ABCDEFGHIJKLMNOPQRSTUVWXYZ
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( a )
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Design of composite columns
( b )
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according to ECP no. 205-2001
( c )
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( Working loads )
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II
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1- Appreviations :
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fcu = 28-days cube strength of concrete (N/mm2)
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l = Slenderness ratio = kl/rm
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rm = Modified radius of gyration of the composite section (cm)
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Fym = Modified yield stress (t/cm2)
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Fy = Yield stress of steel section (t/cm2)
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Fyr = Yield stress of longitudinal reinforcing bars (kg/cm2)
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Em = Modified Young's modulus (t/cm2) >= Es
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Es = Young's modulus of steel (t/cm2)
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Ec = Young's modulus of concrete (N/mm2)
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As = Area of steel section (cm2)
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Ar = Area of longitudinal reinforcing bars (cm2)
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Ac = Area of concrete (cm2) excluding As and Ar
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c1,c2,c3 = Numerical coefficients
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Fc = Allowable compressivestress for composite section (t/cm2)
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fca = Allowable compressivestress due to axial force computed on steel section only (t/cm2)
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Cmx,Cmy = Moment modification factors as per Clause 2.6.7.1
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fbx,fby = Applied bending stress based on moments about the X and Y axes respectively and
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neglecting composite action (t/cm2)
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femx,femy = Modified elastic buckling stress for buckling in X and Y directions respectively (t/cm2)
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2- Requirements :
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a- The total cross-sectional area of steel section shall not be less than four percent (4%) of the gross column area.
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b- The characteristic 28-day cube strength of concrete, fcu, shall not be less than 250 kg/cm2, nor greater than 500 kg/cm2.
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c- Multiple steel shapes in the same cross-section shall be interconnected with lacing, tie plates, or batten plates to prevent
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buckling of individual shapes before hardening of concrete.
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d- For concrete encasement, the spacing of lateral ties shall not exceed two thirds of the least dimension of the composite
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section, or 30 cm, whichever is samller. Concrete cover over lateral ties shall not be less than 4 cm.
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f- To avoid local buckling, the minimum wall thickness of steel rectangular tubing filled shall be taken as b(Fy/3Es)^1/2
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and for circular section shall be taken as D(Fy/8Es)^1/2.
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3- Input Data :
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Composite section case =
( a )
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Concrete Sec.
Reinforcement
Steel Section
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fcu =30N/mm2Fyr =400kg/cm2Es =2100,00t/cm2
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b1 =50cm
D of long bars =
18mmFy =2,40t/cm2
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b2 =50cm
No of long bars =
10As =196,00cm2As min =100cm2
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Ec =24099,79253N/mm2Ar =25,43cm2Zx =3139,00cm3
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Zy =3139,00cm3
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rx =20,01cm
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ry =20,01cm
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1,00
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4- Straining Action :
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Case Lodaing
II
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N =120tMx =20m.tMy =10,00m.t
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Lx =1000,00cmLy =1000,00cm
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Kbx =1,2Kby =1,20
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5- Check Stresses :
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Acg =2500,00cm2Ac =2278,57cm2
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c1 =0,70c2 =0,48c3 =0,20
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rmx =20,01cmrmy =20,01cm
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lx =
Kbx * Lx / rmx =
59,97<=180safe
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ly =
Kby * Ly / rmy =
59,97<=180safe
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lmax =59,97<=180safe<=100
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Fym =
Fy + c1 * Fyr * ( Ar / As ) + c2 * fcu * ( Ac / As ) =
2,60t/cm2
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Em =
Es + c3 * Ec * ( Ac / As ) =
2660,34t/cm2
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a =
( 0.58 * 104 * Fym - 3.57 * Em ) / ( 104 * Fym )2 =
0,000008267
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Fc =
( 0.58 - a * Fym * lmax2 ) * Fym =
1,31t/cm2
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Femx=2,64t/cm2
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Femy=2,64t/cm2
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fca =N / As =0,61t/cm2
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fca / Fc=0,47>= 0.15
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fbx=0,64t/cm2
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fby=0,32t/cm2
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Cmx=1,00
per Clause 2.6.7.1
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Cmy=1,00
per Clause 2.6.7.1
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A1=1,30
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A2=1,30
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Interaction Equation :