132 



THE CIVIL ENGINEER AND ARCHITECTS JOtTRNAL. 



[May 



career. Bio^aphical notices of architects we most undeniably 

 have, yet scarcely anythinf? really deservinf? tlie name of architec- 

 tural biography, — nothinp: written in e.rtenno and fully developed. 

 Passing over other studies which are strangely claimed for the ar- 

 chitect, Iwill point out what, although overlooked,! myself conceive 

 to be very essential qualifications — I say essential, not indis])ensable, 

 — because daily experience convinces us that dispensed with they 

 are. Now I sliould say that talent for Invention and Contrivance 

 stJinds almost foremost among the qualifications for an architect. 

 Without it, he can be little more than a barren copier,— the crea- 

 ture of comme-il-fuut routine ; a very respectable automaton, but 

 not an artist. If we care only for mechanical skiU and excellence, 

 let us boldly say so at once, and desist from that maudlin, namby- 

 pamby prating' about architecture as art, — except it be just that 

 brevet grade of the latter, by virtue of which tailoring and 

 cookery claim to be enrolled among the so-called arts. For the 

 display of other talent and merits, the opportunities are compara- 

 tively few ; but those for tlie exercise of Contrivance are con- 

 tinually presenting themselves. It is wliat so far from requiring 

 favourable circumstances, is most of all called into operation by 

 disadvantageous ones, and by difficulties and untoward circum- 

 stances which, by a little exercise of it, might be overcome, not 

 only sufficiently well, but even happily, and so as to be productive 

 of both conveniences and beauties that would not have been 

 thought of but for the obstacles which prevent compliance with 

 usual matter-of-course proceeding. A taste for and acquaintance 

 with art generally, as well as his own particular branch of it, is also 

 highly desirable, if not indispensable, for the architect — a taste not 

 so much, perhaps, expressly for painting and sculpture tliemselves, 

 as for pictorial and sculpturesque decoration ; and as regards an 

 eye for colour, effect, and various combinations of form. 



ON THE STABILITY OF ARCHES. 



On the Stahilitii of Arches, with practical methods for determining, 

 according to the Pressures to which they will be subjected, the best form of 

 Section, or variable depth of Voussoir, for any given Intrados or Estra- 

 das. By George Snell, Assoc. Inst. C.E. — (From a paper read at 

 the Institution of Civil Engineers.) 



The first section of this paper treats of the general conditions of 

 stability in structures composed of many blocks of materials, as 

 walls, arches, &c. The second and third sections discuss the con- 

 ditions of stability of an arch, the form of which and the pressures 

 sustained by it, as regards position, direction, and amount, are 

 similar on either side of the crown of the arch ; such as an arch 

 sustaining its own weight only, or that of a symmetrical super- 

 structure. In the second section the arch is supposed to be formed 

 of blocks of an incompressible material; but in the third section 

 the limited strength of materials is taken into consideration. The 

 fourth section discusses the conditions of stability of an arch, acted 

 upon by forces of any.,amount, applied in any position and direction 

 in the plane of the section, or of an arch whose form is not similar 

 on both sides of the crown. 



The effect of the adliesion of the cement is not taken in any case 

 into consideration. 



Section I. 



Art. 1. — A structure built of blocks of stone or other material, 

 as A B C D, diagram 1, may yield under the pressure to which it is 

 subjected ; first, by the slipi)iug of certain of its surfaces of contact 



Dlagra m 1. Diagram 2. Diagram 3. Diagram 4. Diagram 5. 



one upon another, as diagram 2; — secondly, by the blocks turning 

 over on e upon the edge of another, as diagram 3 ;— or thirdly, by 



the yielding of the materials of which the structure is composed, 

 as diagram 4'. For the first effect to take place, it is necessary 

 tliat the resultant V„, of the pressure P,, on one of the blocks A, 

 and weight of A, should act in a direction inclined to a perpendi- 

 cular drawn from the surfaces of contact, at an angle greater than 

 L A R, the "limiting angle of resistance" of those surfaces. For 

 example, if the materials are calcareous oolite, this angle, LA R, 

 is 36° 30' ; and if, as in diagi-am 2, the direction of the resultant is 

 moi'e inclined from the perpendicular than this angle, failure vvill 

 take place, from tlie one block slipping on the other. 



For the second effect to take place, the resultant pressure must 

 act in a direction which passes without the joint, as in diagram 3. 

 The third effect depends, first, on the strength of the material ; 

 secondly, on the amount of the resultant pressure ; and thirdly, on 

 the position and direction of that pressure. Thus the material 

 may be capable of sustaining the pressure, if it acts through the 

 axis of the stone; the pressure in that case being equally distri- 

 buted over the whole surface of contact ; but if tlie direction of 

 the pressure approaches very closely to one of the edges, so that 

 one portion of the block sustains a much greater pressure per 

 square inch than another, then the material may yield and failure 

 ensue, as in diagram 4. 



If, however, none of the resultant pressures Pj Pj P^ P5, dia- 

 gram 5, fulfil any of the above conditions, that is, if none are in- 

 clined from a periiendicular to the surface of contact at an angle 

 greater than the limiting angle of resistance of those surfaces, nor 

 fall without the joint, nor approach so near to the edge as to cause 

 the material to yield, then the structure will withstand the pres- 

 sure P,. Also, if instead of the pressure P,, the structure be acted 

 on by a pressure;),, and the resultants p^ p^ p^ p^, do none of them 

 fulfil any of the conditions of failure, it will withstand tliis pres- 

 sure. In like manner, an endless variety of pressures, or systems 

 of pressures, may be sustained by the structure, each giving a dif- 

 ferent series of resultants on the successive joints. 



Art. 2. — If any other joints are made in the structure, the posi- 

 tion and direction of the resultant pressures on them, also, must be 

 drawn and examined, before the stability of the arch is determined ; 

 if, however, a curve such as that in diagram 5 could be traced, the 

 property of which curve should be, that at any point in it the 

 tangent should represent the position and direction of the resultant 

 pressure, as the arrows P^ P., P4 P5, which are tangents to the 

 curve, and which also show the position and direction of the re- 

 sultants ; then if no part of this curve passed without the structure, 

 or so near to the edges of it, as to cause the material to yield, the 

 structure would be stable, however numerous, or in whatever di- 

 rection the joints might be, provided that the perpendicular from 

 the joint were inclined to the tangent to the curve, at an angle less 

 than the limiting angle of resistance. This curve is known as the 

 "line of resistance,' and its properties were discussed for the 

 first time by Professor Moseley, in essays published in the " Cam- 

 bridge Philosophical Transactions ;"* it can be traced by applica- 

 tion of difficult mathematical analysis, as shown in the fourth part 

 of the " Jlechanical Principles of ("ivil Engineering and Architec- 

 ture," p. 403. If, however, the resultant pressures are determined 

 for a series of joints, the line of resistance can be traced with suffi- 

 cient accuracy from joint to joint, by means of a bent whalebone, 

 or a metal spring, or by hand as in diagram 5. 



Art. 3. Problem 1. — To find the position, direction, and amount 

 of the resultant pressure on every joint of a structure, the result- 

 ant pressure on one of the blocks being given in position, direc- 

 tion, and amount, and the specific gravity of the material forming 

 the structure being also known. 



Diagram 6 represents a structure of seven blocks of stone, or 

 other material, the pressure on the first block being 80 cwt., and 

 its position and direction represented by the arrow ; it is required 

 to determine the position, direction, and amount of the resultant 

 pressures on all the other blocks. 



Construct a scale of equal parts, each part to represent one cwt., 

 or one pound, &c., as may be convenient. In this figure each 

 equal part represents one cwt. Calculate the weight of each stone 

 (in this example, if the first block weighs 15 cwt., the weight of the 

 others are as figured on them in the diagram). 



Find the centres of gravity of the blocks : {they are indicated in 

 this and the follnwing diagrams by this mark + ). 



Then the pressures on the second block are, first, the weight of 

 the first block := 15 cwt., which may be represented by a pressure 

 of 15 cwt. acting vertically downwards through the centre of gra- 

 vity of the block ; draw the line W,, representing the position 

 and direction of this pressure : secondly, the pressure on the first 

 block, which acts in the direction and position indicated by the 



* Vide Pliil. Trans., Cambridge, Toi. v. p. 293 ; voi. vi. p. 463. 



