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Resistance of wrought iron tubes to external and internal pressure
Resistance of Wrought Iron Tubes.
393
In conclusion, I would remark that it is seldom that a report of 38 pages of printed matter, giving the results of an extensive set of experiments upon an important subject, has not some point so weak that it may be successfully assailed; and if the paper to which this is reply is the heaviest artillery that can be brought against it, the :Board have abundant reason for congratulation that they have been so successful.
To Clteck ttte Warping of Planks. The face of the planks should be cut in the direction which lay from east to west as the tree stood. I f this be done, the planks will warp much less than in the opposite direction. The strongest side of a piece of timber is that which in its natural position faced the north.--Dingler's _Pol2/teeh. Jour. ~ull. Soc. d'.Encour, pour l'Zndus. !Vation. For the Journal of the Franklin Institute.
Resistance of Wrought Iron Tubes to ~'xternal and Internal _Pressure. Deduced from Experiments of W. Fairbairn. By CuAs. H. HASW~LL, C . E . (Continued
from page 306.)
:No. 2. ~esistance of Wrought Iron C1jlindrical Tubes to Internal _Pressure. Taking the mean of the results of Experiments 31 and 34 on iron tubes, r' × d 425 × 6 1,-- 2 t 'Or2x'043----29~651 Ibs., and 2 t x r ---pt . . . .
d, or~
2x'043×29,651 425
=
6ins.,
~x2t ..... ~ pt. d Hence, To ascertain the Thickness of a Wrought Iron rlt,eted Tube or JFlue,'the Diameter of the tube and the _Pressure in pounds per square inch being given. Rur, E.--Multiply the pressure in pounds per square inch, by the diameter of the tube in inches, and divide the product by twice the tensile resistance of the metal in pounds per square inch. EXAMPLE.--The diameter of a wrought iron ilue is 6 inches, and the pressure to which it is to be submitted is 425 lbs. per square inch, what should be the thickness of the metal ? Assume the tensile strength to be as above, 29,651 lbs. 425 X 6 2550 ............ 043 in. 29651 X 2 59302 The tenacity or tensile resistance of wrought iron boiler plates, ranges from 62,000 to 42,000 lbs.* per square inch ; hence it appears, and
* Including English plates.
394
Mechanics, Physics, and Chemistry.
that in the cases given, are duetion of tenacity of about "4 must be made. From Experiments 7, 8, 10, and 11, and 31, 32, 33, and 34, it appears that tubes or flues subjected to internal pressure or bursting, have much greater resistance than when subjected to external pressure or collapsing; in the cases given where the lengths of the col= lapsed tubes were 2"5 feet, the difference is about 6"2 times. The difference, however, between these strains cannot be determined as a rule, for the reason that the resistance to internal pressure is inversely as the diameter of the tube or flue alone, without regard to its length ; whereas, with the resistance to collapse, the stress is inversely as the product of the diameter and the length.
Application to Construction of tl~e Results of the ff,xperiments. Throughout the experiments here enumerated, it has been proved that the resistance to collapse from a uniform external pressure, in cylindrical tubes or flues, varies iu the inverse ratio of the lengths. This law has been tested to lengths not exceeding fifteen diameters of the tube or flue ; hut the point at which it ceases to hold true is as yet undetermined, and it can only be ascertained by a series of experiments on tubes and flues of greater length, in which the strength of the material modifies the above law of resistance to collapse. Such experiments are desirable, but the results already obtained appear to supply the data necessary for calculating the resistance, and proportioning the material in ordinary cases. Thus, with drawn or brazed tubes, when there are no courses and consequent laps; their length is an essential element in an estimate of their resistance to collapse; but with riveted flues, constructed in courses, the objection to length is removed, as the addition of the laps is a source of great resistance to collapse, rendering the flue alike to a series of lengths, each equal to the distance between the centres of the courses.
In a boiler of the ordinary construction, of 30 feet in length and 3 feet 6 inches in diameter, with two flues 16 inches in diameter, the cylindrical external shell has 2"8 times resistance to the force tending to burst it, than the flues have to resist the same force to collapse them. This being the case, it is not surprising that the collapse of the internal flues so frequently occurs. To remedy this, and to place the security of boilers upon a more certain basis, it is essential that every part should be of uniform strength to resist the st'ress upon it. The equalization of the powers of resistance is the more important, as the increased s~rength of the outer shell is absolutely of no value, so long as the internal flues remain liable to be destroyed by collapse, at a pressure of only one-third of that required to burst the envelope which contains them. The following Table, deduced from experiments, exhibits the collapsing pressure of flues, and bursting pressure of boilers of different diameters and thickness of metal : - -
tlesistanee of Wrought Iron Tubes.
395
TxaLm of the Resistance of Wrouzht Iron Flues to an External or Collapsing Pres-
sure, and of the Shells of Boilers to an Internal or Bursting Pressure. Tensile resistance of the Plates without rivetin~ is taken at a mean o f 5 5 , 0 0 0 pounds per square inch. FLUES,
SItELLS,
Bursting Pressure persquareinch.
~z -~
~
"~"Z O~
~.~
5 Ins,
Feet.
6 6.5 7
17
"2
~
"2
"
"25
"
"2
"
"25
7.5
Ins. "2
8
"
.25
"
'25
"
.2
"
"25
8"5 9
9.5 I0
10'5
11
11"5
12
12"5 13 135 14 14"5 15 15"5
16
12
417 385 357 580 333 542 312 5O8 294 478 278 451 ~63 427 227 354 612 216 337 583 206 322 557 197 308 532 153 239 415 229 398 220 384 212 369 176 3O5 169 294 157 276 152 267 148 23I
Feet.
I[)S.
2 2'6 3 3'4
"25 .25 .25 .25 ,3125 .25 .3125 .25 • 3 ! 25 .25 .3125 .25
3"6 4 4"6 5
•3 t 2 5
5"6
6'6 7 7'6 8 8'6 9 9"6 0
0"6
1
1"6 2
.25 "3125 '375 "25 "3125 "375 "3125 "375 "3125 *375 "3125 "375 "312 "375 "312 "375 "312 "375 "312 "375 "312 '375 "5 "312 "375 "5 "375 .5 "375 "5 "375 i "5
382 318 398
I i [
596 496 414 5t8
32~
t
4~6
409 286 358 254 318 229 286 208 260 312 191 239 286 220 264 204 245 191 229 179 215 168 202 t59 19I 150 18I 143 172 229 136 163 218 156 208 149 199 143 191
i i / I I /
532 372 i65 33[ 413 298 372 270 338 406 248 3II 372 287 344 266 319 248 298 233 279 219 263 2(}7 248 196 235 186 224 298 177 212 284 203 271 194 259 186 248
I
396
Mechanics, _Physics, and Chemistry.
NoTs.--The single riveted are estimated at "5 the resistance of the plates, and the double riveted at "65; this reduction from "56 and "7, as determined by Fairbairn, is to meet defects of rivets, cracks of plates from the priming of rivet holes, kc., his experiments having been made with rivets and plates in a normal condition. ~kPPLICATION OF TIIE PRECEDING TABLE.
To ascertain the Ultimate Collapsing Resistance of a ~lue. When the thickness of the metal is not given in the above Table. R~LE.--Take the square of the thickness of the metal, if given in decimals of an inch, or that due to the number of it, if given by a wire gauge, and multiply it by its proportional unit or multiplier from the table preceding (page 395), the thickness and length being duly considered, and divide the product by the product of the diameter of the flue in inches, and the length of it in feet. ExAMPL~.--The diameter of a flue is 15 ins., the thickness of the metal No. 3 U. S. wire gauge ( = "23 in.), and the length of it is 30 feet ; what is its ultimate resistance to collapse per square inch ? Multipliers for thicknesses from "125¢to "25 in., and for a length of 30 feet, are 8t0,000 to 920,000, the difference of which is (920,000 --810,000) ---- 110,000, and the difference in thickness ( ' 2 5 - "125) ---- "125 Then, as "125 : 110,000 :: "105 ( ' 2 3 - - " 1 2 5 ) : 92,400. ]Difference in length (35 - - 25) ~ 10. Then, as 10 : 110,000 : : 5 ( 3 5 - - 30) : 55,000. Consequently, 92,400 +2 55,000 ----73,700,
a mean multiplier of
thicknesses and length, which added to 810,000, the multiplier for •125 in. in thickness and 25 feet in length, ~ 883,700. •23 ~ .0529 Hence, 30 X 15 X 883,700 ~ 4---50 X 883,700 ~- 103"88 lbs.
To ascertain the Ultimate Bursting Resistance of the Shell of a Boiler. When the thickness of the metal is not given in the above table. RULE.--Double the thickness given, or as ascertained, for a wire gauge, and multiply the sum by the tensile resistance of the metal, and divide the product by the diameter of the flue in inches. ExAMPLE.--The diameter of the shell of a wrought iron boiler, single riveted, is 5 feet, and the thickness of the metal is "28 in. ; what is the ultimate resistance to a bursting pressure ? : "28 + "28 X 55,000 = 30,800, and 30,800 ~,5i3,331bs., which X "5 for reduction of resistance of the plates for single riveting -~ 256"67 15s. ~O~E.--From the results given in the table and deduced from the
_7~esistanee of Wrought Iron Tubes.
397
rules, such allowances for the resistance and wear of the plates, oxidation, &c., &c, are to be made, as the character of the metal, the nature of the service, and the circumstance of using fresh or salt water~ &c., &e., will render necessary. In plates single riveted, it is customary in practice to estimate the tensile resistance of the metal at one-fifth of its ultimate resistance, and, when they are double riveted, at one-fourth of it. Comparison between the Resistance to External and Internal Pressure in Wrought Iron Single Riveted Flues ~f different Diameters and Lengths. :External pressure per sq. inch.
Internal pressure per sq. ineh.
Diameter.
Thickness.
Length.
Ins°
Ins,
Feet.
]bs.
ibm
6 12 t8
•15 •2 •25
l0 15 20
205 163 135
1375 917 764
Ratio.
1 to 6.7 I " 5'6 1 " 5"6
RESISTANCE OF L E A D TUBES TO INTERNAL PRESSURIe,
°
RZMARXS.
Iris*
Ins.
Ins.
]bs,
3
14½
"25
374
3
31
"25
364
I
Ruptured in body of tube.
Assuming 370 as the mean of the pressure of rupture in lbs. per square inch, P= and
PP X D
2---/-'
2tXP - - p i ...... d,
or or
370 × 3
2 ×'2--~5~ 2220 lbs.,
2X.25X2220 370
3ins. '
and
e X 2 t== pr. d Hence, To ascertain the Thickness of a Zead _Pipe, the .Diameter and the _Pressure in pounds per square inch being given. RuLE.--Multiply the pressure in pounds per square inch by the diameter of the pipe in inches, and divide the product by twice the tensile resistance of the metal in pounds per square inch. EXAMPLE.--The diameter of a lead pipe is 3 inches, and the pressure to which it is to be submitted is 370 lbs. per square inch ; wha: should be the thickness of the metal ? 370 X 3 1110 •25 in. 2220 X 2 -- 4440 -VoL. XLII.--THmD SERIES.~rO° 6.--DEcE~ER, 1861.
34
Mechanics, _Physics, and Chemistry.
398
:RZSlSVANCE OF GLASS GLOB~S ASI) CYLINDERS TO COLLXPSZ~G (Fairbairn). (~LOBES.
CYLINDERS. °
Diameters. ,,j Ins. 5.05 5.08 4.95 5.60 8.22 8.20 8.~0
Ins.
][us.
lbs.
Ins.
Ins.
Ins.
lbs.
4"76
"015
4"70
•0 1 9
292 410 470 475 350 420 600
4'06 4"02 4"05 4'05 3"09 3"08 3'25
]3.75 14 7 7 14 14 14
"045 -065 .046 '034 '024 '032 '042
lS0 297 380 202 850 103 175
4"72 7"45 7"30 7"40
I
"021 "020 '010 "012 "015
From which it appears that the resistance of cylindrical vessels exposed to a uniform external pressure , varies inversely as their lengths. For the Journal of the Franklin Institute°
~trength of Cast Iron and Timber Pillars: A series of Tables showing the Breaking Weight of Cast Iron, Dantzic Oak, and Red Deal Pillars.
By W~. B~£soN, Cir. Eng. (Continued from page 330.)
Mr. Hodgkinson gives the following formula for the strength of a solid pillar of east iron : W ~
Ds.5 m X L1.6S
m representing a weight which varied from 49"94 tons in the strongest iron tried, to 38"60 tons in the weakest. Mr. H. also gives the following formulm for the strength of a hollow pillar of Low Moor iron, :No. 2: w =- 46"65 Ds'55- dS'55 LI.7
w --~ 42"347 ~s's - - ds'~ L hS3
" I t was found that when the length was the same, the strength varied as the 3"5 power of the diameter, and when the diameter was the same and the length varied, the strength was inversely as the 1"63 power of the length ; both of these were obtained from mean results of many experiments." N o T z . ~ T h e above formulm are deduced from experiments on pillars 10 feet long, and from 2~ inches to 4 inches diameter. It was shown at p. IS6 of this Journat, and by the several tables, that similar formuhe were applicable for solid pillars when the length exceeded 25 diameters, and for hollow pillars when the length varied from about 28 to 34 diameters, the variability depending a good deal upon the sectional thickness.
393
In conclusion, I would remark that it is seldom that a report of 38 pages of printed matter, giving the results of an extensive set of experiments upon an important subject, has not some point so weak that it may be successfully assailed; and if the paper to which this is reply is the heaviest artillery that can be brought against it, the :Board have abundant reason for congratulation that they have been so successful.
To Clteck ttte Warping of Planks. The face of the planks should be cut in the direction which lay from east to west as the tree stood. I f this be done, the planks will warp much less than in the opposite direction. The strongest side of a piece of timber is that which in its natural position faced the north.--Dingler's _Pol2/teeh. Jour. ~ull. Soc. d'.Encour, pour l'Zndus. !Vation. For the Journal of the Franklin Institute.
Resistance of Wrought Iron Tubes to ~'xternal and Internal _Pressure. Deduced from Experiments of W. Fairbairn. By CuAs. H. HASW~LL, C . E . (Continued
from page 306.)
:No. 2. ~esistance of Wrought Iron C1jlindrical Tubes to Internal _Pressure. Taking the mean of the results of Experiments 31 and 34 on iron tubes, r' × d 425 × 6 1,-- 2 t 'Or2x'043----29~651 Ibs., and 2 t x r ---pt . . . .
d, or~
2x'043×29,651 425
=
6ins.,
~x2t ..... ~ pt. d Hence, To ascertain the Thickness of a Wrought Iron rlt,eted Tube or JFlue,'the Diameter of the tube and the _Pressure in pounds per square inch being given. Rur, E.--Multiply the pressure in pounds per square inch, by the diameter of the tube in inches, and divide the product by twice the tensile resistance of the metal in pounds per square inch. EXAMPLE.--The diameter of a wrought iron ilue is 6 inches, and the pressure to which it is to be submitted is 425 lbs. per square inch, what should be the thickness of the metal ? Assume the tensile strength to be as above, 29,651 lbs. 425 X 6 2550 ............ 043 in. 29651 X 2 59302 The tenacity or tensile resistance of wrought iron boiler plates, ranges from 62,000 to 42,000 lbs.* per square inch ; hence it appears, and
* Including English plates.
394
Mechanics, Physics, and Chemistry.
that in the cases given, are duetion of tenacity of about "4 must be made. From Experiments 7, 8, 10, and 11, and 31, 32, 33, and 34, it appears that tubes or flues subjected to internal pressure or bursting, have much greater resistance than when subjected to external pressure or collapsing; in the cases given where the lengths of the col= lapsed tubes were 2"5 feet, the difference is about 6"2 times. The difference, however, between these strains cannot be determined as a rule, for the reason that the resistance to internal pressure is inversely as the diameter of the tube or flue alone, without regard to its length ; whereas, with the resistance to collapse, the stress is inversely as the product of the diameter and the length.
Application to Construction of tl~e Results of the ff,xperiments. Throughout the experiments here enumerated, it has been proved that the resistance to collapse from a uniform external pressure, in cylindrical tubes or flues, varies iu the inverse ratio of the lengths. This law has been tested to lengths not exceeding fifteen diameters of the tube or flue ; hut the point at which it ceases to hold true is as yet undetermined, and it can only be ascertained by a series of experiments on tubes and flues of greater length, in which the strength of the material modifies the above law of resistance to collapse. Such experiments are desirable, but the results already obtained appear to supply the data necessary for calculating the resistance, and proportioning the material in ordinary cases. Thus, with drawn or brazed tubes, when there are no courses and consequent laps; their length is an essential element in an estimate of their resistance to collapse; but with riveted flues, constructed in courses, the objection to length is removed, as the addition of the laps is a source of great resistance to collapse, rendering the flue alike to a series of lengths, each equal to the distance between the centres of the courses.
In a boiler of the ordinary construction, of 30 feet in length and 3 feet 6 inches in diameter, with two flues 16 inches in diameter, the cylindrical external shell has 2"8 times resistance to the force tending to burst it, than the flues have to resist the same force to collapse them. This being the case, it is not surprising that the collapse of the internal flues so frequently occurs. To remedy this, and to place the security of boilers upon a more certain basis, it is essential that every part should be of uniform strength to resist the st'ress upon it. The equalization of the powers of resistance is the more important, as the increased s~rength of the outer shell is absolutely of no value, so long as the internal flues remain liable to be destroyed by collapse, at a pressure of only one-third of that required to burst the envelope which contains them. The following Table, deduced from experiments, exhibits the collapsing pressure of flues, and bursting pressure of boilers of different diameters and thickness of metal : - -
tlesistanee of Wrought Iron Tubes.
395
TxaLm of the Resistance of Wrouzht Iron Flues to an External or Collapsing Pres-
sure, and of the Shells of Boilers to an Internal or Bursting Pressure. Tensile resistance of the Plates without rivetin~ is taken at a mean o f 5 5 , 0 0 0 pounds per square inch. FLUES,
SItELLS,
Bursting Pressure persquareinch.
~z -~
~
"~"Z O~
~.~
5 Ins,
Feet.
6 6.5 7
17
"2
~
"2
"
"25
"
"2
"
"25
7.5
Ins. "2
8
"
.25
"
'25
"
.2
"
"25
8"5 9
9.5 I0
10'5
11
11"5
12
12"5 13 135 14 14"5 15 15"5
16
12
417 385 357 580 333 542 312 5O8 294 478 278 451 ~63 427 227 354 612 216 337 583 206 322 557 197 308 532 153 239 415 229 398 220 384 212 369 176 3O5 169 294 157 276 152 267 148 23I
Feet.
I[)S.
2 2'6 3 3'4
"25 .25 .25 .25 ,3125 .25 .3125 .25 • 3 ! 25 .25 .3125 .25
3"6 4 4"6 5
•3 t 2 5
5"6
6'6 7 7'6 8 8'6 9 9"6 0
0"6
1
1"6 2
.25 "3125 '375 "25 "3125 "375 "3125 "375 "3125 *375 "3125 "375 "312 "375 "312 "375 "312 "375 "312 "375 "312 '375 "5 "312 "375 "5 "375 .5 "375 "5 "375 i "5
382 318 398
I i [
596 496 414 5t8
32~
t
4~6
409 286 358 254 318 229 286 208 260 312 191 239 286 220 264 204 245 191 229 179 215 168 202 t59 19I 150 18I 143 172 229 136 163 218 156 208 149 199 143 191
i i / I I /
532 372 i65 33[ 413 298 372 270 338 406 248 3II 372 287 344 266 319 248 298 233 279 219 263 2(}7 248 196 235 186 224 298 177 212 284 203 271 194 259 186 248
I
396
Mechanics, _Physics, and Chemistry.
NoTs.--The single riveted are estimated at "5 the resistance of the plates, and the double riveted at "65; this reduction from "56 and "7, as determined by Fairbairn, is to meet defects of rivets, cracks of plates from the priming of rivet holes, kc., his experiments having been made with rivets and plates in a normal condition. ~kPPLICATION OF TIIE PRECEDING TABLE.
To ascertain the Ultimate Collapsing Resistance of a ~lue. When the thickness of the metal is not given in the above Table. R~LE.--Take the square of the thickness of the metal, if given in decimals of an inch, or that due to the number of it, if given by a wire gauge, and multiply it by its proportional unit or multiplier from the table preceding (page 395), the thickness and length being duly considered, and divide the product by the product of the diameter of the flue in inches, and the length of it in feet. ExAMPL~.--The diameter of a flue is 15 ins., the thickness of the metal No. 3 U. S. wire gauge ( = "23 in.), and the length of it is 30 feet ; what is its ultimate resistance to collapse per square inch ? Multipliers for thicknesses from "125¢to "25 in., and for a length of 30 feet, are 8t0,000 to 920,000, the difference of which is (920,000 --810,000) ---- 110,000, and the difference in thickness ( ' 2 5 - "125) ---- "125 Then, as "125 : 110,000 :: "105 ( ' 2 3 - - " 1 2 5 ) : 92,400. ]Difference in length (35 - - 25) ~ 10. Then, as 10 : 110,000 : : 5 ( 3 5 - - 30) : 55,000. Consequently, 92,400 +2 55,000 ----73,700,
a mean multiplier of
thicknesses and length, which added to 810,000, the multiplier for •125 in. in thickness and 25 feet in length, ~ 883,700. •23 ~ .0529 Hence, 30 X 15 X 883,700 ~ 4---50 X 883,700 ~- 103"88 lbs.
To ascertain the Ultimate Bursting Resistance of the Shell of a Boiler. When the thickness of the metal is not given in the above table. RULE.--Double the thickness given, or as ascertained, for a wire gauge, and multiply the sum by the tensile resistance of the metal, and divide the product by the diameter of the flue in inches. ExAMPLE.--The diameter of the shell of a wrought iron boiler, single riveted, is 5 feet, and the thickness of the metal is "28 in. ; what is the ultimate resistance to a bursting pressure ? : "28 + "28 X 55,000 = 30,800, and 30,800 ~,5i3,331bs., which X "5 for reduction of resistance of the plates for single riveting -~ 256"67 15s. ~O~E.--From the results given in the table and deduced from the
_7~esistanee of Wrought Iron Tubes.
397
rules, such allowances for the resistance and wear of the plates, oxidation, &c., &c, are to be made, as the character of the metal, the nature of the service, and the circumstance of using fresh or salt water~ &c., &e., will render necessary. In plates single riveted, it is customary in practice to estimate the tensile resistance of the metal at one-fifth of its ultimate resistance, and, when they are double riveted, at one-fourth of it. Comparison between the Resistance to External and Internal Pressure in Wrought Iron Single Riveted Flues ~f different Diameters and Lengths. :External pressure per sq. inch.
Internal pressure per sq. ineh.
Diameter.
Thickness.
Length.
Ins°
Ins,
Feet.
]bs.
ibm
6 12 t8
•15 •2 •25
l0 15 20
205 163 135
1375 917 764
Ratio.
1 to 6.7 I " 5'6 1 " 5"6
RESISTANCE OF L E A D TUBES TO INTERNAL PRESSURIe,
°
RZMARXS.
Iris*
Ins.
Ins.
]bs,
3
14½
"25
374
3
31
"25
364
I
Ruptured in body of tube.
Assuming 370 as the mean of the pressure of rupture in lbs. per square inch, P= and
PP X D
2---/-'
2tXP - - p i ...... d,
or or
370 × 3
2 ×'2--~5~ 2220 lbs.,
2X.25X2220 370
3ins. '
and
e X 2 t== pr. d Hence, To ascertain the Thickness of a Zead _Pipe, the .Diameter and the _Pressure in pounds per square inch being given. RuLE.--Multiply the pressure in pounds per square inch by the diameter of the pipe in inches, and divide the product by twice the tensile resistance of the metal in pounds per square inch. EXAMPLE.--The diameter of a lead pipe is 3 inches, and the pressure to which it is to be submitted is 370 lbs. per square inch ; wha: should be the thickness of the metal ? 370 X 3 1110 •25 in. 2220 X 2 -- 4440 -VoL. XLII.--THmD SERIES.~rO° 6.--DEcE~ER, 1861.
34
Mechanics, _Physics, and Chemistry.
398
:RZSlSVANCE OF GLASS GLOB~S ASI) CYLINDERS TO COLLXPSZ~G (Fairbairn). (~LOBES.
CYLINDERS. °
Diameters. ,,j Ins. 5.05 5.08 4.95 5.60 8.22 8.20 8.~0
Ins.
][us.
lbs.
Ins.
Ins.
Ins.
lbs.
4"76
"015
4"70
•0 1 9
292 410 470 475 350 420 600
4'06 4"02 4"05 4'05 3"09 3"08 3'25
]3.75 14 7 7 14 14 14
"045 -065 .046 '034 '024 '032 '042
lS0 297 380 202 850 103 175
4"72 7"45 7"30 7"40
I
"021 "020 '010 "012 "015
From which it appears that the resistance of cylindrical vessels exposed to a uniform external pressure , varies inversely as their lengths. For the Journal of the Franklin Institute°
~trength of Cast Iron and Timber Pillars: A series of Tables showing the Breaking Weight of Cast Iron, Dantzic Oak, and Red Deal Pillars.
By W~. B~£soN, Cir. Eng. (Continued from page 330.)
Mr. Hodgkinson gives the following formula for the strength of a solid pillar of east iron : W ~
Ds.5 m X L1.6S
m representing a weight which varied from 49"94 tons in the strongest iron tried, to 38"60 tons in the weakest. Mr. H. also gives the following formulm for the strength of a hollow pillar of Low Moor iron, :No. 2: w =- 46"65 Ds'55- dS'55 LI.7
w --~ 42"347 ~s's - - ds'~ L hS3
" I t was found that when the length was the same, the strength varied as the 3"5 power of the diameter, and when the diameter was the same and the length varied, the strength was inversely as the 1"63 power of the length ; both of these were obtained from mean results of many experiments." N o T z . ~ T h e above formulm are deduced from experiments on pillars 10 feet long, and from 2~ inches to 4 inches diameter. It was shown at p. IS6 of this Journat, and by the several tables, that similar formuhe were applicable for solid pillars when the length exceeded 25 diameters, and for hollow pillars when the length varied from about 28 to 34 diameters, the variability depending a good deal upon the sectional thickness.