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T-BEAMS

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OBJECTIVES Explain why the neutral axis falls below the slab. is!uss the assu"ptions use# in the #esi$n of T-

bea"s

Apply the ACI spe!i%!ations in the #esi$n of T-bea". Assess whi!h between a T-bea" an# a

re!tan$ular is better to be use# in ter"s ofstren$th an# pra!ti!ality reasons.

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In "u!h reinfor!e# !on!rete !onstru!tion an#parti!ularly in &oor syste"s' a !on!rete slab is!ast "onolithi!ally with an# !onne!te# tore!tan$ular bea"s for"in$ a T-bea".

The %$ure below is a !ross-se!tion of a !on!rete&oor syste" whi!h is !o"pose# of bea"s an#slabs.

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It is assu"e#' within !ertain li"itations' thatthe re!tan$ular bea"' whi!h has a wi#th bw

a!ts stru!turally with the slab'b

wi#e an#hf

thi!). This then for"s a T-bea" shown.

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If the neutral axis of the se!tion falls within the slabof &an$e of the T-bea" as shown' then the analysisfor the se!tion is the sa"e as for a re!tan$ular bea".

Be!ause the e*e!t of the !on!rete below the neutralaxis has been ne$le!te#' the +alue for bw !oul# beanythin$' an# the bea" woul# be analy,e# as asi"ple re!tan$ular bea" with wi#th b.

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If howe+er' the area of the &an$e is not !apable ofresistin$ the !o"pressi+e for!e' then the neutral axis fallsbelow the slab.

i$ure is si"ilar to the #ia$ra" for a re!tan$ular bea"ex!ept that the lo!ation of the !entroi# of the !o"pressi+efor!e is not as rea#ily #eter"ine#.

/en!e' the #eri+ations are "ore !o"plex. The #eri+ationsof the for"ulas for a T-bea" are si"ilar to the re!tan$ular

bea".

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The prin!ipal expressions use# in thealternate #esi$n "etho# for reinfor!e#

!on!rete T-bea"s

If the !o"pressi+e stress in the ste" isne$le!te#' the su""ation of hori,ontalfor!es is C0 T.

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Sin!e the !o"pressi+e for!e is boun#e# by atrape,oi#' 1 f! 2 3f!4)#53)#-hf5 bhf 0 Asfs or

6earran$in$ 78

fc 2 kd hf ( ) bhf

2 kd

=As fs.

fc 2 kd hf ( ). bhf .

fs 2. kd.

=

As=

b. d. or fc

fs

= 2 . b. d2.

2 kd. hf ( ) h.

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Substitutin$ for fc in e9uation ' we obtain8

The #istan!e z "ay be foun# by su""in$"o"ents about the !entroi# of the !o"pressi+efor!es8

ro" %$ure :' ;# 0 #

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The resistin$ "o"ent of the !on!rete woul# beM! 0 C;# or M! 0 f!37 < hf4 )#5bhf;#.

If 6 0 f!;37 < hf4 )#53hf4#5' then M! 0 6b# an# #0 M!46b

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These expressions were #e+elope# assu"in$ thatthe !o"pressi+e stress in the ste" portion isne$li$ible an# that the bea" has tensilereinfor!e"ent only.

ACI Co#e spe!i%es that the e*e!ti+e wi#th of slabor &an$e shall be ta)en as follows8

It shall not ex!ee# one-fourth of the span len$th of thebea".

The o+erhan$in$ wi#th of the &an$e in either si#e of the

ste" or web shall not ex!ee# > ti"es the slab thi!)ness. In any !ase' the &an$e wi#th "ust not be $reater thanthe #istan!e !enter to !enter of a#;a!ent bea"s.

Mini"u" bw 0 ?? ""