1846.] 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



147 



Having in the month of August last year been requested to render 

 assistance, principally in a scientific point of view, wilh respect to the 

 experiments to ascertain the practicability of erecting a Tubular Bridge 

 across the Menai Straits, of suflicient strength for railway trains to pass 

 through it with safety, I attended twice in London for that purpose : and 

 as the experiments made there were on tubes of various forms of section, 

 including several elliptical and circular ones, I investigated formulas for 

 reducing the strength of the leading ones. It appeared evident to nie, 

 however, that any conclusions deduced from received principles, with 

 respect to the strength of thin tubes, could only be approximations ; for 

 these tubes usually give way by the top or compressed side becoming 

 wrinkled, and unable to offer resistance, long before the parts subjected to 

 tension are strained to the utmost they would bear. To ascertain how far 

 this defect, which had not been coutemplated in the theory, would atfect 

 the truth of computations on the strength of the lubes proposed to be used 

 in the bridge, — and also to show whether the principles generally received 

 could be applied with certainty in reasoning as to the strength of the 

 bridge from that of models comparatively very small, — lor these two pur- 

 poses I urged the necessity of a number of fundamental experiments, 

 which, besides supplying the wants above mentioned, might enable me to 

 obtain additional information to that from Mr. Fairbairu s experimenis, 

 wilh respect to the proportions that the dilTerent parts of the section of such 

 a bridge ought to have, as well as what form it should be of, in order to 

 bear the most. 



Feeling that there might be objections against allowing me to follow the 

 courses I proposed, however necessary it might appear to myself, I sug- 

 gested a much more limited series of experirueuts than now appear to me 

 to be necessary ; and, as the time consumed in getting the plates rolled and 

 the tubes prepared, caused the experimenis to be deUyed till the beginning 

 of the year, the time given me has beeen too limited to obtain all the facts 

 which the few experiments proposed would have ati'orded. 



I will now give the results, so far as they have been obtained and seem 

 worthy of reliance, subject to correction from future experiments ; begin- 

 ning with the reduction of Mr. Fairbairn's experiments on the strength of 

 tubes of wrought iron made of plates rivetted together. 



Cylindrical Tubes. — The strength of a cylindrical tube, supported at the 

 ends, and loaded in the middle, is expressed by the formula 



'a I 



{a*-a">). 



)■ Mean 29887 lb.= 1334 tons. 



Where I is the distance between the supports ; a, a' the external and 

 internal radii ; w the breaking weight ; / the strain upon a unity of sec- 

 tion, as a square inch, at the top aud bottom of the tube, in consequence 

 of the weight «•; ir = 3'1415'J. 



From this formula we obtain 



wl a 

 ■^^ n{a^-a'*)' 



As it will be convenient to know the strain /per square inch, which the 

 metal at the top aud bottom of the tube is bearing when rupture takes 

 place, this value will be obtained from each of Mr. Fairbairn's experi- 

 ments : the value to being made to include, besides the wei",ht laid on at 

 the time of fracture, the pressure from the weight of the lube between the 

 supports, this last being equal to half that weight. Computing the results 

 wtr have, from 



Experiment 1, / =33456 



2, / =33420 



3, / =35462 



4, / = 32415 

 „ 5, / =30078 



6, /= 33869 

 „ 7, / =22528 



„ 8, /= 22653 



„ 9, / =25095 J 



Fracture in all cases took place either by the tube failing at the lop, or 

 tearing across at the rivet holes ; this happened on the average, as appears 

 from above, when the metal was strained 13^ tons per square inch, or litlle 

 more than half its full tensile sirengih. 



Elliptical Tubes. — The value of/ in an elliptical tube broken as before, 

 (the transverse axis being vertical), is expressed by the formula 



w la 

 f= 



•' IT (ba^ — 6' a"-') 



Where a, a' are the semitransverse external and internal diameters ; 



b, b' the semi-conjugate external and internal diainclers ; and the rest as 



before, w including in all cases the pressure from the weight of the beam. 



Computing the results from Mr. Fairbairn's experiments we have from 



Experiment 20, / = 36938 lb. ] 



„ 21, /=29144 ^ Mean 37089 lb. = 16-55 tons. 



24, / =45185 J 

 Rectangular Tubes— li in a rectangular tube, employed as a beam, the 

 thickness of the top and boitom be equal, and the sides are of any thick- 

 ness at pleasure, then we have 



3u<ld 



■^"^2 (bd'-f d'->)' 

 in which d, d' are the external and internal depths respectively ; b, b' the 

 external aud internal breadths ; and the rest as before. 

 Mr. Fairbairn's experiment No. 14 gives by reduction 

 / = 18495 lb. = 8-2566 tons. 



This is, however, much below the value which some of my own experi- 

 ments give, as will be seen further on. 



The value of /, which represents the strain upon the top or bottom of 

 the tube when it gives way, is the quantity per square inch which the 

 material will bear either before it becomes crushed at the top side or torn 

 asunder at the bottom. U ut it has been mentioned before, that tbin sheets 

 of iron take a corrugated form with a much less pressure than would be 

 required to tear them asuuder; and therefore the value of/, as obtained 

 from the preceding experiments, is generally the resistance of the material 

 to crushing, and would have been so in every instance if the plates on the 

 bottom side (subjected to tension) had not been rendered neaker by rivet- 

 ting. 



The experiments made by myself were directed principally to two 

 objects : — 



I. — To ascertain how far this value of/ would be affected by changing 

 the thickness of the metal, the other dimensions of the tube being the 

 same. 



II. — To obtain the strength of tubes, precisely similar to other tubes 

 fixed on, — but proportionately less than the former in all their dimensions, 

 as length, breadth, depth, and thickness, — in order to enable us to reason 

 as 10 strength from one size to another, with more certainty than hitherto, 

 as mentioned before. Another object not far pursued, was to seek fur the 

 proper proportion of metal in the top and bottom of tlie lube. Much more 

 is required in this direction. 



In the three series of experiments made, the tubes were rectangular, 

 and the dimensions and other values are given below. 



The tube placed first in each series, is intended to be proportional in 

 every leading dimension, as distance between supports, breaiith, depth, 

 and thickness of metal, — aud any variations are allowed for in the com- 

 pulaliou. Thus the three first lubes of each series are intended to be 

 similar ; and in the same manner of the other tubes, &c. 



Looking at the breaking weights of the tubes varying only in thickness, 

 we find a great falling oil' in the strength of the thinner ones ; aud the 

 values of y show that in these — the thickness of the plates being -525, 

 •272, -124 inch— the resislance, per square inch, will be 1917, 14-47, aud 

 7-74 Ions respectively. The breaking weights here employed, do not 

 include the pressure from the weight of the beam. 



The value of/ is usually constant in questions on the strength of bodies 

 of the same nature, and represents the tensile strength of the material, but 

 it appears from these expennienls that it is varittble in tubes, aud repre- 

 sents their power to resist crippling. It depends upon the thickness of 

 the matter in the tubes, when the depth or diameter is the same ; or upon 

 the thickness divided by the depth when that varies. The determinatiou 

 of the value of /, which cau only be obtained by experiment, forms the 

 chief obstacle to obtaining a formula for the strength of tubes of every 

 form. When/ is known the rest appears to depenU upon recened prin- 

 ciples, and the computation of the strength may be made as in the Appli- 

 cation de la Mecanique of Navier, Part 1st, Article iV. ; or as in Papers 

 of my own in the Memoirs of the Literary and Philosophical Society of 

 Manchester, vols 4 and 5, second series. I have, however, maile for the 

 present purpose, further invesiigatious on this subject, but defer giving 

 them till additional information is obtained on the tlitferent points alluded 

 to in this report ; and this may account lor other omissions. 



In the last table of experiments tlie tubes were devised to lessen or to 

 avoid the anomalies which rivettiug lutrocluces, in order to render the pro- 

 perties sought for more obvious. Hence, the results are somewhat higher 

 than those vihich would be obtained by rivetting as geueiallj applied. 



The tube 31 feet 6 inches long, 24 cwt. 1 qr. weight, aud -:i72 inch in 

 thickness of plates, was broken by crushing at the tup with i;i-7o tons. 

 This tube was afterwards rendered straight, and had its weak top replaced 

 by one of a given thickness, which I had obtained from coiupulatiuu ; and 

 the result was, that by a small addition of metal, applied in its proper 

 proportion to the weakest part, the tube was increased in strength from 

 22-75 tons to 32-53 tons ; aud the top and the bottom gave way together. 



If it be determined to erect a bridge of lubes, I would beg to recom- 

 mend that suspension chains be employed as an auxiliary, otherwise great 

 thickness of metal would be required to pioduce adequate stitiuess and 

 streDgth. 



EATU^ HODGKINSON, 



19* 



