BRIDGE. 



505 



hrory. ofenquiry. It depends intimately upon the corpuscular 

 v action: of the particles of stone; subject Ofl which, we 

 regret to say, that our information has been hitherto 

 very scanty. The writers of this article have, at pre- 

 sent, a series of experiments in some forwardness, which 

 will thniw much light on this, as well aa on many other 

 dt; of architecture. Meanwhile, that we may 



not disappoint the reader by leaving the subject un- 

 touched, we shall endeavour to draw some information 

 respecting it, from the present state of our knowledge, 

 and the dimensions of structures already existing. 



The question evidently depends on the amount of 

 the tangential pressure. At the crown this is the 

 horizontal thrust. We shall suppose all the joints 

 to be duly drawn to equilibration, the sections fairly 

 abutting on each other, and no weakness arising from 

 aciue angles. 



Stone, it is said, will carry from 250,000 to 

 850,000 tt) avoirdupois per foot square, and brick 

 300,000ft. They have been made practically to 

 carry of this, and even more. The pillar in the 

 cu 1 ^ of the Chapter House at Elgin carries up- 

 wards of 40,000 lt< on the square foot, and there was 

 formerly a heavy lead roof on it. It is a red sand 

 stone, and has borne this pressure for centuries. 



We shall therefore take 50,000 lt> per foot as a 

 load, which may be safely laid on every square foot 

 in the arch. A cubic foot of stone weighs about 160 fb 

 per foot ; and brick weighs less. Suppose, there- 

 fore, the arch to be one foot thick at the crown, and 

 the keystone one cubic foot, it will bear a horizontal 

 thrust of 50,000 Jb, that is, 312* times its weight. 



But, 50,000 : 160 :: R : Tang. 1 1' 0" 3"', which will 

 be the angle of the key-stone in that case. So that 

 an arch of 312^ feet radius, or a semicircular arch of 

 6'25 feet span, might bear to have a key-stone of a 

 foot deep, without risking its being crushed more 

 than in structures which have already stood for many 

 years. And this may be called the limit of stone 

 arch building ; for if we double the depth of the stone, 

 we will thereby double the weight also, and its ratio 

 to the horizontal thrust will still be the same. In- 

 deed this limit does not much exceed what has been 

 actually executed. A considerable portion of the 

 bridge of Neuilly is an arch of 250 feet radius ; and 

 Gautier mentions a platband in the church of the 

 Jesuits at Nismes, the camber of which, after set- 

 tling, would make it a portion of an arch of 280 feet 

 radius. The length or span is 26^ French feet, the rise 

 only 4 inches, and therefore the diameter of its circle 

 would be 560 English feet. 



This singularly bold platband was made under the 

 conduct of Pere Mourgues, after the design of Cubi- 

 sol, an able architect. The stones are 1 foot thick, 

 their depth is 2 feet towards the key, and 2 feet 4 

 inches at each end. It had a camber given it of about 

 (J or 7 inches, and descended near 3 inches on striking 

 the centres. (Gantier. ) 



We see, that the horizontal pressure does not de- 

 termine the vertical thickness of the arch-rtone. But 

 as we pass down the arch, it is plain that the butting 

 surfaces must increase, in proportion to the increasing 

 tangential pressure. 



At sixty degrees from the vertex, granting that 



YOL. IT. PART II. 



the arch is equilibrated, the depth of the arch-stones 'i 



must be doubled ; and though tin n be ' "\p~~~ 



carried no farther, yet, at the :-.|>riii.;ir ; or hoi / >utal 

 joint, a small increase will l ;. The 



ratio will soon be found. To the square of the 

 weight of the semi-arch, add the square of the hori- 

 zontal thrust, the square root of the sum is the pres- 

 sure at the springing. If we divide this by the hori- 

 zontal thrust, it will give the thickness at the spring- 

 ing, compared with that which is necessary at the 

 crown. Or if we divide it by 312J, it will give the 

 smallest depth of joint which should be used at the 

 springing. The thrust and weight are supposed to 

 be given in solid feet. If given in pounds, divide the 

 above quotient by 160, or divide at once by 50,000. 

 Example. Required the thickness of the lower 

 joints for a semicircular arch, when the weight of a 

 section of a foot in breadth from the crown of the 

 arch to the springing is 60,000 Ib, and the horizontal 

 thrust is 20,000 lt>, which answers nearly to a 60 

 feet arch, 4 feet thick at the crown. 



60 20 50,000)63,250( 



60 20 -j^265 feet, 



StiOO 400 or I foot 3f inches nearly ; of 



400 course the vertical section, or 



key stone, might be only 

 -S-=f of a foot, or 4f 

 inches, if it were necessary so 

 to reduce it. 



4000(63.25 

 36 



123)400 

 369 



310 &c. 



For another example, take a 50 feet arch, having 

 5 feet thickness at crown. The semi-arch may be 

 found sufficiently near, by multiplying the half span 

 into the half height to the road, viz. 25 X I5=-C." 

 And the horizontal thrust 5 X 25=125 feet of stone, 

 375 1 =140600, 125'=13625, their sum is 156250, 

 the square root of which, divided by 312^, gives 

 1.265, or 1 foot 3 inches; and here again the verti- 

 cal section might be - , or 44 inches only. 

 3121- 



If we calculate upon the same principles, the depth 

 of arch stone at the spring course of a semi-circle of 

 100 feet span, 10 feet thick at crown, we shall 

 find it to be 5 feet, and at the crown the depth may 

 be 19 inches. In the great arches of the bridge of 

 Neuilly, the thickness at the crown is about 4 feet 8 

 inches, the span 128.2 feet, and height 32. The ho- 

 rizontal thrust is great, the crown being drawn with, 

 a radius of 150 feet ; consequently this arch would 

 require a depth at springing of about 4 feet. But 

 when the centre was struck, the crown of this arch 

 descended 23 inches, which has rendered it a portion 

 of a much larger circle, and has greatly increased 

 the horizontal thrust. After all, the pressure at 

 the springing is scarcely greater than in the last 

 example, and the depth of joint there need not 

 have exceeded 5 feet. It is nearly three times that, 

 and even at the crown the thickness is i greater 

 than the increased thrust would require. We trust, 

 therefore, that, in spite of the great risk this singular 

 arch has run, it may yet long remain a monument of 

 the skill and boldness of the able architect who de- 

 signed it. 



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