60302536 Unit 14 Design of Slender Columns

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    REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/

    UNIT 14

    DESIGN OF SLENDER COLUMNS

    GENERAL OBJECTIVE

    To be able to identify te b!a"ed #lende! "ol$%n# de#i&n '!in"i'le# a""o!din& to

    B( )110 !e*$i!e%ent#+

    At te end of ti# $nit yo$ ,ill be able to "al"$late-

    1+ te %ini%$% e""ent!i"ity.%in

    e +

    + te defle"tion . ua $#in& e*$ation 3

    3+ te !ed$"tion fa"to!. $#in& e*$ation 33

    4+ te additional %o%ent $#in& e*$ation 3

    + te initial end %o%ent# $#in& e*$ation 32

    2+ te a!ea of lon&it$dinal !einfo!"e%ent+

    + te #ie and #'a"in& of late!al !einfo!"e%ent 5tie#6+

    )+ #7et" te !einfo!"e%ent# detail# in #lende! "ol$%n#+

    1

    OBJECTIVES

    (8ECI9IC OBJECTIVE(

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    REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/

    14+1 Slender Columns

    A b!a"ed #lende! "ol$%n i# defined a# a "ol$%n in ,i" te effe"ti:e

    ei&t/de't !atio i# &!eate! tan 1+ Te #t!en&t of #lende! "ol$%n# i#

    #i&nifi"antly !ed$"ed by t!an#:e!#e defle"tion#+ Te #lende!ne## effe"t !ed$"e# it#

    load;"a!!yin& "a'a"ity+ If te "ol$%n i# #o!t. te defle"tion i# #%all and en"e

    te additional %o%ent i# ne&li&ible. "o%'a!ed ,it te initial %o%ent+ If te

    "ol$%n i# #lende!. te defle"tion i# no lon&e! #%all. ten te additional %o%ent

    be"o%e# #i&nifi"ant "o%'a!ed to te initial %o%ent+ Te additional %o%ent

    #o$ld ten be "on#ide!ed if te effe"ti:e ei&t/de't !atio i# &!eate! tan 1+ If

    te "ol$%n i# :e!y #lende!. te "ol$%n ,ill *$i"7ly "olla'#e and #$" a fail$!e i#

    "alled in#tability fail$!e+

    Te additional %o%ent. addM i# "a$#ed by te defle"tion of #lende! "ol$%n+

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    REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/

    Now do !e "ollow#n$%

    14+1 A b!a"ed #lende! "ol$%n i# a "ol$%n in ,en bot te !atio#h

    lex andb

    ley

    a!e &!eate! tan ===========================+

    14+ An $nb!a"ed #lende! "ol$%n i# one in ,i" bot !atio# h

    lex

    and b

    ley

    i#

    &!eate! tan =========================+

    14+3 Te #t!en&t of a #lende! "ol$%n i# !ed$"ed by =====================+

    14+4 Te defle"tion of #lende! "ol$%n i# #i&nifi"ant "o%'a!ed ,it te

    ======================== %o%ent+

    14+ 9o! #lende! "ol$%n#. ================= #o$ld be "on#ide!ed+

    14+2 Te additional %o%ent of #lende! "ol$%n i# "a$#ed by te "ol$%n

    ========================+

    3

    ACTIVIT& 14'

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    REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/

    Now (!e() *our 'nswers%

    14%1 1

    14%+ 10

    14%, t!an#:e!#e defle"tion

    14%4 initial %o%ent

    14%- additional %o%ent

    14%. defle"tion+

    I" 'll *our 'nswers 're (orre(/ 0le'se 0ro(eed% O!erw#se 0le'se $o '() o

    !e IN2UT #n !#s se(#on 'nd do !e '(#3#*%

    4

    FEEDBAC 14'

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    REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/

    14%5 Add##on'l Momen/ addM

    Con#ide! a "ol$%n a"ted by a>ial load N and an end %o%ent ?ia# #o,n belo,@

    Te additional %o%ent. addM i# "al"$lated a# follo,#@

    N

    a$

    IN2UT +

    N

    9i&$!e 14+1- efle"tion of a !e"tan&$la! "ol$%n+

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    REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/

    uadd NaM =

    e!e. N te $lti%ate a>ial load

    ua "ol$%n defle"tion at $lti%ate li%it+

    ua i# "al"$lated $#in& e*$ation 3 of te "ode &i:en belo, @

    And Dai# "al"$lated $#in& e*$ation 34 a# follo,#@

    Da "an al#o be obtained f!o% Table 3+3 of B( )110. ,i" in de'endent on te

    !atioE

    b

    le ,e!e el i# te effe"ti:e ei&t of "ol$%n in te 'lane "on#ide!ed and

    bb =E . i# te di%en#ion of te #%alle! "ol$%n+

    2

    Kha au =

    /

    E/000

    1

    =

    b

    le

    a

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    REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/

    ial bendin&. ,e!e

    addM a!e '!e#ent in bot a>e#. > and y. te :al$e E

    b

    le i# e*$al to

    h

    lex and

    b

    ley+

    i# te !ed$"tion fa"to! to "o!!e"t te defle"tion and to ta7e into "on#ide!ation

    te effe"t of a>ial load+ "an be "al"$lated $#in& e*$ation 33 of te "ode+ Ti# i#

    #o,n belo,-

    e!e. scyccuuz AfAfN )+04+0 += and bdfN cubal /+0=

    5$#ed fo! #y%%et!i"al !einfo!"ed "on"!ete "ol$%n#6+

    Te!efo!e. addM "an be !e,!itten a#@

    uzN de'end# on scA b$t scA i# not yet 7no,n. i# ten ta7en a# 1+0+ Te

    ite!ation '!o"e## i# to be "ontin$ed $ntil te :al$e obtained i# e*$al to o!

    a''!o>i%ately e*$al to te :al$e a##$%ed ea!lie!+

    1=

    baluz

    uz

    NNNNK

    Kb

    lNhM eadd

    /

    E/000

    =

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    REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/

    Now do !e "ollow#n$ e6er(#se% F#ll #n !e l'n)s%

    14+ Te additional %o%ent. addM i# "al"$lated $#in& e*$ation

    =========================+

    14+) Te defle"tion. a$i# "al"$lated $#in& e*$ation ================+

    14+F a "an be obtained f!o% Table ==================of te "ode+

    14+10 ================== i# te !ed$"tion fa"to! to "o!!e"t defle"tion+

    14+11 Te !ed$"tion fa"to! "an be "al"$lated $#in& e*$ation

    ========================+

    14+1 en 1/E=

    b

    le . a i# e*$al to =====================+

    14+13 en 20E=

    b

    le . a i# e*$al to ======================+

    14+14 en 00 %%. 1+0. a ======================+

    14+1 en ua 00%% and N 3000 7N. te additional %o%ent i# e*$al to

    ========= 7N+

    14+12 A "ol$%n of di%en#ion 300%% > 400%% i# !einfo!"ed ,it 4T3 ba!#+ If

    f"$ 40 N/%%and fy 420 N/%%

    . "al"$late uzN +

    )

    ACTIVIT& 14

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    REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/

    14+1 Cal"$late balN fo! te "ol$%n #e"tion &i:en belo, $#in& f"$a# 40 N/%%+

    14+1) Cal"$late te !ed$"tion fa"to!. if uzN 3007N. balN 3000 7N and

    N 3100 7N+

    0 %%

    400%%

    F

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    REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/

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    REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/

    310040040/+0

    00 7N

    14+1) baluz

    uz

    NN

    NN

    K

    =

    3000300

    3100300

    00

    400

    0+) 1

    11

    IN2UT ,

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    REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/

    14%17 Slender Br'(ed Columns

    Con#ide! a "ol$%n e>'e!ien"in& an ea!lie! e""ent!i"ity of a>ial load a# #o,n

    belo,@

    Te total %o%ent i# addit MMM += + Te initial %o%ent ?ito be $#ed i# #i%'ly

    te initial %o%ent at an end of te "ol$%n+ B()110 !e"o%%end# tat ?ibe ta7en

    a#-

    1/ 4+02+0 MMMi += 5?bein& te la!&e!6 fo! #y%%et!i"al bendin&

    N

    e a$

    1

    9i&$!e14+- efle"tion of (lende! B!a"ed Col$%n

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    REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/

    And. 1/ 4+02+0 MMMi = /4+0 M b$t not le## tan /4+0 M fo!

    a##y%%et!i"al bendin& i+e+ bendin& in do$ble "$!:at$!e+ Ti# i# #o,n in

    9i& 3+0. B( )110+

    Te t,o e*$ation# "an be "o%bined a# follo,#-

    e!e.

    ?ii# te #%alle! initial end %o%ent 5ta7en a# ne&ati:e if te "ol$%n i#

    bent in do$ble "$!:at$!e6 and ?i# te la!&e! initial end %o%ent. ,i" i# al,ay#

    ta7en a# 'o#iti:e+

    B()110 i%'o#e# a f$!te! "ondition tat addt MMM/

    11+

    A "ol$%n in any "a#e i# de#i&ned fo! a %o%ent of at lea#t Ne%in+

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    REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/

    Now do !e "ollow#n$ e6er(#se%

    9ill in te blan7#+

    14+1F =================== i# e*$al to te #$% of initial %o%ent. iM and

    te additional %o%ent addM

    14+0 9o! #y%%et!i"al bendin&. te initial %o%ent i# e*$al to

    ============================+

    14+1 9o! ================= bendin&. 1/ 4+02+0 MMMi =

    14+ ====================== i# bendin& in do$ble "$!:at$!e+

    14+3 A #lende! "ol$%n i# de#i&ned fo! a %ini%$% %o%ent of

    ==========================+

    14+4 Te de#i&n %ini%$% e""ent!i"ity i# ta7en a# =========== o! 0 %%

    ,i"e:e! i# le##+

    14+ 8i"7 fo$! 546 f!o% te follo,in& "!ite!ia in dete!%inin& te %a>i%$%

    de#i&n %o%ent @

    14

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    REINFORCED CONCRETE STRUCTURAL DESIGN C4301/UNIT14/

    a6 /M

    b6 14+0 M

    "6 /2+0 M

    d6 addi MM +

    e6/

    1add

    MM +

    f6 /4+0 M

    &6 /1 2+04+0 MM +

    6 Ne%in

    14+2 9o! te #lende! "ol$%n e>'e!ien"in& initial %o%ent# at bot end# 5#o,n

    belo,6. dete!%ine te :al$e# of 1M and /M a##$%in& do$ble "$!:at$!e+

    14+ Cal"$late iM of te "ol$%n in $e#tion ) a##$%in&