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\2014_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\2014_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 'in2'
3 Ag = Cross sectional area of concrete in 'in2'
4 Ash = Total cross sectional area transverse reinforcement (including cross ties) within spacing S in 'in2'
5 Avd = Area of diagonal reinforcement in coupler beam in 'in2'
6 As = Area of Tension reinforcement required in 'in2'
7 As,min = Minimum area of flexural reinforcement in 'in2'
8 As,nominal = Nominal area of reinforcement in 'in2'
9 Al = Area of longitudinal reinforcement required to resist torsion in 'in2'
10 Al,face = Area of longitudinal reinforcement required on each face to resist torsion in 'in2'
11 At Torsion = Area of closed stirrups resisting torsion in 'in2'
12 AstPrv = Area of longitudinal reinforcement provided at given section in 'in2'
13 Av = Area of shear reinforcement required per meter length in 'in2'
14 Av,min = Minimum area of shear reinforcement in 'in2'
15 Al,min = Minimum area of longitudinal torsional reinforcement in 'in2'
16 Av Total Reqd = Total area of shear reinforcement required, including that for torsion in 'in2'
17 Av Total Prv = Total area of shear reinforcement provided, including that for torsion in 'in2'
18 Ao = Gross area enclosed by shear flow path in 'in2'
19 Aoh = Area enclosed by centerline of the outermost closed transverse torsional reinforcement in 'in2'
20 Ast = Total area of longitudinal reinforcement calculated at a given section in 'in2'
21 Asr = Area of Skin reinforcement calculated for given section in 'in2'
22 Asc = Area of Compression reinforcement required for doubly reinforced section or if torsion exists in 'in2'
23 Asv Reqd Sway = Area of shear reinforcement required for sway condition in 'in2'
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 Sprv = Stirrup spacing provided in 'in'
56 Tcr = Cracking torque under pure Torsion in 'kip-ft'
57 Tu = Factored Torsional Moment at a section in 'kip-ft'
58 VD+L = Shear due to Dead and Live load in Simply supported beam in 'kip'
59 Ve = Earthquake induced shear in 'kip-ft'
60 φVc = Reduced Shear strength provided by concrete in 'kip'
61 φVc sway = Reduced Shear strength provided by concrete for sway condition in 'kip'
62 Vu = Factored Shear Force at a section in 'kip'
63 Vu-A1(sway Left) = VD+Lleft - (Mpr1left + Mpr2right / L ) in 'kip'
64 Vu-A2(sway Left) = VD+Lleft + (Mpr2left + Mpr1right / L ) in 'kip'
65 Vu-B1(sway Right) = VDLRight - (Mpr1left + Mpr2right / L ) in 'kip'
66 Vu-B2(sway Right) = VDLRight + (Mpr2left + Mpr1right / L ) in 'kip'
67 Vud = Design Shear Force due to sway in 'kip'
68 Vs = Nominal shear strength provided by shear reinforcement in 'kip'
69 Vs Sway = Nominal shear strength provided by shear reinforcement for sway condition in 'kip'
70 Vu sway = Max (Vu-A1,Vu-A2) & (Vu-B1,Vu-B2) in 'kip'
71 y = Neutral axis depth.
72 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

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 - 14
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 : 327.85 kip-ft
As,min (flex) (B) : 0.82 in2
As,nominal (Bn) : 0.32 in2
As,min(user input)(B') : 0.32 in2
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
= 0.07 < 0.08, 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 in2
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) (in2) (C) - 0 - 0.04 0.01 0.04
Asc (flex) (in2) (A) - - - - - -
Tu (kip-ft) - - - - - -
Tcr/4 (kip-ft) - - - - - -
Al, min(in2)(Tor.) (D) - - - - - -
Al (in2) (Tor.) (E) - - - - - -
Al (Dist) (in2) (D) - - - - - -
Ast (in2) 0.32 0.32 0.32 0.32 0.32 0.32
AstPrv (in2) 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) (in2) = 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) 19.92 19.92 19.92
Vs (kip) - - -
Aoh (in2) - - -
At (in2/ft) - - -
Av (in2/ft) 0.12 0.12 0.12
Tu (kip-ft) 0 0 0
At Torsion (in2/ft) - - -
Av Total Reqd (in2/ft) 0.12 0.12 0.12
Asv Reqd (in2/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 (in2/ft) 0.26 0.26 0.26
Hoop link for diagonal bars as per ACI 318 - 14
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 = 4 in
Hence Link spacing, S = Maximum (Minimum Spacing, Minimum (6db, Maximum Spacing))
= 4 in
Hoop dimension, bc = 5.6 in
Gross area of column, Ag = B" x D"
= 119.16 in2
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 in2
Hoop Link Criteria:
Ash1 = 0.3 x S x bc x (Fck/Fy) x (Ag/Ach-1)
= 0.19 in2
Ash2 = 0.09 x S x bc x (Fck/Fy)
= 0.1 in2
Ash = Maximum (Ash1, Ash2)
= 0.19 in2
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
 
Skin reinforcement
  
Beam Width = 11.81 in
Beam Depth = 23.62 in
Depth = 23.62 <= 36,     Hence Skin Reinforcement is not required.