S T 0
457
S T 0
Of 4L . ,
joints may be varied about 20°, perhaps 30°, fromH equilibrium, before any derangement can arise froming of the arch-stones.
j| v -^ois is a most important conclusion, and leads to exten-of" Practical consequences. It affords a true explanation^ ac dity with which arches are everywhere constructed,V the common country mason.
Pfa ■ r t ^ 1 ' 3 reason ) therefore, we approve highly of theWe ct ice, which we believe is very general among artificers,8 ef taea n that of backing up the arch with solid masonry, forOl courses above the springing. If great security isOn 7§ht necessary, cement, being a compressible substance,1 to ' 3e sparingly employed in the vertical joints at the.. °f the arch-stones.
,“Th,
e friction of the sections of the arch, as it permits a
lovable variation to take place in the position of the
?°ni
4*. Will also admit of a considerable deviation from thea which is necessary for equilibrium over any point of<, j Ul we.
Hi^ would not be difficult to investigate the extent to%ll t ' l ’ s variation of weight might be carried. But wehrt . at Present only remind the reader, that, as we find aatl °n of 20° practicable in the position of the joints, heHl t r. c °»clude that each section will admit of its load beingeiti. to that which would suit a point in the curve 20° onT? «ide of it.
Une
6ll t of
thing only remains to be considered in this depart-our SL| hject, which is, the lateral pressure likely toto ta . ° n the back of the arch, from the materials employedu Jp e the structure to the horizontal line.
1 the materials employed here be only a solid mass ofit it is not easy to see, everything being steady, how
If4 act in any other way than in the vertical direction.,ri at^' Vever , a motion takes place in the arch, the mass of>01* lying nearly over the springing, when the arch is''’•’Us r • different from a semicircle, will have such an enor-fiction, if well built and bonded together, as woulde fiual to the resistance of any pressure that is likely to
opposed
“ter
its
to it. And when the arch is a segment much
than a semicircle, the rules we have already givene fiuilibration must be considered. But, instead offilhjj c °Urses of masonry, the haunches of arches are often’•'ere with coarse gravel, or shiver, and sometimes with•Ue at) or sand. Materials of this description do by nos li<] e 8 ae t by mere dead weight. They have a tendency toPo Ss <lo Wn towards a horizontal position; and, of course,r ‘f a 3 >n some slight degree, the quaquaver sum, pressure••e\ v Ul 'l- This may act on our arch in a manner altogether•io produce strains for which hitherto we have madefii|° j' s i°n. We shall first consider the back of the arch
c Ur Ve r 7 part will be in a direction perpendicular to thePerp ’ a !*d will be proportional to the depth. A pressureVti„ | cular to the curve will be equivalent, in effect, to a°f t) le . Pressure, which exceeds it in the ratio of the secant\ p Ilc lination to the vertical. Of course, the pressure atViJ/ ln g>ng, when all is equilibrated, must be equal to the“ r pj thrust in a semicircular arch.
•lei, « 10u ?h the action of sand, gravel, or mould, in situations?lo\ V ' S ^is, be not exactly the same with that of water, inH ' n » the laws of hydrostatical pressure ; yet these mate->r| i(] ( ]l e esetll ble water, and may be conceived to hold theSr, e Place between the fluid and the solid backing. In*Vy a es Pects they are more advantageous than the fluid.n r(i ^ e _stiffer, so to speak, affording a lateral abutment tois likely to yield ; and as the parts have a great
up with a fluid substance, as water. The pressure
•on
among themselves, it will require a much greater6 A
pressure, acting horizontally, to make the matter rise, thanin the case of a fluid. We must not, however, be too con-fident. Materials of this kind are compressible ; and wehave already seen that very slight shifts are attended withdangerous consequences. At the same time, we need not bemuch afraid of a trivial departure from exact equilibration ;for it is not likely that materials of this kind will act withthe powerful effort of hydrostatical pressure.
“But there is another case, where matter of this kind islikely to be attended with more pernicious effects than evena fluid of equal density would be. We mean, when the backof the arch is gorged up with water from land-floods : if thebacking be open gravel, or shiver, we have superadded to itsweight that of the whole quantity of water admitted into thestructure. This, even if it acts equally on both sides, mustbe a dangerous experiment on any arch; but where it isconfined to one side, as is generally the case, and betweenlofty side-walls, the effects are likely to be serious indeed.Accordingly, the builder forms gutters in the side-wall tolet off the water ere it collects;—a practice which is in generalhighly useful, but which, in the case of sand, clay, or mould,is of small service. The water enters into such matter byits capillary attraction; and fills it to the upper surface, inspite of our gutters. It of course expands it, and this witha force which we cannot measure, but which we are sure isvery great. Here the friction of the parts, which was souseful in the former instance, proves extremely hurtful. Foras the matter cannot easily rise, and probably the adhesion ofits particles is increased by the water, the expanding forcebecomes an enormous hydrostatical pressure acting perpen-dicularly on the side-walls and extrados of our arch, andwhich in all probability they may not sustain.
“ The dangerous consequences of this mode of backing are,in some degree, prevented by ramming the layers of matter,especially if it consists of mould or the like : or, by puddlingthem, so as to form a mass impervious to water. And herewe should observe, that as this ramming will produce anextraordinary lateral pressure, we must attend to equilibra-tion, as we rise along the arch, and secure the side-wallsby thickening them below, or curving them horizontally orvertically.
“ The thickness of the arch-stones is an important depart-ment of the theory of arches. It is natural that we shouldendeavour to make them as small as possible. That willdiminish the expense of the structure, lessen the pressuresin the arch, and increase the security at the springing. Butthere is an evident limit to this diminution ; for though wetake every pains to render the joints close, the stones maycome at length to be so small as to crush by the thrust of thearch. This is, indeed, a curious branch of inquiry. Itdepends intimately upon the corpuscular actions of the par-ticles of stone ; a subject on which, we regret to say, ourinformation has been hitherto very scanty.
“ The question evidently depends on the amount of thetangential pressure. At the crown this is the horizontalthrust. We shall suppose all the joints to be duly drawn toequilibration, the sections fairly abutting on each other, andno weakness arising from acute angles.
“Stone, it is said, will carry from 250,000 to 850,0001b.avoirdupois per foot square, and brick 300,0001b. Theyhave been made practically to carry one-sixth of this, and evenmore. The pillar in the centre of the Chapter-house atElgin carries upwards of 40,0001b. on the square foot, andthere was formerly a heavy lead roof on it. It is a red sand-stone, and has borne this pressure for centuries.
“ We shall therefore take 50,0001b. per foot as a loadwhich may be safely laid on every square foot in the arch.