CAP and BUTTON, are two small islands, or rather rocks, lying in longitude 105° 48' 30" east; and in latitude, the former 5° 58' 30", the latter 5° 49' south. They were visited by some of the persons attending Lord Macartney on his embassy to China; and are thus described by Sir George Staunton.
"At a little distance they might be mistaken for the remains of old castles, mouldering into heaps of ruins, with tall trees already growing upon the tops; but at a nearer view, they betrayed evident marks of a volcanic origin. Explosions from subterraneous fires produce, for the most part, hills of a regular shape, and terminating in truncated cones; but when from a subaqueous volcano eruptions are thrown up above the surface of the sea, the materials falling back into the water, are more irregularly dispersed, and generally leave the sides of the new creation naked and marshy, as in the instance of AMSTERDAM, and of those smaller spots called, from some resemblance in shape, the Cap and Button.
"In the Cap were found two caverns, running horizontally into the side of the rock; and in these were a number of those birds' nests so much prized by the Chinese epicures. They seemed to be composed of fine filaments cemented together by a transparent viscid matter, not unlike what is left by the foam of the sea upon stones alternately covered by the tide, or those gelatinous animal substances found floating on every coast. The nests adhere to each other, and to the sides of the cavern, mostly in rows, without any break or interruption. The birds that build these nests are small grey swallows, with bellies of a dirty white. They were flying about in considerable numbers; but they were so small, and their flight so quick, that they eluded the shot fired at them. The same nests are said also to be found in deep caverns, at the foot of the highest mountains in the middle of Java, and at a distance from the sea, from which the birds, it is thought, derive no materials, either for their food or the construction of their nests; as it does not appear probable they should fly, in search of either, over the intermediate mountains, which are very high, or against the boisterous winds prevailing thereabouts. They feed on insects, which they find hovering over stagnated pools between the mountains, and for catching which their wide opening beaks are particularly adapted. They prepare their nests from the best remnants of their food. Their greatest enemy is the kite, who often intercepts them in their passage to and from the caverns, which are generally surrounded with rocks of grey limestone or white marble. The nests are placed in horizontal rows at different depths, from 50 to 500 feet. The colour and value of the nests depend on the quantity and quality of the insects caught, and perhaps also on the situation where they are built. Their value is chiefly determined by the uniform fineness and delicacy of their texture; those that are white and transparent being most esteemed, and fetching often in China their weight in silver. These nests are a considerable object of traffic among the Javanese, and many are employed in it from their infancy. The birds having spent near two months in preparing their nests, lay each two eggs, which are hatched in about fifteen days. When the young birds become fledged, it is thought time to seize upon their nests, which is done regularly thrice a-year, and is effected by means of ladders of bamboo and reeds, by which the people descend into the cavern; but when it is very deep, rope ladders are preferred. This operation is attended with much danger; and several break their necks in the attempt. The inhabitants of the mountains generally employed in it begin always by sacrificing a buffalo; which custom is constantly observed by the Javanese on the eve of every extraordinary enterprise. They also pronounce some prayers, anoint themselves with sweet-scented oil, and smoke the entrance of the cavern with gum-benjamin. Near some of those caverns a tutelar goddeis is worshipped, whose priest burns incense, and lays his protecting hands on every person preparing to descend into the cavern. A flambeau is carefully prepared at the same time, with a gum which exudes from a tree growing in the vicinity, and is not easily extinguished by fixed air or subterranean vapours. The swallow, which builds these nests, CARPENTRY,
The art of framing timber for the purposes of architecture, machinery, and, in general, for all considerable structures.
It is not intended in this article to give a full account of carpentry as a mechanical art, or to describe the various ways of executing its different works, suited to the variety of materials employed, the processes which must be followed for fashioning and framing them for our purposes, and the tools which must be used, and the manner in which they must be handled: This would be an occupation for volumes; and though of great importance, must be entirely omitted here. Our only aim at present will be to deduce, from the principles and laws of mechanics, and the knowledge which experience and judicious inferences from it have given us concerning the strength of timber, in relation to the strain laid on it, such maxims of construction as will unite economy with strength and efficacy.
This object is to be attained by a knowledge, 1st, of the strength of our materials, and of the absolute strain that is to be laid on them; 2dly, of the modifications of this strain, by the place and direction in which it is exerted, and the changes that can be made by a proper disposition of the parts of our structure; and, 3dly, having disposed every piece in such a manner as to derive the utmost advantage from its relative strength, we must know how to form the joints and other connections in such a manner as to secure the advantages derived from this disposition.
This is, evidently, a branch of mechanical science, which makes carpentry a liberal art, constitutes part of the learning of the Engineer, and distinguishes him from the workman. Its importance in all times and states of civil society is manifest and great. In the present condition of these kingdoms, raised, by the active ingenuity and energy of our countrymen, to a pitch of prosperity and influence unequalled in the history of the world, a condition which consists chiefly in the superiority of our manufactures, attained by prodigious multiplication of engines of every description, and for every species of labour, the Science (so to term it) of carpentry is of immense consequence. We regret therefore exceedingly, that none of our celebrated artists have done honour to themselves and their country, by digesting into a body of consecutive doctrines the results of their great experience, so as to form a system from which their pupils might derive the first principles of their education. The many volumes called Complete Instructors, Manuals, Jewels, &c. take a much humbler flight, and content themselves with instructing the mere workman, or sometimes give the master builder a few approved forms of roofs and other framings, with the rules for drawing them on paper; and from thence forming the working draughts which must guide the saw and the chisel of the workman. Hardly any of them offer any thing that can be called a principle, applicable to many particular cases, with the rules for this adaptation. We are indebted for the greatest part of our knowledge of this subject to the labours of literary men, chiefly foreigners, who have published in the memoirs of the learned academies dissertations on different parts of what may be termed the science of carpentry. It is singular, that the members of the Royal Society of London, and even of that established and supported by the patriotism of these days for the encouragement of the arts, have contributed so little to the public instruction in this respect. We observe of late some beginnings of this kind, such as the last part of Nicholson's Carpenters and Joiners Assistant, published by J. Taylor, Holburn, 1797. And it is with pleasure that we can say, that we were told by the editor, that this work was prompted in a great measure by what has been delivered in the Encyclopaedia Britannica in the articles Roof and Strength of Materials. It abounds more in important and new observations than any book of the kind that we are acquainted with. We again call on such as have given a scientific attention to this subject, and pray that they would render a meritorious service to their country by imparting the result of their researches. The very limited nature of this work does not allow us to treat the subject in detail; and we must confine our observations to the fundamental and leading propositions.
The theory (so to term it) of carpentry is founded Theory, on two distinct portions of mechanical science, namely, a knowledge of the strains to which framings of what timber are exposed, and a knowledge of their relative strength.
We shall therefore attempt to bring into one point of view the propositions of mechanical science that are more immediately applicable to the art of carpentry, and are to be found in various articles of our works. particularly Roof and Strength of Materials. From these propositions we hope to deduce such principles as shall enable an attentive reader to comprehend distinctly what is to be aimed at in framing timber, and how to attain this object with certainty; and we shall illustrate and confirm our principles by examples of pieces of carpentry which are acknowledged to be excellent in their kind.
The most important proposition of general mechanics to the carpenter is that which exhibits the composition and resolution of forces; and we beg our practical readers to endeavour to form very distinct conceptions of it, and to make it very familiar to their mind. When accommodated to their chief purposes, it may be thus expressed:
1. If a body, or any part of a body, be at once pressed in the two directions AB, AC (fig. 1.), and if the intensity or force of those pressures be in the proportion of those two lines, the body is affected in the same manner as if it were pressed by a single force acting in the direction AD, which is the diagonal of the parallelogram ABDC formed by the two lines, and whose intensity has the same proportion to the intensity of each of the other two that AD has to AB or AC.
Such of our readers as have studied the laws of motion, know that this is fully demonstrated. We refer them to the article Mechanics, no. 5, &c., where it is treated at some length. Such as wish for a very accurate view of this proposition, will do well to read the demonstration given by D. Bernoulli, in the first volume of the Comment. Petropol. and the improvement of this demonstration by D'Alembert in his Oeuvres, and in the Comment. Taurinensis. The practitioner in carpentry will get more useful confidence in the doctrine, if he will shut his book, and verify the theoretical demonstrations by actual experiments. They are remarkably easy and convincing. Therefore it is our request that the artist, who is not so habitually acquainted with the subject, do not proceed further till he has made it quite familiar to his thoughts. Nothing is so conducive to this as the actual experiment; and since this only requires the trifling expense of two small pulleys and a few yards of whipcord, we hope that none of our practical readers will omit it: They will thank us for this injunction.
2. Let the threads Ad, Afh, and Ae (fig. 2.), have the weights d, b, and c, appended to them, and let two of the threads be laid over the pulleys F and E. By this apparatus the knot A will be drawn in the directions AB, AC, and AK. If the sum of the weights b and c be greater than the single weight d, the assemblage will of itself settle in a certain determined form; if you pull the knot A out of its place, it will always return to it again, and will rest in no other position. For example, if the three weights are equal, the threads will always make equal angles, of 120 degrees each, round the knot. If one of the weights be three pounds, another four, and the third five, the angle opposite to the thread stretched by five pounds will always be square, &c.
When the knot A is thus in equilibrium, we must infer that the action of the weight d, in the direction Ad, is in direct opposition to the combined action of b, in the direction AB, and of c, in the direction AC. Therefore, if we produce dA to any point D, and take AD to represent the magnitude of the force, or pressure exerted by the weight d, the pressures exerted on A by the weights b and c, in the directions AB, AC, are in fact equivalent to a pressure acting in the direction AD, whose intensity we have represented by AD. If we now measure off by a scale on AF and AE the lines AB and AC, having the same proportions to AD that the weights b and c have to the weight d, and if we draw DB and DC, we shall find DC to be equal and parallel to AB, and DB equal and parallel to AC; so that AD is the diagonal of a parallelogram ABDC. We shall find this always to be the case, whatever are the weights made use of; only we must take care that the weight which we cause to act without the intervention of a pulley be less than the sum of the other two: if any one of the weights exceeds the sum of the other two, it will prevail, and drag them along with it.
Now, since we know that the weight d would just balance an equal weight g, pulling directly upwards by the intervention of the pulley G; and since we see that it just balances the weights b and c, acting in the directions AB, AC, we must infer, that the knot A is affected in the same manner by those two weights, or by the single weight g; and therefore, that two pressures, acting in the directions, and with the intensities, AB, AC, are equivalent to a single pressure having the direction and proportion of AD. In like manner, the pressures AB, AK, are equivalent to AH, which is equal and opposite to AC. Also AK and AC are equivalent to AI, which is equal and opposite to AB.
We shall consider this combination of pressures a little more particularly.
Suppose an upright beam BA (fig. 3.) pushed in the direction of its length by a load B, and abutting on the ends of two beams AC, AD, which are firmly fitted at their extreme points C and D, which rest on two blocks, but are nowise joined to them: these two beams can resist no way but in the directions CA, DA; and therefore the pressures which they sustain from the beam BA are in the directions AC, AD. We wish to know how much each sustains? Produce BA to E, taking AE from a scale of equal parts, to represent the number of tons or pounds by which BA is pressed. Draw EF and EG parallel to AD and AC; then AF, measured on the same scale, will give us the number of pounds by which AC is strained or crushed, and AG will give the strain on AD.
It deserves particular remark here, that the length of AC or AD has no influence on the strain, arising from the thrust of BA, while the directions remain the same. The effects, however, of this strain are modified by the length of the piece on which it is exerted. This strain compresses the beam, and will therefore compress a beam of double length twice as much. This may change the form of the assemblage. If AC, for example, be very much shorter than AD, it will be much less compressed: The line CA will turn about the centre C, while DA will hardly change its position; and the angle CAD will grow more open, the point A sinking down. The artist will find it of great consequence to pay a very minute attention to this circumstance, and to be able to see clearly the change of shape which necessarily results from these mutual strains. He will see in this the cause of failure in many very great works.—By thus changing shape, strains are often produced in places places where there were none before, and frequently of the very worst kind, tending to break the beams across.
The dotted lines of this figure show another position of the beam AD'. This makes a prodigious change, not only in the strain on AD', but also in that on AC. Both of them are much increased; AG is almost doubled, and AF is four times greater than before. This addition was made to the figure, to show what enormous strains may be produced by a very moderate force AE, when it is exerted on a very obtuse angle.
The 4th and 5th figures will affix the most uninstructed reader in conceiving how the very same strains AF, AG, are laid on these beams, by a weight firmly hang- ing from a billet resting on A, pressing hard on AD, and also leaning a little on AC; or by an upright piece AE, joggled on the two beams AC, AD, and per- forming the office of an ordinary king-post. The read- er will thus learn to call off his attention from the means by which the strains are produced, and learn to consider them abstractedly, merely as strains, in whatever situation he finds them, and from whatever cause they arise.
We presume that every reader will perceive, that the proportions of these strains will be precisely the same if everything be inverted, and each beam be drawn or pulled in the opposite direction. In the same way that we have substituted a rope and weight in fig. 4, or a king-post in fig. 5, for the loaded beam BA of fig. 3, we might have substituted the framing of fig. 6, which is a very useful practice. In this framing, the batten DA is stretched by a force AG, and the piece AC is compressed by a force AF. It is evident, that we may employ a rope, or an iron rod hooked on at D, in place of the batten DA, and the strains will be the same as before.
This seemingly simple matter is still full of instruc- tion; and we hope that the well-informed reader will pardon us, though we dwell a little longer on it for the sake of the young artist.
By changing the form of this framing, as in fig. 7, we produce the same strains as in the disposition repre- sented by the dotted lines in fig. 3. The strains on both the battens AD, AC, are now greatly increased.
The same consequences result from an improper change of the position of AC. If it is placed as in fig. 8, the strains on both are vastly increased. In short, the rule is general; that the more open we make the angle against which the push is exerted, the greater are the strains which are brought on the struts or ties which form the sides of the angle.
The reader may not readily conceive the piece AC of fig. 8, as sustaining a compression; for the weight B appears to hang from AC as much as from AD. But his doubts will be removed by considering whether he could employ a rope in place of AC. He cannot: But AD may be exchanged for a rope. AC is there- fore a strut, and not a tie.
In fig. 9, AD is again a strut, butting on the block D, and AC is a tie; and the batten AC may be re- placed by a rope. While AD is compressed by the force AG, AC is stretched by the force AF.
If we give AC the position represented by the dotted lines, the compression of AD is now AG'; and the force stretching AC is now AF'; both much greater than they were before. This disposition is analogous to fig. 8, and to the dotted lines in fig. 3. Nor will the young artist have any doubts of AC' being on the stretch, if he consider whether AD can be replaced by a rope. It cannot, but AC may; and it is therefore not com- pressed, but stretched.
In fig. 10, all the three pieces, AC, AD, and AB, are tied, on the stretch. This is the complete inversion of fig. 3; and the dotted position of AC induces the same changes in the forces AF, AG', as in fig. 3.
Thus have we gone over all the varieties which can happen in the bearings of three pieces on one point. All calculations about the strength of carpentry are reduc- ed to this case; for when more ties or braces meet in a point (a thing that rarely happens), we reduce them to three, by substituting for any two the force which results from their combination, and then combining this with another; and so on.
The young artist must be particularly careful not to mistake the kind of strain that is exerted on any piece of the framing, and suppose a piece to be a brace which is really a tie. It is very easy to avoid all mistakes in this matter by the following rule, which has no excep- tion.
Take notice of the direction in which the piece acts from which the strain proceeds. Draw a line in that direction from the point on which the strain is exerted; and let its length (measured on some scale of equal proportion) express the magnitude of this action in pounds, extension, hundreds, or tons. From its remote extremity draw lines parallel to the pieces on which the strain is exerted. The line parallel to one piece will necessarily cut the other, or its direction produced; if it cut the piece itself, that piece is compressed by the strain, and it is performing the office of a strut or brace; if it cut its direction produced, the piece is stretched, and it is a tie. In short, the strains on the pieces AC, AD, are to be estimated in the direction of the points F and G from the strained point A. Thus, in fig. 3, the up- right piece BA, loaded with the weight B, presses the point A in the direction AE; so does the rope AB in the other figures, or the batten AB in fig. 5.
In general, if the straining piece is within the angle formed by the pieces which are strained, the strains which they sustain are of the opposite kind to that which it exerts. If it be pushing, they are drawing; but if it be within the angle formed by their directions produced, the strains which they sustain are of the same kind. All the three are either drawing or pressing. If the straining piece lie within the angle formed by one piece and the produced direction of the other, its own strain, whether compression or extension, is of the same kind with that of the most remote of the other two, and opposite to that of the nearest. Thus, in fig. 9, where AB is drawing, the remote piece AC is also drawing, while AD is pushing or resisting compression.
In all that has been said on this subject, we have not spoken of any joints. In the calculations with which we are occupied at present, the reliance of joints has no share; and we must not suppose that they exert any force which tends to prevent the angles from changing. The joints are supposed perfectly flexible, or to be like compass joints; the pin of which only keeps the pieces together when one or more of the pieces draws or pulls. The carpenter must always suppose them all compass joints when he calculates the thrusts and draughts of the different pieces of his frames. The strains on joints, and their power to produce or balance them, are of a different kind, and require a very different examination.
Seeing that the angles which the pieces make with each other are of such importance to the magnitude and the proportion of the excited strains, it is proper to find out some way of readily and commodiously conceiving and expressing this analogy.
In general, the strain on any piece is proportional to the straining force. This is evident.
Secondly, the strain on any piece AC is proportional to the sine of the angle which the straining force makes with the other piece directly, and to the sine of the angle which the pieces make with each other inversely.
For it is plain, that the three pressures AE, AF, and AG, which are exerted at the point A, are in the proportion of the lines AE, AF, and FE (because FE is equal to AG). But because the sides of a triangle are proportional to the sines of the opposite angles, the strains are proportional to the sines of the angles AFE, AEF, and FAE. But the sine of AFE is the same with the sine of the angle CAD, which the two pieces AC and AD make with each other; and the sine of AEF is the same with the sine of EAD, which the straining piece BA makes with the piece AC. Therefore we have this analogy, Sin. CAD : Sin. EAD = AE : AF, and AF = AE × Sin. EAD / Sin. CAD. Now the fine of angles are most conveniently conceived as decimal fractions of the radius, which is considered as unity. Thus, Sin. 30° is the same thing with 0.5, or 1/2, and so of others. Therefore, to have the strain on AC, arising from any load AE acting in the direction AE, multiply AE by the sine of EAD, and divide the product by the sine of CAD.
This rule shows how great the strains must be when the angle CAD becomes very open, approaching to 180 degrees. But when the angle CAD becomes very small, its fine (which is our divisor) is also very small; and we should expect a very great quotient in this case also. But we must observe, that in this case the fine of EAD is also very small; and this is our multiplier. In such a case, the quotient cannot exceed unity.
But it is unnecessary to consider the calculation by the tables of sines more particularly. The angles are seldom known any otherwise but by drawing the figure of the frame of carpentry. In this case, we can always obtain the measures of the strains from the same scale, with equal accuracy, by drawing the parallelogram AFCG.
Hitherto we have considered the strains excited at A only as they affect the pieces on which they are exerted. But the pieces, in order to sustain, or be subject to, any strain, must be supported at their ends C and D; and we may consider them as mere intermediaries, by which these strains are made to act on those points of support: Therefore AF and AG are also measures of the forces which press or pull at C and D. Thus we learn the supports which must be found for these points. There may be infinitely various. We shall attend only to such as somehow depend on the framing itself.
Such a structure as fig. 11. very frequently occurs, where a beam BA is strongly pressed to the end of another beam AD, which is prevented from yielding, both because it lies on another beam HD, and because its end D is hindered from sliding backwards. It is indifferent from what this pressure arises: we have represented it as owing to a weight hung on at B, while B is withheld from yielding by a rod or rope hooked to the wall. The beam AD may be supposed at full liberty to exert all its pressure on D, as if it were supported on rollers lodged in the beam HD; but the loaded beam BA presses both on the beam AD and on HD. We wish only to know what strain is borne by AD?
All bodies act on each other in the direction perpendicular to their touching surfaces; therefore the support given by HD is in a direction perpendicular to it. We may therefore supply its place at A by a beam AC, perpendicular to HD, and firmly supported at C. In this case, therefore, we may take AE, as before, to represent the pressure exerted by the loaded beam, and draw EG perpendicular to AD, and EF parallel to it, meeting the perpendicular AC in F. Then AG is the strain compelling AD, and AF is the pressure on the beam HD.
It may be thought, that since we assume as a principle that the mutual pressures of solid bodies are exerted at the directions of their touching surfaces, this balance of pressures, in framings of timbers, depends on the directions of their butting joints: but it does not, as will readily appear by considering the present case.
Let the joint or abutment of the two pieces BA, AD be mitred, in the usual manner, in the direction of AF. Therefore, if AE be drawn perpendicular to AF, it will be the direction of the actual pressure exerted by the loaded beam BA on the beam AD. But the reaction of AD, in the opposite direction AR, will not balance the pressure of BA; because it is not in the direction precisely opposite. BA will therefore slide along the joint, and press on the beam HD. AE represents the load on the mitre joint A. Draw EG perpendicular to AE, and EF parallel to it. The pressure AE will be balanced by the reactions EA and FA; or, the pressure AE produces the pressures AE and AF, of which AF must be resisted by the beam HD, and AE by the beam AD. The pressure AF not being perpendicular to HD, cannot be fully resisted by it; because (by our assumed principle) it acts only in a direction perpendicular to its surface. Therefore draw FA, FI parallel to HD, and perpendicular to it. The pressure AF will be resisted by HD with the force PA; but there is required another force IA, to prevent the beam BA from slipping outwards. This must be furnished by the reaction of the beam DA. In like manner, the other force AE cannot be fully resisted by the beam AD, or rather by the prop D, acting by the intervention of the beam; for the action of that prop is exerted through the beam in the direction DA. The beam AD, therefore, is prefaced to the beam HD by the force AR, as well as by AF. To find what this pressure on HD is, draw EG perpendicular to HD, and EF parallel to it, cutting EG in r. The forces GA and GA will resist, and balance AE.
Thus we see, that the two forces AE and AF, which are equivalent to AE, are equivalent also to AP, AI, AE, and AG. But because AF and AE are equal and parallel, and ER and FI are also parallel, as also ER and FP, it is evident, that IF is equal to rE, or to rF; and IA is equal to rE, or to G. Therefore the four forces... A, A', A", A', A", are equal to AG and AF. Therefore AG is the compression of the beam AD, or the force pressing it on D, and AF is the force pressing it on the beam HD. The proportion of these pressures, therefore, is not affected by the form of the joint.
This remark is important; for many carpenters think the form and direction of the butt joint of great importance; and even the theorist, by not prosecuting the general principle through all its consequences, may be led into an error. The form of the joint is of no importance, in so far as it affects the strains in the direction of the beams; but it is often of great consequence, in respect to its own firmness, and the effect it may have in bringing the piece on which it acts, or being crippled by it.
The same compression of AE, and the same thrust on the point D by the intervention of AD, will obtain, in whatever way the original pressure on the end A is produced. Thus supposing that a chord is made fast at A, and pulled in the direction AE, and with the same force, the beam AD will be equally compressed, and the prop D must react with the same force.
But it often happens that the obliquity of the pressure on AD, instead of compressing it, stretches it; and we desire to know what tension it sustains. Of this we have a familiar example in a common roof. Let the two rafters AC and AD (fig. 12.), press on the tie-beam DC. We may suppose the whole weight to press vertically on the ridge A, as if a weight B were hung on there. We may represent this weight by the portion A b of the vertical or plumb line, intercepted between the ridge and the beam. Then drawing b f and b g parallel to AD and AC, A g and A f will represent the pressures on AC and AD. Produce AC till CH be equal to A f. The point C is forced out in this direction, and with a force represented by this line. As this force is not perpendicularly across the beam, it evidently stretches it; and this extending force must be withstood by an equal force pulling it in the opposite direction. This must arise from a similar oblique thrust of the opposite rafter on the other end D. We concern ourselves only with this extension at present; but we see that the cohesion of the beam does nothing but supply the balance to the extending forces. It must still be supported externally, that it may resist, and, by resisting obliquely, be stretched. The points C and D are supported on the walls, which they press in the directions CK and DO, parallel to A b. If we draw HK parallel to DC, and HT parallel to CK (that is, to A b), meeting DC produced in I, it follows from the composition of forces, that the point C would be supported by the two forces KC and IC. In like manner, making DN = A g, and completing the parallelogram DMNO, the point D would be supported by the forces OD and MD. If we draw g o and f k parallel to DC, it is plain that they are equal to NO and CK, while A o and A k are equal to DO and CK, and A b is equal to the sum of DO and CK (because it is equal to A o + A k). The weight of the roof is equal to its vertical pressure on the walls.
Thus we see, that while a pressure on A, in the direction A b, produces the strains A f and A g, on the pieces AC and AD, it also excites a strain CI or DM in the piece DC. And this completes the mechanism of a frame; for all derive their efficacy from the triangles of which they are composed, as will appear more clearly as we proceed.
But there is more to be learned from this. The external consideration of the strains on the two pieces AD and DC, by the action of a force at A, only showed them frame, as the means of propagating the same strains in their own direction to the points of support. But, by adding the strains exerted in DC, we see that the frame becomes an intermediate, by which exertions may be made on other bodies, in certain directions and proportions; so that this frame may become part of a more complicated one, and, as it were, an element of its constitution. It is worth while to ascertain the proportion of the pressures CK and DO, which are thus exerted on the walls. The similarity of triangles gives the following analogies:
\[ \frac{DO}{DM} = \frac{Ab}{bD} \]
\[ CI, \text{or } DM : CK = Cb : Ab \]
Therefore \( DO : CK = Cb : bD \).
Or, the pressures on the points C and D, in the direction of the straining force A b, are reciprocally proportional to the portions of DC intercepted by A b.
Also, since \( Ab = DO + CK \), we have
\[ Ab : CK = Cb + bD \text{ (or } CD) : bD, \text{ and } \]
\[ Ab : DO = CD : bC. \]
In general, any two of the three parallel forces A b, DO, CK, are to each other in the reciprocal proportion of the parts of CD, intercepted between their directions and the direction of the third.
And this explains a still more important office of the frame ADC. If one of the points, such as D, be supported, an external power acting at A, in the direction A b, and with an intensity which may be measured by A b, may be set in equilibrium, with another acting at C, in the direction CL, opposite to CK or A b, and with an intensity represented by CK: for since the pressure CH is partly withstood by the force IC, or the firmness of the beam DC supported at D, the force KC will complete the balance. When we do not attend to the support at D, we conceive the force A b to be balanced by KC, or KC to be balanced by A b. And, in like manner, we may neglect the support or force acting at A, and consider the force DO as balanced by CK.
Thus our frame becomes a lever, and we are able to trace the interior mechanical procedure which gives it a lever, its efficacy: it is by the intervention of the forces of cohesion, which connect the points to which the external forces are applied with the supported point or fulcrum, and with each other.
These strains or pressures A b, DO, and CK, not being in the directions of the beams, may be called transverse. We see that by their means a frame of carpentry may be considered as a solid body; but the example which brought this to our view is too limited for explaining the efficacy which may be given to such constructions. We shall therefore give a general proposition, which will more distinctly explain the procedure of nature, and enable us to trace the strains as they are propagated through all the parts of the most complicated framing, finally producing the exertion of its most distant points.
We presume that the reader is now pretty well habituated to the conception of the strains as they are propagated along the lines joining the points of a frame, and we shall therefore employ a very simple figure. Let the strong lines ACBD (fig. 13.) represent a frame of carpentry. Suppose that it is pulled at the point A by a force acting in the direction AE, but that it rests on a fixed point C, and that the other extreme point B is held back by a power which resists in the direction BF. It is required to determine the proportion of the strains excited in its different parts, the proportion of the external pressures at A and B, and the pressure which is produced on the obstacle or fulcrum C.
It is evident that each of the external forces at A and B tend one way, or to one side of the frame, and that each would cause it to turn round C if the other did not prevent it; and that if, notwithstanding their action, it is turned neither way, the forces in actual exertion are in equilibrium by the intervention of the frame. It is no less evident that these forces concur in pressing the frame on the prop C. Therefore, if the piece CD were away, and if the joints C and D be perfectly flexible, the pieces CA, CB would be turned round the prop C, and the pieces AD, DB would also turn with them, and the whole frame change its form. This shows, by the way, and we desire it to be carefully kept in mind, that the firmness or stiffness of framing depends entirely on the triangles bounded by beams which are contained in it. An open quadrilateral may always change its shape, the sides revolving round the angles. A quadrilateral may have an infinity of forms, without any change of its sides, by merely pushing two opposite angles towards each other, or drawing them farther. But when the three sides of a triangle are determined, its shape is also invariably determined; and if two angles be held fast, the third cannot be moved. It is thus that, by inserting the bar CD, the figure becomes unchangeable; and any attempt to change it by applying a force to an angle A, immediately excites forces of attraction or repulsion between the particles of the stuff which form its sides. Thus it happens, in the present instance, that a change of shape is prevented by the bar CD. The power at A presses its end against the prop; and in doing this it puts the bar AD on the stretch, and also the bar DB. Their places might therefore be supplied by cords or metal wires. Hence it is evident that DC is compressed, as is also AC; and, for the same reason, CB is also in a state of compression; for either A or B may be considered as the point that is impelled or withheld. Therefore DA and DB are stretched, and are resisting with attractive forces. DC and CB are compressed, and are resisting with repulsive forces. DB is also acting with repulsive forces, being compressed in like manner; and thus the support of the prop, combined with the firmness of DC, puts the frame ABCD into the condition of the two frames in fig. 8. and fig. 9. Therefore the external force at A is really in equilibrium with an attracting force acting in the direction AD, and a repulsive force acting in the direction AK. And since all the connecting forces are mutual and equal, the point D is pulled or drawn in the direction DA. The condition of the point B is similar to that of A, and D is also drawn in the direction DB. Thus the point D, being urged by the forces in the directions DA and DB, presses the beam DC on the prop, and the prop resists in the opposite direction. Therefore the line DC is the diagonal of the parallelogram, whose sides have the proportion of the forces which connect D with A and B. This is the principle on which the rest of our investigation proceeds. We may take DC as the representation and measure of their joint effect. Therefore draw CH, CG, parallel to DA, DB. Draw HL, GO, parallel to CA, CB, cutting AE, BF in L and O, and cutting DA, DB in I and M. Complete the parallelograms ILKA, MONB. Then DG and AI are the equal and opposite forces which connect A and D; for GD = CH = AI. In like manner DH and BM are the forces which connect D and B.
The external force at A is in immediate equilibrium with the combined forces, connecting A with D and with C. AI is one of them; Therefore AK is the other; and AL is the compound force with which the external force at A is in immediate equilibrium. This external force is therefore equal and opposite to AL. In like manner, the external force at B is equal and opposite to BO; and AL is to BO as the external force at A to the external force at B. The prop C resists with forces equal to those which are propagated to it from the points D, A, and C. Therefore it resists with forces CH, CG, equal and opposite to DG, DH; and it resists the compressions KA, NB, with equal and opposite forces CL, CN. Draw KL, no parallel to AD, BD, and draw CIQ, CO P: it is plain that KCH is a parallelogram equal to KAI, and that CI is equal to AL. In like manner CO is equal to BO. Now the forces CK, CH, exerted by the prop, compose the force CI; and CN, CG compose the force CO. These two forces CI, CO are equal and parallel to AL and BO; and therefore they are equal and opposite to the external forces acting at A and B. But they are (primitively) equal and opposite to the pressures (or at least the compounds of the pressures) exerted on the prop, by the forces propagated to C from A, D, and B. Therefore the pressures exerted on the prop are the same as if the external forces were applied there in the same directions as they are applied to A and B. Now if we make CV, CZ equal to CI and CO, and complete the parallelogram CVYZ; it is plain that the force YC is in equilibrium with IC and OC. Therefore the pressures at A, C, and B, are such as would balance if applied to one point.
Lastly, in order to determine their proportions, draw CS and CR perpendicular to DA and DB. Also draw Ad, Bf perpendicular to CQ and CP; and draw Cg, Ci perpendicular to AE, BF.
The triangles CPR and BPf are similar, having a common angle P, and a right angle at R and f.
In like manner the triangles CPS and AQd are similar. Also the triangles CHR, CGS are similar, by reason of the equal angles at H and G, and the right angles at R and S. Hence we obtain the following analogies:
\[ \frac{CO}{CP} = \frac{On}{PB} = \frac{CG}{PB} \] \[ \frac{CP}{CR} = \frac{PB}{fB} \] \[ \frac{CR}{CS} = \frac{CH}{CG} \] \[ \frac{CS}{CQ} = \frac{Ad}{AQ} \] \[ \frac{CQ}{CI} = \frac{AQ}{Kl} = \frac{AQ}{CH} \]
Therefore, by equality,
\[ \frac{CO}{CI} = \frac{Ad}{fB} \] or \( \frac{BO}{AL} = \frac{Cg}{CI} \)
That is, the external forces are reciprocally proportional. This proposition (sufficiently general for our purpose) is fertile in consequences, and furnishes many useful instructions to the artist. The strains LA, OB, CY, that are excited, occur in many, we may say in all, framings of carpentry, whether for edifices or engines, and are the sources of their efficacy. It is also evident, that the doctrine of the transverse strength of timber is contained in this proposition; for every piece of timber may be considered as an assemblage of parts connected by forces which act in the direction of the lines which join the strained points on the matter which lies between those points, and also act on the rest of the matter, exciting those lateral forces which produce the inflexibility of the whole. See Strength of Materials, Encycl.
Thus it appears that this proposition contains the principles which direct the artist to frame the most powerful levers; to secure uprights by shores or braces, or by ties and ropes; to secure scaffoldings for the erection of spires, and many other most delicate problems of his art. He also learns, from this proposition, how to ascertain the strains that are produced, without his intention, by pieces which he intended for other offices, and which, by their transverse action, put his work in hazard. In short, this proposition is the key to the science of his art.
We would now counsel the artist, after he has made the tracing of the strains and thrusts through the various parts of a frame familiar to his mind, and even amused himself with some complicated fancy framings, to read over with care the articles Strength of Materials and Roof in the Encyclopedia Britannica. He will now conceive its doctrines much more clearly than when he was considering them as abstract theories. The mutual action of the woody fibres will now be easily comprehended, and his confidence in the results will be greatly increased.
There is a proposition (no. 19, in the article Roof) which has been called in question by several very intelligent persons; and they say that Belidor has demonstrated, in his Science des Ingénieurs, that a beam firmly fixed at both ends is not twice as strong as when simply lying on the props, and that its strength is increased only in the proportion of 2 to 3; and they support this determination by a list of experiments recited by Belidor, which agree precisely with it. Belidor also says, that Pito had the same result in his experiments. These are respectable authorities; but Belidor's reasoning is anything but demonstration; and his experiments are described in such an imperfect manner, that we cannot build much on them. It is not said in what manner the battens were secured at the ends, any farther than that it was by chevalets. If by this word is meant a trefoil, we cannot conceive how they were employed; but we see it sometimes used for a wedge or key. If the battens were wedged in the holes, their resistance to fracture may be made what we please; they may be loose, and therefore resist little more than when simply laid on the props. They may be (and probably were) wedged very tight, and bruised or crippled.
Our proposition mentioned distinctly the security given to the ends of the beams. They were mortised into remote posts. Our precise meaning was, that they were simply kept from rising by these mortises, but at full liberty to bend up between E and I, and between G and K. Our assertion was not made from theory alone (although we think the reasoning incontrovertible), but was agreeable to numerous experiments made in those precise circumstances. Had we mortised the beams firmly into two very stout posts, which could not be drawn nearer to each other by bending, the beam would have borne a much greater weight, as we have verified by experiment. We hope that the following mode of conceiving this case will remove all doubts.
Let LM be a long beam (fig. 14.) divided into five equal parts, in the points D, B, A, C, E. Let it be firmly supported at L, B, C, M. Let it be cut thro' at A, and have compass joints at B and C. Let FB, GC be two equal uprights, resting on B and C, but without any connection. Let AH be a similar and equal piece, to be occasionally applied at the seam A. Now let a thread or wire AGE be extended over the piece GC, and made fast at A, G, and E. Let the same thing be done on the other side of A. If a weight be now laid on at A, the wires AFD, AGE will be strained, and may be broken. In the instant of fracture we may suppose their strains to be represented by AF and
(a) The learned reader will perceive, that this analogy is precisely the same with that of forces which are in equilibrium by the intervention of a lever. In fact, this whole frame of carpentry is nothing else than a built or framed lever in equilibrium. It is acting in the same manner as a solid, which occupies the whole figure compressed in the frame, or as a body of any size and shape whatever that will admit the three points of application A, C, and B. It is always in equilibrium in the case first stated; because the pressure produced at B by a force applied to A is always such as balances it. The reader may also perceive, in this proposition, the analysis or tracing of those internal mechanical forces which are indispensible requisite for the functions of a lever. The mechanicians have been extremely puzzled to find a legitimate demonstration of the equilibrium of a lever ever since the days of Archimedes. Mr Vince has the honour of first demonstrating, most ingeniously, the principle assumed by Archimedes, but without sufficient ground, for his demonstration; but Mr Vince's demonstration is only a putting the mind into that perplexed state which makes it acknowledge the proposition, but without a clear perception of its truth. The difficulty has proceeded from the abstract notion of a lever, conceiving it as a mathematical line—inflexible, without reflecting how it is inflexible—for the very source of this indispensible quality furnishes the mechanical connection between the remote pressures and the fulcrum; and this supplies the demonstration (without the least difficulty) of the desperate case of a straight lever urged by parallel forces. See Rotation, no. 11. Encycl. and A.g. Complete the parallelogram, and A.a is the magnitude of the weight. It is plain that nothing is concerned here but the cohesion of the wires; for the beam is sawed through at A, and its parts are perfectly moveable round B and C.
Instead of this process apply the piece AH below A, and keep it there by fastening the same wire BHC over it. Now lay on a weight. It must press down the ends of BA and CA, and cause the piece AH to strain the wire BHC. In the instant of fracture of the same wire, its resistances H.b and H.c must be equal to A.f and A.g, and the weight b.H which breaks them must be equal to A.a.
Lastly, employ all the three pieces FB, AH, GC, with the same wire attached as before. There can be no doubt but that the weight which breaks all the four wires must be = a.A + b.H, or twice A.a.
The reader cannot but see that the wires perform the very same office with the fibres of an entire beam I.M held fast in the four holes D, E, C, and E, of some upright posts.
In the experiments for verifying this, by breaking slender bars of fine deal, we get complete demonstration, by measuring the curvatures produced in the parts of the beam thus held down, and comparing them with the curvature of a beam simply laid on the props B and C; and there are many curious inferences to be made from these observations, but we have not room for them in this place.
We may observe, by the way, that we learn from this case, that purlins are able to carry twice the load when notched into the rafters that they carry when mortised into them, which is the most usual manner of framing them. So would the binding joists of floors; but this would double the thickness of the flooring. But this method should be followed in every possible case, such as breast timbers, lintels over several pillars, &c. These should never be cut off and mortised into the sides of every upright; numberless cases will occur which show the importance of the maxim.
We must here remark, that the proportion of the spaces BC and CM, or BC and J.B, has a very sensible effect on the strength of the beam BC; but we have not yet satisfied our minds as to the rationale of this effect. It is undoubtedly connected with the serpentine form of the curve of the beam before fracture. This should be attended to in the construction of the springs of carriages. These are frequently supported at a middle point (and it is an excellent practice), and there is a certain proportion which will give the easiest motion to the body of the carriage. We also think that it is connected with that deviation from the best theory observable in Buffon's experiments on various lengths of the same scantling. The force of the beams diminished much more than in the inverse proportion of their lengths.
We have seen that it depends entirely on the position of the pieces in respect of their points of ultimate support, and of the direction of the external force which produces the strains, whether any particular piece is in a state of extension or of compression. The knowledge of this circumstance may greatly influence us in the choice of the construction. In many cases we may substitute slender iron rods for massive beams, when the piece is to act the part of a tie. But we must not invert this disposition; for when a piece of timber acts as a strut, and is in a state of compression, it is next to certain that it is not equally compressible in its opposite sides through the whole length of the piece, and that the compressing force on the abutting joint is not acting in the most equable manner all over the joint. A very trifling inequality in either of these circumstances (especially in the first) will compress the beam more on one side than on the other. This cannot be without the beam's bending, and becoming concave on that side on which it is most compressed. When this happens, the frame is in danger of being crushed, and soon going to ruin. It is therefore indispensably necessary to make use of beams in all cases where struts are required of considerable length, rather than of metal rods of slender dimensions, unless in situations where we can effectually prevent their bending, as in trussing a girder internally, where a cast iron strut may be firmly cased in it, so as not to bend in the smallest degree. In cases where the pressures are enormous, as in the very oblique struts of a centre or arch frame, we must be particularly cautious to do nothing which can facilitate the compression of either side. No mortises should be cut near to one side; no lateral pressures, even the slightest, should be allowed to touch it. We have seen a pillar of fir 12 inches long and one inch in section, when loaded with three tons, snap in an instant when pressed on one side by 16 pounds, while another bore 4½ tons without hurt, because it was inclosed (loosely) in a stout pipe of iron.
In such cases of enormous compression, it is of great importance that the compressing force bear equally on the whole abutting surface. The German carpenters are accustomed to put a plate of lead over the joint. This prevents, in some measure, the penetration of the end fibres. Mr. Perrotot, the celebrated French architect, formed his abutments into arches of circles, the centre of which was the remote end of the strut. By this contrivance the unavoidable change of form of the triangle made no partial bearing of either angle of the abutment. This always has a tendency to splinter off the heel of the beam where it presses strongest. It is a very judicious practice.
When circumstances allow it, we should rather employ ties than struts for securing a beam against lateral strains. When an upright pillar, such as a flag-staff, a mast, or the uprights of a very tall scaffolding, are to be hoisted up, the dependence is more certain on those braces that are stretched by the strain than on those which are compressed. The scaffolding of the iron bridge near Sunderland had some ties very judiciously disposed, and others with less judgment.
We should proceed to consider the transverse strains as they affect the various parts of a frame of carpentry; but we have very little to add to what has been said already in the article Strength of Materials (Encyc.) and in the article Roof. What we shall add in this article will find a place in our occasional remarks on different works. It may, however, be of use to recall to the reader's memory the following propositions.
1. When a beam AB (fig. 15,) is firmly fixed at the general end A, and a straining force acts perpendicularly to its length at any point B, the strain occasioned at any section C between B and A is proportional to CB, and may therefore be represented by the product W×CB; that is, by the product of the number of tons, pounds, &c. which measure the straining force, and the number of feet, inches, &c. contained in CB. As the loads on a beam are easily conceived, we shall substitute this for any other straining force.
1. If the strain or load is uniformly distributed along any part of the beam lying beyond C (that is, further from A), the strain at C is the same as if the load were all collected at the middle point of that part; for that point is the centre of gravity of the load.
2. The strain on any section D of a beam AB (fig. 16.) resting freely on two props A and B, is \( w \times \frac{AD \times DB}{AB} \) (see Roof, n° 19. and Strength of Materials, n° 92, &c. Encycl.) Therefore,
3. The strain on the middle point, by a force applied there, is one fourth of the strain which the same force would produce, if applied to one end of a beam of the same length, having the other end fixed.
4. The strain on any section C of a beam, resting on two props A and B, occasioned by a force applied perpendicularly to another point D, is proportional to the rectangle of the exterior segments, or is equal to \( w \times \frac{AC \times DB}{AB} \). Therefore
The strain at C occasioned by the pressure on D, is the same with the strain at D occasioned by the same pressure on C.
5. The strain on any section D, occasioned by a load uniformly diffused over any part EF, is the same as if the two parts ED, DF of the load were collected at their middle points e and f. Therefore
The strain on any part D, occasioned by a load uniformly distributed over the whole beam, is one-half of the strain that is produced when the same load is laid on at D; and
The strain on the middle point C, occasioned by a load uniformly distributed over the whole beam, is the same which half that load would produce if laid on at C.
7. A beam supported at both ends on two props B and C (fig. 14.), will carry twice as much when the ends beyond the props are kept from rising, as it will carry when it rests loosely on the props.
8. Lastly, the transverse strain on any section, occasioned by a force applied obliquely, is diminished in the proportion of the sine of the angle which the direction of the force makes with the beam. Thus, if it be inclined to it in an angle of thirty degrees, the strain is one half of the strain occasioned by the same force acting perpendicularly.
On the other hand, the relative strength of a beam, or its power in any particular section to resist any transverse strain, is proportional to the absolute cohesion of the section directly, to the distance of its centre of effort from the axis of fracture directly, and to the distance from the strained point inversely.
Thus in a rectangular section of the beam, of which b is the breadth, d the depth (that is, the dimension in the direction of the straining force), measured in inches, and f the number of pounds which one square inch will just support without being torn asunder, we must have \( f \times b \times d^2 \), proportional to \( w \times CB \) (fig. 15.). Or, \( f \times b \times d^2 \), multiplied by some number m, depending on the nature of the timber, must be equal to \( w \times CB \). Or, in the case of the section C of fig. 16., that is strained by the force \( w \) applied at D, we must have \( m \times f \times b \times d^2 = w \times \frac{AC \times DB}{AB} \). Thus if the beam is of found oak, m is very nearly \( \frac{1}{2} \) (see Strength of Materials, n° 116, Encycl.) Therefore we have \( \frac{f \times b \times d^2}{9} = w \times \frac{AC \times CB}{AB} \).
Hence we can tell the precise force \( w \) which any section C can just resist when that force is applied in any way whatever. For the above mentioned formula gives \( w = \frac{f \times b \times d^2}{9 \times CB} \), for the case represented by fig. 15. But
the case represented in fig. 16., having the straining force applied at D, gives the strain at C (\( w = f \times \frac{b \times d^2 \times AB}{9 \times AC \times CB} \)).
Example. Let an oak beam, four inches square, rest freely on the props A and B, seven feet apart, or 84 inches. What weight will it just support at its middle point C, on the supposition that a square inch rod will just carry 16,000 pounds, pulling it asunder?
The formula becomes \( w = \frac{16000 \times 4 \times 16 \times 84}{9 \times 42 \times 42} \)
or \( w = \frac{86016000}{15876} = 5418 \) pounds. This is very near what was employed in Buffon's experiment, which was 5312.
Had the straining force acted on a point D, half way between C and B, the force sufficient to break the beam at C would be \( \frac{16000 \times 4 \times 16 \times 84}{9 \times 42 \times 24} = 10836 \) lbs.
Had the beam been found red fir, we must have taken \( f = 10,000 \) nearly, and \( m \) nearly 8; for although fir be less cohesive than oak in the proportion of 5 to 8 nearly, it is less compressible, and its axis of fracture is therefore nearer to the concave side.
Having considered at sufficient length the strains of joints of different kinds which arise from the form of the parts of a frame of carpentry, and the direction of the external forces which act on it, whether considered as impelling or as supporting its different parts, we must now proceed to consider the means by which this form is to be secured, and the connections by which those strains are excited and communicated.
The joinings practised in carpentry are almost infinitely various, and each has advantages which make it preferable in some circumstances. Many varieties are employed merely to please the eye. We do not concern ourselves with these: Nor shall we consider those which are only employed in connecting small works, and can never appear on a great scale; yet even in some of these, the skill of the carpenter may be discovered by his choice; for in all cases, it is wise to make every, even the smallest, part of his work as strong as the materials will admit. He will be particularly attentive to the changes which will necessarily happen by the shrinking of timber as it dries, and will consider what dimensions of his framing will be affected by this, and what will not; and will then dispose the pieces which are least essential to the strength of the whole, in such a manner that their tendency to shrink shall be in the same direction with the shrinking of the whole framing. If he do otherwise, the seams will widen, and parts will be split asunder. He will dispose his boardings in such a manner as to contribute to the stiffness of the whole, avoiding at the same time the giving them positions which will produce lateral strains on truss beams which bear great pressures; recollecting, that although a single board has little force, yet many united have a great deal, and may frequently perform the office of very powerful struts.
Our limits confine us to the joinings which are most essential for connecting the parts of a single piece of a frame when it cannot be formed of one beam, either for want of the necessary thickness or length; and the joints for connecting the different sides of a trussed frame.
Much ingenuity and contrivance has been bestowed on the manner of building up a great beam of many thicknesses, and many singular methods are practised as great novelties by different artists; but when we consider the manner in which the cohesion of the fibres performs its office, we will clearly see that the simplest are equally effectual with the most refined, and that they are less apt to lead us into false notions of the strength of the assemblage.
Thus, were it required to build up a beam for a great lever or a girder, so that it may act nearly as a beam of the same size of one log—it may either be done by plain joggling, as in fig. 17, A, or by scarfing, as in fig. 17, B or C. If it is to act as a lever, having the gudgeon on the lower side at C, we believe that most artists will prefer the form B and C; at least this has been the case with nine-tenths of those to whom we have proposed the question. The bell informed only hesitated; but the ordinary artists were all confident in its superiority; and we found their views of the matter very coincident. They considered the upper piece as grasping the lower in its hooks; and several imagined that, by driving the one very tight on the other, the beam would be stronger than an entire log; but if we attend carefully to the internal procedure in the loaded lever, we shall find the upper one clearly the strongest. If they are formed of equal logs, the upper one is thicker than the other by the depth of the joggling or scarfing, which we suppose to be the same in both; consequently, if the cohesion of the fibres in the intervals is able to bring the uppermost filaments into full action, the form A is stronger than B, in the proportion of the greater distance of the upper filaments from the axis of the fracture: this may be greater than the difference of the thickness, if the wood is very compressible. If the gudgeon be in the middle, the effect, both of the joggles and the scarfings, is considerably diminished; and if it is on the upper side, the scarfings act in a very different way. In this situation, if the loads on the arms are also applied to the upper side, the joggled beam is still more superior to the scarfed one. This will be best understood by resolving it in imagination into a trussed frame. But when a gudgeon is thus put on that side of the lever which grows convex by the strain, it is usual to connect it with the rest by a powerful strap, which embraces the beam, and causes the opposite point to become the resisting point. This greatly changes the internal actions of the filaments, and, in some measure, brings it into the same state as the first, with the gudgeon below. Were it possible to have the gudgeon on the upper side, and to bring the whole into action without a strap, it would be the strongest of all; because, in general, the resistance to compression is greater than to extension. In every situation the joggled beam has the advantage; and it is the easiest executed.
We may frequently gain a considerable accession of strength by this building up of a beam; especially if the part which is stretched by the strain be of oak, and the other part be fir. Fir being so much superior to oak as a pillar (if Muffchenbrock's experiments may be considered), and oak so much preferable as a tie, this construction seems to unite both advantages. But we shall see much better methods of making powerful levers, girders, &c., by trussing.
Observe, that the efficacy of both methods depends entirely on the difficulty of canting the piece between the cross joints to slide along the timber to which it adheres. Therefore, if this be moderate, it is wrong to make the notches deep; for as soon as they are too deep that their ends have a force sufficient to push the fibre along the line of junction, nothing is gained by making them deeper; and this requires a greater expenditure of timber.
Scarlings are frequently made oblique, as in fig. 18, but we imagine that this is a bad practice. It begins to yield at the point, where the wood is crippled and splintered off, or at least bruised out a little; as the pressure increases, this part, by squeezing broader, causes the solid parts rise to a little upwards, and gives them some tendency, not only to push their antagonists along the base, but even to tear them up a little. For similar reasons, we disapprove of the favourite practice of many artists, to make the angles of their scarfings acute, as in fig. 19. This often causes the two pieces to tear each other up. The abutments should always be perpendicular to the directions of the pressures. Let it be forgotten in its proper place, we may extend this injunction also to the abutments of different pieces of a frame, and recommend it to the artist even to attend to the shrinking of the timbers by drying. When two timbers abut obliquely, the joint should be most full at the obtuse angle of the end; because, by drying, that angle grows more obtuse, and the beam would then be in danger of splintering off at the acute angle.
It is evident, that the nicest work is indispensible in necessary in building up a beam. The parts must abut not on each other completely, and the smallest play or void takes away the whole efficacy. It is usual to give the butt joint a small taper to one side of the beam, so that they may require moderate blows of a maul to force them in, and the joints may be perfectly close when the external surfaces are even on each side of the beam. But we must not exceed in the least degree; for a very taper wedge has great force; and if we have driven the pieces together by very heavy blows, we leave the whole in a state of violent strain, and the abutments are perhaps ready to splinter off by a small addition of pressure. This is like too severe a proof for artillery; which, though not sufficient to burst the pieces, has weakened them to such a degree, that the strain of ordinary service is sufficient to complete the fracture. The workman is tempted to exceed in this, because it smooths off and conceals all uneven seams; but he must be watched. It is not unusual to leave some abutments open enough to admit a thin wedge reaching through Nor is this a bad practice, if the wedge is of materials which is not compressed by the driving or the strain of service. Iron would be preferable for this purpose, and for the joggles, were it not that by its too great hardness it cripples the fibres of timber to some degree. In consequence of this, it often happens that, in beams which are subjected to deflatory and sudden strains (as in the levers of reciprocating engines), the joggles or wedges widen the holes, and work themselves loose: Therefore skilful engineers never admit them, and indeed as few bolts as possible, for the same reason; but when resisting a steady or dead pull, they are not improper, and are frequently used.
Beams are built up, not only to increase their dimensions in the direction of the strain (which we have hitherto called their depth), but also to increase their breadth or the dimensions perpendicular to the strain. We sometimes double the breadth of a girder, which is thought too weak for its load, and where we must not increase the thickness of the flooring. The mast of a great ship of war must be made bigger athwartship, as well as fore and aft. This is one of the nicest problems of the art; and professional men are by no means agreed in their opinions about it. We do not presume to decide; and shall content ourselves with exhibiting the different methods.
The most obvious and natural method is that shown in fig. 20. It is plain that (independent of the connection of cross bolts, which are used in them all when the beams are square) the piece C cannot bend in the direction of the plane of the figure without bending the piece D along with it. This method is much used in the French navy; but it is undoubtedly imperfect. Hardly any two great trees are of equal quality, and swell or shrink alike. If C shrinks more than D, the feather of C becomes loose in the groove wrought in D to receive it; and when the beam bends, the parts can slide on each other like the plates of a coach spring; and if the bending is in the direction ef, there is nothing to hinder this sliding but the bolts, which soon work themselves loose in the bolt-holes.
Fig. 21. exhibits another method. The two halves of the beam are tabled into each other in the same manner as in fig. 17. It is plain that this will not be affected by the unequal swelling or shrinking, because this is insensible in the direction of the fibres; but when bent in the direction ab, the beam is weaker than fig. 20. bent in the direction ef. Each half of fig. 20. has, in every part of its length, a thickness greater than half the thickness of the beam. It is the contrary in the alternate portions of the halves of fig. 21. When one of them is bent in the direction AB, it is plain that it drags the other with it by means of the cross buttments of its tables, and there can be no longitudinal sliding. But unless the work is accurately executed, and each hollow completely filled up by the table of the other piece, there will be a lateral slide along the cross joints sufficient to compensate for the curvature; and this will hinder the one from compressing or stretching the other in conformity to this curvature.
The imperfection of this method is so obvious, that it has seldom been practised; but it has been combined with the other, as is represented in fig. 22, where the beams are divided along the middle, and the tables in each half are alternated, and alternate also with the tables of the other half. Thus 1, 3, 5, are prominent, and 2, 4, 6, are depressed. This construction evidently puts a stop to both slides, and obliges every pair of both pieces to move together. ab and cd show sections of the built-up beam corresponding to AB and CD.
No more is intended in this practice by any intelligent artist, than the causing the two pieces to act together in all their parts, although the strains may be unequally distributed on them. Thus, in a building girder, the binding joints are frequently morticed into very different parts of the two sides. But many seem to aim at making the beam stronger than if it were of one piece; and this inconsiderate project has given rise to many whimsical modes of tabling and fastening, which we need not regard.
The practice in the British dock yards is somewhat different from any of these methods. The pieces are methodically joined as in fig. 22, but the tables are not thin parallel prisms, but thin prisms. The two outward joints on visible beams are straight lines, and the table rises gradually to its greatest thickness in the axis. In like manner, the hollow for receiving the opposite tables, sinks gradually from the edge to its greatest depth in the axis. Fig. 23. represents a section of a round piece of timber built up in this way, where the full line EFGH is the section corresponding to AB of fig. 22, and the dotted line EGFR is the section corresponding to CD.
This construction, by making the external seam straight, leaves no lodgement for water, and looks much fairer to the eye; but it appears to us that it does not give such firm hold when the mast is bent in the direction EH. The exterior parts are most stretched and most compressed by this bending; but there is hardly any abutment in the exterior parts of these tables. In the very axis, where the abutment is the firmest, there is little or no difference of extension and compression.
But this construction has an advantage, which we imagine much more than compensates for these imperfections, at least in the particular case of a round mast: it will draw together by hooping incomparably better than any of the others. If the cavity be made somewhat too shallow for the prominence of the tables, and if this be done uniformly along the whole length, it will make a somewhat open seam; and this opening can be regulated with the utmost exactness from end to end by the plane. The heart of those vast trunks is very sensibly softer than the exterior circles; therefore, when the whole is hooped, and the hoops hard driven, and at considerable intervals between each fell —we are confident that all may be compressed till the seam disappears; and then the whole makes one piece, much stronger than if it were an original log of that size, because the middle has become, by compression, as solid as the crust, which was naturally firmer, and resisted further compression. We verified this beyond a doubt, by hooping a built stick of a timber which has this inequality of firmness in a remarkable degree, and it was nearly twice as strong as another of the same size.
Our mastmakers are not without their fancies and whimsies; and the manner in which our masts and yards... are generally built up, is not near so simple as fig. 25; but it consists of the same essential parts, acting in the very same manner, and derives all its efficacy from the principles which are here employed.
This construction is particularly suited to the situation and office of a ship's mast. It has no bolts; or, at least, none of any magnitude, or that make very important parts of its construction. The most violent strains perhaps that it is exposed to, is that of twisting, when the lower yards are close braced up by the force of many men acting by a long lever. This form resists a twist with peculiar energy: it is therefore an excellent method for building up a great shaft for a mill. The way in which they are usually built up is by reducing a central log to a polygonal prism, and then filling it up to the intended size by planting pieces of timber along its sides, either spiking them down, or cocking them into it by a feather, or joggling them by slips of hard wood sunk into the central log and into the slips. N.B. Joggles of elm are sometimes used in the middle of the large tables of masts; and when sunk into the firm wood near the surface, they must contribute much to the strength. But it is very necessary to employ wood not much harder than the pine; otherwise it will soon enlarge its bed, and become loose; for the timber of these large trunks is very soft.
The most general reason for piecing a beam is to increase its length. This is frequently necessary, in order to procure tie-beams for very wide roofs. Two pieces must be scarfed together.—Numberless are the modes of doing this; and almost every master carpenter has his favourite method. Some of them are very ingenious: but here, as in other cases, the most simple are commonly the strongest. We do not imagine that any, of the most ingenious, is equally strong with a tie consisting of two pieces of the same scantling laid over each other for a certain length, and firmly bolted together. We acknowledge that this will appear an artless and clumsy tie-beam; but we only say that it will be stronger than any that is more artificially made up of the same thickness of timber. This, we imagine, will appear sufficiently certain.
The simplest and most obvious scarfing (after the one now mentioned) is that represented in fig. 24, n° 1. and 2. If considered merely as two pieces of wood joined, it is plain that, as a tie, it has but half the strength of an entire piece, supposing that the bolts (which are the only connections) are fast in their holes. No 2. requires a bolt in the middle of the scarf to give it that strength; and, in every other part, is weaker on one side or the other.
But the bolts are very apt to bend by the violent strain, and require to be strengthened by uniting their ends by iron plates; in which case it is no longer a wooden tie. The form of n° 1. is better adapted to the office of a pillar than n° 2.; especially if its ends be formed in the manner shewn in the elevation n° 3. By the fully given to the ends, the scarf resists an effort to bend it in that direction. Besides, the form of n° 2., is unsuitable for a post; because the pieces, by sliding on each other by the pressure, are apt to splinter off the tongue which confines their extremity.
Fig. 25. and 26. exhibit the most approved form of a scarf, whether for a tie or for a post. The key presented in the middle is not essentially necessary; the two pieces might simply meet square there. This form, without a key, needs no bolts (although they strengthen it greatly); but, if worked very true and close, and with square abutments, will hold together, and will resist bending in any direction. But the key is an ingenious and a very great improvement, and will force the parts together with perfect tightness. The same precaution must be observed that we mentioned on another occasion, not to produce a constant internal strain on the parts by overdriving the key. The form of fig. 25. is by far the best; because the triangle of 26. is much easier splintered off by the strain, or by the key, than the square wood of 25. It is far preferable for a post, for the reason given when speaking of fig. 24. n° 1. and n° 2. Both may be formed with a fall at the ends equal to the breadth of the key. In this shape fig. 25. is vastly well suited for joining the parts of the long corner posts of spires and other wooden towers. Fig. 25. n° 2. differs from n° 1. only by having three keys. The principle and the longitudinal strength are the same. The long scarf of n° 2. tightened by the three keys, enables it to resist a bending much better.
None of these scarfed tie-beams can have more than one-third of the strength of an entire piece, unless with the affluence of iron plates; for if the key be made thinner than one-third, it has less than one-third of the fibres to pull by.
We are convinced, therefore, that when the heads of the bolts are connected by plates, the simple form of fig. 24. n° 1. is stronger than those more ingenious scarfings. It may be strengthened against lateral bending by a little tongue, or by a fall; but it cannot have both.
The strongest of all methods of piecing a tie-beam would be to set the parts end to end, and grasp them between other pieces on each side, as in fig. 27. This is what the ship carpenter calls fishking a beam; and is a frequent practice for occasional repairs. Mr Perronet used it for the tie-beams or stretchers, by which he connected the opposite feet of a centre, which was yielding to its load, and had pushed aside one of the piers above four inches. Six of these not only withstood a strain of 1800 tons, but, by wedging behind them, he brought the feet of the truss 2½ inches nearer. The stretchers were 14 inches by 11 of found oak, and could have withstood three times that strain. Mr Perronet, fearing that the great length of the bolts employed to connect the beams of these stretchers would expose them to the risk of bending, scarfed the two side pieces into the middle piece. The scarfing was of the triangular kind (Traité de Jupiter), and only an inch deep, each face being two feet long, and the bolt passed through close to the angle.
In piecing the pump rods, and other wooden stretchers of great engines, no dependence is had on scarfing; and the engineer connects everything by iron straps. We doubt the propriety of this, at least in cases where the bulk of the wooden connection is not inconvenient. These observations must suffice for the methods employed for connecting the parts of a beam; and we now proceed to consider what are more usually called the joints of a piece of carpentry.
Where the beams stand square with each other, and square the joints— The strains are also square with the beams, and in the plane of the frame, the common mortise and tenon is the most perfect junction. A pin is generally put through both, in order to keep the pieces united, in opposition to any force which tends to part them. Every carpenter knows how to bore the hole for this pin, so that it shall draw the tenon tight into the mortise, and cause the shoulder to butt close, and make neat work; and he knows the risk of tearing out the bit of the tenon beyond the pin, if he draw it too much. We may just observe, that square holes and pins are much preferable to round ones for this purpose, bringing more of the wood into action, with less tendency to split it. The ship carpenters have an ingenious method of making long wooden bolts, which do not pass completely through, take a very fast hold, though not nicely fitted to their holes, which they must not be, lest they should be crippled in driving. They call it "football wedging." They stick into the point of the bolt a very thin wedge of hard wood, so as to project a proper distance; when this reaches the bottom of the hole by driving the bolt, it splits the end of it, and squeezes it hard to the side. This may be practised with advantage in carpentry. If the ends of the mortise are widened inwards, and a thin wedge be put into the end of the tenon, it will have the same effect, and make the joint equal to a dovetail. But this risks the splitting the piece beyond the shoulder of the tenon, which would be unsightly. This may be avoided as follows: Let the tenon T, fig. 28, have two very thin wedges a and c fixed in near its angles, projecting equally: at a very small distance within these, put in two shorter ones b, d, and more within these if necessary. In driving this tenon, the wedges a and c will take first, and split off a thin slice, which will easily bend without breaking. The wedges b, d, will act next, and have a similar effect, and the others in succession. The thickness of all the wedges taken together must be equal to the enlargement of the mortise toward the bottom.
When the strain is transverse to the plane of the two beams, the principles laid down in n° 85, 86, of the article Strength of Materials, will direct the artist in placing his mortise. Thus the mortise in a girder for receiving the tenon of a binding joint of a floor should be as near the upper side as possible, because the girder becomes concave on that side by the strain. But as this exposes the tenon of the binding-joint to the risk of being torn off, we are obliged to mortise farther down. The form (fig. 29.) generally given to this joint is extremely judicious. The sloping part a b gives a very firm support to the additional bearing c d, without much weakening of the girder. This form should be copied in every case where the strain has a similar direction.
The joint that most of all demands the careful attention of the artist, is that which connects the ends of beams, one of which pushes the other very obliquely, putting it into a state of extension. The most familiar instance of this is the foot or a rafter pressing on the tie-beam, and thereby drawing it away from the other wall. When the direction is very oblique (in which case the extending strain is the greatest), it is difficult to give the foot of the rafter such a hold of the tie-beam as to bring many of its fibres into the proper action. There would be little difficulty if we could allow the end of the tie-beam to project to a small distance beyond the foot of the rafter; but, indeed, the dimensions which are given to tie-beams, for other reasons, are always sufficient to give enough of abutment when judiciously employed. Unfortunately this joint is much exposed to failure by the effects of the weather. It is much exposed, and frequently perishes by rot, or becomes so soft and friable that a very small force is sufficient, either for pulling the filaments out of the tie beam, or for crumbling them together. We are therefore obliged to secure it with particular attention, and to avail ourselves of every circumstance of construction.
One is naturally disposed to give the rafter a deep hold by a long tenon; but it has been frequently observed in old roofs that such tenons break off. Frequently they are observed to tear up the wood that is above them, and push their way through the end of the tie-beam. This in all probability arises from the first faggoting of the roof, by the compression of the rafters and of the head of the king post. The head of the rafter descends, the angle with the tie-beam is diminished by the rafter revolving round its step in the tie-beam. By this motion the heel or inner angle of the rafter becomes a fulcrum to a very long and powerful lever much loaded. The tenon is the other arm, very short, and being still fresh, it is therefore very powerful. It therefore forces up the wood that is above it, tearing it out from between the cheeks of the mortise, and then pushes it along. Carpenters have therefore given up long tenons, and give to the toe of the tenon a shape which abuts firmly, in the direction of the thrust, on the solid bottom of the mortise, which is well supported on the under side by the wall plate. This form has the further advantage of having no tendency to tear up the end of the mortise. This form is represented in fig. 30. The tenon has a small portion a b cut perpendicular to the surface of the tie-beam, and the rest b c is perpendicular to the rafter.
But if the tenon is not sufficiently strong (and it is not so strong as the rafter, which is thought not to be stronger than is necessary), it will be crushed, and then the rafter will shade out along the surface of the beam. It is therefore necessary to call in the assistance of the whole rafter. It is in this distribution of the strain among the various abutting parts that the varieties of joints and their merits chiefly consist. It would be endless to describe every nostrum, and we shall only mention a few that are most generally approved of.
The aim in fig. 31. is to make the abutments exactly perpendicular to the thrusts. It does this very perfectly; and the share which the tenon and the shoulder forms, have of the whole may be what we please, by the portion of the beam that we notch down. If the wall plate lie duly before the heel of the rafter, there is no risk of straining the tie across or breaking it, because the thrust is made direct to that point where the beam is supported. The action is the same as against the joggle on the head or foot of a king post. We have no doubt but that this is a very effectual joint. It is not, however, much practised. It is said that the sloping beam at the shoulder lodges water; but the great reason seems to be a secret notion that it weakens the tie-beam. If we consider the direction in which it acts as a tie, we must acknowledge that this form takes the best method for bringing the whole of it into action.
Fig. 32. exhibits a form that is more general, but certainly worse. What part of the thrust that is not borne by the tenon acts obliquely on the joint of the shoulder, and gives the whole a tendency to rise up and slide outward.
The shoulder joint is sometimes formed like the dotted line \(abcdefg\) of fig. 32. This is much more agreeable to the true principle, and would be a very perfect method, were it not that the intervals \(bd\) and \(df\) are so short that the little wooden triangles \(bed\) and \(def\) will be easily pushed off their bases \(bd, df\).
Fig. 33. seems to have the most general approbation. It is the joint recommended by Price (page 7.), and copied into all books of carpentry as the true joint for a rafter foot. The visible shoulder joint is flush with the upper surface of the tie beam. The angle of the tenon at the tie nearly bisects the obtuse angle formed by the rafter and the beam, and is therefore somewhat oblique to the thrust. The inner shoulder \(ac\) is nearly perpendicular to \(bd\). The lower angle of the tenon is cut off horizontally as at \(ed\). Fig. 34. is a section of the beam and rafter foot, shewing the different shoulders.
We do not perceive the peculiar merit of this joint. The effect of the three oblique abutments \(ab, ac, ed\) is undoubtedly to make the whole bear on the outer end of the mortise, and there is no other part of the tie-beam that makes immediate resistance. Its only advantage over a tenon extending in the direction of the thrust is, that it will not tear up the wood above it. Had the inner shoulder had the form \(eei\), having its face \(ic\) perpendicular, it would certainly have acted more powerfully in stretching many filaments of the tie-beam, and would have had much less tendency to force out the end of the mortise. The little bit \(ei\) would have prevented the sliding upwards along \(ee\). At any rate, the joint \(ab\) being flush with the beam, prevents any tendible abutment on the shoulder \(ac\).
Fig. 33. No. 2. is a simpler, and in our opinion a preferable, joint. We observe it practised by the most eminent carpenters for all oblique thrusts; but it rarely employs less of the cohesion of the tie-beam than might be used without weakening it, at least when it is supported on the other side by the wall plate.
Fig. 33. No. 3. is also much practised by the first carpenters.
Fig. 35. is proposed by Mr Nicholson (page 65.) as preferable to fig. 33. No. 3. because the abutment of the inner part is better supported. This is certainly the case; but it supposes the whole rafter to go to the bottom of the socket, and the beam to be thicker than the rafter. Some may think that this will weaken the beam too much, when it is no broader than the rafter is thick; in which case they think that it requires a deeper socket than Nicholson has given it. Perhaps the advantages of Nicholson's construction may be had by a joint like fig. 35. No. 2.
Whatever is the form of these butting joints, great care should be taken that all parts bear alike, and the be attended artist will attend to the magnitude of the different surfaces. In the general compression, the greater surfaces will be less compressed, and the smaller will therefore change most. When all has settled, every part should be equally close. Because great logs are moved with difficulty, it is very troublesome to try the joint frequently to see how the parts fit; therefore we must expect less accuracy in the interior parts. This should make us prefer those joints whose efficacy depends chiefly on the visible joint.
It appears from all that we have said on this subject, that a very small part of the cohesion of the tie-beam is sufficient for withstanding the horizontal thrust of a roof, even though very low pitched. If therefore no other use is made of the tie-beam, one much slenderer may be used, and blocks may be firmly fixed to the ends, on which the rafters might abut, as they do on the joggles on the head and foot of a king post. Although a tie-beam has commonly floors or ceilings to carry, and sometimes the workshops and store-rooms of a theatre, and therefore requires a great scantling, yet there frequently occur in machines and engines very oblique stretchers, which have no other office, and are generally made of dimensions quite inadequate to their situation, often containing ten times the necessary quantity of timber. It is therefore of importance to ascertain the most perfect manner of executing such a joint. We have directed the attention to the principles that are really concerned in the effect. In all hazardous cases, the carpenter calls in the assistance of iron straps; and they are frequently necessary, even in roofs, notwithstanding this superabundant strength of the tie-beam. But this is generally owing to bad construction of the wooden joint, or to the failure of it by time. Straps will be considered in their place.
There needs but little to be said of the joints at a joggle worked out of solid timber; they are not near so difficult as the last. When the size of a log will allow the joggle to receive the whole breadth of the abutting brace, it ought certainly to be made with a square shoulder; or, which is still better, an arch of a circle, having the other end of the brace for its centre. Indeed this in general will not sensibly differ from a straight line perpendicular to the brace. By this circular form, the settling of the roof makes no change in the abutment; but when there is not sufficient stuff for this, we must avoid bevel joints at the shoulders, because they always tend to make the brace slide off. The brace in fig. 36. must not be joined as at \(a\), but as at \(b\), or some equivalent manner. Observe the joints at the head of the main posts of Drury Lane theatre, fig. D.
When the very oblique action of one side of a frame of carpentry does not extend but compresses the piece on which it abuts (as in fig. 11.), there is no difficulty in the joint. Indeed a joining is unnecessary, and it is enough that the pieces shut on each other; and we have only to take care that the mutual pressure be equally borne by all the parts, and that it do not produce lateral pressures, which may cause one of the pieces to slide on the butting joint. A very slight mortise and tenon is sufficient at the joggle of a king post with a rafter or framing beam. It is best, in general, to make the butting plane, bisecting the angle formed by the sides, or else perpendicular to one of the pieces. In fig. 36. No. 2., where the framing beam \(ab\) cannot slip away from the pressure, the joint \(a\) is preferable to \(b\), or indeed After having attempted to give a systematic view of the principles of framing carpentry, we shall conclude by giving some examples which will illustrate and confirm the foregoing principles.
Fig. 38. is the roof of the chapel of the Royal Hospital at Greenwich, constructed by Mr S. Wyatt.
| A.A. | Is the tie-beam, 57 feet long, spanning | |------|-------------------------------------| | | 14 by 12 | | C.C. | Queen posts | | D.D. | Braces | | E.E. | Truss beam | | F.F. | Straining piece | | G.G. | Principal rafters | | H.H. | A cambered beam for the platform | | B.B. | An iron string supporting the tie-beam |
The trusses are 7 feet apart, and the whole is covered with lead, the boarding being supported by horizontal ledgers 4, 6, or 6 by 4 inches.
This is a beautiful roof, and contains less timber than most of its dimensions. The parts are all disposed with great judgment. Perhaps the iron rod is unnecessary; but it adds great stiffness to the whole.
The iron straps at the rafter feet would have had more effect if not so oblique. Those at the head of the posts are very effective.
We may observe, however, that the joints between the straining beam and its braces are not of the best kind, and tend to bruise both the straining beam and the truss beam above it.
Fig. 39. the roof of St Paul's, Covent Garden, constructed by Mr Wapshot in 1796.
| A.A. | Tie-beam spanning 30 feet 2 inches | |------|-----------------------------------| | B.B. | Queen post | | C.C. | Truss beam | | D.D. | King post (at the joggle) | | E.E. | Brace | | F.F. | Principal brace (at bottom) | | H.H. | Principal rafter (at bottom) | | S.S. | Studs supporting the rafter |
This roof far exceeds the original one put up by Inigo Jones. One of its trusses contains 198 feet of timber. One of the old roof had 273, but had many inactive timbers, and others ill disposed. (N.B. The figure which we gave of it in the article Roof, copied from Price, is very erroneous). The internal truss P.C.F. is admirably contrived for supporting the exterior rafters, without any pressure on the far projecting ends of the tie-beam. The former roof had bent them greatly, so as to appear unsightly.
We think that the camber (six inches) of the tie-beam is rather hurtful; because by settling, the beam lengthens; and this must be accompanied by a considerable sinking of the roof. This will appear by calculation.
Fig. 40. the roof of Birmingham theatre, constructed by Mr Geo. Saunders. The span is 80 feet clear, and the trusses are 10 feet apart.
| A.A. | Is an oak corbel | |------|------------------------------------| | B.B. | Inner plate | | C.C. | Wall plate | | D.D. | Pole plate |
As for those that are necessary for the turning joints of great engines constructed of timber, they make no part of the art of carpentry. This roof is a fine specimen of British carpentry, and is one of the boldest and lightest roofs in Europe. The straining fill Q gives a firm abutment to the principal braces, and the space between the posts is 19 feet wide, affording roomy workshops for the carpenters and other workmen connected with a theatre. The contrivance for taking double hold of the wall, which is very thin, is excellent. There is also added a beam (marked R), bolted down to the tie-beams. The intention of this was to prevent the total failure of to hold a trussing, if any of the tie-beams should fail at the end by rot.
Akin to this roof is fig. 41, the roof of Drury Lane theatre, 80 feet 3 inches in the clear, and the trusses 15 feet apart, constructed by Mr. Edward Grey Saunders.
The main beams are trussed in the middle space with oak trusses 5 inches square. This was necessary for its width of 32 feet, occupied by the carpenters, painters, &c. The great space between the trusses afford good store-rooms, dressing rooms, &c.
It is probable that this roof has not its equal in the world for lightness, stiffness, and strength. The main truss is so judiciously framed, that each of them will safely bear a load of near 300 tons; so it is not likely that they will ever be quarter loaded. The division of the whole into three parts makes the exterior roofing very light. The struts are admirably kept from the walls, and the walls are even firmly bound together by the roof. They also take off the dead weight from the main truss one-third.
The intelligent reader will perceive that all these roofs are on one principle, depending on a truss of three pieces and a straight tie-beam. This is indeed the great principle of a truss, and is a step beyond the roof with two rafters and a king post. It admits of much greater variety of forms, and of greater extent. We may see, that even the middle part may be carried to any space, and yet be flat at top; for the truss-beam may be supported in the middle by an inverted king post (of timber, not iron), carried by iron or wooden ties from its extremities: And the same ties may carry the horizontal tie-beam K; for till K be torn asunder, or M, M, and P be crippled, nothing can fail.
The roof of St Martin's church in the Fields is constructed on good principles, and every piece properly disposed. But although its span does not exceed 40 feet from column to column, it contains more timber in a truss than there is in one of Drury Lane theatre. The roof of the chapel at Greenwich, that of St Paul's, Covent Garden, that of Birmingham, and that of Drury Lane theatres, form a series gradually more perfect. Such specimens afford excellent lessons to the artists. We therefore account them a useful present to the public.
There is a very ingenious project offered to the public by Mr. Nicholson (Carpenter's Assistant, p. 68.) He proposes iron rods for king posts, queen posts, and all other situations where beams perform the office of ties. This is in prosecution of the notions which we published in the article Roof of the Encyclopædia (see no. 36, 37.) He receives the feet of the braces and trusses in a socket very well connected with the foot of his iron king post; and he secures the feet of his queen posts from being pulled inwards, by interposing a straining fill. He does not even mortise the foot of his principal rafter into the end of the tie-beam, but sets it in a socket like a shoe, at the end of an iron bar, which is bolted into the tie-beam a good way back. All the parts are formed and disposed with the precision of a person thoroughly acquainted with the subject; and we have not the smallest doubt of the success of the project, and the complete security and durability of his roofs, and we expect to see many of them executed. We abound in iron, but we must send abroad for building timber. This is therefore a valuable project; at the same time, however, let us not over-rate its value. Iron is but about 12 times stronger than red fir, and is more than 12 times heavier; nor is it cheaper, weight for weight, or strength for strength.
Our illustrations and examples have been chiefly taken from roofs, because they are the most familiar instances of the difficult problems of the art. We could have wished for more room even on this subject. The construction of dome roofs has been (we think) mistaken, and the difficulty is much less than is imagined. We mean in respect of strength; for we grant that the obliquity of the joints, and a general intricacy, increases the trouble of workmanship exceedingly. Another opportunity may perhaps occur for considering this subject. Wooden bridges form another class equally difficult and important; but our limits are already overpassed, and will not admit them. The principle on which they should all be constructed, without exception, is that of a truss, avoiding all lateral bearings on any of the timbers. In the application of this principle, we must farther remark, that the angles of our truss should be as acute as possible; therefore we should make it of as few and as long pieces as we can, taking care to prevent the bending of the truss beams by bridles, which embrace them, but without pressing them to either side. When the truss consists of many pieces, the angles are very obtuse; and the thrusts increase nearly in the duplicate proportion of the number of angles. The proper maxims will readily occur to the artist who considers with attention the specimens of centres or coombs, which we shall give in the article Centre.
With With respect to the frames of carpentry which occur in engines and great machines, the varieties are such that it would require a volume to treat of them properly. The principles are already laid down; and if the reader be really interested in the study, he will engage in it with seriousness, and cannot fail of being instructed. We recommend to his consideration, as a specimen of what may be done in this way, the working beam of Hornblower's steam engine (see Steam Engine, no. 84. Encycl.) When the beam must act by chains hung from the upper end of arch heads, the framing there given seems very scientifically constructed; at the same time, we think that a strap of wrought iron, reaching the whole length of the upper bar (see the figure), would be vastly preferable to those partial plates which the engineer has put there; for the bolts will soon work loose.
But when arches are not necessary, the form employed by Mr Watt is vastly preferable, both for simplicity and for strength. It consists of a simple beam AB (fig. 42.), having the gudgeon C on the upper side. The two piston rods are attached to wrought iron joints A and B. Two strong struts DC, EC rest on the upper side of the gudgeon, and carry an iron string ADE, consisting of three pieces, connected with the struts by proper joints of wrought iron. A more minute description is not needed for a clear conception of the principle. No part of this is exposed to a cross strain; even the beam AB might be sawed through at the middle. The iron string is the only part which is stretched; for AC, DC, EC, BC, are all in a state of compression. We have made the angles equal, that all may be as great as possible, and the pressure on the struts and strings a minimum. Mr Watt makes them much lower, as A'deB, or A'c'B. But this is for economy, because the strength is almost insuperable. It might be made with wooden fittings; but the workmanship of the joints would more than compensate the cheapness of the materials.
We offer this article to the public with deference; conclusions and we hope for an indulgent reception of our essay on a subject which is in a manner new, and would require much study. We have bestowed our chief attention on the strength of the construction, because it is here that persons of the profession have the most scanty information. We beg them not to consider our observations as too refined, and that they will study them with care. One principle runs through the whole; and when that is clearly conceived and familiar to the mind, we venture to say that the practitioner will find it of easy application, and that he will improve every performance by a continual reference to it.
If this attempt to instruct our most valuable and much esteemed artists shall appear to meet with their approbation, it may encourage us to engage in the serious task of composing a system on the subject. But this is a great work, and will require much time and liberal contribution of knowledge from the eminent carpenters who do honour to this country by their works.