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Des ign of Bolts or Rivets Subject to CombinedShe a r a n d TensionPaper presented by ALFRED ZWEIG (April, 1966, issue)

Discussion by W. B E R T W E L LM U C H HAS BEEN WRITTEN on the subject of structurals teel b rackets , the la tes t being the p a p e r by Mr. Z w e i gin the Ap r i l , 1966 Engineering Journal. U n f o r t u n a t e l y ,t h e b as i c as su m p t io n of his d e v e l o p m e n t t h a t then eu t r a l ax i s of the c o n n e c t i o n is at the cen t ro id of thef as t en er sis d i sp u t ab l e , to say the least . One of theb e s t t r e a t m e n t s of th is subject was p resen t ed by P r o fessor J. E. L o t h e r s , in A S C E P a p e r N o . 2 3 4 7 , V o l . 116of Transactions. Professor Lothers found the n e u t r a lax is to be a b o u t 0.94 of the l e n g t h of the angles f romt h e i r top.

In v i ew of the m a n y v a r i a b l e s , it is d o u b t fu l t h a tg r e a t a c c u r a c y is w a r r a n t e d . T h e r e f o r e , it has b e e n thewri t e r ' s p rac t i ce to t ak e the n eu t r a l ax i s at the b o t t o mof the an g les . The ca l cu l a t i o n s r eq u i r ed are t h e n ext r em ely s im p le . The to tal tension in all the bol ts is them o m e n t d i v i d e d by % the h e i g h t of the c o n n e c t i o n ,a n d the m a x i m u m b o l t t e n s i o n is twice the a v e r a g e ,p lu s a co r rec t i o n d escr ib ed b e lo w. I t seem s ev id en tt h a t the co m p ara t i v e ly g rea t f l ex ib i l i t y 'of the a n g l elegs in " f l a t " b en d in g j u s ti f ies t h i s p ro ced u re .

Th e m o s t c r i t i ca l i t em s in su ch co n n ec t io n s areu su a l ly the b en d in g s t r es s in the angle legs carry ing theb o l t s wh ich are in tension , and the co r resp o n d in g s t r es sin the e l e m e n t of the m e m b e r to w h i c h the b r a c k e ti s a t t ach ed . In the case of the angle, using ProfessorLo th er s ' t e rm in o lo g y , the stress in the u p p e r i n c h ofeach an g le is

(V - 0.6R)s = 4 . 5 M - t2h 2i n wh ich

s = U n i t s t r es s in the an g leM = T o t a l m o m e n t on the c o n n e c t i o n

W. Bertwell is Ch ief Structural Engineer, Ka iser Engineers, Oak land,Calif.

g = G a g e of angle less its th icknessh = H e i g h t of co n n ec t io n ( l en g th of an g le )R = R a d i u s of angle fi l lett = Th ick n ess of a n g l e

T h e r a d i u s ofthe f il let i s take n in to acc oun t abov e in aso m ewh at d i f f e ren t way f ro m th a t of Professor Lothers ,b u t the resu l t is a lm o s t i d en t i ca l . It may be o m i t t e da l t o g e th er for g rea t e r s im p l i c i t y but a g rea t e r v a lu e of twil l then be r e q u i r e d .

A fur ther obvious safety measure is to use, as al imi t ing s t ress , the b en d in g s t r es s on the ne t sect ion of t h ean g le leg, t h u s :

h~e\/ 0.5p + e \, ~ T / \0.Sp + e - d)

w h e r ee = End dis tance beyond most h ighly s t ressed bol td = D i a m e t e r of h o lep = Pi t ch of the bol ts

T h e c o m p u t a t i o n s for b e n d i n g , as noted before,m u s t be r e p e a t e d for the column flanges, or the ap p ro p r i a t e su p p o r t i n g p ar t . In some cases a s t ress comb i n a t i o n at the b r a c k e t m i g h t be ser ious.

T o o b t a i n the a d d i t i o n to the b o l t t en s io n m en t io n edab o v e , the "p ry in g ac t i o n " d escr ib ed in the c o m m e n t a r yto the AISG sp ec i f i ca t i o n m u s t be a p p r o x i m a t e d . R e f e r r i n g to L. E. G r i n t e r ' s " D e s i g n of M o d e r n S te e l S t r u c t u r e s " , this ' is

tM _ 2 \ l%g - 0 . 6 f l \VAhN)X\ q jw h e r e

N = The t o t a l n u m b e r of bol tsq = The d i s t an ce f ro m cen t e r of b o l t s to toe of

an g leF in a l l y , Ex am p le 4 of M r . Z w e i g 's p a p e r is e r r o n e o u s

in assign ing equal effect iveness to all the r i v e t s . Th o sein the outer rows wi l l p rovide l i t t le or no tensile resista n c e , and should be d i s reg ard ed ex cep t in sh ear . Thep a t t e r n of bol ts in E x a m p l e 3 is a l so o b j ec t i o n ab l e , fors imi lar reasons.

M a x . s = A.5M(g - 0.6R)

O C T O B E R / 1 9 6 6

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Discussion by A L F R E D Z W E I GM R . B ER T W E LL ' S cr i t i c i sm can b e su m m ar i zed i n t h rees t a t e m e n t s :

1. Th e n eu t r a l ax i s sh o u ld b e p l aced a t t h e b o t to m o fth e c l i p an g l es r a th er t h an a t t h e cen t e r o f t h efas t en er g ro u p .

2. T he a ddi t ion al force in the bo l ts resu l t ing f rom the"p ry in g ac t i o n " sh o u ld b e co n s id ered .

3 I n cl ip angles wi th tw o gag e l ines , bo l ts o r r ivetsin the ou ter row should be d isregarded in tension .

I t was , o f co u r se , k n o wn an d s t a t ed so i n t h e p a p e ru n d er d i scu ss io n t h a t t h e n e u t r a l ax i s is b e lo w th e ce n t e r -l ine and i t w a s . n o oversigh t to assume i t a t the cen ter o fth e f as t en er g ro u p . Th i s was d o n e d e l i b era t e ly t oco n fo rm to co m m o n p rac t i ce , a s d em o n s t r a t ed i n t h eex am p le o n p ag e 4 -5 1 o f t h e l a t es t M an u a l o f S t ee lC o n s t r u c t i o n .

T he assu mp t ion is obviously on the safe s ide and i tm ig h t t h e re fo re b e c r i t ic i zed as cau s in g u n d u e was t e ,s ince i t assumes tensi le forces in the ex t reme connectorswh ic h a re u p t o an d m o re t h a n twice as m u ch as t h o seobtained f rom the locat ion of a neut ral ax is proposedb y M r . B e r t w e l l .

Th i s p ro b l em sh o u ld b e r ev i ewed , h o wev er , i n i t swh o le co n t ex t wh ich b r in g s u s t o t h e seco n d p o in t o fM r . Ber twel l , t h a t of t h e o m iss io n o f t h e "p ry i n g ac t i o n " .For those w ho are no t famil ia r w i th th is expression itm ig h t b e wel l t o ex p l a in t h a t M r . Ber twel l h as t h e reb ym ad e r e fe ren ce t o t h e ad d i t i o n a l t en s io n i n t h e b o l t a s aco n seq u en ce o f t h e en d r es t r a in t o ccu r r in g i n t h ec l i p an g l es . Th i s en d r es t r a in t p e rm i t s u s t o d es ig n t h esean g les for b en d in g m o m en t s o f h a l f t h e m ag n i tu d eco m p ar ed t o t h o se o ccu r r in g i n u n res t r a in ed co n nect io ns as show n in the design exam ple on pa ge 4-67of t h e A I S G M a n u a l .

To assu re t h is en d r es t r a in t , h o wev er , co n s id erab l efo rce is i n d u ce d i n to t h e co n n e c to r . G r in t e r h as sh o wnin t h e r e fe ren ce c i t ed b y M r . Ber twel l t h a t t h i s ad d i t i o n a lforce i s l ikely to almost d ou ble the basic bo l t s t ress ,d ep en d in g u p o n s i ze an d t h i ck n ess o f t h e c l i p an g l e .

I f we n o w co m b in e t h e two ap p are n t e r ro r s m en t i o n ed b y M r . Ber twel l , t h a t r esu l t i n g f ro m a l o werlocat io n of the neu t ra l ax is an d tha t resu l t in g f romnegle ct ing the so cal led "p ry in g act i on" , we f ind that inmost cases these errors wi l l more or less offset o r comp le t e ly can ce l each o th er . I t , t h e re fo re , b eco m es ev id en tth a t t h e co m m o n ly u sed as su m p t io n o f p l ac in g t h eneutral ax is in the cen ter o f the fastener group is wel ljust i f ied as i t permi ts no t on ly a very s imple so lu t ionto the problem but i t a lso resu l ts in answers which arev ery c lo se t o t h o se o b t a in ed b y t h e m o re c i r cu i t o u sap p ro a ch su g ges t ed b y M r . Ber twel l .Alfred Zweig is Chief Structural Engineer, Albert Kahn Associated

Architects & Engineers, Detroit, Mich.

N ow f inally a few wo rds abou t the th i rd ob jec t ionra i sed b y M r . Ber twel l , t h a t is h i s su m m a r i l y s t a t edasse r t i o n t h a t co n n ec to r s i n t h e o u t e r ro w wi l l p ro v id el i t t le o r no tensi le res is tance and should be d isregardedex cep t i n sh ear .

I t i s obviou s that h is s tatem en t i s based o n theassu mp t ion th at tensi le forces in the ou ter row wi l loverst ress the cl ip angle to such an ex ten t that theseconnectors wi l l become pract ical ly ineffect ive in tensionan d sh o u ld t h ere fo re b e d i s r eg ard ed .

I t s hould b e s tate d , f i rst , tha t i t wa s the in ten t o f thetab les pr in ted in the Apri l i ssue so lely to s impl i fy thedesign of the fasteners of bracket connect ions in thel igh t o f the new speci f icat ions per tain ing to combinedsh ear an d t en s io n an d n o th in g e l se . N e i th er t h e t ab l esn o r t h e e x am p les were i n t en d e d t o b e u sed i n t h e d es ig nof the cl ip angles . I t i s , o f course, assumed that the cl ipangles must be s t rong enough to res is t the forces inducedby the fasteners an d i t i s also kn ow n tha t f reque nt lythe s ize of the cl ip angles rather than that o f the fas tenerswi l l d e t e rm in e t h e s t r en g th o f t h e b rack e t co n n ec t io n .

As t h i s sp ec i f i c cau t io n ary s t a t em en t was o m i t t edin t h e o r ig in a l p ap er , M r . Ber twel l ' s wa rn in g wo u ld b ecom plete ly just i f ied a nd val id i f i t we re no t wor ded ins u c h g e n e r a l t e r m s .

The effect iveness of the connector in the ou ts idero w d e p en d s u p o n th e b en d in g s t r es s in t h e c li p an g l e ,wh ich in tu r n i s a funct ion of the tensi le force in th eco n n ec to r an d o f t h e an g l e t h i ck n ess . I n ex t r em e casesi t was fo u n d n ecessa ry t o weld h o r i zo n t a l d i a p h r ag m sin to the cl ip angles when the angle th ickness was inadequate to res is t the bending s t resses therein .

Th e fu n c t io n of su ch a h o r i zo n t a l d i ap h ra g m can b erep l ace d by the top p lat e of the brac ket . I f the to pplates of the brackets shown in Figs . 2 to 5 in the Apri li ssue are welded to the cl ip angles they wi l l be s t rongenough to res is t the hor izontal pu l l , and for th is reasonthe fasteners in the ou ts ide row can be assumed toresis t the fu l l tensi le force as the hor izontal force at theb rack e t t o p is t r an s fe r r ed t o t h e v er t i ca l p l a t e t h ro u g hth e h o r i zo n t a l p l a t e r a th er t h an t h e weak an g le l eg s .

In the l igh t o f these observat ions except ion must bet ak en t o M r . Ber twel l ' s s t a t em en t t h a t "E x a m p le 4 ise r ro n eo u s . . . an d Ex a m p le 3 is a l so o b j ec t i o n ab l e . "

Wh i l e i t is t h u s sh o wn th a t M r . Ber twel l ' s co m m e n t sd id n o t i n v a l i d a t e t h e t ab l es p resen t ed i n t h e Ap r i li s su e , h i s o b serv a t i o n s a r e welco m e an d o f g rea t v a lu ein asm u ch as t h ey b ro u g h t ag a in b efo re t h e p ro fess ionth e b ac k g ro u n d for t h e d es ig n o f s t eel b rack e t s an despecial ly the necessi ty to invest igate no t on ly thes t r en g th o f t h e fas t en er s b u t a l so th e s t ru c tu ra l ad e q u a cyof the cl ip angles .*

* M r . Zweig, w ho submitted this discussion, also suggested thatfurther comments by Mr. Bertwell might be helpful to the reader.Accordingly, here are the supplementary remarks by Mr. Bertwell:

166A I S C E N G I N E E R I N G J O U R N A L

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1. Amplification of expression for stress in connection angle. Th edistance (g 0.6R) is illustrated in the sketch below . The effectivespan betw een points of fixity of angle leg is assumed to be (g 0.6R).This gives the strengthening effect of the fillet about the same as calculated by Professor Lothers.

. 585 R .6R1

I AU,45 "V

g - .6R

porting m ember as triangular, as assumed by Professor L. E. Grinter{paragraph 35, pp. 53-54 of his book), this moment is

()Equating these two exp ressions for the moment in the angle

c - ! F ^Then c= m\N h 3 (g - 0.6R) ]

an dtotal bolt pull = 3M 3MT 3(g-0.6R\\Nh +L ~ Nhl7 + 4\ q )\

The connection is made up of two angles. The maximum forceper inch at the top of one angle is

A = (S x *) 3 MMom ent in angle leg at center of bolt is

fg - 0.6R\ 3Mi^i) 4h 2 (g ~ 0.6R)Then

? [ 3M (g h 20.6R)1 4.5M(g - 0.6R)In order to take account, roughly and on the safe side, of the bolt

hole in the angle, the above stress may be multiplied by two ratios:distance from N.A. to