BEAM DESIGN CALCULATION
Project Name	:	Unassigned
Client Name	:	Unassigned
Engineer Name	:	Unassigned
Design File	:	D:\Bentley\Common data\Bentley Communities\ACI\ACI_English_validation Sheet\2019_English\Beam_Coupling\STAAD file\Coupling beam-testing-model-2-Beam-1-49.2125 ft.rcdx
Analysis File	:	D:\Bentley\Common data\Bentley Communities\ACI\ACI_English_validation Sheet\2019_English\Beam_Coupling\STAAD file\Coupling beam-testing-model-2.std
Analysis Last Modified	:	3/3/2023 1:25:18 PM
Level Designed	:	49.2125 ft

Sr.No.	Symbol		Definitions
1	α	=	Angle formed with horizontal line along length of Beam
2	Ach	=	Cross sectional area of structural member measures to the outside edge of transverse reinforcement in 'in^2'
3	Ag	=	Cross sectional area of concrete in 'in^2'
4	Ash	=	Total cross sectional area transverse reinforcement (including cross ties) within spacing S in 'in^2'
5	Avd	=	Area of diagonal reinforcement in coupler beam in 'in^2'
6	As	=	Area of Tension reinforcement required in 'in^2'
7	As,min	=	Minimum area of flexural reinforcement in 'in^2'
8	As,nominal	=	Nominal area of reinforcement in 'in^2'
9	Al	=	Area of longitudinal reinforcement required to resist torsion in 'in^2'
10	Al,face	=	Area of longitudinal reinforcement required on each face to resist torsion in 'in^2'
11	At Torsion	=	Area of closed stirrups resisting torsion in 'in^2'
12	AstPrv	=	Area of longitudinal reinforcement provided at given section in 'in^2'
13	Av	=	Area of shear reinforcement required per meter length in 'in^2'
14	Av,min	=	Minimum area of shear reinforcement in 'in^2'
15	Al,min	=	Minimum area of longitudinal torsional reinforcement in 'in^2'
16	Av Total Reqd	=	Total area of shear reinforcement required, including that for torsion in 'in^2'
17	Av Total Prv	=	Total area of shear reinforcement provided, including that for torsion in 'in^2'
18	Ao	=	Gross area enclosed by shear flow path in 'in^2'
19	Aoh	=	Area enclosed by centerline of the outermost closed transverse torsional reinforcement in 'in^2'
20	Ast	=	Total area of longitudinal reinforcement calculated at a given section in 'in^2'
21	Asr	=	Area of Skin reinforcement calculated for given section in 'in^2'
22	Asc	=	Area of Compression reinforcement required for doubly reinforced section or if torsion exists in 'in^2'
23	Asv Reqd Sway	=	Area of shear reinforcement required for sway condition in 'in^2'
24	b	=	Width of the Beam in 'in'
25	bw	=	Width of Web ( For flanged Beam ) in 'in'
26	b'	=	C/C distance between longitudinal reinforcement along B in 'in'
27	bc	=	Oustside dimension of transverse reinforcement in 'in'
28	Cc	=	Effective Cover to tension reinforcement in 'in'
29	Cmin	=	Clear cover to top and bottom reinforcement in 'in'
30	Cside	=	Clear cover to side reinforcement in 'in'
31	c'	=	Effective cover to reinforcement at compression face in 'in'
32	d	=	Effective depth of Beam in 'in'
33	d'	=	C/C distance between longitudinal reinforcement along D in 'in'
34	D	=	Depth of Beam in 'in'
35	Es	=	Modulus of elasticity of steel in 'ksi'
36	f'c	=	Specified compressive strength of concrete in cylinder in 'ksi'
37	fs	=	Calculated tensile stress in reinforcement at service loads, 'ksi'
38	Hf	=	Thickness of Flange in 'in'
39	hx	=	Maximum C/C horizontal spacing of hoops legs on all faces in 'in'
40	Icr	=	Moment Of Inertia Of concrete crack section
41	l	=	Effective Length Of Beam (Clear Span) in 'in'
42	Legs	=	Number Of legs Of the shear reinforcement
43	Mcr	=	Cracking Moment
44	Mh	=	Hogging moments of resistance of member at the joint faces in 'kip-ft'
45	Mpr1	=	Hogging moments Of resistance Of member at the joint faces in 'kip-ft'
46	Mpr2	=	Sagging moments Of resistance Of member at the joint faces in 'kip-ft'
47	Ms	=	Sagging moments Of resistance Of member at the joint faces in 'kip-ft'
48	Mu	=	Factored Bending Moment at a section in 'kip-ft'
49	Mubal	=	Nominal flexural strength Of Singly Reinforced Section At Balance Neutral Axis in 'kip-ft'
50	Ptmin	=	Minimum percentage steel
51	PtPrv	=	Provided percentage steel
52	Stirrup	=	Bar mark representing shear stirrup
53	S	=	spacing Of confining links in 'in'
54	SCalc	=	Stirrup spacing calculated As per Asv in 'in'
55	Spc-trans	=	Spacing of shear links along width of the beam in 'in'
56	Sprv	=	Stirrup spacing provided in 'in'
57	Tcr	=	Cracking torque under pure Torsion in 'kip-ft'
58	Tu	=	Factored Torsional Moment at a section in 'kip-ft'
59	V^D+L	=	Shear due to Dead and Live load in Simply supported beam in 'kip'
60	Ve	=	Earthquake induced shear in 'kip-ft'
61	φVc	=	Reduced Shear strength provided by concrete in 'kip'
62	φVc sway	=	Reduced Shear strength provided by concrete for sway condition in 'kip'
63	Vu	=	Factored Shear Force at a section in 'kip'
64	Vu-A1(sway Left)	=	V^D+Lleft - (Mpr1left + Mpr2right / L ) in 'kip'
65	Vu-A2(sway Left)	=	V^D+Lleft + (Mpr2left + Mpr1right / L ) in 'kip'
66	Vu-B1(sway Right)	=	V^DLRight - (Mpr1left + Mpr2right / L ) in 'kip'
67	Vu-B2(sway Right)	=	V^DLRight + (Mpr2left + Mpr1right / L ) in 'kip'
68	Vud	=	Design Shear Force due to sway in 'kip'
69	Vs	=	Nominal shear strength provided by shear reinforcement in 'kip'
70	Vs Sway	=	Nominal shear strength provided by shear reinforcement for sway condition in 'kip'
71	Vu sway	=	Max (Vu-A1,Vu-A2) & (Vu-B1,Vu-B2) in 'kip'
72	y	=	Neutral axis depth.
73	Φ	=	Strength reduction factor
All Forces are in 'kip', 'kip-ft', Stress in 'ksi' & Dimension are in 'in'.

Code References
Sr.No.	Item		Clause / Table
1.	Ptmax	:	7.3.3.1, 8.3.3.1, 9.3.3.1
2.	As,min (flex) (B)	:	9.6.1.1, 9.6.1.2
3.	As,min	:	9.6.1.3
4.	Vc	:	22.5
5.	Asv	:	22.5.10.5 & 22.6.7
6.	Min Shear Reinf	:	9.6.3.1
7.	Max Stirrup Spacing	:	9.7.62
8.	Shear Reinf - Torsion	:	22.7.3.1
9.	Side Face Reinforcement	:	9.7.2.3
10.	Tcr	:	9.5.4.1
11.	fs,perm	:	10.6.4
12.	fc,perm	:	10.2.7.1
13.	Wcr	:	Eq 4.2(a)
14.	Ptmin	:	18.6.3.1
15.	Asmin	:	18.6.3.1
16.	Sclc	:	18.6.4.1 & 18.6.4.4
17.	Bidirectional one-way shear effects	:	22.5.1.10 & 22.5.1.11

Group	:	G2
Beam No	:	B2
Analysis Reference (Member)	:	1304 (49.2125 ft)
Beam Length	:	39.37	in
Breadth (B)	:	11.81	in
Depth (D)	:	23.62	in
Effective Depth (d)	:	20.94	in
Design Code	:	ACI 318 - 19
Beam Type	:	Coupling Beam
Grade Of Concrete (f'c)	:	C3	ksi
Grade Of Steel (Main)	:	Fy60	ksi
Grade Of Steel (Shear)	:	Fy60	ksi
Grade Of Steel - Flexural Design	:	Fy60	ksi
Grade Of Steel - Shear Design	:	Fy60	ksi
Grade Of Steel - Torsion Design	:	Fy60	ksi
Top/Bottom Clear Cover (Cmin)	:	1.5	in
Side Clear Cover	:	1.5	in
Es	:	29007.55	ksi
Mubal	:	414.36	kip-ft
As,min (flex) (B)	:	0.82	in^2
As,nominal (Bn)	:	0.32	in^2
As,min(user input)(B')	:	0.32	in^2
Strength Reduction Factor φ (Shear)	:	0.6

Check for coupling action
Design of diagonal reinforcement
Clear Span of Beam, Ln	=	39.37	in
Beam Depth, D	=	23.62	in
Effective Depth, deff	=	20.94	in
Angle with horizontal, (α)	=	27.646	deg
Shear for EQ case, Vu	=	104.14	kip
λ	=	1
Φ	=	0.85
Criteria
1.	=	Ln/D
	=	39.37/23.62
	=	1.67 < 2, Hence coupling beam is applicable
2.   Vc	=	4 x  λ  x sqrt(fck) x B x D
	=	61.12	kip
	=	Vc  <  Vu
	=	Hence, Beam Is coupling beam
Vn	=	10 x sqrt(fck) x B x Deff
	=	135.46	kip
Vu	<	Vn	Hence Ok
Avd	=	(Vu x 1000 / (2 x Fy x sinα)) / Φ
	=	2.2	in^2
Reinforcement provided	=	4-#5 4-#5 Both diagonals

Flexure Design (For Vertical Load Only)
	Beam Bottom			Beam Top
	Left	Mid	Right	Left	Mid	Right
Critical L/C - Analysis	-	13	-	13	13	13
Critical L/C - RCDC	-	3	-	3	3	3
Mu (kip-ft)	-	0.17	-	3.61	0.8	3.61
As (flex) (in^2) (C)	-	0	-	0.04	0.01	0.04
Asc (flex) (in^2) (A)	-	-	-	-	-	-
Tu (kip-ft)	-	-	-	-	-	-
Tcr/4 (kip-ft)	-	-	-	-	-	-
Al, min(in^2)(Tor.) (D)	-	-	-	-	-	-
Al (in^2) (Tor.) (E)	-	-	-	-	-	-
Al (Dist) (in^2) (D)	-	-	-	-	-	-
Ast (in^2)	0.32	0.32	0.32	0.32	0.32	0.32
AstPrv (in^2)	0.33	0.33	0.33	0.33	0.33	0.33
Reinforcement Provided	3-#3	3-#3	3-#3	3-#3	3-#3	3-#3

Note: Calculation of Ast
Ast	=	Max {B, C+D, A+D} (for Mu > 0 and C x 1.33 > B)
Ast	=	Max{B', C x 1.33 + D, A+D} (for Mu > 0 and C x 1.33 < B)
Ast	=	Bn (for Mu = 0)
Where,
A	=	Asc (flex)	=	Compression reinforcement required for bending moment
B	=	As,min (flex)	=	Min area of flexural reinforcement
Bn	=	As,nominal	=	Nominal area of reinforcement
C	=	As (flex)	=	Total area of longitudinal reinforcement calculated at a given section
D	=	Al (Dist)	=	Distributed longitudinal torsional reinforcement at section considered
E	=	A s,reqd Crack	=	Area of reinforcement required for Crack Width
Ast (Dist) (in^2)			=	Max(Al,min (Tor), Al (Tor)) x ((2B) / (2B + 2D))

Shear Design (For Vertical Load Only)
	Left	Mid	Right
Critical L/C - RCDC	3	3	3
PtPrv (%)	0.133	0.133	0.133
Vu (kip)	4.52	1.66	4.52
Mu-Sect (kip-ft)	3.61	0.26	3.61
Φ Vc (kip)	20.32	20.32	20.32
Vs (kip)	-	-	-
Aoh (in^2)	-	-	-
At (in^2/ft)	-	-	-
Av (in^2/ft)	0.12	0.12	0.12
Tu (kip-ft)	0	0	0
At Torsion (in^2/ft)	-	-	-
Av Total Reqd (in^2/ft)	0.12	0.12	0.12
Asv Reqd (in^2/ft)	0.12	0.12	0.12
Legs	2	2	2
Stirrup Rebar	3	3	3
SCalc (in)	10	10	10
SPrv (in)	10	10	10
Av Total Prv (in^2/ft)	0.26	0.26	0.26

Hoop link for diagonal bars as per ACI 318 - 19
Spacing Criteria:
Effective Width, (B")	=	8	in
Effective Depth, (D")	=	16	in
6 X diameter of longitudinal bar (db)	=	3.76	in
Maximum Spacing	=	6	in
Minimum Spacing	=	2	in
Hence Link spacing, S	=	Maximum (Minimum Spacing, Minimum (6db, Maximum Spacing))
	=	3	in
Hoop dimension, bc	=	5.6	in
Gross area of column, Ag	=	B" x D"
	=	119.16	in^2
Core area of column, Ach	=	(B" - 2 x Cside + 2 x Outer Link Rebar) x (D" - 2 x Cmin + 2 x Outer Link Rebar)
	=	76.66	in^2
Hoop Link Criteria:
Ash1	=	0.3 x S x bc x (Fck/Fy) x (Ag/Ach-1)
	=	0.14	in^2
Ash2	=	0.09 x S x bc x (Fck/Fy)
	=	0.08	in^2
Ash	=	Maximum (Ash1, Ash2)
	=	0.14	in^2
Link Rebar (Outer)	=	4
Link Rebar (Internal)	=	3

Maximum Spacing Criteria

Basic

                4 Sqrt(f'c)Bd

=

54.18

kip

	Left	Mid	Right
Vs (kip)	0	0	0
Check	Vs <= 4 Sqrt(f'c)Bd	Vs <= 4 Sqrt(f'c)Bd	Vs <= 4 Sqrt(f'c)Bd
Spc1 (in)	d/2=10.47	d/2=10.47	d/2=10.47
Spc2 (in)	24	24	24

Maximum Spacing Criteria Along Beam Width
4 Sqrt(f'c)Bd	=	54.18	kip

	Left	Mid	Right
Vs (kip)	0	0	0
Check	Vs <= 4 Sqrt(f'c)Bd	Vs <= 4 Sqrt(f'c)Bd	Vs <= 4 Sqrt(f'c)Bd
Spc-trans 1 (in)	d = 20.94	d = 20.94	d = 20.94
Spc- trans 2 (in)	24	24	24
Spc-trans actual (in)	9.19	9.19	9.19

Skin reinforcement
Beam Width	=	11.81	in
Beam Depth	=	23.62	in
Depth	=	23.62 <= 36,     Hence Skin Reinforcement is not required.