Mat Chapter 26

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Mat Chapter 26
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  STEEL-CONCRETE COMPOSITE COLUMNS-II   STEEL-CONCRETE COMPOSITE COLUMNS-II 1.0 INTRODUCTION In a previous chapter, the design of a stee-concrete co!posite cou!n under a iaoading #as discussed$ This chapter deas #ith the design of stee-concrete co!positecou!ns su%&ected to %oth a ia oad and %ending$ To   design a co!posite cou!n under co!%ined co!pression and %ending, it is first isoated fro! the fra!e#or', and the end!o!ents #hich resut fro! the ana(sis of the s(ste! as a #hoe are ta'en to act on thecou!n under consideration$ Interna !o!ents and forces #ithin the cou!n ength aredeter!ined fro! the structura consideration of end !o!ents, a ia and transverse oads$)or each a is of s(!!etr(, the %uc'ing resistance to co!pression is first chec'ed #iththe reevant non-di!ensiona senderness of the co!posite cou!n$ Thereafter the!o!ent resistance of the co!posite cross-section is chec'ed in the presence of appied!o!ent a%out each a is, e$g$  x-x  and  y-y  a is, #ith the reevant non-di!ensionasenderness vaues of the co!posite cou!n$ )or sender cou!ns, %oth the effects of ongter! oading and the second order effects are incuded$ 2.0COMBINED COMPRESSION AND UNI-AXIAL BENDING The design !ethod descri%ed here is an e tension of the si!pified design !ethoddiscussed in the previous chapter for the design of stee-concrete co!posite cou!nsunder a ia oad$ 2.1 Interaction Cr!e or Co#$re%%ion an& Uni-a'ia( Ben&in) The resistance of the co!posite cou!n to co!%ined co!pression and %ending isdeter!ined using an interaction curve$ )ig$ 1 represents the non-di!ensiona interactioncurve for co!pression and uni-a ia %ending for a co!posite cross-section$ In a t(pica interaction curve of a cou!n #ith stee section on(, it is o%served that the!o!ent of resistance undergoes a continuous reduction #ith an increase in the a ia oad$*o#ever, a short co!posite cou!n #i often e hi%it increases in the !o!ent resistance %e(ond pastic !o!ent under reative( o# vaues of a ia oad$ This is %ecause under so!e favoura%e conditions, the co!pressive a ia oad #oud prevent concrete crac'ingand !a'e the co!posite cross-section of a short cou!n !ore effective in resisting!o!ents$ The interaction curve for a short co!posite cou!n can %e o%tained %(considering severa positions of the neutra a is of the cross-section, h n , and deter!iningthe interna forces and !o!ents fro! the resuting stress %oc's$+ Cop(right reserved *er%ion II2+-1 2+  STEEL-CONCRETE COMPOSITE COLUMNS-II   It shoud %e noted %( #a( of contrast that  IS: 456-1978  for reinforced concrete cou!nsspecifies a 2 cm  eccentricit( irrespective of cou!n geo!etr($ The !ethod suggestedhere, using EC, ao#s for an eccentricit( of oad appication %( the ter! α    andtherefore no further provision is necessar( for stee cou!ns$ .nother note#orth( featureis the prescription of strain i!itation in  IS: 456-1978 , #hereas EC does not i!pose sucha i!itation$ The reevant provision in the Indian Code i!its the concrete strain to 0.0035 !inus 0.75  ti!es the strain at the east co!pressed e tre!e fi%re/)ig$ 2  sho#s an interaction curve dra#n using si!pified design !ethod suggested in the UK   Nationa .ppication 0ocu!ent for EC   (NAD).  This negects the increase in!o!ent capacit( %e(ond  M   P    discussed a%ove, under reative( o# a ia co!pressiveoads/$ *er%ion II2+-2 Fig. 1 Interaction curve for compression and uni-axial bending   M  P  1 = λ   PP   p  MM   ! 01.01.0   # A D Fig. 2 Interaction curve for compression and uni-axial bending using the simplified method  M   !  P  c  A #   P  M 0 P   ! 0  STEEL-CONCRETE COMPOSITE COLUMNS-II   )ig$ 3 sho#s the stress distri%utions in the cross-section of a concrete fied rectanguar tu%uar section at each point,  A$ # and    of the interaction curve given in )ig$ 2.  It isi!portant to note that2 ã Point  A  !ar's the pastic resistance of the cross-section to co!pression at this pointthe %ending !o!ent is 3ero/$  P   A % P   !   4  A & .'   y  5 γ    a  6 α  c $  A  c.  ('  c   ) cy 5 γ   c  6  A    .'      5 γ    s  7/  M   A  % 0  8/ ã Point  # corresponds to the pastic !o!ent resistance of the cross-section the a iaco!pression is 3ero/$  P   # %0  9/  M   #  % M   !  % !  y  (*   !& -*   !&n  )+    !    (*   ! -*   !n  )+    ! c  (*   !c -*   !cn  )  / #here   *   !  $ *   !& , and  *   !c  are pastic section !odui of the reinforce!ent, stee section, andconcrete a%out their o#n centroids respective($   *   !n  $ *   !&n   and  *   !cn  are pastic section !odui of the reinforce!ent, stee section, andconcrete a%out neutra a is respective($   ã .t point   , the co!pressive and the !o!ent resistances of the cou!n are given asfoo#s:  P     % P  c %    A c  ! c.   ;/  M     % M   !   </ ã The e pressions !a( %e o%tained %( co!%ining the stress distri%utions of the cross-section at points  #  and   : the co!pression area of the concrete at point  #  is e=ua tothe tension area of the concrete at point .  The !o!ent resistance at point    is e=uato that at point  # , since the stress resutants fro! the additiona( co!pressed partsnuif( each other in the centra region of the cross-section$ *o#ever, theseadditiona( co!pressed regions create an interna a ia force, #hich is e=ua to the pastic resistance to co!pression of the concrete  $ P  c   aone$ *er%ion II2+-,  STEEL-CONCRETE COMPOSITE COLUMNS-II   It isi!portant to note that the positions of the neutra a is for points  #  and   , h n , can %edeter!ined fro! the difference in stresses at points  #  and   $ The resuting a ia forces,#hich are dependent on the position of the neutra a is of the cross-section, h n , can easi( %e deter!ined as sho#n in )ig$ 4 $ The su! of these forces is e=ua to  P  c $ This cacuationena%es the e=uation defining h n to %e deter!ined, #hich is different for various t(pes of sections$ (1)  or concrete enca%e& %tee( %ection%*er%ion II2+-/  ! c  2 !  y  P  c 2h n   Fig. 4(a) Variation in the neutral axis positions  y x Fig.  !tress distributions for the points of the interaction curve for concrete filled rectangular tubular sections  y P,n A ! c   !  y  !     P   !  N, m,m/n  x ! c   !  y   !     P,n # M   # %M   !  */, &x& ',c/h n  y x P,n      ! c   !  y  !    2h n    M  %M   !  P     %P  c
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