8/13/2019 Discussion- Torsion of Rolled Steel Sections in Building Structures

1/2

  i s c u s s i o n

91

Torsion  o f Rol led Stee l S ect ions inBui ld ing S t ruc turesPaper presented by JO HN   G. HOTCH KISS (January , 1966, Issue)

Discussion  by J O H N  C B U R T O NI  S HOULD LI KE  to suggest a very careful dimensionalanalysis   of  E x a m p l e  4 on  p a g e  30 for I  feel such  ananalysis  may rev ea l  an  e r r o r  of the  m a g n i t u d e  of 10 int h e ca l cu l a t i o n s .Discussion  by J O H N  G H O T C H K I S SW E A P PR E C I A TE  y o u r ca l l i n g a t t en t i o n  to  E x a m p l e  4.Th e e r ro r i n v o lv ed  the  in co r rec t so lu t io n  for the  m a x i m u m w a r p i n g m o m e n t  at  m i d s p a n  as  d e t e r m i n e d f r omJohn  C. Burton  is Associate Civil E ngineer,  San Diego  Gas Electric

Company,  San Diego,  Calif.John  G. Hotchkiss  is  Senior Regional E ngineer, A merican Institute  of

Steel Construction,  New  York,  N. Y.

A P R I L /  1 9 6 6

8/13/2019 Discussion- Torsion of Rolled Steel Sections in Building Structures

2/2

w  = 2 k / f t

ftl

ro102 J 2

A-k.T2 12

11 600 psi1

1 ^

4 3 , 2 0 0 psi

- l l , 6 0 0 p s i 43 ,200ps i

Figures  17 and 18  {corrected)

T a b l e 2 . T h e c o r r e c t e q u a t i o n a p p e a r i n g i n T a b l e 2 ,D2ml2S h o r t M e t h o d , p a g e 4 1 , s h o u l d r e a d , m a x  Mw  = — - —h

( l b - in . ) . Th e t e rm   h was o m i t t e d i n t h e o r ig in a l a r tw o rk .A t y p o g r a p h i c e r r o r i n t h e N o m e n c l a t u r e o n p a g e 3 1

should also be no ted . The def in i t ion of   m  sh o u ld r eadU n i fo rm ly d i s t r i b u t ed t o r s io n a l l o ad ( l b - in . / i n . o r

l b - f t / f t ) '5 .E x a m p l e 4 r e v i s e d )Given:  A b e a m b u i l t - u p b y w e l d i n g t h r e e p l a te s r e s e m

bl ing an I -sect ion i s loa ded wi th a un i form ly d ist r ib u te d tors ional m om en t m = 1 ,000 lb-f t / f t over theen t i r e sp an o f 4 6 f t. Th e en d co n n ec t io n s a re as su m e dto b e b o l t ed web c l i p an g l es , Ty p e 2 co n s t ru c t i o n .De te rm in e i f t h e ad d i t i v e t o r s io n a l n o rm al s t res ses a rew i t h i n p e r m i s si b l e l i m it s b y t h e Q u i c k M e t h o d a n dch eck r esu l t s b y t h e Ex ac t m eth o d ,  e =  6 in . ,  w  =2,000 lb / f t , see Fig . 17 .)

Solution:m =  (2 ,0 0 0 X 6 ) /1 2

m o m en t , s ee F ig . 5 )1 ,000 lb- in . / in . (posi t ive

Dete rm in e t h e t o r s io n a l co n s t an t s an d p ro p er t i e sf ro m Ch ar t 1 :Cw  = -b*m =  — 123  X  5 3 . 52  X 0 . 5 024 24

= 103 ,000 in . 62 1K =   -bfi  +  -hh*

J

=  - X 1 2 X 0 . 5 0 3  + - X 53 X 0 .5 03= 3 .2 1 i n .4

bh   1 2 X 5 3 . 5  2W m « =  — =  = 1 6 0 , 5 m /4 4X = 0 . 6 2 \ — = 0 . 6 2 ^ - ^ ^ = 0 . 0 0 3 4 1 i n . - 1*C W  ^ 1 0 3 , 0 0 0

\l =  0 .0 0 3 4 1 X 552 = 1 .8 8Cw  103 ,000ow =  642 in .4W max  1 6 0 . 5

D e t e r m i n e t h e m o m e n t o f i n e r t i a  Iy/2 :S in ce  Sw  =  a n d  Cw  —

ly  U a , X Z^nth en - = ;—2  h2/26 4 2 X 1 6 0 . 5

5 3 . 5 2 / 2 72 in.4

D e t e r m i n e m a x i m u m w a r p i n g m o m e n t a t m i d s p a nf r o m T a b l e 2 , S h o r t M e t h o d . ( N o t e t h e m o m e n t   Mwas u sed i n Tab le 2 is expressed in lb - in . an d shou ld n otbe confused wi th  Mw  th e b im o m en t ex p ressed as l b -in .2  u sed e l sewh ere i n t h i s p ap er . ) S in ce  \l =  1 .88 , al i n e a r i n t e r p o l a t i o n b e t w e e n  \l =  1 .5 an d 2 .0 g iv esD2  =  0 . 0 9 1 1 .

D 2ml2  0 .0 91 1 X 1 ,000 X 5522T h e n m a x  Mw  — 5 3 . 5

m a x  aw= 518 ,000 lb- in .

M w  518 ,000 X 6

= 43 ,200 psi (where  a = b/2)

D e t e r m i n e m a x i m u m m o m e n t d u e to p l a n e b e n d i n g a tm i d s p a n :m a x  Mb  = wP   2 ,000 X 46

2- 529 ,000 lb-ft

M b  529 ,000 X 12m a x  ab  = — —  —— = 11 ,600 psiSx  547C o m b i n e d n o r m a l s t r e s s e s : m a x  aw  + m a x