91 



THE CIVIL ENGINEER AND ARCHITECT'S JOURNAL. 



[Mabcu, 



In Tallies V. and IX., on thp transverse strenfrth of bars, of 

 wrought and cast-iron mixed, ive find a similar I'allinf; off to that 

 aliove, in the stren;;th of the larger hars l>elo«- that of the smaller 

 ones, as is shown in the following extracts: — 



Size of Bir 

 Ft. Spun, In. sq 



9 2 



Streuijth 'o bear U^rzuatal Pres&ure. 



•11 



lb. 



230 from 1 cxperiraonts on 1st sample 



fX|)-'i intents nil 2iHi bani[»Ie 



630 frcni -I experinicnts on Isl sample 



505 foni 4 experiments on 2nil sample 



r2230 fro 

 •■ \ l.Mo fro 



..{-■ 



Ultim.->te rii-aectl'n 

 from 

 HoilzontHi Pressure 

 2 -20 in. 

 2 258 

 1-4995 

 1 320 



Gi'iicriil lieninrkx nit the Riijiidity cf Increase of Traiisvprse Strnujth 

 oj' Square liursjhr Smat/ Inrrenients oj' their Sectional Dinieiiiioiii. 



The rapiility with which the transverse strength of square bars 

 increases for small increments of their sectional dimensions does 

 not appear to have been always adequately considered in experi- 

 mental inquiries. For -square bars ofcunstant length between the sap- 

 jiurts, the trunnverxe xtrciiyth varies as the cube of the side of the square, 

 consequently, for bars not greatly e.xceeding 1 inch square, — 

 such as have most frerpiently been subjected to series of experi- 

 ments, — an error of -J^th of an inch (for example) in the sectional 

 dimensions, will produce an error of nearly f^rd in estimating the 

 transverse strength. It is, however, by no means unusual to 

 assume bars, cast to be 1 inch square, to have exactly their nominal 

 dimension; variations of the actual dimensions, sometimes approach- 

 ing to, or even exceeding iiith of an inch, being neglected. 



This source of error has been avoided in the present series of 

 experiments, — and in nearly all others by the author, — by measur- 

 ing the transverse dimensions of each bar to thousands of an inch, 

 and reducing the results by theory to those for the intended size 

 of the casting. The nature and extent of the error will be easily 

 seen by the following table, in which is exhibited the difference of 

 strength of square bars, of which the transverse dimension increases 

 by hundredths of an inch. The breaking weight of the bar 1 inch 

 square is taken at 4tSlb. (from the mean of experiments on east 

 iron). It w ill be observed from this table, that .an error of less 

 than -nrth of an inch in the measure of the side of the square bar 

 produces an error of ith of the strength. A similar error of y^th 

 of an inch produces an error of ^rd the strength, and an error of 

 less than ^th of an inch produces an error of i the strength. 



Comparative Transverse Stretiyth of Bars of Sections slightly differing 

 from 1 square inch. 



NEW WEST.MINSTER BRIDGE. 



Sir — Several designs have been given in for building a new 

 bridge across the river Thames at Westminster. The designs have 

 been lithographed, and are to be found in the " Third Report, 

 AV'estminster Bridge and New Palace, ordered by the House of 

 Commons to be printed 5th August, 1S46." 



The design proposed by Mr. Walker, for a stone bridge, consists 

 of five arches, segments of circles, ami the information regarding 

 those arches, as stated in the design, is as follows: — 

 " Span of centre arrh, 150 feet. 

 Span of side arches, 140 and 120 feet. 

 SufBt of centre arch above Trinity standard, 24 feet." 



The versed sine or heights of those five arches above the springing 

 line liave not been figured in on the design, nor the radius of any 

 of tlie arches. The figured dimensions of the piers are oniitteil, 



and also the radius of the curve which the soffits of the five arches 

 should tangent; but by measuring on the design, the versed sines 

 or heights of the first and last arches between the springing line 

 and their soffits have been found to be each 15 feet, and the centre 

 arch about 20 feet. The tliickness of the piers, measured on the 

 plan, 18, 20, 20, and 18 feet, making a total of 76 feet. The dis- 

 tance across the river, between the abutments, 7+6 feet, and the 

 clear waterway 670 feet. Tlie horizontal distance, or length of the 

 chord line between the versed sines of the first and last arches, is 

 626 feet. 



The spans of the arches of 150, 14-0, and 120 feet, have all dif- 

 ferent radii. Have they been |)ut into the design at random? or 

 have they been the result of calculation emanating from some rule 

 of science? Has this been the reason of the engineer having 

 omitted to figure in the versed sines of the five arches on the 

 plan ? 



A design for an iron bridge is also given by Mr. Walker, with a 

 short note, as follows: — 



"Span of centre arch, 150 feet. 

 Span of side arches, 140 and 130 feet. 

 Soffit of centre arch above Trinity standard, 21 feet." 

 This makes a clear waterway of 690 feet, whereas Mr. Walker's 

 design for a stone bridge gives only a waterway of 670 feet, being 

 a difference of 20 feet of waterway between the two designs. This 

 is the very limited and variable information contained in Mr. 

 Walker's two designs for a bridge over the Thames at ^V'est- 

 minster. 



Mr. George Rennie has given in a design for a stone bridge, con- 

 sisting of seven elliptic arches; the spans of the arches and their 

 heights have been figured in on the design. The waterway of the 

 seven ellijitic arches is 760 feet, and the width between the abut- 

 ments, 832 feet, which varies greatly from the dimensions given by 

 Mr. Walker. 



Waterway. 



.Mr. Rennie's bridge of seven arches 760 



Mr. V^'alker's stone bridge, five arches 670 



Difference 90 



Mr. Rennie's bridge of seven arches 760 



Mr. Walker's iron bridge, five arches 690 



Difference 70 



Mr. ^Valker's iron bridge, five arches 690 



Mr. M'alker's stone bridge, five arches 670 



Width 



heiiveen 



Abutiieiii!!. 



832 



7+6 



66 



832 



756 



756 

 746 



Difference 20 10 



Mr. Barry's iron bridge of five arclies has a waterway of about 

 720 feet, but no figured dimensions have been given. 



As your Jnnrual is read by many intelligent persons w-ell ac- 

 quainted witli calculations and the properties of the circle, perhaps 

 some of them would be kindly pleased to give the solution of the 

 following problem, and the formula; on which the solution and cal- 

 culations have been based. 



Elements given. 



Pier Pier a' Pier Pier 



a' 18 feet. 18 feet. 18 feet. 18 lect. a' 



Distance between tlie abutments, C, C 746 



Ordinates between .\, a 15 



Ordinates between .\, a 20 



Ordinates between A, a' 15 



Horizontal distance between the ordinates 313 



The width of each of the five segment arches by cal- 



cul.ation, all of the same radii, to span a waterway of 670 

 Four piers, two on each side of the centre arch to be 

 20 feet thick each, and two at the side arches 18 

 feet thick each; the breadth or thickness of the 



whole four piers 76 



6, b, i>, h, line, from which the arches are to spring. 

 «', «', «', three points through wliich a curve line shall 

 pass, and tangent the soffits of the five segment 

 arches. 



