276

For the Journal of the Frankl in Ins t i tu te .

On tt~e ~roportlons of Cast Iron Steam or Water Pipes~ with _~aeed _Flange Joints. By ROBERT BaronS.

The proportions for cast iron pipes with faced flanges given by the following formulas and tables, have been reached after many years experience in their manufacture and use.

Those dimensions which are given by the first set of formulas (for 75 lbs, pressure) have been quite extensively adopted in the practice of engineers and machinists, the past eight or ten years. They give the minimum diameters to the flanges which will allow .six sided nuts of proper diameters to be turned, and they give also such thickness to each flange, as has been found practically ample when the joint is faced all over, and either no packing or a very thin one over the whole joint surface is used. After the manufacture of many thousand of lengths, to these dimensions, no instance of failure to give tight joints or of breakage from unequal shrinking of the casting, or of break- age from want of strength is remembered. And the' great excess of strength to withstand the internal pressure at which it is proposed to use them is made evident by the formulas. There has been found, however, a demand for flanged cast iron pipes to carry about 100 lbs. pressure, united with a requirement for flanges so large that the common square nuts (which have their inscribed diameters equal to twice that of the bolts on which they belong) can be readily turned on the back of the flanges, and also with a requirement for flanges so thick as to with- stand the unfair strains occasioned by the use of packing rings made of yielding materials and placed within the diameters of the bolts as a substitute for surface packing.

It is of no avail to argue with those, who from false economy, pur- chase bolts and nuts by weight with little question as to quality, neither is it advisable to demonstrate the unworkmanlike character of the joints made by packing rings or the unmeehanical procedure of mak- ing up lengths or getting small angles in this way. It is enough that flanges can be made sufficiently large and heavy to overcome these defects in construction and also sufficiently accurate to be used in the legitimate way. To meet these conditions the second set of formu- las and tables have been made. It is not proposed at this time to enter into a discussion of the derivation or the character of the for- mulas, We will only say as regards the thickness, that on the smaller sizes, say below 12 inches diameter, the constant of thickness required for sound castings is very much in excess of that demanded to resist internal pressure and that the formulas establishing the number and size of bolts have been based on the assumption that for 75 lbs. pres- sure, four inch pipes require 5 - ~ inch bolts, or for 100 Ibs. pressure, the same size of pipes require 5--~ inch bolts, and that for both 75 Ibs. and 100 lbs. pressure, forty-eight inch pipes require 36 - 1½ inch bolts. The results of this assumption as a whole system have been carefully investigated and found to give a value for the tensile strength of the wrought iron below the roots of the threads of the bolts, as compared with

t~roTortlom of Cast Iron ~ e a m and Water _Pipes. 277

the tensile strength of the cast iron demanded to sustain internal lon- gitudinal pressure, in the ratios of 2½ to 3½ times, the lesser ratio being on the larger bolts where the danger of overstraining by the workman in screwing up the bolts is the least.

l¢ormula for Thicknesses of Pipes, ~¢. Let v m_ th ickness of pipes in inches, s = thickness necessary for sound

D = diameter of pipes " cast ings for smallest pipe. d = d iameter of bolt " n = d iameter of pipe which has such ~x = o u t s i d e d iameter of flange in ins. th ickness tha t no addit ion for A1 = diameter of centre of bolt, " sound cast ings is required. ar = tensile s t reng th of cast iron. P = pressure per square inch im c = co-efficient of safety above proof, pounds. c I = co-efficient of proof above work-

ing pressure. The genera l equation of th ickness then becomes,

T - - P D C c ' ' F S ( 1 - - ~ ) 2 K

Suppose x = 18,000 lbs per square inch, P = 7 5 i b s .

c = 3 t , e I = 4 , e c l ~ 15. n = 48 inches diameter.

C a ~ " ~ I "~"~ which gives for seventy-five lbs. pressure and 15

- -~ ~ 1 ¢ " ~ " ~ times absolute strength, witl~o.t constant for sound castings

i ; ~ .'. T = 0 " 0 ~ 6 0 4 n + 0 . 2 5 ] i , ~ ~ suppose as before except that ! ' - - ~ - - - ' ~ - - - - - ~ P ~--- 100 lbs., e : 3.28, c I -~- 4, e c l = 13.125, !!i ~ : ~ / / / / ~ J T ~ / . . ~ ~ which gives for I00 lbs. pressure and 13'125 times , . ~ absolute strength, without constant for sound east- i! tugs, ~! ! ~ zcr/oA, or mHcu

1st. Thickness of pipe, 2d. Thickness of boss, 3d. L e n g t h of boss,

. . . T = 0 . 0 3 0 4 n + 0 . 2 9 2

Formula for the Flanges. 75 lbs.

~r = 0.026 I)+0.25 ~ = 0"03 D+0 ' 31 = 0"05 D + I ' I O

100 lbs. = 0.0304 D-}-0.292 ~' = 0.035 ])+}-0'44 ~--- 0.05 ~)+1.10 = 0.04 D40"6 = 0.045 D+0-85 = 0.008 D+0"16 = 1"25 d+0"05

=1"25 d + 0 " l

4th. Thickness of flange finished, = 0.033~ D+0"4 5th. Thickness of flange in the rough, = 0.036~ D + 0 ' 4 5 6th. Radius of hollow, none g iven 7th. Centre of bolt to outside of f l a n g e , = 1 .1d+0 .1

{ 1-04d+0.2 } 8th. Centre of bolt to hollow at root o f to root itself flange,

9th. d iameter of holes in flange, = 1.03 d + 0 . 0 3 = 1 0 3 d + 0 . 0 3 zx = outside diameter of flange, -~1 .06 D + 4 . 2 8 d + l . 2 2 = 1 ' 0 8 6 D + 5 d + l . 5 0 41 = diameter of centre of holes, = 1.06 v + 2 . 0 8 d + l . 0 2 = l - 0 8 6 D + 2 . 5 d + l - 4 0 ~ = n u m b e r of bolts, ~--- 0.7046 ])+2.182

d :=diameter of bolts, --_ 1 • 182 4 0 ' 0 1 7 8 5 A 1 2 + 0 " 2 0 5 2 + 0 .0492 * N

• The va lue of A, under the radical in this formula, is taken at an average com- puted one of A, = 1.1048 D + 2"0127

VOL. X L I X . m T H I R D SERIES.~{O. 4 . - -APRIL, 1865. 24

278 ~TTeehanlcs, -physics, and Chemistry. In the t~bles following the exact figures obtained for a, a,, :% and

d, by the formulas are not given but instead, the aliquot figures in inches or sixteenths nearest to fractional ones derived by computation.

There is besides the dimensions derived from the formulas, two col- umns giving the convenient lengths for each piece and the calculated weight of each length with the flanges in the rough.

Table of dimensions for Flanged Joint Cast I r on Pipes, in tended to curry 75 Ibs. er square inch work ing pressure.

2.

8 10 12 10

10 12 16

¢ 9 0

.328 "341 "354 .380 .406 .458 .510 '563 "667

'40 1"25 I "415 1"28

-43 1"30 • 46 1 "35 • 49 1"40 .55 1 ' 5 0 • 61 ~1'60 • 67 1"70 • 79 1"90

i

in. [ in. .3832 .545 • 3984 I '563 • 4136] "580 • 4440[ "615 '4744~ '650 '5352 "720 '5960 '790 '6568 '860 7784 11,000

"50 "511 '53 "56 • 60 t "66 "73 "80

0 , 0 bJ

m ~ ~ 0 ~

~ I ~ ~ 1 . ~ ~ ~

"56 "57] .59~ '62~ .67 -73~ "81 "89

t'01~

z ~ . ~ - " ~

I No in,

• 61 ~.61 6 ~

• 68 110~ 8t~ 6 • 68/12.] lO~ I 8 ~ • 81/1 13¢ lO • 93 ~17~ 157~ 10 • 93 [22 191s ~ 14

Table of dimensions for Flanged Joint Cast Iron Pipes intended to ca r ry 100 lbs . p e r square inch working pressure.

in. l in. in. in. [ in. in. in. No.[ 1"2! -72 '8 "184~ "61 7.] 6 1.2t . 7 4 - 8 2 .188/-61 8 6] 1.3( .- 9 17~ .84 1 9 2 / 6 8

s 9 .200/ .68 1o o*, 1"3£ 1"4( "84 "93 .208| "68 i1 9~ 1'5( "92 "02 .224| "68 13.} 11¼ 1'6C l '00 "11 .240~ "81 16 14 1"70 [ '08 "20 .286| "93 t9 16~ 4 1"90 ['24 "38 .288~ "98 ,)3~ 121

!

6 8

10 10 14

¢J#:~

~. i lbs.

8 94 8 113 8 134 8 176 9 250 9 360 9 5]4 9 685 9 1110

f~.

8 8 8 8 9 9 9 9 9

lbs. 118~ 139 166 217 303 451 624 832

1809

4 - - ~ bolts could be used for this joint in place of the tabular n u m b e r and size, but the jo in t will be better i f the number and dimensions given are followed.

t :~ The 3½ inch pipe flanges can have 4 - - ,~ bolts and 4 inch can have 4 - - ~ bolts, bu t the jo in t will no t be so well made as with the tabular numbers and diameters.

_Puddling by Machinery. From the London Builder, No. 1150.

Amongst the papers set down to be read at the annual meeting of the Institution of Mechanical Engineers in Birmingham, on the 26th ult., was one upon "machine puddling," by Mr. Menelaus. The