Design of columns
Columns ( A ) Short columns : The columns is considered to be shot if λ≤ 10
(unbraced )
λ ≤ 15
( braced )
where λ is slenderness ratio
b T Where H0 : is the free space between beams bracing column in direction considered . b,t : column dimenntions . K : factor . Short columns can be designed as either tied or spiral :
( 1 ) Tied column design : P = 0.35 fcu Ac +067 fy As
(ultimate )
P = fc0 Ac + 044 fy As
( working ) Page 1
Design of columns
Then assume As = .008 ---- .012 Ac Get Ac then assume ( b ) to get ( t ) We have Ac so we can get As . --If we used st 36 And fcu 250 and assumed As = .01Ac the equation will be
Ac = pu /111.32 Ac = p /75.84
( ultimate ) ( working )
( 2 )Spiral column design : This column should be circular .
( 1 ) pu = 0.4 fcu Ac +0.76 fy As .
( ultimate )
P = 1.14 fc0 Ac + 051 fy As .
( working )
( 2 ) pu=0.35 fcu Ak+0.67fy As+1.38 fysp Vsp.(ultimate ) P=fc0 Ak+0.44fy As + 0.92 fysp Vsp. (3)
đ?œ‹
( working )
Get ( pitch )
Where : Ak : area of cross section without cover . Fysp : 2400 .
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Design of columns
( B ) Long columns :
b
If λt > 10
( unbraced )
If λt > 15
(braced )
If λb > 10
( unbraced )
If λb > 15
( braced )
t
If the section is long in one or two direction there will be additional moment can be calvulated by
Mxadd = Pu.δt
where
δt = λt2.t / 2000
where
δb = λb2.b / 2000
And Myadd = Pu.δb
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Design of columns
In this case we may have initial and additional moment so we have to compute equvilent of moment .
* In case of Braced columns : ( 1 ) Minitial // Madditional
Mx Final is the maximum of (1) Mx2 (2) Mx1 +Mxadd / 2 (3) Mi + Mxadd (where) Mi=0.4Mx1+0.6Mx2 ≼0.4 m , M2 is the bigger . And if It was (double curvature ) we take (4)Pu . emin
Mx1 (-ve).
where e min is the min of 2 cm or .05 t .
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Design of columns
( 2 ) M initial ┴ M additional
My final is the max. of (1) My add (2) Pu . emin Mx final = Mx2 Now we have Mx , My This is called Biaxial moment and should be transformed into uniaxial moment . where t - = t- cover
Get (
where b - = b – cover
( If
>
design for Mx-
Mx- = Mx +[ β * My ( ) ] Page 5
Design of columns
or If
>
design for My-
My- = My +[ β * Mx ( ) ] * In case of unbraced columns :
Mx final is the max of (a) Mx +Mxadd (b) pu . emin And so on My final . After that we transform biaxial moment into uniaxial moment as we did before . *Design of sections subjected to ( P, M ) : (a) if e/t ≤ 0.05
where e = M/P
Neglect ( M ) and design for ( P ) as short column .
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Design of columns
≤ 0.04
( b ) if
Neglect ( P ) and design for ( M ) 0nly as beam . > 0.04
( c ) if e/t ≥ 0.5 , es = e + t/2 -cover Ms = p . es
And use this moment for design as beam. use I.D
( d ) if 0.05 < e/t <0.5 ) From charts we get ( ρ μ = ρ fcu 10-5 As = μ b t
مالحظات : .1فىىىأل مدة ىىى ا كمن م العىىىلن م نل لىىىا لاىىى م ىىى مد عىىىأل لتسىىىللل م ىىىى أل %8.0ىىى سىىىل ا م لىىىىلى م سىىىلعأل م ىلىىىى س ب سىىىىلىلل ةلىىىىأل للىىىى ةىىىى %8.6ىىىى سل ا م ل ىلى م فن لأل ك ك فأل ل ا مدة ا م short =0.25+0.052 λb ل مدة ا م longتا .2فىىأل مدة ىى ا كمن م العىىلن م ل علىىا لاىى م ىى مد عىىأل لتسىىىىللل م ىىىىى أل %1ىىىى سىىىىل ا م لىىىىىلى م الىىىىأل Page 7
Design of columns
سىىىل ا م للىىىس م
%1.2ىىى له ل اى . .3ت ل ى عسىىىا م تسىىللل م ى ى أل م لأل ى ة فىىأل مدة ى ا ة ى : %4ألة ىىى ا م سىىىىلا %5ألة ىىى ا م ى فلىىىا %6 ألة ا م اعلا . .4لجىىس عىىل ل ت ى ة م ن ى ةلىىأل سىىلل ى ى أل فىىأل ا ى ا ى العه . .5عأل قى ألسللخ م ى لا ه 12م . قىىىى سىىىس ىىىاله هىىى .6عىىىأل لىىىل عىىىلأ م ن ىىى 288م . .7اىى لىىل عىىلأ ة ى ل عىىأ ىىىه سىىللخ ىلد اىىل فلىىى هىىى 388ىىىم م لجىىىس عىىىأ سىىىللخ ت سىىىىا ةلىىىأل سىىلفلن قألىىلهل 258ىىم لجىىس ىىىى مدسىىللخ ىالعىىلن لألىىىىا مكم م ن م سىىىىلفا ىىىىىل مدسىىىىللخ م ت سىىىىىا للىى مدسىىللخ م ى ىىىا ةلىىأل 158ىىم ا ىىل لجىىس ة مدسللخ فأل م لىلى م مئ ة ة . 6 .0لجىىس ت لىى م سىىلفا ىىىل م العىىلن فىىأل م تجىىل م ىىى أل لن ىى ةلىىأل 15ىى ا قىىى ألىى سىىلل ىىى أل ى ىى قألأل 288م . .9عىىأل قىىى لالعىىلن هىى 8.25قىىى اىىى سىىلل ىىى أل ةلىىأل للىى ةىى 0ىىم قىى جىىم لالعىىلن % 8.25 جم م سلعا . .18لجىىىىس تسىىىىت م العىىىىلن م نل لىىىىا م ل علىىىىا علىق م تللء مدة ا ىل ا من . م Page 8
ىىى ىل العىىىلن م ل علىىىا
Design of columns
قألىىىأل ىىىى ا لالعىىىلن م ل علىىىا هىىىأل 08ىىىم .11 ىىىى ا هىىىأل 38ىىىم لفعىىى م تفىىىل ىىىىل ى ا ألىىى ثلىتىىىا ىىىأ ة ىىى ثىىىات من ةعىىى اىىى ىىىى ى ىىىى ا تسىىل ة عأل ى م ى ى ا م نل لىىا ىىأ ثعىىأل ى ى سىىلل م ىىأل للىى ةىى 188ىىم 18ىى من م ىى م لىىىلى ىىىى قى سلل م العا. .12لجىىس للىى ألىى قىىى لالعىىلن م ل علىىا ةىى 0م. .13فىىأل ل ىىا ىىل مكم العىىن تىىىا سىىلعا مدة ى ا ةلىىأل ىىى % 148تىىىىا سىىىلعا م سىىىل لجىىىس ت للىىىق ىىى م ت مىلن م تلا : ىى مدة ىى ا ىى لىىتم ألىىس جىى مء م سىىل ب تىىىىا سىىىلعا مدة ىىى ا ىىىأ مةىىىلا سىىىلعا ىىىىعف ت ت ى مدسىىىل م نل لىىا هىىك مدج ى مء ى ىىل لل ى ة ى 688 ىىم ى جىىه مدة ى ا ىىأ ىىك م تللىىىلن م تىىأل تتع ى سىىلعا م سىىل سىىلعا هىىك مدج ى مء ت ىىلم م ى ىى ىىىل م لىا ىهل . لىىتم سىىلس م لل ىىا م لألىى ة ألة ىى ا ةلىىأل بس سىىل م تىىىا مد عىىأل ل سىىلعا ىىأ مسىىت مم ىىلل سىىلا العىىلن ل علىىا سىىس م لجىىا ى ىىل لت تىىس ةللىىه فض م لل ا م لأل ة ألة ا . بج ألة ىىىى ا م لىىىىىا جلعىلىىىىل ىىىى ىىىىىأ جهىىىىلن ىا ىىى من كمن ة ىىىلق تسىىىل لا تل لىىىىل ىاىىىىلن فلعىىىه ل اىى سىىلس م لل ىىا م لألىى ة اة ىى ا مةت ىىل م ةلىىأل قل ىىا مفت معىىلا لل ىىا م عىى ى سىىلعا م ألىىلا ىىىل م ن ىىىى م سىىىىل تسىىىىل ة لألىىىى ج ىىىىأ % 75ىىىى Page 9
Design of columns
سىىلعا م سىىل ى ىى ى سىىلعا مدة ى ا م سىىل
سىىلعا مدة ىى ا % 35ىى ة ى م لىىل ا م عسىىىا ىىىل تىتىىأل –فأل هك م ل ا -ة . 2.5 .14لجىىىس علىىى ج لىىىأ م لىىى ة م نىىى م م ىىى ث ا ةعىىى قلةىى ا م ن ىى م ىىأل م للةىى ا ىل تاىىل ةلىىأل م سىىلعا ىألىىىىلس م تسىىىىللل ب ىىىىلل – ألىىىىان .مكم تعىىىى عن ى ىىل ن م ت ل ى م ى م ا ةلىىأل م للة ى ا م ت ىىل ج ى فلجىىس لل تىىه ىألىىلس م تسىىللل فلىىى ىىأ ع ى ا مسىىتلفلء ل ىىىا ىىى م ت ىىى خ ا ىىىل لجىىىس ت لىىى قىىىلم مجهىىىل من م للةىى ا ةىى م لىىلم م ىى م ا م تاىىل اىى ىى م ن ىى ىىىل ا .اىىك ك لجىىس لاىى ألىىلس م تسىىللل م ىىلل م ألىىان الفلىىا لل ىىا ا ى ق ى ة م ع ى ى م تىىأل ت ل ى ةلىىأل لل ىىا م تاىىل ا ى ى م للة ى ا م ن ى ى لىىت تلىىى ةىىى تسىىىللل م ن ىىى .فىىىأل ل ىىىا جىىى قىىى ة جلكىلىىىا تىىى ث ةلىىىأل سىىىىل م ىىىتا لىىىتم عللهىىىل ى مسىىىىا م تالك م لص ىى للا ة علسىا .
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