LRFD_composite_beam_design (www.theengineeringcommunity.org).xlsm

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1				PROJECT	150123 Portsea North Apartments				SECTION	1	LRFD
2				TITLE	Floor support beams				DATE	4/5/2026	CODE SPECS.
3				FILE	150123 LRFD_composite_beam_design.xls				TIME	11:09 PM
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5	SIMPLY SUPPORTED I SECTION COMPOSITE BEAM DESIGN
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29	DESCRIPTION
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31	-Check design shear and flexure strength of a simply supported I section composite beam to AISC LRFD 3rd Ed.
32	-Note that for "unshored" construction, total deflection is sum of deflection of the steel beam under its own load, and deflection of the composite beam
33	under dead and live loads. For "shored" construction, total deflection is sum of deflection under dead and live loads for the composite section only.
34	-Based on methods used in "Steel Structures Design and Behaviour" by: Salmon & Johnson (see pages 1010-1061)
35	-Transformed Section method has been used to calculate elastic section properties
36	-It is assumed that all shear will be transferred through Headed Studs and that concrete and steel sections form a fully composite section
37	-Steel Material assumed to conform to ASTM A922
38	-See AISC LRFD Specifications Chapter I
39
40	INPUT PARAMETERS
41		Structure
42		-Beam Span	Lb	=	8000		17,41	[ft]	5306	[mm]
43		-Specified Uniformly Distributed Live Load	LL	=			0,18667	[kip/ft]	3	[kN/m]
44		-Specified Uniformly Distributed Dead Load	DL	=			0,88	[kip/ft]	13	[kN/m]
45		-Live Load Factor	Lf	=			1,6	[]	2	[]
46		-Dead Load Factor	Df	=			1,2	[]	1	[]
47		-Factored Maximum Moment	Mu	=	(LfLL+DfDL)*Lb^2/8	=	51	[kip-ft]	68	[kN-m]
48		-Factored Maximum Shear	Vu	=	(LfLL+DfDL)Lb0.5	=	12	[kip]	52	[kN]
49		-Shear Stud Diameter	Sd	=			0,75	[in]	19	[mm]
50		Section Dimensions
51		-Effective Width	be	=			110	[in]	2794	[mm]
52		-Slab Thickness	ts	=			8	[in]	203,2	[mm]
53		-Steel Section	Des	=			ST10X37.5	[]
54		Material Properties
55		-Steel Yield Strength	Fy	=		=	36	[ksi]	248	[MPa]
56		-Shear Stud Ultimate Strength	Fu	=			58	[ksi]	400	[MPa]
57		-Concrete Compressive Strength	fc	=		=	3500	[psi]	24138	[MPa]
58		-Steel Elastic Modulus	Es	=		=	29000	[ksi]	200000	[MPa]
59		-Steel Elastic Modulus	Ec	=	Es/index(C_Table,Match(fc,Comp,0),2)	=	3412	[ksi]	23529	[MPa]
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61		-Table Row	row	=	Match(Des,section,0)	=	795
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63	CALCULATIONS
64		Section Properties
65		-Area of Steel	As	=	index(table,row,4)	=	11,00	[in^2]	7096,8	[mm^2]
66		-Height to web thickness ratio	hc	=	index(table,row,25)	=	13,6	[]	13,60	[]
67		-Moment of Inertia about x-x	Ix	=	index(table,row,31)	=	109,0	[in^4]	45369225	[mm^4]
68		-Beam Depth	BD	=	index(table,row,5)	=	10,00	[in]	254	[mm]
69		-Flange Width	bf	=	index(table,row,8)	=	6,39	[in]	162,306	[mm]
70		-Flange Thickness	tf	=	index(table,row,12)	=	0,795	[in]	20,193	[mm]
71		-Steel to Concrete E ratio	nn	=	index(C_Table,Match(fc,Comp,0),2)	=	8,5	[]	9	[]
72		-Check whether we use Plastic or Elastic Stress Distr.	Chk1	=	if(hc<=3.76*sqrt(Es/Fy),"Plastic","Elastic")	=	Plastic				LRFD I3.2
73		Elastic Section Properties
74		-Concrete Transformed width	bet	=	be/nn	=	12,9	[in]	328,7058824	[mm]
75		-Location of Composite Elastic Neutral Axis	yd	=	(((AsBD/2)+(betts(BD+ts/2)))/(As+tsbet))	=	13,14	[in]	334	[mm]
76		-Moment of Inertia of Composite section about x-x	Itr	=	Ix+(As(yd-BD/2)^2)+(1/12ts^3bet)+(tsbet)*(yd-BD-ts/2)^2	=	1466,58	[in^4]	610436930	[mm^4]
77		-Extreme fiber tension section modulus	Str	=	Itr/yd	=	111,65	[in^3]	1829605,2	[mm^3]
78		-Extreme fiber compression section modulus	Sconc	=	Itr/(BD+ts-yd)	=	301,5	[in^3]	4940571,6	[mm^3]
79		Flexural Strength Calculations
80		-Flexural Strength Based on Elastic Stress	Mn1	=	if(Chk1="Elastic", min(0.90.85Sconcfc,0.9Str*Fy)/12,"See Below")	=	See Below	[kip-ft]	#VALUE!	[kN-m]	LRFD I3.2
81		Case-1 Plastic Neutral Axis (PNA) in Slab
82		-Uniform Compression stress depth	ad	=	(AsFy)/(0.85fc*be/1000)	=	1,210	[in]	31	[mm]	(16.7.3)
83		-Compressive force in case 1	C1	=	0.85fc/1000ad*be	=	396,0	[kip]	1760	[kN]	(16.7.1)
84		-Tensile force in case 1	T1	=	As*Fy	=	396,0	[kip]	1760	[kN]	(16.7.2)
85		-Factored Nominal Flexural Strength based on Case 1	Mn2	=	if(ts>ad,0.85AsFy*(BD/2+ts-ad/2)/12,"N/A")	=	348	[kip-ft]	464	[kN-m]	(16.7.5)
86		Case-2 Plastic Neutral Axis (PNA) in Steel Beam
87		-Compressive force in concrete	Cc	=	0.85fcbe*ts/1000	=	2618	[kip]	11636	[kN]	(16.7.6)
88		-Tension force in steel	Cs	=	((As*Fy)-Cc)/2	=	-1111	[kip]	-4938	[kN]	(16.7.9)
89		-Thickness of flange in compression	df	=	Cs/(bf*Fy)	=	-4,830	[in]	-123	[mm]
90		-Check if PNA within flange	Chk2	=	if(df<0,"N/A",if(tf<bf,"PNA in Flange","PNA in Web"))	=	N/A
91		-Distance to the centroid of tension portion of steel beam	yct	=	if(Cs<0,"N/A",((AsBD/2)-(dfbf(BD-df)))/(As-bfdf))	=	N/A	[in]	N/A	[mm]
92		-Factored Nominal Flexural Strength based on Case 2	Mn3	=	if(Cs<0,"N/A",0.85(Cc(BD+ts/2-yct)+Cs*(BD-yct-df/2))/12)	=	N/A	[kip-ft]	N/A	[kN-m]	(16.7.10)
93		Shear Strength Calculations
94		-Required stud shear strength	Vnh	=	min(0.85fcbets/1000,AsFy)	=	396,0	[kip]	1760	[kN]
95		-Nominal stud shear strength	Qn	=	0.5pi()Sd^2/4sqrt(fcEc/1000)	=	24,14	[kip]	107	[kN]
96		-Number of required Studs	Ns	=	round(Vnh/Qn,0)	=	16	[]	16	[]
97		-Maximum Stud Spacing	ps	=	min(8ts,Lb12/Ns)	=	13	[in]	332	[mm]
98		Deflections
99		-Dead Load Deflection	DDL	=	5DL(Lb12)^4/(384Es*Ix)	=	6,90	[in]	175,2	[mm]
100		-Live Load Deflection	DLL	=	5LL(Lb12)^4/(384Es*Itr)	=	0,11	[in]	2,8	[mm]