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 Sway shear\STAAD file\Sample Model_R0-Beam-1-24 ft.rcdx
Analysis File : D:\Bentley\Common data\Bentley Communities\ACI\ACI_English_validation Sheet\2014_English\Beam Sway shear\STAAD file\Sample Model_R0.STD
Analysis Last Modified : 2/16/2023 10:07:18 PM
Level Designed : 24 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 : G3
Beam No : B7
Analysis Reference (Member) : 33 (24 ft)
Beam Length : 204 in
Breadth (B) : 15 in
Depth (D) : 30 in
Effective Depth (d) : 27.32 in
Design Code : ACI 318 - 14
Beam Type : Ductile Beam (Special Frame)
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 : 708.61 kip-ft
As,min (flex) (B) : 1.37 in2
As,nominal (Bn) : 0.53 in2
As,min(user input)(B') : 0.53 in2
Maximum percentage steel (User Defined) : 4 %
Maximum percentage steel (Special Frame) : Min (4 , 2.5)
: 2.5 %
Strength Reduction Factor φ (Shear) : 0.6
 
For Longitudinal Reinf
Beam Bottom Beam Top
Left Mid Right Left Mid Right
Critical L/C - Analysis 10 6 12 12 - 10
Critical L/C - RCDC 6 2 8 8 - 6
Mu (kip-ft) 57.41 152.15 53.6 81.23 - 85.75
As (flex) (in2) (C) 0.47 1.29 0.44 0.67 - 0.71
Asc (flex) (in2) (A) - - - - - -
Tu (kip-ft) 0.89 1.48 1.14 1.14 - 0.89
Tcr/4 (kip-ft) 7.7 7.7 7.7 7.7 - 7.7
Al, min(in2)(Tor.) (D) - - - - - -
Al (in2) (Tor.) (E) - - - - - -
Al (Dist) (in2) (D) - - - - - -
Ast (in2) 0.63 1.37 0.59 0.9 0.53 0.95
AstPrv (in2) 0.98 1.37 0.59 0.98 0.55 0.98
Reinforcement Provided 5-#4 5-#4
2-#4
3-#4 5-#4 5-#3 5-#4
 
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))
 
For Transverse Reinf
Left Mid Right
Critical L/C - RCDC 2 2 2
PtPrv (%) 0.24 0.335 0.24
Vu (kip) 53.33 18.35 54.19
Mu-Sect (kip-ft) 72.64 125.56 79.92
Φ Vc (kip) 0 0 0
Vs (kip) 88.89 30.58 90.32
Aoh (in2) - - -
At (in2/ft) - - -
Av (in2/ft) 0.65 0.22 0.66
Tu (kip-ft) 1.48 1.48 1.48
At Torsion (in2/ft) 0 0 0
Av Total Reqd (in2/ft) 0.65 0.22 0.66
Asv Reqd (in2/ft) 0.65 0.22 0.66
For Sway Shear
VD+L (kip) 44.61 14.83 44.54
Mh (kip-ft) 161.93 0 161.93
Ms (kip-ft) 161.93 0 98.56
Sway-Right (kip) 23.72 35.72 65.44
Sway-Left (kip) 61.42 1.98 27.74
Vu-Sway (kip) 61.42 35.72 65.44
Vud (kip) 61.42 35.72 65.44
Φ Vc Sway(kip) 0 0 0
Vs Sway(kip) 102.36 59.53 109.06
Asv Reqd Sway(in2/ft) 0.75 0.44 0.8
Asv Reqd Final = max (Asv Reqd , Asv Reqd Sway ) (in2/ft) 0.75 0.44 0.8
Legs 2 2 2
Stirrup Rebar 3 3 3
SCalc (in) 2.5 5.5 2.5
SPrv (in) 2.5 5.5 2.5
Av Total Prv (in2/ft) 1.05 0.48 1.05
          
 
Maximum Spacing Criteria
    
       Basic                               
                4 Sqrt(f'c)Bd = 89.78 kip
Left Mid Right
Vs (kip) 88.89 30.58 90.32
Check Vs <= 4 Sqrt(f'c)Bd Vs <= 4 Sqrt(f'c)Bd Vs > 4 Sqrt(f'c)Bd
Spc1 (in) d/2=13.66 d/2=13.66 d/4=6.83
Spc2 (in) 24 24 12
      
For Torsion
                                
                (X1 = 12.4, Y1 = 27.4)
                Spc3 = 12 in
                Spc4=(X1+Y1)/4 = 9.9 in
   
 
     For Ductility (Special Frames)        
       Left Section,  Right Section
              Spc5 = 6 x Small Longitudinal Dia = 3 in
              Spc6 = d / 4 = 6.8 in
              Spc7 = 5.9 in
             Provided Spacing = 2.5 in
       
       Mid Section
              Provided Spacing = 11.8 in
       
 
Skin reinforcement
  
Beam Width = 15 in
Beam Depth = 30 in
Depth = 30 <= 36,     Hence Skin Reinforcement is not required.