Design of Composite Beam

• Materials
• Input data
• Loads
• Verification of Construction Stage
• Verification of Final Stage
  
  

Assumptions
a) Simply supported beam
b) Internal beam
c) Sheeting with ribs transverse to the supporting beams
d) equal concrete flange

Input Data of Composite Beam
Type		Data			Check	Reference
Steel Beam
	Beam Span L	L=		m	Input data
	beam spacing	B =		m	Input data
Structural steel		S235≤16 S235≤40 S235≤63 S235≤80 S235≤100 S275≤16 S275≤40 S275≤63 S275≤80 S275≤100 S335≤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
		IPE AA 80 IPE A 80 IPE 80 IPE AA 100 IPE A 100 IPE 100 IPE AA 120 IPE A 120 IPE 120 IPE AA 140 IPE A 140 IPE 140 IPE AA 160 IPE A 160 IPE 160 IPE AA 180 IPE A 180 IPE 180 IPE O 180 IPE AA 200 IPE A 200 IPE 200 IPE O 200 IPE AA 220 IPE A 220 IPE 220 IPE O 220 IPE AA 240 IPE A 240 IPE 240 IPE O 240 IPE A 270 IPE 270 IPE O 270 IPE A 300 IPE 300 IPE O 300 IPE A 330 IPE 330 IPE O 330 IPE A 360 IPE 360 IPE O 360 IPE A 400 IPE 400 IPE O 400 IPE A 450 IPE 450 IPE O 450 IPE A 500 IPE 500 IPE O 500 IPE A 550 IPE 550 IPE O 550 IPE A 600 IPE 600 IPE O 600 IPE 750 x 137 IPE 750 x 147 IPE 750 x 173 IPE 750 x 196 User Input			Choose steel cross-section
	Mass	m=		kg/m
	Depth	h=		mm
	Width	b=		mm
	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
Properties of profiled sheeting
Use the re-entrant composite floor deck		RF 55/1.0 decking
	Depth of decking	hp =		mm	Input data
	Pitch of deck ribs	b1 =		mm	Input data
	For re-entrant profiles, the minimum width should be used.	b0 =		mm	Input data
	Deck weight	gp =		KN/m2	Input data
	Characteristic yield strength	fyk,p =		N/mm2	Input data
	Design thickness	tp =		mm	Input data
	Effective area of cross-section	Ap =		mm2/m	Input data
	Second moment of area of steel core	Ip =		mm4/m	Input data
	Design value of modulus of elasticity	Ep =		N/mm2	Input data
Slab data
	Overall slab depth	ht=		mm	Input data
	Slab depth above steel decking	hc=		mm
	Volumn of concrete	vc =		m3/m2	Input data
Properties of materials
Concrete
	Concrete grade	C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60 C55/67 C60/75
	Concrete wet density	rwc =		kg/m3	Input data
	Concrete dry density	rc =		kg/m3	Input data
	Characteristic value of compressive strength	fck=		N/mm2
	Partial safety factor	γc=
	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	γs=
	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

Loadings per unit length of composite beam for each stage are shown in Table, assumming that the beam are internal beam.

Loads
	Load					Partial factors of safety		ULS Loading		SLS Loading
Construction stage						ULS	SLS
Self weight of composite slab					kN/m	1.35	1.0		kN/m		kN/m
Self weight of steel beam			m x 9.81 =		kN/m	1.35	1.0		kN/m		kN/m
Construction load	0.75	kN/m2	q1 = q1k x B =		kN/m	1.5	1.0		kN/m		kN/m
Total									kN/m		kN/m
Composite stage
Self weight of composite slab					kN/m	1.35	1.0		kN/m		kN/m
Self weight of steel beam			m x 9.81 =		kN/m	1.35	1.0		kN/m		kN/m
Finishes and services	1	kN/m2	q2k x B =		kN/m	1.35	1.0		kN/m		kN/m
Imposed load (for office)	5	kN/m2	q = q3kx B =		kN/m	1.5	1.0		kN/m		kN/m
Total									kN/m		kN/m

Verification for construction stage
Ultimate limit state
Total loads (ULS):		w=		kN/m
The mid-span bending moment is:		MEd=		kNm
The design vertical shear is:		VEd=		kN
The plastic moment resistance is		Mpl,a,Rd=		kNm
Check		Mpl,a,Rd	<	MEd	Recalculate
					The section is adequate in bending.
Serviceability limit state - end of construction
Total loads (SLS):		w=		kN/m
The maximum deflection is:		δ=		mm
Allowable deflection is:				mm
Check deflection		δ	<		Recalculate
The mid-span bending moment is:		MEd=		kNm
Maximum bending stress:				N/mm2
Check stress			<	fy	Recalculate
The section is still in elastic region at the end of construction.
All design checks are OK at both the ultimate limit state and the serviceability limit state.

Verification for composite stage
Section classification
The parameter e :		ε=
Outstand of compression flange		c=		mm
		c/tf=
		9ε=			The limiting value for class 1
		10ε=			The limiting value for class 2
		14ε=			The limiting value for class 3
Internal compression part:		c=		mm
		c/tw=
		72ε=			The limiting value for class 1
		83ε=			The limiting value for class 2
		124ε=			The limiting value for class 3
The class of the cross-section is Class 1
Effective width of concrete flange
At the midspan:		beff=		m	Section with equal concrete flange.	nr=1, b0=0
		be=		m		nr=2, b0=100mm
Design shear resistance of a headed stud
The design shear resistance of a shear connector is		PRd1=		kN
		PRd2=		kN
		hsc/d=
		α=			Check
		γv=
For sheeting with ribs transverse to the supporting beam, the reduction factor for shear resistance is:		kt=			Assumption for tranverse ribs arrangement
		kmax=				nr=2, kmax=0.70
		nr=	1 2		Input data
		kt=
The design shear resistance should be determined by:		PRd=		kN
Degree of shear connection
Number of shear connectors studs for half span:		n=				nr=2, n is even number
Total resistance of shear connectors		Nq=		kN
Compression resistance of concrete slab		Ncf=		kN	P.N.A in steel beam
Tensile resistance of the steel section		Npl,a=		kN
Degree of shear connector:		η=			Partial shear connection
Checking the condition of minimum degree of partial shear connection
The minimum degree of shear connection is		ηmin≥			Recalculate	if the connection is full shear connection, not check it
Verification of bending resistance (plastic resistance moment)
Total loads (factored load used for ULS):		w=		kN/m
The mid-span bending moment is:		MEd=		kNm
The design vertical shear is:		VEd=		kN
Interpolation method:
Concrete flange resistance with partial shear connection		Nc=		kN		if the connection is full shear connection, calculate next part
Plastic moment capacity of steel section		Mpl,a,Rd=		kNm
MRd could be defined from the interpolated equation:
Mpl,Rd is plastic moment resistance with full shear connection.
		Npl,a'=		kN		P.N.A in concrete slab
Check the P.N.A						P.N.A in steel flange
						P.N.A in steel web
The depth of plastic neutral xpl		xpl=		mm		P.N.A in concrete slab
the resistance moment in full shear connection is		Mpl,Rd=		kNm		P.N.A in steel flange
The resistance moment MRd with patial shear connection is		MRd=		kNm		P.N.A in steel web
Check		MRd	<	MEd	recalculate
Verification of vertical shear resistance
The shear area of the steel beam is		Avz=		mm2		EN 1994-1-1 6.2.1.3 (3)
		ηhwtw=		mm2
		η=
		Avz=	<	ηhwtw	Take the larger one
Shear plastic resistance		Vpl,a,Rd=		kN
		Vpl,a,Rd	<	VEd	recalculate
Note that the verification to shear buckling is not required when:		hw/tw=
		72ε/η=
		hw/tw	>	72ε/η	verification to shear buckling is required
Note that the reduction in bending resistance is not required when:		VEd/Vpl,a,Rd=			ok, reduction to bending resistance is not required
Longitudinal Shear resistance
Transverse reinforcement
The plastic longitudinal shear stresses is given by:		vEd=		N/mm2
		△x=		m
		△Fd=		kN
To prevent crushing of the compression struts in the concrete flange, the following condition should be satisfied:		vfcdsinθfcosθf=		N/mm2
		v=
		θf=			Input data
		vfcdsinθfcosθf	<	vEd	Recalculate
Continuous profiled decking with ribs perpendicular to the beam span
In practice, it is usual to neglect the decking
the area of transverse reinforcement per unit length is		Asf/sf ≥		mm2/m
The reinforcement provided is		As=		mm2/m	recalculate
Diameter of reinofrcement bars		d=		mm	Input data
Space		s=		mm	Input data
Serviceability limit state verification
The modula ratio for variable loading is n0, and the modular ratio for permanent load is around 3n0. But, for simplicity, creep will be allowed for by using n = 2n0 for all loading.
		n=
Distance from the top surface of the concrete slab to centre of area		zg=		mm
The neutral-axis depth is given by						for the neutral-axis depth x to be less than hc
		x=		mm
The second moment of area is:		I=		cm4		for the neutral-axis depth x to be larger than hc
The deflection of steel beam due to permanent load is		δa=		mm
The deflection of composite beam is		δc=		mm
The total deflection is		δ=		mm
Allowable deflection is:		[δ]=		mm
Check		δ	>	[δ]	recalculate

Back to Top