BEAM DESIGN CALCULATION
Project Name	:	Sample
Client Name	:	Sample
Engineer Name	:	Sample
Design File	:	D:\Bentley\Common data\Bentley Communities\AS\Validation Problem\RCDC Files\Beam design file_AS code.rcdx
Analysis File	:	D:\Bentley\000 RCDC 2010\11.1.0\Standard model for Demo\Staad\RCDC-Staad-Demo -with RCC wall.std
Analysis Last Modified	:	3/17/2021 4:34:09 PM
Level Designed	:	7.858 m

Sr.No.	Symbol		Definitions
1	A_c,eff	=	The effective area of concrete in tension surrounding the bar with depth hc,eff in 'sqmm'
2	Acp	=	Total area enclosed by outside perimeter of concrete section in 'sqmm'
3	Ao	=	Area enclosed by shear flow path in 'sqmm'
4	Aoh	=	Area enclosed by centre line of exterior closed transverse torsion reinforcement in 'sqmm'
5	Ast required	=	Area of longitudinal tensile reinforcement required at a cross section in 'mm'
6	Astmin	=	Minimum cross sectional area of longitudinal tensile reinfocement in 'sqmm'
7	Asv/s	=	Cross sectional area of shear reinforcement per m length of section in sqmm/m
8	Asv/s min	=	Cross sectional area of minimum shear reinforcement per m length of section in sqmm/m
9	b	=	Width of rectangular cross section in 'mm'
10	Bef	=	Effetive width of flange for T or L beam in 'mm'
11	bv	=	Effective width of a web for shear in 'mm'
12	D	=	Overall depth of a cross section in the plane of bending in 'mm'
13	do	=	Distance from the extreme compression fibre of the concrete to the centroid of the outermost layer of tensile reinforcement in 'mm'
14	d_sc	=	Distance from the extreme compressive fibre of the concrete to the centroid of compressive reinforcement in 'mm'
15	dv	=	Effective depth to be considered for shear check in 'mm'
16	Ec	=	Modulus of elasticity of concrete due to creep in 'N/sqmm'
17	Ecj	=	Modulus of elasticity of concrete in 'N/sqmm'
18	Es	=	Modulus of elasticity of steel in 'N/sqmm'
19	f^'c	=	Characteristic compressive (cylinder) strength of concrete at 28 days in 'N/sqmm'
20	f_cm	=	Mean value of cylinder strength in 'N/sqmm'
21	f_cmi	=	Mean value of the in site compressive strength of concrete at relavent age in 'N/sqmm'
22	f^'ct	=	Characterstic flexural tensile strength of concrete at 28 days in 'N/sqmm'
23	f^'ct f	=	Characterstic uniaxial tensile strength of concrete in 'N/sqmm'
24	fsc	=	Characteristic compressive strength of reinforcement in 'N/sqmm'
25	fsy	=	Characteristic yield strength of reinforcement in 'N/sqmm'
26	fsy.f	=	Characteristic yield strength of reinforcement used as fitment in 'N/sqmm'
27	k1	=	Coefficient that accounts for bond properties of the bonded reinforcement
28	k2	=	Coefficient that accounts for the longitudinal strain distribution
29	k2	=	Coefficient used for the creep calculation
30	k3	=	Coefficient depend on the age of concrete at loadings used for the creep calculation
31	k4	=	Coefficient depend on the enviroment condition used for the creep calculation
32	k5	=	A modification factor for high strength concrete used for creep calculation
33	k6	=	Coefficient accounts for the non linear creep that develops at sustained stress level of 0.45 fcmi
34	kd	=	The depth of the neutral axis on the cracked section in 'mm'
35	ku	=	Neutral axis parameter being the ratio,at ultimate strength under any combination of bending and compression, of the depth to the neutral axis from the extreme compressive fibre to d
36	kud	=	Ratio, at ultimate strength without axial force of the depth to the neutral axis from the extreme compression fibre to effective depth do
37	kv	=	Constant to calculate concrete section Ultimate shear strength excluding shear reinforcement
38	Legs	=	Number Of legs Of the shear reinforcement
39	M^*	=	Design Bending Moment at cross section in 'kNm'
40	M^*(shear)	=	Design Bending Moment at cross section related to Shear force considered in 'kNm'
41	Mnh	=	Hogging moments of resistance of member at the joint faces in 'kNm'
42	Mns	=	Sagging moments Of resistance Of member at the joint faces in 'kNm'
43	Muo	=	Ultimate strength in bending, without axial force at a cross section in 'kNm'
44	Scalc	=	Shear reinforcement spacing calculated as per Asv in 'mm'
45	Sprv	=	Shear reinforcement spacing provided in 'mm'
46	S_{r, max}	=	Maximum crack spacing in 'mm'
47	t	=	Time since commencement of drying starts in concrete in days
48	T^*	=	Torsional moment on cross section in 'kNm'
49	Tcr	=	Torsional cracking moment in 'kNm'
50	th	=	Hypothetical thickness of a memebr used in determining creep and shrinkage in 'mm'
51	Tus	=	Torsional resistance in 'kN'
52	uc	=	The length of outside perimater of concrete cross section in 'mm'
53	uh	=	Perimeter of the centre line of the closed transverse torsion reinforcement in 'mm'
54	V^*	=	Design shear force at a cross section in 'kN'
55	V^*-A1(sway Left)	=	V^D+L_left - (Mns_left + Mnh_right / L ) in 'kN'
56	V^*-A2(sway Left)	=	V^D+L_Right + (Mns_left + Mnh_right / L ) in 'kN'
57	V^*-B1(sway Right)	=	V^DL_left - (Mnh_left + Mns_right / L ) in 'kN'
58	V^*-B2(sway Right)	=	V^DL_Right + (Mnh_left + Mns_right / L ) in 'kN'
59	V^*d	=	Design shear force at a cr oss section for sway condition in 'kN'
60	V^*eq	=	Equivalent factored Shear force for co-existing applied shear force and applied torsion in 'kN'
61	V^*-Sway	=	Max (V^-A1,V^-A2) & (V^-B1,V^-B2) in 'kN'
62	V^D+L	=	Shear due to Dead and Live load in Simply supported beam in 'kN'
63	Vu,max	=	Ultimate shear strength limited by web crushing failure in 'kN'
64	Vuc	=	Ultimate shear strength excluding shear reinforcement in 'kN'
65	Vuc sway	=	Ultimate shear strength excluding shear reinforcement for sway condition in 'kN'
66	Vus	=	Contribution of shear reinforcement to the ultimate shear strength of a beam or wall in 'kN'
67	Vus Sway	=	Contribution of shear reinforcement to the ultimate shear strength of a beam for sway condition in 'kN'
68	w	=	Calculated maximum crackwidth in the concrete member in 'mm'
69	w^'_max	=	Maximum permissible crackwidth in a concrete member in 'mm'
70	x^'	=	Centre line distance of the closed transverse torsion reinforcement along width of section in 'mm'
71	y^'	=	Centre line distance of the closed transverse torsion reinforcement along depth of section in 'mm'
72	y1	=	Larger overall dimension of the closed fitment in 'kN'
73	α₂	=	Constant used for calculation of stress in concrete for rectangular stress block
74	α_{2(crackwidth)}	=	Constant used for crackwidth calculation based on Hypothetical thickness of section (th)
75	α₃	=	Coefficient used for creep calculation, 0.7x (k4 x α2)
76	αv	=	Angle between the inclined shear reinforcement and the longitudinal tensile reinforcement in Degree
77	γ	=	The ratio, under design bending or design combined bending and compression, of the depth of the assumed rectangulat compressive stress block to kud
78	εcc	=	The creep strain in the concrete
79	εsc	=	Strain at level where compressive reinforcement is provided in case of doubly reinforced beam
80	εx	=	Longitudinal strain in concrete
81	ηe	=	Effective modular ratio
82	θv	=	Angle between the axis of the concrete compression strut and the longitudinal axis of the member in Degree
83	σ_o	=	The compressive stress in concrete assuming a cracked section in 'N/sqmm'
84	σ_o,Perm	=	Permissible compressive stress in concrete assuming a cracked section in 'N/sqmm'
85	σscr	=	The stress in the tensile reinforcement assuming a cracked section in 'N/sqmm'
86	σ_scr,Perm	=	Permissible stress in the tensile reinforcement assuming a cracked section in 'N/sqmm'
87	τ	=	Age of concrete at loadings in days
88	Φ	=	Capacity reduction factor for design using linear elastic analysis
89	φcc	=	Design creep coefficient for concrete
90	φcc.b	=	Basic creep co-efficient

All Forces are in 'kN', 'kNm', Stress in 'N/sqmm' & Dimension are in 'mm'.

Code References
Sr.No.	Item		Clause / Table
1.	Capacity reduction factor	:	Table 2.2.2
2.	Astmin	:	8.1.6.1
3.	V^*eq	:	8.2.1.2
4.	Asw min	:	8.2.5.5
5.	Vus	:	8.2.3.1
6.	Vuc	:	8.2.4.1
7.	Max Fitment Spacing	:	8.3.2.2
8.	Asv.min	:	8.2.1.7
9.	Vu,max	:	8.2.3.3
10.	Side Face Reinforcement	:	8.6.4
11.	Tcr	:	8.2.1.2
12.	α2	:	8.1.3
13.	γ	:	8.1.3
14.	Design creep coefficient	:	3.1.8
15.	Crack width calculation	:	8.6.2.3
16.	Shear reinforcement -IMRF	:	14.5.2.2
17.	Flanged Beam	:	8.8
18.	Intermediate Moment Resisting Frames (IMRF)	:	14.5
19.	Design strength in Bending	:	8.1.5

Group		:	G24
Beam No		:	B6
Analysis Reference (Member)	7.858 m	:	5006
Beam Length		:	8000	mm
Breadth (b)		:	450	mm
Depth (D)		:	800	mm
Effective Depth (do)		:	730	mm
Effective width for flanged beam		:	730	mm
Design Code		:	AS 3600 : 2018
Beam Type		:	IMRF Beam
Category		:	Internal
Grade Of Concrete (f'c)		:	N25	N/sqmm
Grade Of Steel (fsy)		:	500N	N/sqmm
Clear Cover (c)		:	40	mm
Es		:	2x10^5	N/sqmm
α2		:	0.81
γ		:	0.91
Φ Muo		:	832.79	kNm
As,min (flex) (B)		:	473.42	sqmm
As,nominal (Bn)		:	468	sqmm
As,min(user input)(B')		:	427.05	sqmm

Flexure Design
	Beam Bottom			Beam Top
	Left	Mid	Right	Left	Mid	Right
Critical L/C - RCDC	5	6	6	6	6	5
M^* (kNm)	5.18	153.64	20.68	378.52	30.8	356.17
ku	0	0.04	0.01	0.11	0.01	0.1
kud (Distance Of N.A.) (mm)	1.01	30.43	4.03	77.25	6.01	72.46
Doubly Reinforced Section
M^*2 (Excess Moment for Doubly Reinforced section) (kNm)	0	0	0	0	0	0
fsc (Compressive Stress in Steel) (N/sqmm)	0	0	0	0	0	0
Asc (Area of Compression Reinf.) ( sqmm) (C)	0	0	0	0	0	0
ρ (%) (Flexural)	0.005	0.154	0.02	0.39	0.24	0.366
Ast (sqmm) (A)	16.7	504.76	66.83	1281.6	99.65	1202.17
Asc (ku > 0.36 & M^*>0.8 Φ Muo)
Ac compression (kud x b) (sqmm)	0	0	0	0	0	0
Asc (sqmm) (D)	0	0	0	0	0	0
Asc reqd (sqmm)	0	0	0	0	0	0
Ast reqd (sqmm)	473.42	504.76	473.42	1281.6	473.42	1202.17
A_{st prov} (sqmm)	565.5	565.5	565.5	1357.14	603.18	1357.14
Reinforcement Provided	5-N12	5-N12	5-N12	3-N24	3-N16	3-N24

Note: Calculation of Ast

Ast reqd	=	Max(B,B^',A) (for Mu > 0)
Ast reqd	=	Bn (for Mu = 0)
Asc reqd	=	Max(C,D)
Where,
A	=	Ast	=	Tension reinforcement required for bending moment
B	=	Ast min (flex)	=	Minimum area of flexural reinforcement
B^'	=	Ast min(user input)	=	Minimum area of flexural reinforcement defined by User
Bn	=	Ast nominal	=	Nominal area of reinforcement
C	=	Asc	=	Compression reinforcement required for bending moment
D	=	Asc (ku > 0.36 & M^*>0.8 Φ Muo)	=	Compression reinforcement required for condition (ku > 0.36 & M^*>0.8 Φ Muo)

Shear Design
Aoh	=	277400	sqmm
uc	=	2500	mm
uh	=	2220	mm
Asv/s.min	=	360	sqmm/m
Tcr	=	85.54	kNm
0.25ΦTcr	=	16.04	kNm
Asw/s min (torsion)	=	0	sqmm/m

For Transverse Reinf
	Left	Mid	Right
Critical L/C - RCDC	6	6	5
PtPrv (%)	0.413	0.184	0.413
V* (kN)	194.03	139.95	188.35
M*-Sect (kNm)	378.52	30.8	356.17
T* (kNm)	0.31	0.31	0.31
0.9xT*x uh/2Ao (N)	0	0	0
V*eq (kN)	194.03	139.95	188.35
εx x 10^^-3	1.42	1.16	1.35
kv	0.13	0.15	0.13
cot θv	1.24	1.32	1.26
v* (stress due to V* + T*) (N/sqmm)	0.66	0.47	0.64
Φ Vu,max / (bv x dv) (N/sqmm)	5.04	4.96	5.02
Φ Vuc (kN)	141.77	161.84	136.31
Φ Vus (kN)	69.67	29.19	182.77
Legs	2	2	2
Fitment Rebar	10	10	10
Asw/s (T*) (sqmm/m)	0	0	0
Asw /s (Tcr) (sqmm/m)	0	0	0
Asw /s (torsion) (sqmm/m)	0	0	0
Asv/s Reqd (sqmm/m)	476.69	360	458.91
For Sway Shear
V^D+L (kN)	189.22	128.27	189.83
Mnh (kNm)	426.68	0	426.68
Mns (kNm)	183.35	0	183.35
Sway-Right (kN)	105.65	44.7	273.39
Sway-Left (kN)	272.78	211.83	106.26
V*-Sway (kN)	272.78	211.83	273.39
Vu (2*Eq Comb) (kN)	220.26	166.18	214.58
V*d (kN)	220.26	211.83	220.26
Φ Vuc Sway(kN)	132.55	122.04	136.31
Φ Vus Sway(kN)	186.97	119.73	182.77
Asv Reqd Sway(sqmm/m)	476.69	450	458.91
Asv Reqd Final = max (Asv Reqd , Asv Reqd Sway ) (sqmm/m)	476.69	450	458.91
SCalc (mm)	95	265	95
SPrv (mm)	95	265	95
Av Total Prv (sqmm/m)	1653.47	592.75	1653.47


Maximum Spacing Criteria

Basic
Spc1	=	400	mm
Spc2	=	300	mm
For Torsion
(x' = 380, y' = 730)
Spc3	=	300	mm
Spc4= 0.12 x 2 x (x'+y')	=	266	mm


For IMRF
Left Section, Right Section
Spc5 = 8 x db	=	96	mm
Spc6 = 24 x df	=	240	mm
Spc7 = 0.25 x do	=	182	mm
Spc8	=	300	mm
Provided Spacing	=	95	mm

Mid Section
Spc9 = 0.5 x D	=	400	mm
Provided Spacing	=	300	mm

Side face reinforcement

Beam Width	=	450	mm
Depth of the Beam	=	800	mm
		Beam Depth > 750 ,
		Hence, Side face reinforcement is Provided

Spacing Criteria

SFR Rebar	=	12	mm
Number of Rebar (EF)	=	3
Maximum Spacing Permitted	=	200	mm
Spacing Provided	=	175	mm Hence, OK