تصميم الاعمدة

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 .

Page 2

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

Page 3

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 .

Page 4

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 .

Page 6

‫‪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 ‪.‬‬

‫‪Page 10‬‬