at least to mitigate calamities which, in certain regions of
the world, are continually repeated. The subject is an extensive one,
and what is here said about it must be regarded only as a contribution
to the work of future writers who may give it the attention it
deservedly requires.
_The Destruction produced by Earthquakes is not irregular._—If we
were suddenly placed amongst the ruins of a large city which had
been shattered by an earthquake, it is doubtful whether we should at
once recognise any law as to the relative position of the masses of
_débris_ and the general destruction with which we are surrounded.
The results of observation have, however, shown us that, amongst the
apparently chaotic ruin produced by earthquakes, there is in many cases
more or less law governing the position of bodies which have fallen,
the direction and position of cracks in walls, and the various other
phenomena which result from such destructive disturbances.
Mallet, at the commencement of his first volume, describing the
Neapolitan earthquake of 1857, discusses the general effect produced by
various shocks upon differently constructed buildings. First he shows
that, if we have a rectangular building, the walls at right angles to
the shock will be more likely to be overthrown than those which are
parallel to it. Experience teaches a similar lesson. Thus Darwin, when
speaking of the earthquake at Concepcion in 1835,[20] tells us that
the town was built in the usual Spanish fashion, with all the streets
running at right angles to each other. One set ranged S.W. by W. and
N.E. by E. and the other N.W. by N. and S.E. by S. The walls in the
former direction certainly stood better than those in the latter. The
undulations came from the S.W.
In Caraccas it is said that every house has its _laga securo_, or safe
side, where the inhabitants place their fragile property. This _laga
securo_ is the north side, and it was chosen because about two out of
every three destructive shocks traversed the city from west to east,
so that the walls in these sides of a building have been stricken
broadside on.[21]
_Cracks in Buildings._—Results like the above come from destructive
earthquakes rather than from movements such as those we have to deal
with ordinarily. When a building is subjected to a slight movement
it is assumed that the walls at right angles to the direction of the
shock move backwards and forwards as a whole, and there is little or
no tendency for them to be fractured at their weaker parts, these
weaker parts being those over the various openings. The walls, however,
which are parallel to the direction of the movement are, so to speak,
extended and contracted along their length, and in consequence they may
be expected to give way over the various openings. This tendency for
extension and contraction of a wall along its length may be supposed,
for instance, to be due to the different portions of a wall, owing to
differences in dimensions and elasticity, having different periods of
natural vibration, or possibly for two portions of a long line of wall
to be simultaneously affected by portions of waves in different phases.
As an illustration of the giving way of a building in the manner here
suggested we may take the case of a large brick structure which was
recently being erected in Tokio. This building, at the time of the
earthquake, was only some fourteen or fifteen feet above the surface
of the ground. The length of the building stretched from N.W. to S.E.,
and it was intersected by many walls at right angles to this direction.
Through all the walls of this building there were many arched openings.
In the central part of the transverse walls, which walls were fully
five feet in thickness, the arches which joined them together were 4
feet 4 inches in thickness. The arches therefore formed a comparatively
lightly constructed link between heavy masses of brickwork.
On March 3, 1879, at 4.43 P.M., an earthquake was felt throughout
Tokio, the strength of which, as judged by our feelings, was above that
of an average shock. As registered by one of Palmieri’s instruments, it
had a direction S.S.W. to N.N.E. and an intensity of 11°. On the same
day there were several smaller shocks having the same direction, and
these were succeeded by others on the 9th of the month.
Immediately after these shakings it was discovered that almost every
arch in the internal walls of the building here referred to had been
cracked across the crown in a direction about N. 40° W. All the
other arches of the building, of which there were a great number in
walls at right angles to the direction of the shock, were found not
to have sustained any injury. To this statement, however, there was
one exception, which was subsequently proved to have been due to a
settlement taking place.
After examining these cracks the only cause to which they could be
attributed was the series of shakings which they had just experienced.
It seemed as if the heavy walls right and left of the arches had been
in vibration without synchronism in their periods, and as a consequence
the arches which connected them had been torn asunder.
Although the time at which the cracks were formed and the peculiar
positions in which they were only to be found pointed distinctly to
their origin, to be certain that they were not due to settlement of the
foundations, horizontal lines were ruled upon the brickwork and from
time to time subsequently observed.
The points to which the various cracks extended were also marked and
observed. Beneath the walls as foundations there were beds of concrete
about three feet thick and about ten feet in width. These had been
under the pressure of the partially built walls for two years before
the arches had been put in. As these foundations were unusually strong,
being intended to carry so very much greater weight than that to which
they had been subjected, if any settlement had been detected it would
have been a matter of surprise.
Some weeks after the formation of these cracks it was observed that
they gradually closed. This was probably due to the gradual falling
inwards of the two broken portions of the arch, their position when
open being one of instability.
[Illustration: FIG. 16.—Cracks in a corner house, Belluno, June 29,
1873 (Bittner).]
Had this building been more complete at the time of the shock, and
the heavy walls been tied together at higher points, although the
archways would have been points of weakness, it is quite possible
that fracture would not have taken place. This illustration shows us
that when a building is shaken in a definite direction there will be
some rule as to the positions in which fractures occur. As another
example, we may take the observations of Alexander Bittner upon the
buildings of Belluno after the shock of June 29, 1873 (see Beiträge
zur Kenntniss des Erdbebens von Belluno am 29 Juni, 1873, p. 40. Von
Alexander Bittner. Aus dem LXIX. Bande der Sitzungsb. der K. Akad. der
Wissensch., II. Abth., April-Heft. Jahrg. 1874).
Speaking generally, he remarks that ‘Houses similarly situated have
suffered in corresponding walls and corners in a similar manner. In
Belluno there is a certain kind of damage which is repeated everywhere,
making a peculiar system of splits in the S.W. and N.E. corners of the
houses.’ This is well shown in the accompanying sketch, which evidently
illustrates the effect of a shock oblique to the direction of two walls
at right angles to each other.
[Illustration: FIG. 17.—Brick buildings in Tokio, showing
fractures.]
_Buildings in Tokio._—For the purpose of finding out what has been the
effect produced by earthquakes upon the buildings of Tokio, and at
the same time for ascertaining whether blocks of buildings ranging in
different directions suffered to the same extent, the author examined,
in company with Mr. Josiah Conder, a large number of foreign-built
houses in the district of the Ginza. The chief reason for choosing
this was because it was the only district where a large number of
_similar_ buildings could be found. By examining houses or buildings of
different constructions, the effects produced upon them by earthquakes
are very often likely to show so many differences that it becomes
almost an impossibility to determine what the general effect has
been—unsymmetrical construction involving unsymmetrical ruin.
A number of similarly constructed buildings in one locality may be
regarded as a number of seismographs, the effect upon any one of them
being judged of by the average of the general effect which has been
produced upon the whole. The general form of two of these houses
which were examined is shown in fig. 17. In this figure the general
character of the fractures which have been produced can also be seen.
The houses are built of brick, and are in many cases faced with a thin
coat of white plaster. Projecting from the level of the upper floor
there is a balcony fronted by a low balustrade. This is supported by
small beams which at their outer extremity are carried on a row of
cylindrical columns. This forms a covered way in front of each row of
houses. The roofs are covered with thick tiles. It will be observed
that the arches of the upper windows spring _sharply_ from their
abutments, and at their crown they carry a heavy key-stone. The lower
openings, which have a span of 9 feet, have evidently been constructed
in imitation of the open front of an ordinary Japanese house. These
archways curve out _gently_ from their abutments. The outside walls
have a thickness of 13½ inches.
The results obtained from a careful examination of 174 houses in
streets running N.E. and 156 houses in streets running N.W., all of
these houses being similar, were as follows:—
1. In the upper windows nearly all the cracks ran from the springing,
which formed an angle with the abutment.
2. In the lower arches, which _curved_ into the abutments, not a single
crack was observed at the springway. The cracks in these arches were
near the crown, where beams projected to carry the balcony. In many
instances the cracks proceeded from such beams, even if there were
no arch beneath. That cracks should occur in peculiar positions, as
is here indicated, is shown in the illustrations which accompany the
accounts of many earthquakes.
3. The houses which were most cracked were in the streets running
parallel to the direction in which the greater number and most powerful
set of shocks cross the city.
The results showed that, in order to avoid the effects of small shocks,
all walls containing principal openings should be placed as nearly
as possible at right angles to the direction in which the shocks of
the districts usually travel. The blank walls, or those containing
unimportant openings, would then be parallel to the direction of the
shocks—that is, presuming our building to be made up of two sets of
walls at right angles to each other.
Another point of importance would be to build archways _curving_ into
the supporting buttresses; the archways over doors and windows which we
find in earthquake countries do not appear to be in any way different
from those which are built in countries free from earthquakes. In
the one country these structures have simply to withstand vertical
pressures applied statically; in the other, they have to withstand more
or less horizontal stresses, applied suddenly.
_Relation of Destruction to Earthquake Motion._—The relations which
exist between the overturning and projection of bodies and the motion
of the ground have already been discussed. It may be interesting
to call attention to the fact that in the formulæ showing three
relationships, it was the _shape_ rather than the _weight_ of a body
which determined whether it should be overturned or projected by a
motion at its base.
As an interesting proof that light bodies may be overturned as easily
as heavy ones. Mallet refers to the overturning of several large
haystacks as one of the results of the Neapolitan earthquake.
If masses of material are displaced or fractured, then Mallet remarks
_____
that the maximum velocity will exceed √2_gh_, where _h_ is the
amplitude of the wave. Should the maximum velocity be less than this
quantity, the masses which are acted upon will be simply raised and
lowered, and there will be no relative displacements even if the
emergence of the wave be nearly or quite vertical.
When we get a vertical wave acting upon an irregular mass of masonry,
the heavier portions of the masonry, by their inertia, tend to descend
relatively to the remaining portions, and in this way vertical fissures
will be produced. For this reason it would not be advisable to use
heavy materials above archways, heavy roofs, or heavy floors. The
vertical fissures, Mallet remarks, would have their widest opening at
the base.
In considering cases of fracture produced by earthquake motion, it
must be remembered that these are due to stresses applied _suddenly_,
and that if the same amount of stress had been _slowly_ applied to a
building, fractures might not have occurred.
If a disturbance is horizontal, and has a direction parallel to the
length of a wall, the wall is carried forward at its foundations. This
motion is opposed by the inertia of the upper portion of the wall and
the various loads it carries. The wall being elastic, distortion takes
place, and cracks, which are widest at the top, will be formed. In a
uniform wall the two most prominent fissures ought to be near the ends.
If the horizontal backward and forward movement has a direction
oblique to the plane of the wall, the wall will be either overthrown,
fractured, or have a triangular fragment thrown off towards the origin
from the end last reached.
Should the wave emerge steeply, diagonal fissures at right angles to
the direction of transit will be formed, or else triangular pieces will
be projected.
The accompanying figures are reduced from Mallet’s ‘Account of the
Neapolitan Earthquake of 1857.’
[Illustration: FIG. 18.—Cathedral Church, Potenza (Mallet).]
Taking _a_ _b_ as the general direction of the fractures in fig. 18,
then _c_ _d_ will represent the direction in which the shock emerged,
which is at an angle of 23°·20′ to the horizon. It might be argued that
the direction of these fractures was due to the direction in which
surface undulations had travelled, or to the relative strengths and
proportions of different portions of the building. The directions of
cracks in a building are undoubtedly due to a complexity of causes, but
for buildings situated in the region of shock the impulsive effect of
the shock is probably the most important function to be considered.
The method of applying the directions of emergence, deduced from
observations on fractures, to determine the origin of a disturbance
will be referred to in Chapter X.
[Illustration: FIG. 19.—The Cathedral, Paterno (Mallet).
Neapolitan Earthquake of 1857.]
Mallet observed that, although two ends of a building might be nearly
the same, the fissures and joints do not occur at equal distances from
the ends, nor are they equally opened.
The end where the joints are the most opened is that which was first
acted upon, and this phenomenon may be sufficiently well pronounced
to indicate the direction in which we must look to find the origin
of a disturbance. Amongst possible explanations for this disposition
of fractures in a wall. Mallet suggests that they may be due to real
differences in the two semiphases of the wave of shock, the second
semiphase being described with a somewhat slower velocity than the
first. This, it will be observed, is contrary to the indications of
seismographs.
Fig. 19, of the cathedral at Paterno, shows the effect of a subnormal
shock striking a wall obliquely and projecting one of its corners.
MEASUREMENTS OF THE RELATIVE MOTION OF PARTS OF A
BUILDING AT THE TIME OF AN EARTHQUAKE.
In 1880 a series of observations was made in Tokio to determine whether
at the time of an earthquake the various parts of the arched openings
which we see in many buildings synchronised in their vibrations, or,
for want of synchronism, were caused to approach and recede from each
other. The arches experimented on were heavy brick arches forming the
two corridors of the Imperial College of Engineering. The direction of
one set of these corridors is N. 40° E. and that of the other N. 50° W.
The thickness of the walls in which these arches are placed is 1 ft.
11 in. They are built of Japanese bricks bound together with ordinary
lime. The span of the arches is 8 ft. 3 in., and the height of the arch
from the springing-line to the crown 4 ft. 1 in. The height of the
abutments is 7 ft. 1½ in. The voussoirs of the arch are formed of a
light grey soft volcanic rock, and on their faces show a depth of 12
inches. The width of the intermediate columns between the arches is 4
ft. 6⅞ in.
To determine whether at the time of an earthquake there was any
variation in the dimensions of these arches, a light stiff deal
rod, about 2 in. by ½ in. in cross section, was placed across the
springing-line of the arch. One end of this was firmly fixed to the
top of one abutment by means of a spike; on the other end, which was
to indicate any horizontal movement if the abutments approached each
other, there was fixed a pointer made out of a piece of steel wire.
This rested on a piece of smoked glass fixed to the ledge on which
the loose end of the rod was resting. If the abutments approached or
receded from each other a line would be drawn measuring the extent of
the motion. As a further indication of motion, a second smoked glass
plate was fixed on the transverse rod, which plate was marked on by a
pointer attached to a vertical rod hanging down from the crown of the
arch.
As a general result of these experiments it may be said that the
portions of the building which were examined usually either did not
move at all, or else they practically synchronised in their movements.
When they did move, the extent of motion was small, and the small
differences in movement which were observed were in every probability
far within the elastic limits of the structure.
_Observations on Cracks._—To determine whether the walls of a building
which have once been cracked, when subjected to a series of shocks,
similar to those which they experienced before being cracked, still
continued to give way, the extremities of a considerable number of
cracks in the N.E. end of the museum buildings of the Engineering
College were marked with pencil. Although since the time of marking
there had been many severe shocks, these cracks did not visibly extend.
These marks were made on the outside wall of the building. On the
inside, one of these same cracks showed itself as a fissure about ¼
inch in width. Across this crack a horizontal steel wire pointer was
placed. One end of this wire was fixed in the wall; the other end,
which was pointed, rested on the surface of a smoked glass plate placed
on the other side of the crack. After small earthquakes there was no
indication of motion having taken place, but after a shock on February
21, as indicated by a line upon the smoked glass plate, it was seen
that the sides of the crack had approached and receded from each other
through a distance of about 1/16 inch.
By similar contrivances placed on cracks in a neighbouring building
exactly similar results were obtained, namely, that during small
earthquakes the two sides of the crack had retained their relative
positions, but at the time of a large shock this position had been
changed.
In this building it was also observed that the cracks in many instances
increased their length.
By attaching levers to the end of the pointers to multiply any motion
that might take place, no doubt the indications would be more frequent
and more definite. It would also be easier to note the relative
distances of motion in two directions, namely, how far the cracks
had closed and how far they had opened. As to whether motion would
occur or not, much would no doubt depend upon the direction of the
earthquake.
_Prevention of Fractures._—One conclusion which may perhaps be drawn
from these observations is, that a cracked building at the time of an
earthquake shows a certain amount of flexibility. Whether a building
which had been designed with cracks or joints between those parts
which were likely to have different periods of vibration would be more
stable, so far as earthquake shakings are concerned, than a similar
building put up in an ordinary manner, is a matter to be decided by
experiment. Certainly some of the cracks which have been examined
indicate that if they had not existed, the strain upon the portion of
the building where they occur would have been extremely great.
_Direction of Cracks._—In looking at the cracks produced by small
earthquakes it is interesting to note the manner of their extension.
The basements of the buildings which have been most carefully examined
are, for a height of two or three feet, built of large rectangular
blocks of a greyish-coloured volcanic rock. In these parts the cracks
pass in and out between the joints of the stone, indicating that
the stones have evidently been stronger than the mortar which bound
them together, and as a consequence the latter had to give way.
Above this basement when the cracks enter the brickwork, they no
longer exclusively confine themselves to the joints, but run in an
irregular line through all they meet with, sometimes across the bricks
and sometimes through the mortar joints. In places where they have
traversed the brickwork, we can say that the mortar has been stronger
than the bricks. This traversing of the bricks rather than the joints
is, I think, the general rule for the direction of the cracks in the
brickwork of Tokio buildings.
_The Pitch of Roofs._—From observation of the effects produced by
earthquakes, it appears to us that the houses which lost the greater
number of tiles appear to be those with the steepest pitch, and those
where the tiles were simply laid upon the roof and not in any manner
fastened down. It would seem that destruction of this sort might to a
great extent be obviated by giving the roofs a less inclination and
fixing the tiles with nails. It was also noticed that the greatest
disturbance amongst the tiles was upon the ridges of the roofs.
Destruction of this sort might be overcome by giving especial attention
to these portions during the construction of the roof.
[Illustration: FIG. 20. FIG. 21.]
_Relative Position of Openings in Walls._—From what has been said about
the fractures in the buildings of Tokio it will have been seen that,
with but few exceptions, they have all taken place above openings
like doorways and windows. If architecture demands that openings like
arches should be placed one above another in heavy walls of this kind,
as in fig. 17, there will be lines of weakness running through the
openings parallel to the dotted lines. As arches are only intended
to resist vertical thrusts, special construction must be adopted to
make them strong enough to resist horizontal pulls. For instance, a
flat arch would offer more resistance to horizontal pulls than an
arch put together with ordinary voussoirs, there being in the former
case more friction to prevent the component parts sliding over each
other. Or again, above each arch an iron girder or wooden lintel might
be inserted in the brick or stone arch. It was suggested to me by my
colleague, Mr. Perry, that the best form calculated to give a wall
uniform strength, would be to build it so that the openings of each
tier would occupy alternate positions, that is to say, along lines
parallel to the struts and ties of a girder. In this way we should have
our materials so arranged that they would offer the same resistance to
horizontal as to vertical movements. Such a wall is shown in fig. 20:
the dotted lines running through the openings, and all similar lines
parallel to the former, representing lines of weakness. If we compare
this with fig. 21, we shall see that in the case of a horizontal
movement _a_ _b_ or of a vertical movement _c_ _d_, we should rather
expect to find fractures in a house built like fig. 21 than in one
built like fig. 20. If, however, these two buildings were shaken by a
shock which had an angle of emergence of about 45° in the direction _e_
_f_, the effects might be reversed. Usually, however, and always in a
town like Tokio which is visited by shocks originating at a distance,
the movements are practically horizontal ones, and, therefore,
buildings erected on the principles illustrated by fig. 20 should
be much superior, so far as resisting earthquakes is concerned, to
buildings constructed in the ordinary manner, as in fig. 21. Fractures
following a vertical line of weakness are shown in the accompanying
drawing, fig. 22, of the Church of St. Augustin, at Manilla, shattered
by the earthquakes of 1880.
_The last House in a Row._—When an earthquake shock enters a line
of buildings, and proceeds in a direction coincident with that of
the buildings, we should expect that the last of these houses, being
unsupported on one side, would be in the position of the last person in
Tyndall’s row of boys. From this it would seem that the end house in a
row would show the greatest tendency to fly away from its neighbours.
If the last house stood upon the edge of a deep canal or a cliff,
there would be a layer of ground, equal in thickness to the depth of
the canal or to the height of the cliff, as the case may be, which
would also be in a position to be thrown forward. The effect which is
sometimes produced upon an end building is shown in fig. 23, which is
taken from the photograph of a house shattered in 1868 at San Francisco.
[Illustration: FIG. 22.—Church of St. Augustin, Manilla.
Earthquakes of July 18–20, 1880.]
_The Swing of Buildings._—The distance through which buildings are
moved at the time of an earthquake depends partly on their construction
and partly on the extent, nature, and duration of the movement
communicated to them at their foundations. By violent shocks buildings
may be completely overthrown. In the case of small earthquakes, the
upper portion of a house may frequently move through a much greater
distance than the ground at its foundation. For instance, during the
Yokohama earthquake of February, 1880, when the maximum amplitude of
the earth’s motion was probably under ¾ of an inch, from the slow swing
of long Japanese pictures, from three to six feet in length, which
oscillated backwards and forwards on the wall, it is very probable
that the extent through which the upper portion of houses moved was
very considerable. In some instances these pictures seem to have swung
as much as two feet, and from the manner in which they swung they
evidently synchronised with the natural swing of the house.
[Illustration: FIG. 23.—Webber House, San Francisco. Oct. 21, 1868.]
From this it would seem that such a house must have rocked from side to
side one foot out of its normal perpendicular position. That the motion
was great is testified by nearly all who tried to stand at the time of
the shock, it having been impossible to walk steadily across the floor
of a room in an upper story. The houses here referred to are either
those which are purely Japanese, or else those which are framed of wood
and built on European models, a class of building which is very common
in Tokio and Yokohama.
Perry and Ayrton calculated the period of a complete natural vibration
of different structures. For a square house whose outer and inner
sections were respectively 30 and 26 feet, and whose height was 30
feet, the period calculated would be about ·06 second.
At the time of the above earthquake many houses seem to have moved like
inverted pendulums. On the morning after the shock my neighbour, who
was living upstairs in a tall wooden house with a tile roof, told me
that he endeavoured to count the vibrations, and was of the impression
that to make a complete swing it took about 2 seconds.
Assuming now that the distance through which the top of a wooden house
moved was about 1 foot, and the number of vibrations which it made per
second was about ·5, then the greatest velocity of a point on the top
of such a house must have been about 6 feet per second.
Mallet, who made observations upon the vibrations of various
structures, tells us that Salisbury spire moves to and fro in a gale
more than 3 inches. A well-constructed brick and mortar wall, 40 feet
high and 1 foot 6 inches thick, was observed to vibrate in a gale 2
feet transversely before it fell.
An octagonal chimney with a heavy granite capping, 160 feet high, was
observed instrumentally to vibrate at the top nearly 5 inches.[22]
At the time of a severe earthquake it does not seem impossible but that
a building may be swung completely over. The accompanying illustration,
fig. 24, taken from a photograph,[23] apparently indicates a movement
of description.
[Illustration: FIG. 24.—Stud Mill at Haywards, California. Oct. 21,
1868.]
_Principle of relative Vibrational Period._—If a lath or thin pole
loaded at one end with a weight fixed to the ground, so as to stand
vertically, be shaken by an earthquake it will be caused to rock to
and fro like an inverted pendulum. The period of its swing will be
chiefly dependent on its dimensions, its elasticity, and its load. In
a building we have to consider the vibration of a number of parts,
the periods of which, if they were independent of each other, would be
different. On account of this difference in period, whilst one portion
of a building is endeavouring to move towards the right, another
is pulling towards the left, and, in consequence, either the bonds
which join them or else they themselves are strained or broken. This
was strikingly illustrated by many of the chimneys in the houses at
Yokohama, which by the earthquake of February 20, 1880, were shorn off
just above the roof. The chimneys were shafts of brick, and probably
had a slower period of vibration than the roof through which they
passed, this latter vibrating with the main portion of the house, which
was framed of wood.
A particularly instructive example of this kind which came under my
notice is roughly sketched in fig. 25.
[Illustration: FIG. 25.]
This is a chimney standing alone, which, for the sake of support, was
strapped by an iron band to an adjoining building. It would seem that
at the time of the shock, the building moving one way and the chimney
another, the swing of the heavy building gave the chimney a sharp jerk
and cut it off. The upper portion, being then loose upon the lower
part, rotated under the influence of the oscillations in manner similar
to that in which gravestones are rotated.
Mallet made observations similar to these in Italy. He tells us that a
buttress may often not have time to transmit its stability to a wall.
The wall and the buttress have different periods of vibration, and
therefore they exert impulsive actions on each other. Effects like
these were strikingly observable in many of the rural Italian churches
where the belfry tower is built into one of the quoins of the main
rectangular building.
Not only have we to consider the relative vibrations of the various
parts of a building amongst themselves, but we have to consider the
relation of the natural vibrations of any one of them or the vibration
of the building as a whole, with regard to the earth, the vibrations of
which it must be remembered are not strictly periodic.
Some of the more important results dependent upon the principle of
‘relative vibrational periods’ may be understood from the following
experiments:—
[Illustration: FIG. 26.]
In fig. 26 A, B, and C are three flat springs made out of strips of
bamboo, and loaded at the top with pieces of lead. At the bottom they
are fixed into a piece of board D E, and the whole rests on a table F
G. The legs of this table being slightly loose, by placing the fingers
on the top of it, a quick short backward and forward movement can be
produced. The weights on A and B are the same, but they are larger than
the weight on C. Consequently the periods of A and B are the same, but
different to the period of C. The dimensions of these springs are as
follows: height, 18 inches; A and B each carry weights equal to 320
grammes, and they make one vibration per second; C has a weight of 199
grammes, and makes 0·75 vibrations per second.
_First Experiment._—It will be found that by giving the table a gentle
backward and forward movement, the extent of which movement may be so
small that it will be difficult to detect it with the eye, either A
and B may be made to oscillate violently whilst C remains still; or
_vice versâ_, C may be caused to oscillate whilst A and B remain still.
In the one case the period of shaking will have been synchronous with
the natural period of A and B, whilst in the latter it will have been
synchronous with that of C. This would seem to show us that if the
natural period of vibration of a house, or of parts of it, at any time
agree with the period of the shock, it may be readily thrown into a
state of oscillation which will be dangerous for its safety.
_Second Experiment._—Bind A and B together with a strip of paper
pasted between them. (The paper used was three-eighths of an inch
broad and would carry a weight of nearly three pounds.) If the table
be now shaken as before, A and B will always have similar movements,
and tend to remain at the same distance apart, and as a consequence
the strip of paper will not be broken. From this experiment it would
seem that so long as the different portions of a building have almost
the same periods of vibration, there will be little or no strain upon
the tie-rods or whatever contrivance may be used in connecting the
different parts.
_Third Experiment._—Join A and C, or B and C with a strip of paper in a
manner similar to the last experiment. If the table be now shaken with
a period approximating either to that of A and B, or with that of C,
the paper will be suddenly snapped.
This indicates that if we have different portions of a building of
such heights and thicknesses that their natural periods of vibration
are different, the strain upon the portions which connect such parts
is enormous, and it would seem, as a consequence, that either the
vibrators themselves, or else their connections, must, of a necessity,
give way. This was very forcibly illustrated in the Yokohama earthquake
of February 1880 by the knocking over of chimneys. The particular case
of the chimneys is, however, better illustrated by the next experiment.
_Fourth Experiment._—Take a little block of wood three-quarters of an
inch square and about one inch high, and place it on the top of A, B,
or C. It will be found that, although the spring on which it stands
is caused to swing backwards and forwards through a distance of three
inches, the little block will retain its position.
This little block we may regard as the upper part of a chimney standing
on a vibrating stack, and we see that, so long as this upper portion is
light, it has no tendency to fall.
_Fifth Experiment._—Repeat the fourth experiment, having first placed a
small leaden cap on the top of the block representing the chimney. (The
cap used only weighed a few grammes.) When vibration commences it will
be found that the block quickly falls. This would seem to indicate that
chimneys with heavy tops are more likely to fall than light ones.
_Sixth Experiment._—Bind A and B together with a strip of paper and
stand the little block upon the top of either. It will be found that
the block will stand as in the fourth experiment.
_Seventh Experiment._—Bind A and C, or B and C together, and place
the block upon the top of either of them. When vibration commences,
although the paper may not be broken, the little block will quickly
fall.
_Eighth Experiment._—Take two pencils or pieces of glass tube and
place them under the board D E. If the table F G be now shaken in the
direction D E, it will be found that the springs will not vibrate.
In a similar manner if a house or portion of a house were carried on
balls or rollers, as has already been suggested, it would seem that the
house might be saved from much vibration.
_Ninth Experiment._—Set any of the springs in violent vibration by
gently shaking D E instead of the table, and then suddenly cease the
actuating motion. It will be observed that at the moment of cessation
the board and the springs will have a sudden and very decided motion
of translation in the same direction as that in which the springs were
last moving, and although the springs were at the time swinging through
a considerable arc, all motion will suddenly cease.
This shows, that if a house is in a state of vibration the strain at
the foundations must be very great.
It would not be difficult to devise other experiments to illustrate
other phenomena connected with the principle of relative vibrational
periods, but these may perhaps be sufficient to show to those who have
not considered this matter its great importance in the construction
of buildings. Perhaps the greater portion of what is here said may by
many be regarded as self-evident truisms hardly worth the trouble of
demonstration. Their importance, however, seems to be so great that I
hope that their discussion has not been altogether out of place.
I may remark that in the rebuilding of chimneys in Yokohama the
principles here enunciated were taken advantage of by allowing the
chimneys to pass freely through the roofs without coming in contact
with any of the main timbers.
In putting up buildings to resist the effects of an earthquake, besides
the idea of making everything strong because the earthquake is strong,
there are several principles which, like the one just enunciated, might
advantageously be followed which as yet appear to have received but
little attention.