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On the longitudinal riveted joints of steam-boiler shells
Aug., I 8 8 9 . ]
L o n g i t u d i n a l ]¢h,etcd Joz)tts.
I3I
o f the p r o b l e m s presented, and which v a r y w i t h e v e r y building, e v e r y t h i n g b e a r i n g u p o n the s u b j e c t is p a t i e n t l y considered, and with an interest that pertains to seekers for further knowledge. A t the end of ten years, after t a k i n g an interest in matters p e r t a i n i n g to ventilation, I felt I was further back than at the beginning, and at the end of t w e n t y years had made b u t little progress. A t the present time, some ten years later, I am only at the point of s t a r t i n g fresh, hoping, however, to give some i m p e t u s to the cause, and particularly to ineite others to go on to more perfect work.
ON THE L O N G I T U D I N A L R I V E T E D J O I N T S ov STEAM-BOILER SHELLSY BY JOHN H. COOPER.
T h e initial s t a t e m e n t to the English IAoyd's rules for steam boilers is e m b o d i e d in the following words: " T h e strength of circular shells to be calculated from the strength of the longitudinal joints," which assures us that this part of the boiler should be properly proportioned. To these rules a m e m o r a n d u m is added: " I n any case where the s t r e n g t h of the longitudinal joint is satisfactorily shown b y e x p e r i m e n t to be g r e a t e r than given b y this formula (Lloyd's), the actual s t r e n g t h m a y be taken in the calculation." L a t e r on, Lloyd's rules (under the head of " P e r i o d i c a l Surveys," r e g a r d i n g the e x a m i n a t i o n of boilers after t h e y have been several years in service) say: " T h e safe w o r k i n g pressure is to b, d e t e r m i n e d b y their actual condition." T h e s e s t a t e m e n t s lie in the line of practical efficiency, and point to the necessity of providing material in accordance with the r e q u i r e m e n t of the load to be carried. Read at the Nineteenth Meeting of the American Society of Mechanical Engineers, and revised by the author for publication in the.JoURNAL from advance-sheets of the Transactions.
I32
Cooper:
[J. F. 1.,
A n y one who takes the trouble to collect and compare d a t a on this subject c a n n o t fail to notice the g r e a t disparity of rules for d e t e r m i n i n g the w o r k i n g pressure permissible for boilers. T h e case is clear by simple r e a s o n i n g on the d a t a collated, t h a t boilers are held together, it w o u l d seem, more b y conf o r m i t y to rule t h a n by the m a t e r i a l s of which t h e y a r e made. But, of course, the true course to p u r s u e is to give to each m e m b e r its proper allowance of section, in order t h a t the components of the joint shall have an equal chance under strain according to its resisting power. T h e d i m i n i s h e d s t r e n g t h of the shell of a boiler by the l o n g i t u d i n a l joint is well known, and it becomes good engin e e r i n g so to proportion its parts as to obtain t h e greatest s t r e n g t h possible w i t h i n the limits of practical economy. W h e n it became necessary to assure t h e m s e l v e s confidently of the p e r m a n e n t safety of a s t r u c t u r e composed of plates held t o g e t h e r by rivets, engineers were not long in finding o u t t h a t a certain a l l o t m e n t of rivet section to plate section at the joints was necessary, and t h a t these sections were f o u n d to be n e a r l y equal in the s t r o n g e s t joints. T h e e x p e r i m e n t s o f Fairbairn, c o n d u c t e d in the year I 8 3 8 , proved t h a t - - " t h e sectional area of the rivets in a .joint was n e a r l y equal to the sectional a r e a o~ the plate t h r o u g h the rivet holes." S u b s e q u e n t e x p e r i m e n t s by Clark on riveted plates for the Britannia and C o n w a y T u b u l a r Bridge fully corroborate the above s t a t e m e n t ; his conclusion was: " T h e collective area of the rivets is equal to the sectional area of the plate t h r o u g h the rivet holes." T h i s relation of the c o m p o n e n t s of the j o i n t in course of time became e m b o d i e d in the E n g l i s h Board of T r a d e rules and in Lloyd's rules now in force, r e g u l a t i n g the construction of steam boilers. It also forms the basis of the Philadelphia steam-boiler inspection ordinance, first f o r m u l a t e d in 1882. R e f e r r i n g now to those rules only which relate to the proportions of the l o n g i t u d i n a l joints of the cylindrical
Aug., I889.]
Longitmtinal Rivctcd faints,
x33
shells of boilers, we are p r e p a r e d to say t h e y m a y b e most c o n v e n i e n t l y p r e s e n t e d b y t he following n o t a t i o n and formulae : NOTATION.
H = P e r c e n t a g e of p u n c h e d pl at e to t h e solid plate. B = P e r c e n t a g e of d r i v e n r i v e t section to t h e solid plate. ( = T h e p r e s s u r e i n p o u n d s pe r s q u a r e inch, w h i c h the b o iler is allowed to carry. a = A r e a of d r i v e n rivet, or r i v e t hole. d--- D i a m e t e r of r i v e t hole. n .= N u m b e r of rows of rivets. 2 = P i t c h of rivets. t -= T h i c k n e s s of plates. R = R a d i u s of boiler shell. S --= U l t i m a t e sheari," 2 s t r e n g t h of rivets in pounds, per s q u a r e i nch of section. 7"-----Ultimate tensile s t r e n g t h of plates in pounds, per s q u a r e i nch of section. f = F a c t o r of safety. E = L i m i t of e l a s t i c i t y in t h e plates in pounds, per s q u a r e inch of section. = P e r c e n t a g e of j o i n t s t r e n g t h . T h e least of A or .6' s h o u l d be i n s e r t e d in the f o r m u l a C. All d i m e n s i o n s in inches. T h e n o t a t i o n and the f o r m u h e m u t u a l l y explain each other. A =
],
2 -2 :=
a
J
.
n
il)
(2)
•t
C - - t (H orB') T R5
(3)
T h e s e formulae are i n t e n d e d e x c l u s i v e l y for t he g u i d a n c e of the i n s p e c t o r in a s c e r t a i n i n g t he e x a c t s t r e n g t h of t he joints in th e boilers w h i c h com e u n d e r his care, and w h i c h enable h i m to d e t e r m i n e the w o r k i n g p r e s s u r e of s t e a m
34
Cooper :
[ J. F. 1.,
allowable u n d e r the rules. T h e y do not, however, enable the boiler-maker to d e t e r m i n e directly t h a t proportion of pitch which he should use w i t h a n y g i v e n plate thickness and rivet diameter, in order to secure the s t r o n g e s t joint and which will also pass the h i g h e s t inspection. To secure these results, the following simple formulae were devised by the w r i t e r (early in I882), in which the n o t a t i o n given above is similarly employed, and which m a y be t h u s expressed. For single riveted joints, w h e n iron plates are secured by iron rivets and w h e n the plate thickness a n d rivet diameter are given, if it is desired to find a pitch t h a t will secure e q u a l i t y of plate and rivet section, the f o r m u l a will be: ? =
a + d t
(4)
T h i s plainly m e a n s t h a t the pitch is equal to the area of the rivet hole, divided by the thickness of the plate, and to the result of w h i c h the d i a m e t e r of the rivet hole m u s t be added. For m u l t i p l e r i v e t e d joints, w h e n iron plates are secured by iron rivets, the same f o r m u l a is used, w i t h the addition only of n, r e p r e s e n t i n g the n u m b e r of rows of rivets, thus:
p =,
a + d (5) t T h e different resisting power of equal areas of section, as m a n y times f o u n d by tests of the s h e a r i n g stress of the rivets and the tensile stress of the plates, is not taken into a c c o u n t in the make-up of these rules. T h e y are t r e a t e d in all cases as equals u n d e r the strains of c o n t i n u e d use. T h a t is to say: T h e P h i l a d e l p h i a boiler ordinance and the E n g l i s h rules alike impliedly declare: T h e s h e a r i n g s t r e n g t h of the rivets is j u s t equal to the tensional s t r e n g t h of the plates per square inch of area in boilers m a d e of iron plates and iron rivets. If a n y one takes exception to this t r e a t m e n t of the two strains, the formulae p e r m i t h i m to i n t r o d u c e his own figures of difference into their make-up, by which he can get a result
Aug., I889. ]
Longitudinal Riveted joints.
~35
in accordance w i t h his own belief; b u t of the m a t h e m a t i c a l base, e m b o d i e d in the formulae, we are sure. For single a n d m u l t i p l e riveted joints, w h e n steel plates are secured b y iron or steel rivets, the relative resistance of the plates to tension and of the rivets to shear m u s t be inserted in the formula. First, let us assume, as the rules for inspection have done and do in all cases, that, area for area subjected to stress and a c t i n g together, iron plates and iron rivets are equal in resistance. T h e " B e s t " Staffordshire iron boiler plates will s t a n d 48,0oo p o u n d s 7" per square inch of section; b u t the Board of T r a d e and Lloyd's l i m i t all best iron plates and rivets alike to 47,ooo pounds. T h e P h i l a d e l p h i a ordinance will pass iron plates which have shown on test a T o f 5olC~a p o u n d s per square inch, but will allow no more w h a t e v e r the plates m a y show, and will give full credit to a j o i n t in which the driven rivets have equal section to the p u n c h e d plates. A n d y e t we well know it to be a m a t m r of fact t h a t the shearing s t r e n g t h is less t h a n the tensile s t r e n g t h of the same material. ~' Mr. W i l l i a m H. Shock's e x p e r i m e n t s on A m e r i c a n iron gave as a m e a n for single shear 4I,O33 p o u n d s per square inch, and 78,03 ° p o u n d s for double shear, these e x p e r i m e n t s being m a d e upon iron bolts in a s h e a r i n g device which did not include the u n c e r t a i n e l e m e n t of friction by the r o u g h surfaces of the plates when b o u n d closely by the rivets of a riveted joint m a d e in the usual way. W h e n iron rivets are used w i t h steel plates t h e y are accepted u n d e r the rules for j u s t w h a t t h e y are worth under shear and no more. T h e E n g l i s h rules say: " I r o n rivets in steel boilers should have a section of 1~3 of the plate section." Steel rivets m u s t be calculated from their actual s t r e n g t h to resist s h e a r i n g ; and for these the fraction ~s will express the larger area t h e y m u s t h a v e to the plates with which t h e y are used to m a k e joints, simply because steel plates show an u l t i m a t e T of t w e n t y - e i g h t tons, and steel rivets an" u l t i m a t e S of t w e n t y - t h r e e tons per square i n c h of section.
136
Eooper ."
[ J'. ~'. I.,
T h e old rules published by FairbalrtI, and used b y h i m and by m a n y boiler-makers since, are obsolete now, in t h e light of the later m e t h o d of p r o p o r t i o n i n g j o i n t s and the laws which sanction their use, a l t h o u g h he f u r n i s h e d the first m a t e r i a l for the base upon which this law has been built. F r o m an e x t e n d e d list of all iron single joints, proportioned on the principle of e q u a l i t y of sectional areas, the p e r c e n t a g e of joint s t r e n g t h to the solid plate will reach to •64 ar~l in double joints to "78 and be practically t i g h t under pressures up to, say, ~oo p o u n d s of s t e a m per square i n c h - a m a t e r i a l increase over the oft-quoted figures of "56 and •7o, o r i g i n a t e d and r e c o m m e n d e d b y Fairbairn. If we accept the inspection laws referred to, a s s u m i n g even results of the two strains, t h e n R u l e s 4 and 5 will find the proper pitches for boiler joints m a d e of iron plates a n d iron rivets; b u t in composite boiler shells, the i n t r o d u c t i o n of symbols r e p r e s e n t i n g the a c t u a l powers of resistance of the components, will be necessary. W e will t h e n have for double or multiple joints : S' -=-
t 7"
-'- d
(6)
w h i c h can be applied also to an all-iron joint or to joints m a d e of other m a t e r i a l s t h a n the u s u a l iron and steel. In f o r m u l a 6 m a y be inserted the elastic limit/z" of the plates to tension, i n s t e a d of their u l t i m a t e tensile s t r e n g t h , and w i t h this should also be inserted the stress at which the s h e a r i n g of the rivets begins, t o g e t h e r with a fat{or of safety corresponding to the r e q u i r e m e n t of these i m p o r t a n t factors. If we desire to find the pitch of the rivets, w h e n the rivet d i a m e t e r and a certain p e r c e n t a g e of joint s t r e n g t h are given, we m a y use the following f o r m u l a : d~< % + d
i7)
T h i s does not include the thickness of the plates; it relates only to the proportion existing b e t w e e n t h e ' d i s t a n c e
Aug.. 1889. i
Lon~itudina/ lqivrh,d f oints.
137
from centre to centre of the rivet holes and the space between the holes. O t h e r c o n v e n i e n t formulae are readily o b t a i n e d from A, B and C, by transposition. If, for instance, it is desired to know the S to which the rivets are exposed in any particular case after all the e l e m e n t s have been obtained, the formula will take this shape :
.s,=C/K×f t ×-B
('~)
:and will give the p o u n d s per square inch of cross-section to which the rivets are s u b j e c t e d in the seam by the s t e a m pressure C, w h i c h has been o b t a i n e d by the Ordinance formula. ~-,~. T h e rivet hole d e t e r m i n e s the size and m e a s u r e of the rivet after it is driven, because it is t h e n filled by it : and in m a k i n g calculations w i t h the aid of these formulce, the trade sizes of the rivets must not be taken. In p u n c h i n g holes for rivets in boiler plates, it is the u s u a l practice to use punches ~ of an inch g r e a t e r in .diameter t h a n the trade d i a m e t e r of the rivets, and it is .also u s u a l to m a k e the dies w h i c h are used with the l~unches ~ of an inch larger in d i a m e t e r t h a n the punches t o be used w i t h them. T h e result of this m e t h o d is to anake conical holes in the plates, corresponding to the sizes ,of p u n c h and die. If the p u n c h e d holes are net to the d i m e n s i o n s of the ~punch and die here given, and if the m a t e r i a l of the plate i m m e d i a t e l y a r o u n d the hole has not suffered in the act of ~punching, t h e n the proper size of holes to be used in the :formula would be the mean d i a m e t e r of the conical holes so ~made, i n s t e a d of ~ of an inch larger t h a n the punch, as , t h e y are u s u a l l y a s s u m e d to be. It is well k n o w n , however, t h a t the m a t e r i a l of the plates bordering the holes is w e a k e n e d by the detrusion of the p u n c h ; to w h a t distance this reaches from the surface of visible separation of the m e t a l m a y not be definitely known, and m u s t necessarily be different w i t h different materials and punches, b u t it is certain to be a small m e a s u r a b l e distance into the plate a r o u n d the hole.
38
Cooper.
[ J. F. I.,
If we take the d i a m e t e r of the p u n c h e d holes to be equaI to that of the die, we will not b e far from the actual state of the case, especially as some of this d i s t u r b e d metal is r e m o v e d b y the r e a m e r or c r u s h e d b y the drift-pin. W e are safe in this a s s u m p t i o n in so far as the ultimate s t r e n g t h of the j o i n t is concerned, because, as usually h a p p e n s in rupture, the plates give way, while the rivets rarely fail ; and again, the plates suffer loss of s u b s t a n c e by wear and waste, while the rivets are p r e s e r v e d against deterioration, and, therefore, the initial s t r e n g t h of the plates o u g h t to be favored. In view of these facts, the s u g g e s t i o n is here m a d e that w h e n we wish to d e t e r m i n e pitches from given plates ancl rivets, that we use the greater diameter of the p u n c h e d hole, w h a t e v e r that m a y be, for the q u a n t i t y e x p r e s s e d b y a in all of these formula~, and t h a t we a s s u m e the rivet d i a m e t e r to b e that of the lesser diameter, or r e a m e d - o u t d i a m e t e r of the rivet hole. T h e result of this a p p o r t i o n m e n t of the material will be effectively to s t r e n g t h e n the plates, which all experience has proven to be n e c e s s a r y ; so that while this decision appears to be a g a i n s t reason and the isolated facts (If e x p e r i m e n t - - t h e resistance to s h e a r i n g always p r o v i n g less than that to direct tension in the s a m e m a t e r i a l - - i t must c o n s t a n t l y be borne in mind t h a t the strain on the plates and rivets are not dir:ct in the ordinary lap-joint as t h e y are used in a boiler, the plates b e i n g s u b j e c t e d to some trauso verse strain while u n d e r tension, and the rivets to some tensile strain while u n d e r shear. Strictly speaking, the plate loses w h a t i s p u n c h e d out of it, t o g e t h e r with the m e t a l d e s t r o y e d a r o u n d the p u n c h e d hole, and the rivet gains b y w h a t e v e r increased d i a m e t e r it gets in the process of riveting. T h e y should be e s t i m a t e d upon what t h e y actually are w h e n the joint is m a d e up.
L o n g i t u d i n a l ]¢h,etcd Joz)tts.
I3I
o f the p r o b l e m s presented, and which v a r y w i t h e v e r y building, e v e r y t h i n g b e a r i n g u p o n the s u b j e c t is p a t i e n t l y considered, and with an interest that pertains to seekers for further knowledge. A t the end of ten years, after t a k i n g an interest in matters p e r t a i n i n g to ventilation, I felt I was further back than at the beginning, and at the end of t w e n t y years had made b u t little progress. A t the present time, some ten years later, I am only at the point of s t a r t i n g fresh, hoping, however, to give some i m p e t u s to the cause, and particularly to ineite others to go on to more perfect work.
ON THE L O N G I T U D I N A L R I V E T E D J O I N T S ov STEAM-BOILER SHELLSY BY JOHN H. COOPER.
T h e initial s t a t e m e n t to the English IAoyd's rules for steam boilers is e m b o d i e d in the following words: " T h e strength of circular shells to be calculated from the strength of the longitudinal joints," which assures us that this part of the boiler should be properly proportioned. To these rules a m e m o r a n d u m is added: " I n any case where the s t r e n g t h of the longitudinal joint is satisfactorily shown b y e x p e r i m e n t to be g r e a t e r than given b y this formula (Lloyd's), the actual s t r e n g t h m a y be taken in the calculation." L a t e r on, Lloyd's rules (under the head of " P e r i o d i c a l Surveys," r e g a r d i n g the e x a m i n a t i o n of boilers after t h e y have been several years in service) say: " T h e safe w o r k i n g pressure is to b, d e t e r m i n e d b y their actual condition." T h e s e s t a t e m e n t s lie in the line of practical efficiency, and point to the necessity of providing material in accordance with the r e q u i r e m e n t of the load to be carried. Read at the Nineteenth Meeting of the American Society of Mechanical Engineers, and revised by the author for publication in the.JoURNAL from advance-sheets of the Transactions.
I32
Cooper:
[J. F. 1.,
A n y one who takes the trouble to collect and compare d a t a on this subject c a n n o t fail to notice the g r e a t disparity of rules for d e t e r m i n i n g the w o r k i n g pressure permissible for boilers. T h e case is clear by simple r e a s o n i n g on the d a t a collated, t h a t boilers are held together, it w o u l d seem, more b y conf o r m i t y to rule t h a n by the m a t e r i a l s of which t h e y a r e made. But, of course, the true course to p u r s u e is to give to each m e m b e r its proper allowance of section, in order t h a t the components of the joint shall have an equal chance under strain according to its resisting power. T h e d i m i n i s h e d s t r e n g t h of the shell of a boiler by the l o n g i t u d i n a l joint is well known, and it becomes good engin e e r i n g so to proportion its parts as to obtain t h e greatest s t r e n g t h possible w i t h i n the limits of practical economy. W h e n it became necessary to assure t h e m s e l v e s confidently of the p e r m a n e n t safety of a s t r u c t u r e composed of plates held t o g e t h e r by rivets, engineers were not long in finding o u t t h a t a certain a l l o t m e n t of rivet section to plate section at the joints was necessary, and t h a t these sections were f o u n d to be n e a r l y equal in the s t r o n g e s t joints. T h e e x p e r i m e n t s o f Fairbairn, c o n d u c t e d in the year I 8 3 8 , proved t h a t - - " t h e sectional area of the rivets in a .joint was n e a r l y equal to the sectional a r e a o~ the plate t h r o u g h the rivet holes." S u b s e q u e n t e x p e r i m e n t s by Clark on riveted plates for the Britannia and C o n w a y T u b u l a r Bridge fully corroborate the above s t a t e m e n t ; his conclusion was: " T h e collective area of the rivets is equal to the sectional area of the plate t h r o u g h the rivet holes." T h i s relation of the c o m p o n e n t s of the j o i n t in course of time became e m b o d i e d in the E n g l i s h Board of T r a d e rules and in Lloyd's rules now in force, r e g u l a t i n g the construction of steam boilers. It also forms the basis of the Philadelphia steam-boiler inspection ordinance, first f o r m u l a t e d in 1882. R e f e r r i n g now to those rules only which relate to the proportions of the l o n g i t u d i n a l joints of the cylindrical
Aug., I889.]
Longitmtinal Rivctcd faints,
x33
shells of boilers, we are p r e p a r e d to say t h e y m a y b e most c o n v e n i e n t l y p r e s e n t e d b y t he following n o t a t i o n and formulae : NOTATION.
H = P e r c e n t a g e of p u n c h e d pl at e to t h e solid plate. B = P e r c e n t a g e of d r i v e n r i v e t section to t h e solid plate. ( = T h e p r e s s u r e i n p o u n d s pe r s q u a r e inch, w h i c h the b o iler is allowed to carry. a = A r e a of d r i v e n rivet, or r i v e t hole. d--- D i a m e t e r of r i v e t hole. n .= N u m b e r of rows of rivets. 2 = P i t c h of rivets. t -= T h i c k n e s s of plates. R = R a d i u s of boiler shell. S --= U l t i m a t e sheari," 2 s t r e n g t h of rivets in pounds, per s q u a r e i nch of section. 7"-----Ultimate tensile s t r e n g t h of plates in pounds, per s q u a r e i nch of section. f = F a c t o r of safety. E = L i m i t of e l a s t i c i t y in t h e plates in pounds, per s q u a r e inch of section. = P e r c e n t a g e of j o i n t s t r e n g t h . T h e least of A or .6' s h o u l d be i n s e r t e d in the f o r m u l a C. All d i m e n s i o n s in inches. T h e n o t a t i o n and the f o r m u h e m u t u a l l y explain each other. A =
],
2 -2 :=
a
J
.
n
il)
(2)
•t
C - - t (H orB') T R5
(3)
T h e s e formulae are i n t e n d e d e x c l u s i v e l y for t he g u i d a n c e of the i n s p e c t o r in a s c e r t a i n i n g t he e x a c t s t r e n g t h of t he joints in th e boilers w h i c h com e u n d e r his care, and w h i c h enable h i m to d e t e r m i n e the w o r k i n g p r e s s u r e of s t e a m
34
Cooper :
[ J. F. 1.,
allowable u n d e r the rules. T h e y do not, however, enable the boiler-maker to d e t e r m i n e directly t h a t proportion of pitch which he should use w i t h a n y g i v e n plate thickness and rivet diameter, in order to secure the s t r o n g e s t joint and which will also pass the h i g h e s t inspection. To secure these results, the following simple formulae were devised by the w r i t e r (early in I882), in which the n o t a t i o n given above is similarly employed, and which m a y be t h u s expressed. For single riveted joints, w h e n iron plates are secured by iron rivets and w h e n the plate thickness a n d rivet diameter are given, if it is desired to find a pitch t h a t will secure e q u a l i t y of plate and rivet section, the f o r m u l a will be: ? =
a + d t
(4)
T h i s plainly m e a n s t h a t the pitch is equal to the area of the rivet hole, divided by the thickness of the plate, and to the result of w h i c h the d i a m e t e r of the rivet hole m u s t be added. For m u l t i p l e r i v e t e d joints, w h e n iron plates are secured by iron rivets, the same f o r m u l a is used, w i t h the addition only of n, r e p r e s e n t i n g the n u m b e r of rows of rivets, thus:
p =,
a + d (5) t T h e different resisting power of equal areas of section, as m a n y times f o u n d by tests of the s h e a r i n g stress of the rivets and the tensile stress of the plates, is not taken into a c c o u n t in the make-up of these rules. T h e y are t r e a t e d in all cases as equals u n d e r the strains of c o n t i n u e d use. T h a t is to say: T h e P h i l a d e l p h i a boiler ordinance and the E n g l i s h rules alike impliedly declare: T h e s h e a r i n g s t r e n g t h of the rivets is j u s t equal to the tensional s t r e n g t h of the plates per square inch of area in boilers m a d e of iron plates and iron rivets. If a n y one takes exception to this t r e a t m e n t of the two strains, the formulae p e r m i t h i m to i n t r o d u c e his own figures of difference into their make-up, by which he can get a result
Aug., I889. ]
Longitudinal Riveted joints.
~35
in accordance w i t h his own belief; b u t of the m a t h e m a t i c a l base, e m b o d i e d in the formulae, we are sure. For single a n d m u l t i p l e riveted joints, w h e n steel plates are secured b y iron or steel rivets, the relative resistance of the plates to tension and of the rivets to shear m u s t be inserted in the formula. First, let us assume, as the rules for inspection have done and do in all cases, that, area for area subjected to stress and a c t i n g together, iron plates and iron rivets are equal in resistance. T h e " B e s t " Staffordshire iron boiler plates will s t a n d 48,0oo p o u n d s 7" per square inch of section; b u t the Board of T r a d e and Lloyd's l i m i t all best iron plates and rivets alike to 47,ooo pounds. T h e P h i l a d e l p h i a ordinance will pass iron plates which have shown on test a T o f 5olC~a p o u n d s per square inch, but will allow no more w h a t e v e r the plates m a y show, and will give full credit to a j o i n t in which the driven rivets have equal section to the p u n c h e d plates. A n d y e t we well know it to be a m a t m r of fact t h a t the shearing s t r e n g t h is less t h a n the tensile s t r e n g t h of the same material. ~' Mr. W i l l i a m H. Shock's e x p e r i m e n t s on A m e r i c a n iron gave as a m e a n for single shear 4I,O33 p o u n d s per square inch, and 78,03 ° p o u n d s for double shear, these e x p e r i m e n t s being m a d e upon iron bolts in a s h e a r i n g device which did not include the u n c e r t a i n e l e m e n t of friction by the r o u g h surfaces of the plates when b o u n d closely by the rivets of a riveted joint m a d e in the usual way. W h e n iron rivets are used w i t h steel plates t h e y are accepted u n d e r the rules for j u s t w h a t t h e y are worth under shear and no more. T h e E n g l i s h rules say: " I r o n rivets in steel boilers should have a section of 1~3 of the plate section." Steel rivets m u s t be calculated from their actual s t r e n g t h to resist s h e a r i n g ; and for these the fraction ~s will express the larger area t h e y m u s t h a v e to the plates with which t h e y are used to m a k e joints, simply because steel plates show an u l t i m a t e T of t w e n t y - e i g h t tons, and steel rivets an" u l t i m a t e S of t w e n t y - t h r e e tons per square i n c h of section.
136
Eooper ."
[ J'. ~'. I.,
T h e old rules published by FairbalrtI, and used b y h i m and by m a n y boiler-makers since, are obsolete now, in t h e light of the later m e t h o d of p r o p o r t i o n i n g j o i n t s and the laws which sanction their use, a l t h o u g h he f u r n i s h e d the first m a t e r i a l for the base upon which this law has been built. F r o m an e x t e n d e d list of all iron single joints, proportioned on the principle of e q u a l i t y of sectional areas, the p e r c e n t a g e of joint s t r e n g t h to the solid plate will reach to •64 ar~l in double joints to "78 and be practically t i g h t under pressures up to, say, ~oo p o u n d s of s t e a m per square i n c h - a m a t e r i a l increase over the oft-quoted figures of "56 and •7o, o r i g i n a t e d and r e c o m m e n d e d b y Fairbairn. If we accept the inspection laws referred to, a s s u m i n g even results of the two strains, t h e n R u l e s 4 and 5 will find the proper pitches for boiler joints m a d e of iron plates a n d iron rivets; b u t in composite boiler shells, the i n t r o d u c t i o n of symbols r e p r e s e n t i n g the a c t u a l powers of resistance of the components, will be necessary. W e will t h e n have for double or multiple joints : S' -=-
t 7"
-'- d
(6)
w h i c h can be applied also to an all-iron joint or to joints m a d e of other m a t e r i a l s t h a n the u s u a l iron and steel. In f o r m u l a 6 m a y be inserted the elastic limit/z" of the plates to tension, i n s t e a d of their u l t i m a t e tensile s t r e n g t h , and w i t h this should also be inserted the stress at which the s h e a r i n g of the rivets begins, t o g e t h e r with a fat{or of safety corresponding to the r e q u i r e m e n t of these i m p o r t a n t factors. If we desire to find the pitch of the rivets, w h e n the rivet d i a m e t e r and a certain p e r c e n t a g e of joint s t r e n g t h are given, we m a y use the following f o r m u l a : d~< % + d
i7)
T h i s does not include the thickness of the plates; it relates only to the proportion existing b e t w e e n t h e ' d i s t a n c e
Aug.. 1889. i
Lon~itudina/ lqivrh,d f oints.
137
from centre to centre of the rivet holes and the space between the holes. O t h e r c o n v e n i e n t formulae are readily o b t a i n e d from A, B and C, by transposition. If, for instance, it is desired to know the S to which the rivets are exposed in any particular case after all the e l e m e n t s have been obtained, the formula will take this shape :
.s,=C/K×f t ×-B
('~)
:and will give the p o u n d s per square inch of cross-section to which the rivets are s u b j e c t e d in the seam by the s t e a m pressure C, w h i c h has been o b t a i n e d by the Ordinance formula. ~-,~. T h e rivet hole d e t e r m i n e s the size and m e a s u r e of the rivet after it is driven, because it is t h e n filled by it : and in m a k i n g calculations w i t h the aid of these formulce, the trade sizes of the rivets must not be taken. In p u n c h i n g holes for rivets in boiler plates, it is the u s u a l practice to use punches ~ of an inch g r e a t e r in .diameter t h a n the trade d i a m e t e r of the rivets, and it is .also u s u a l to m a k e the dies w h i c h are used with the l~unches ~ of an inch larger in d i a m e t e r t h a n the punches t o be used w i t h them. T h e result of this m e t h o d is to anake conical holes in the plates, corresponding to the sizes ,of p u n c h and die. If the p u n c h e d holes are net to the d i m e n s i o n s of the ~punch and die here given, and if the m a t e r i a l of the plate i m m e d i a t e l y a r o u n d the hole has not suffered in the act of ~punching, t h e n the proper size of holes to be used in the :formula would be the mean d i a m e t e r of the conical holes so ~made, i n s t e a d of ~ of an inch larger t h a n the punch, as , t h e y are u s u a l l y a s s u m e d to be. It is well k n o w n , however, t h a t the m a t e r i a l of the plates bordering the holes is w e a k e n e d by the detrusion of the p u n c h ; to w h a t distance this reaches from the surface of visible separation of the m e t a l m a y not be definitely known, and m u s t necessarily be different w i t h different materials and punches, b u t it is certain to be a small m e a s u r a b l e distance into the plate a r o u n d the hole.
38
Cooper.
[ J. F. I.,
If we take the d i a m e t e r of the p u n c h e d holes to be equaI to that of the die, we will not b e far from the actual state of the case, especially as some of this d i s t u r b e d metal is r e m o v e d b y the r e a m e r or c r u s h e d b y the drift-pin. W e are safe in this a s s u m p t i o n in so far as the ultimate s t r e n g t h of the j o i n t is concerned, because, as usually h a p p e n s in rupture, the plates give way, while the rivets rarely fail ; and again, the plates suffer loss of s u b s t a n c e by wear and waste, while the rivets are p r e s e r v e d against deterioration, and, therefore, the initial s t r e n g t h of the plates o u g h t to be favored. In view of these facts, the s u g g e s t i o n is here m a d e that w h e n we wish to d e t e r m i n e pitches from given plates ancl rivets, that we use the greater diameter of the p u n c h e d hole, w h a t e v e r that m a y be, for the q u a n t i t y e x p r e s s e d b y a in all of these formula~, and t h a t we a s s u m e the rivet d i a m e t e r to b e that of the lesser diameter, or r e a m e d - o u t d i a m e t e r of the rivet hole. T h e result of this a p p o r t i o n m e n t of the material will be effectively to s t r e n g t h e n the plates, which all experience has proven to be n e c e s s a r y ; so that while this decision appears to be a g a i n s t reason and the isolated facts (If e x p e r i m e n t - - t h e resistance to s h e a r i n g always p r o v i n g less than that to direct tension in the s a m e m a t e r i a l - - i t must c o n s t a n t l y be borne in mind t h a t the strain on the plates and rivets are not dir:ct in the ordinary lap-joint as t h e y are used in a boiler, the plates b e i n g s u b j e c t e d to some trauso verse strain while u n d e r tension, and the rivets to some tensile strain while u n d e r shear. Strictly speaking, the plate loses w h a t i s p u n c h e d out of it, t o g e t h e r with the m e t a l d e s t r o y e d a r o u n d the p u n c h e d hole, and the rivet gains b y w h a t e v e r increased d i a m e t e r it gets in the process of riveting. T h e y should be e s t i m a t e d upon what t h e y actually are w h e n the joint is m a d e up.