172 



THE CIVIL ENGINEER AND ARCHITECFS JOURNAL. 



[June, 



Virgin and the Sacrament respectively. In the south aisle are three con- 

 fessional* and the saoristy, and above the south arches in the chancel is 

 the tribune. The light will be obtainid from the east and west windows 

 and from clerestories in the north and south walls. It is worthy of notice 

 that the tracery of no two windows is alike, though the patterns of all 

 of them are extremely rich : the design of the east window espei ially may 

 be safely compared with some of the noblest examples of ancient Deco- 

 rated architecture. With respect, however, to the absence of north and 

 south windows below those of the clerestory, we have already siven a ge- 

 neral and distinct opinion. Our views on this subject have been so recent- 

 ly delailed that we need not now say more than that the examination of 

 the churih which we are describing suggested uoihini; which would modify 

 our opinion. On the contrary, we can state positively that the elTect of 

 the light thrown down from above by no means harmonises with the cha- 

 racter of the church, and that the large surfaces of blank unbroken walls 

 are great defects. We say this the more freely because the excellence 

 of the general design is sufficiently great to afford some drawbacks, and 

 twcause the architect may justly plead the difficulties of the site as an 

 excuse. 



Parts of the interior walls will be plastered and painted with frescoes. 

 This use of plaster is perfectly legitimate, for there is not the slightest 

 pretension of making it look like masonry ; it reveals itself honestly in its 

 true character— that of a ground surface for the pniniing. No deceptive 

 materials whatever are employed in the church. The external masonry is 

 •f Kentish rag ; the mouldings, window-muUions, piers, &c., of Bath 



•tone. 



There is a temporary brick wall at the west-end : this is about to be 

 removed for the purpose of completing the west gable, which will display 

 three windows, with a door b-low the central window, and a trilateral 

 window near the vertex of the gable. There will also be a bell-turret at 

 this end of the church in addition to that now existing over the^ chancel 

 arch. The roofs incline to the horizontal at an angle of about 00° ; on the 

 north and south sides of them are rich perforated parapets. 



We hope to be able hereafter to give a more complete account of the 

 cturch, and to accompany the description by illustrations. 



NOTES ON ENGINEERING, 

 V. 



MENAI TUBULAR BRIDGE. 



Since the former paper (see ante p. 100), on the application of the theory 

 of the strength of beams to the case of the Tubular bridge was published, 

 » report has appeared of experiments by Messrs. Hodgkinson and Fair- 

 bairn, with reference to this particular subject. As far as analogy can be 

 drawn between the method of those experiments and the investigation of 

 which the present paper is a continuation, the results agree exactly. It 

 will be observed however that the experiments had reference solely to the 

 ultimate strength of the girders experimented npon-that is, to the ex- 

 treme weight which they would bear before breaking, the present investi- 

 gation however relates not so much to the strength of the girders as to the 

 ttrain which they must have to bear; and as the results here arrived at 

 are obtained from the fundamental laws of statics, and not from any as. 

 •umptions respecting the nature of the bodies operated upon, the points of 

 resemblance between this theoretical examination and the reported experi- 

 ments are few. It has seemed sufficient in the present paper to point out 

 the precise nature and amount of the forces which the metal will have to 

 resist ; leaving it to the engineer to contrive the proper means of fultilling 

 Ite requirements here pointed out. 



We now proceed with the subject from the point where we left it in the 



former paper. 



5. Form of the Girder of uniform strength. 

 When the girder is of uniform strength throughout, the strain on it is 

 greatest at the centre for two reasons. First, from the weight of the girder 

 iuelf independently of the load: for when a vertical section is made 

 through the centre, it is seen that the molecular forces of the metal have 

 to resist a greater moment of external forces, than when the section is sup- 

 posed to be made elsewhere. Secondly, the load is a moveable one, and 

 has the greatest moment when its centre of gravity is over the centre of the 

 bridge. It is possible to vary the dimensions of the bridge so that the 

 tlrain on ench square inch shall be uniform throughout almost the whole 



length of the bridge. There are three ways of effecting this object — either 

 by increasing the thickness of the plates towards the centre of the bridge, 

 or by increasing the depth of the bridge towards the centre, or by combin- 

 ing both these methods. The second methoil is however the preferable one, 

 because it does not require any considerable addition to the quantity of 

 metal. 



On narrow gauge railways the proportion of the loading of the goods 

 trains to the length of the wagons is such that about 4 tons of load extend 

 over about 9 feet of railway ; consequently on the Menai girders (the length 

 of which is 4.'iO feft; we may take the extreme load to be 200 tons uni- 

 formly distributed over the length. We have now to find the law of the 

 variation of the depth of the girder, so that its own weight, and lb« 

 load together shall produce a uniform strain on the metal. 



Let 21 be the length of the bridge, and m the weight of load and bridge 

 together for a unit of length, and 21 m will be total weight supported. 

 Consequently the pressure on each abutment will be tm. 



Let a vertical section CD' be supposed to be made at a distance x 

 (=AD') from the end of the bridge. Then replacing the molecular 

 actions by a vertical force along C D, and equal horizontal forces at 

 C and D' ; these new forces may be equated with the external forces, 

 which are — first, the vertical pressure at the end A, which, as has been 

 said, is equal to m / ; secondly, the weight of the part A B C D' ( = mx), 

 which may be supposed to act half way between A and D'. And aa wt 



shall hereafter find that the curvature of B' C is very small, it will ba 

 seen that the error arising form this supposition is quite inappreciable. 

 Taking moments about D' and calling the depth C D', y, we have — 



My = m i J- — m X . J X. 

 Now y is supposed to vary so that M remains constant. Consequently 

 the equation to the curve B C will be 



y = jjj- (i X — 1 x') a parabola. 



It will be observed that by this equation y = when x rz or 2 /, th«t », 

 the depth is zero at the two extremities of the beam. It is impossible, 

 however, that this condition could be satisfied, since room must be left for 

 the passage of the train. The height of common railway bridges usually 

 allowed for this purpose is 15 feet, which gives a sufficiently clear spao» 

 above the funnel of the engine ; y, therefore, in the above equation, after 

 it has attained the limit of 15 feet, must remain constant. The only elfecl 

 of this will be that the bridge will be stronger than theory requires it l« 

 be, since, of course, if the depth towards the ends be greater thaa reqai- 

 site, the result is an increased strength in those parts. 



To determine the numerical value of m ; the weight of a square foot of 

 iron one inch thick is about 10 lb. : and since the Menai Bridge is to b« 

 15 feet wide, the weight of one foot of the upper and lower plates together 

 will be 1200 lb. The weight of the train we have supposed 4 tons to 

 feet, or about 1000 1b. to a foot. Consequently m =: 2200 ; we will, fkir 

 convenience of calculation put m = 2240 or 1 ton 



M is to be found by determining its value at the centre of the bridge. 

 Here y = 30 feet and x — 225 feet. Substituting these values in tb« 

 equation to the curve, we find M = 844 tons ; and since i = 225 aotl 

 m = 1, the equation becomes — 



y = Bj,(225-Jx)x. 



The following are some of the values of y, corresponding to given value* 

 of*:— 



