Design of Concrete Encased Composite Column

• Materials
• Input data of concrete encased composite columns
• Design Check of concrete encased composite columns
• Table of I-section

Restrictions on Simplified Design Method
a) columns → doubly symmetrical & uniform cross section
b) steel contribution ratio δ → 0.2 ≤ δ ≤ 0.9
c) non-dimensional slenderness λ ≤ 2
d) 0.3% ≤ As/Ac ≤ 6%
e) minimum & maximum cover are restricted
               minimum cover → 40mm
               maximum cover → cz = 0.3h & cy = 0.4b
f) concrete filled sections → can be fabricated without any reinforcement however concrete encased steel secions → minimum As/Ac = 0.3%
g) ratio of depth to width, 0.2 ≤ h/b ≤ 5

Design Check of Fully Encased Composite Columns
Type		Data			Check	Reference
Composite column specifications
	Column length	L=		m	Input data
	Effective length y-y	Ley=		m
	Effective length z-z	Lez=		m
	Column Type	Fully Encased
Design value of actions
	Design axial force	Nsd=		kN	Input data
	Design bending moment
	about y-y (major) axis	My,top,sd=		kNm	Input data
		My,bot,sd=		kNm	Input data
	about z-z (minor) axis	Mz,top,sd=		kNm	Input data
		Mz,bot,sd=		kNm	Input data
Material properties
Structural steel		S235≤16 S235≤40 S235≤63 S235≤80 S235≤100 S275≤16 S275≤40 S275≤63 S275≤80 S275≤100 S355≤16 S355≤40 S355≤63 S355≤80 S355≤100			Choose the steel grade
	Characteristic yield strength	fy=		N/mm2
	Modulus elastic of steel	Ea=		N/mm2
	Partial safety factor	Ya=
	Design strength	fyd=		N/mm2
Concrete
	Concrete grade	C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60 C55/67 C60/75			Choose the concrete grade
	Type of concrete	Normal Weight Concrete
	Characteristic value of compressive strength	fck=		N/mm2
	Partial safety factor	Yc=
	Design value of compressive strength	fcd=		N/mm2
	Secant modulus of elasticity	Ecm=		N/mm2
Reinforcement
	Characteristic yield strength	fyk=		N/mm2	Input data
	Partial safety factor	Yc=
	Design yield strength	fsd=		N/mm2
	Design value of modulus of elasticity	Es=		N/mm2
Connectors
	Diameter	d=		mm	Input data
	Overall nominal height	hsc=		mm	Input data
	Ultimate tensile strength	fu=		N/mm2	Input data
Cross section geometry and section properties of the selected section
Structural Steel		UC 152 x 152 x 23 UC 152 x 152 x 30 UC 152 x 152 x 37 UC 203 x 203 x 46 UC 203 x 203 x 52 UC 203 x 203 x 60 UC 203 x 203 x 71 UC 203 x 203 x 86 UC 254 x 254 x 73 UC 254 x 254 x 89 UC 254 x 254 x 107 UC 254 x 254 x 132 UC 254 x 254 x 167 UC 305 x 305 x 97 UC 305 x 305 x 118 UC 305 x 305 x 137 UC 305 x 305 x 158 UC 305 x 305 x 198 UC 305 x 305 x 240 UC 305 x 305 x 283 UC 356 x 368 x 129 UC 356 x 368 x 153 UC 356 x 368 x 177 UC 356 x 368 x 202 UC 356 x 406 x 235 UC 356 x 406 x 287 UC 356 x 406 x 340 UC 356 x 406 x 393 UC 356 x 406 x 467 UC 356 x 406 x 551 UC 356 x 406 x 634 600x600x50THK 700x700x50THK 800x800x50THK 900x900x50THK 1000x1000x50THK 1100x1100x50THK 1200x1200x50THK User Input			Choose the steel	steel with other size also can be used
	Mass	m=		kg/m
	Depth	h=		mm
	Width	b=		mm	b/g>Cz Not Ok
	Web thickness	tw=		mm
	Flange thickness	tf=		mm
	Root radius	r=		mm
	Section area	Aa=		cm2
	Second moment of area /yy	Iay=		cm4
	Elastic modulus /yy	Wel,y=		cm3
	Plastic modulus /yy	Wpl,y=		cm3
	Radius of gyration	iy=		cm
	Second moment of area /zz	Iaz=		cm4
	Elastic modulus /zz	Wel,z=		cm3
	Plastic modulus /zz	Wpl,z=		cm3
	Radius of gyration	iz=		cm
	Torsional moment of area	It=		cm4
Concrete
	Concrete width	bc=		mm	Input data
	Concrete depth	hc=		mm	Input data
	Area of concrete	Ac=		cm2
	Second moment of area about major axis: y-y (of columns)	Icy=		cm4
	Second moment of area about minor axis: z-z (of columns)	Icz=		cm4
	Cover	Cy=		mm	Cz<40 Not Ok
	Cover	Cz=		mm	Cz<40 not Ok
Reinforcement
	The number of longitudinal bars	n=			Input data
	Bar diameter	d=		mm	Input data
	Total section area	As=		cm2	0.3%<As/Ac<6% Ok
	Concrete cover			mm	Input data
	Second moment of total area about major axis: y-y (of columns)	Isy=		cm4
	Second moment of total area about minor axis: z-z (of columns)	Isz=		cm4
	Reinforcement ratio	As/Ac=			As/Ac<0.3% Not Ok
Plastic resistance of the composite cross section to compression:
		Npl,Rd=		kN		Eqn 6.30
	Steel contribution factor	δ=			<0.2 Not Ok	Eqn 6.38
Efective elastic flexural stiffness:
	About the major axis (y-y):
		Ke=			Input data	Eqn 6.40
		(EI)ey=		kNm2
	About the minor axis (z-z):
		Ke=			Input data	Eqn 6.40
		(EI)ez=		kNm2
Elastic buckling load:
	About the major axis (y-y):
		Ncry=		kN		Eqn 10 CE5509
	About the minor axis (z-z):
		Ncrz=		kN		Eqn 10 CE5509
Plastic resistance to compression:
		Npl,Rk=		kN		all safety factor = 1
Non-dimesional slenderness ration:
	About the major axis (y-y):
					< 2 Ok	Eqn 14 CE5509
	About the minor axis (z-z):
					< 2 Ok	Eqn 14 CE5509
Evaluate the resistance of the composite column under axial compression:
	Reduction factor:
	strut curve b for major axis and strut curve c for minor axis
	y-y axis
		ay=			Input data	Table 8 CE5509
		fy=				Eqn 16 & 17 CE5509
		χy=				Eqn 16 & 17 CE5509
	z-z axis	az=			Input data	Table 8 CE5509
		fz=				Eqn 16 & 17 CE5509
		χz=				Eqn 16 & 17 CE5509
	Where: a is the imperfection parameter which allows for different levels of imperfections in the columns
					< 1 OK	Eqn 15 CE5509
Checking long term loading:
	Efective elastic flexural stiffness:
		Ec,eff=		N/mm2		Eqn 6.41
		φt=			Input data	Figure 3.1
	assuming permanent load is % of design load	NG,Ed=		kN	Input data
	About the major axis (y-y):
		Ke=			Input data
		(EI)ey=		kNm2
	About the minor axis (z-z):
		Ke=			Input data
		(EI)ez=		kNm2
Elastic buckling load:
	About the major axis (y-y):
		Ncry=		kN		Eqn 10 CE5509
	About the minor axis (z-z):
		Ncrz=		kN		Eqn 10 CE5509
Plastic resistance to compression:
		Npl,Rk=		kN		all safety factor = 1
Non-dimesional slenderness ration:
	About the major axis (y-y):
					< 2 Ok	Eqn 14 CE5509
	About the minor axis (z-z):
					< 2 Ok	Eqn 14 CE5509
Evaluate the resistance of the composite column under axial compression:
	Reduction factor:
	strut curve b for major axis and strut curve c for minor axis
	y-y axis
		ay=			Input data	Eqn 16 & 17 CE5509
		fy=
		χy=
	z-z axis	az=			Input data	Eqn 16 & 17 CE5509
		fz=
		χz=
	Where: α is the imperfection parameter which allows for different levels of imperfections in the columns
					< 1 OK	Eqn 15 CE5509
Checking Resistance of composite section to under combined compression and bending
						Appendix A CE5509
	For fully encased H section:	αc=			Input data
	Major axis bending (y-y):
	Wps: Plastic section modulus for reinforcement
		Wps=		cm3		Appendix B1 CE5509
	Wpsn: Plastic section modulus for reinforcement within the region of 2hn from the middle line
		Wpsn=		cm3		Appendix B1 CE5509
	Neutral axis position:
	Case a Neutral axis in the web hn ≤[h/2-tf]	hn =		mm
	Case b Neutral axis in the flange [h/2-tf] ≤ hn ≤ h/2
	Case c Neutral axis outside the steel section h/2 ≤ hn ≤hc/2
		h/2-tf =		mm
		h/2 =		mm
		hc/2 =		mm
	Wpc: Plastic section modulus for concrete:
		Wpc=		cm3		Appendix B1 CE5509
	Wpan: Plastic section modulus of steel within the region of 2hn from the middle line:
	Case a : tw hn2	Wpan=		cm3		Appendix B1 CE5509
	Case b : bhn2 - [(b-tw)(h-2tf)2/4
	Case c : Wpa
	Wpcn: Plastic section modulus of concrete within the region of 2hn from the middle line:
		Wpcn=		cm3		Appendix B1 CE5509
	The bending resistance
		Mmax,Rd=		kNm		Appendix A CE5509
		Mpl,Rd=		kNm		Appendix A CE5509
	The resistance force
		Npm,Rd=		kN
Interaction Diagram:
	Major axis bending (y-y)
Point
A	Bending Moment M (kNm) M=0	MA=		kNm		Figure 5 CE5509
	Compression force N (kN) N=Npl,Rd	NA=		kN
B	Bending Moment M (kNm) M=Mpl,Rd	MB=		kNm
	Compression force N (kN) N=0	NB=		kN
C	Bending Moment M (kNm) M=Mpl,Rd	MC=		kNm
	Compression force N (kN) N=Npm,Rd	NC=		kN
D	Bending Moment M (kNm) M=Mpm,Rd	MD=		kNm
	Compression force N (kN) N=0.5Npm,Rd	ND=		kN
	Minor axis bending (z-z):
	Wps: Plastic section modulus for reinforcement
		Wps=		cm3
	Wpsn: Plastic section modulus for reinforcement within the region of 2hn from the middle line
		Wpsn=		cm3
	Neutral axis position:
	Case a Neutral axis in the web hn ≤tw/2	hn=		mm
	Case b Neutral axis in the flange tw/2 ≤hn ≤ b/2
	Case c Neutral axis outside the steel section b/2 ≤ hn ≤bc/2
		tw/2 =		mm
		b/2 =		mm
		bc/2 =		mm
	Wpc: Plastic section modulus for concrete:
		Wpc=		cm3
	Wpan: Plastic section modulus of steel within the region of 2hn from the middle line:
	Case a : h hn2	Wpan=		cm3
	Case b : 2 tf hn2 + [(h-2tf)tw2/4]
	Case c : Wpa
	Wpcn: Plastic section modulus of concrete within the region of 2hn from the middle line:
		Wpcn=		cm3
	The bending resistance
		Mmax,Rd=		kNm
		Mpl,Rd=		kNm
	The resistance force
		Npm,Rd=		kN
Interaction Diagram:
	Minor axis bending (z-z)
Point
A	Bending Moment M (kNm) M=0	MA=		kNm
	Compression force N (kN) N=Npl,Rd	NA=		kN
B	Bending Moment M (kNm) M=Mpl,Rd	MB=		kNm
	Compression force N (kN) N=0	NB=		kN
C	Bending Moment M (kNm) M=Mpl,Rd	MC=		kNm
	Compression force N (kN) N=Npm,Rd	NC=		kN
D	Bending Moment M (kNm) M=Mpm,Rd	MD=		kNm
	Compression force N (kN) N=0.5Npm,Rd	ND=		kN
Checking for combined compression and bending:
		(EI)eff,II,y=		kNm2		Effective flexure stiffness Clause 6.7.3.4 Eqn 6.42
		(EI)eff,II,z=		kNm2		Effective flexure stiffness Clause 6.7.3.4 Eqn 6.42
		Ke,II=			Input data
		Ko=			Input data
		Ncr,eff,y=		kN		if Nsd/Ncr >0.1
		Ncr,eff,z=		kN
	for end moment	β=			Input data
	k = β / (1-Ned / Ncr,eff)	k1,y=				Eqn 6.42
		k1,z=				Eqn 6.42
hence	for bending moment from menber imperfection	β=			Input data	equivalent moment factor
	k = β / (1-Ned / Ncr,eff) ≥ 1	k2,y=				Eqn 6.42
		k2,z=				Eqn 6.42
		e0,y=		m		Table 6.5
		e0,z=		m
		My,Ed=		kNm
		μdy Mpl,y,Rd=		kNm
	Case a : μdy = (χ-χd)(1-χn)/(1-χpm)(χ-χn) if χd ≥ χpm	μdy =				Take χ = 1 & χn = 0
	Case b : μdy = 1 - [(1-χ)(χd-χn)/(1-χpm)(χ-χn)]
					as shown in interaction curve
		My,Ed/μdyMpl,y,Rd =
		αM=			Input data
		Mz,Ed=		kNm
		μdz Mpl,z,Rd=		kNm
	Case a : μdz = (χ-χd)(1-χn)/(1-χpm)(χ-χn) if χd ≥ χpm	μdz =				Take χ = 1 & χn = 0
	Case b : μdz = 1 - [(1-χ)(χd-χn)/(1-χpm)(χ-χn)]
					as shown in interaction curve
		Mz,Ed/μdzMpl,z,Rd =
		αM=			Input data
				imperfection only considered in plane in which failure is expected to occur.
Transverse shear
	major axis y-y
	The vertical shear is
		Vy,Ed=		kN
	The design shear resistance is
		Vpl,a,Rd,y=		kN
	Minor axis z-z
		Vz,Ed=		kN
		Vpl,a,Rd,z=		kN
Longitudinal shear
	longitudinal shear force is
		NEd,c=		kN
	longitudinal shear stress				there is no well-established method for calculating longitudinal shear stress, usually based on
				N/mm2
	perimeter of steel section	pa=		mm
	load introduction length	lv=		mm
	design shear strength			N/mm2		Eq 6.49 EN1994-1-1
	if
		PRd1=		kN
		PRd2=		kN
		hsc/d=
		α=
		PRd=		kN
	frictional force	μPRd/2=		kN
	number of headed studs
		n=