208 



THIi: CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[Oct. 



nOTBS ON ENGINEERINQ, 

 VI. 

 MENAI TUBULAR BRIDGE. 



(^Continueil from page 174). 



In the lasl paper on llie Menai Tubular Bridge (ante p. 174), a formula 

 was given for calculating the lioyizontat strains to which the vertical plates 

 of the tube would be subject, and a truth hitherto entirely overlooked was 

 demonstrated, that these plates ought to be sirongcr towards their ei- 

 tremities than at the centre. 



To complete the investigation of the forces to which these plates are 

 subject, the amount of the rertical strains ought also to be determined. 

 But as these papers were already been carried to some length, it is ne- 

 cessary tos'udy brevity; and it will be sufficient to point out the general 

 steps of the calculation. 



The vertical plates consist of two different portions discharging two dif- 

 ferent ollices. That part of each vertical plate which lies over the abut- 

 ments supports the upper horizontal plate upon the lower : the pari between 

 the abutments and clear of them suspends the lower plate /rom the upper. 



In the following diagram, then, the vertical forces of those parts of the 

 vertical rib which are over A a. and B b, are Ihursls.and the vertical forces 

 of the part of A B, tensions. To consider tlie latter first, let us suppose 



41 



sections made at A and B, and that the connection between the upper and 

 lower plates is made not by a continuous rib, but by a number of vertical 

 rods. Then it is clear that we may consider ihe lower plate and the load 

 on it suspended by means of these rods from the upper plate. We must 

 also take into account the vertical molecular at the sections at A B. But 

 as it is impossible to calculate their amount exactly, it will probably be 

 sufficient for practical purposes to suppose that they sustain half the pres- 

 sure of the load, and that the other half is communicated by means of the 

 Suspending rods to the upper plate. Hence the total tension of these rods 

 will be equal to half the weight of the train -\- the weight of one of the 

 horizontal plates. If we suppose the rib couliuuous and not formed of 

 robs, the conclusion will not be widely ditl'erent. A continuous rib indeed 

 would be cut by the section through A and B, but the molecular forces of 

 the rib at the sections would be small compared with the total tension dis- 

 tributed over its whole length. 



Hence we conclude that the vertical plates between A and B must to- 

 gether possess suflicient strength that half the load and the weight, one of 

 the horizontal plates may be suspended from tliem without injuring them. 



To consider next the vertical thrusts on the portions A a, B 6 of the side- 

 plates, it may be easily seen by similar reasoning that these portions sup- 

 port half the load and the weight of one of the horizontal plates resting on 

 them. An important practical conclusion from this is that the portions of 

 Ihe vertical plates over the abutments should be much stronger than the 

 remainder, for they have to resist an equal amount of force distributed over 

 much less surface, and moreover the power of wrought iron to resist thrust 

 is greatly inferior to its power to resist tension. 



We cannot conclude this part of the investigation without expressing a 

 conviction that the connection between the upper and lower plates should 

 be maintained, not by continuous plates, but by a lattice of vertical and 

 horizontal rods, firmly clasped together at the points where they cross 

 each other. The necessary strength of them might be calculated w ith con- 

 siderable accuracy, they would accommodate themselves far better than 

 continuous plates would to the variations of form produced by changes of 

 temperature, would oflTer less resistance to the wind, and v>'ould admit 

 light and air to the interior of the tube. 



7. Variationt of Temperature. 



It may be demonstrated in the simplest manner, that on account of the 

 expansion and construction of the tube from variations of temperature, it 

 would be absolutely necessary that the ends should be left free to move in 

 a horizontal direction. 



It is shown by a very common experiment that a plate of metal if fasten- 

 ed in a horizontal direction between two props, and then considerably 

 heated, will, if prevented from expanding laterally, become bow ed or de- 

 flected. The same thing would happen with the tubular bridge if it were 



so fastened that it could not expan^l laterallv. In order to ascertain the 

 amount of deflection let A B be half of the length of the bridge before, A C 



after, expansion. We will first for sake of simplicity suppose A C a 

 straight line. Then B C is the deflection, and 



BC= = AC» — AB2 = (AC + AB) (AC — AB). 



It is usual to reckon the limits of expansion of iron at j^^ of the length. 

 Therefore if A B be 225 feet or 2700 inches, the expansion to be allowed 

 for is 2J inches each way, . • . A C = 2700J, A C + A B = 5400f, 

 AC— AB = 5. Hence 8^ = 12150 inches, and BC = 1I0 inches 

 nearly. Therefore the amount of deflection by expansion would be rather 

 mare than nine feel. 



A C has been here assumed to be a straight line : if however we suppose 

 as a probable approximation to the truth that it is a segment of a circle we 

 shall find that the amount of deflection is not materially diminished. It 

 may b^ iscertained by a laborious numerical operation which it is not ne- 

 cessary here to repeat that the amount will be about 8 feet. It is clear 

 that a much less distortion than this would suffice to fracture the vertical 

 plates, or wrench them from the horizontal plates. 

 8. Effect of Wind. 



A subject of the utmost importance with respect to llie permanent stabi- 

 lity of the Tubular Bridge is its power of withstanding the lateral pressure 

 of wind. It appears from the experiments of Smeaton, detailed in the 

 Philosophical Transactions for 1757, that the extreme pressure of Ihe wind, 

 when blowing violently, is 49'2 lb. to the square foot. This probably is an 

 amount of pressure which the wind rarely exercises except at sea or when 

 confined between hills. It is said, however, that in March last the force 

 of a gale in Scotland, as registered by an excellent anemometer, was 45 lb. 

 to the square foot. We are also to consider that the situation of the Menai 

 Bridge is one exceedingly subject to Ihe violence of storms, and that Ihe 

 sea-winds confined between the high lands on either side of the strails 

 would exert their force perpendicularly upon the Tubular Bridge, which 

 of course crosses the straits at right angles. 



We therefore shall not be exaggerating if we estimate that 45 or 501b. 

 per square foot is the amount of lateral pressure which the tube ought to 

 be capable of resisting. In this ease we shall find that as the area of one 

 of the vertical sides is 13500 square feet, each span of 450 feet would sus- 

 tain a pressure of 271 or 301 tuns. 



Now the utmost vertical pressure which the weight of a train will exert 

 on the same length of the bridge is 200 tons — that is 71 or 101 tons less 

 than the lateral pressure of the wind. It would therefore seem to follow 

 that whatever precautions be necessary for vertical strength are still nwre 

 necessary for lateral strength, and if it be requisite to strengthen the top 

 and bottom of the tube by a collection of rectangular cells or compart- 

 ments, the same apparatus (or rather one much stronger) ought to be ap- 

 plied to the sides of the tube. It is quite impossible to assign any solid 

 reason for preferring the consideration of vertical strength to that of lateral, 

 or for endeavouring to obtain Ihe two kinds of strength by dissimilar me- 

 thods. Tor it is clear that if the apparatus of cellular compartments be 

 Ihe best possible for ensuring strength vertically, it is also the best for en- 

 suring strength laterally. 



It might be answered perhaps that the cellular compartments gi»e to 

 the top and bottom of the tube an excess of strength which will never be 

 required in practice : but then it may be replied that this excess of strength 

 is just as requisite for Ihe sides of the lube ; for Ihe efl"ecl3 would be 

 equally disastrous whether the structure broke laterally or vertically. If 

 the tube require an excess of \ertical strength, it equally requires an ex- 

 cess of lateral strength : if it do not require an excess of lateral strength, 

 neither does it of vertical. In which latter case the cellular compartments 

 are simply superfluous. , 



The force of the wind on one span only of 450 feet has been reckoned. 

 If we calculate Ihe force of the two spans of that length, and Ihe force on 

 tlie two smaller spans of 250 feet each, we shall have Ihe total force tend- 

 ing to overturn the piers er otherwise displace Ihe structure. 

 9. The hest form (f the vpper and lower sides. 



In calculating Ihe strength of Ihe tube, the course taken in the preced- 

 ing parts of this investigation has been to estimate Ihe sectional area of the 



