BEAM DESIGN CALCULATION
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Engineer Name : GG
Design File : D:\Scube\000 RCDC 2010\10.0.0\Queries\Worley Parsons\Validation sheets\Upper Roof Beam_IMRF Design.rcdx
Analysis File : \\inairwpdfs01v\Shares\Projects$\RPSC-SOR-4-FEED-UPDATE-AND-EARLY-DETAILED-ENGINEERING\11.0-Engineering\11.11 Structural\4.0 Calculations\Substation-806\STAAD\Substation-806_ IFD Rev.std
Analysis Last Modified : 2/26/2020 11:21:52 AM
Level Designed : 15.88m
 
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 'sqmm'
3 Ag = Cross sectional area of concrete in 'sqmm'
4 Ash = Total cross sectional area transverse reinforcement (including cross ties) within spacing S in 'sqmm'
5 Avd = Area of diagonal reinforcement in coupler beam in 'sqmm'
6 As = Area of Tension reinforcement required in 'sqmm'
7 As,min = Minimum area of flexural reinforcement in 'sqmm'
8 As,nominal = Nominal area of reinforcement in 'sqmm'
9 Al = Area of longitudinal reinforcement required to resist torsion in 'sqmm'
10 Al,face = Area of longitudinal reinforcement required on each face to resist torsion in 'sqmm'
11 At Torsion = Area of closed stirrups resisting torsion in 'sqmm'
12 AstPrv = Area of longitudinal reinforcement provided at given section in 'sqmm'
13 Av = Area of shear reinforcement required per meter length in 'sqmm'
14 Av,min = Minimum area of shear reinforcement in as per clause 11.4.6.1 in 'sqmm'
15 Al,min = Minimum area of longitudinal torsional reinforcement as per clause 11.5.5.3 in 'sqmm'
16 Av Total Reqd = Total area of shear reinforcement required, including that for torsion in 'sqmm'
17 Av Total Prv = Total area of shear reinforcement provided, including that for torsion in 'sqmm'
18 Ao = Gross area enclosed by shear flow path in 'sqmm'
19 Aoh = Area enclosed by centerline of the outermost closed transverse torsional reinforcement as per clause 11.5.3.1 in 'sqmm'
20 Ast = Total area of longitudinal reinforcement calculated at a given section in 'sqmm'
21 Asr = Area of Skin reinforcement calculated for given section in 'sqmm'
22 Asc = Area of Compression reinforcement required for doubly reinforced section or if torsion exists in 'sqmm'
23 b = Width of the Beam in 'mm'
24 bw = Width of Web ( For flanged Beam ) in 'mm'
25 b' = C/C distance between longitudinal reinforcement along B in 'mm'
26 bc = Oustside dimension of transverse reinforcement in 'mm'
27 Cc = Effective Cover to tension reinforcement in 'mm'
28 Cmin = Clear cover in 'mm'
29 c' = Effective cover to reinforcement at compression face in 'mm'
30 d = Effective depth of Beam in 'mm'
31 d' = C/C distance between longitudinal reinforcement along D in 'mm'
32 D = Depth of Beam in 'mm'
33 Es = Modulus of elasticity of steel in 'N/sqmm'
34 f'c = Specified compressive strength of concrete in cylinder in 'N/sqmm'
35 fs = Calculated tensile stress in reinforcement at service loads, 'N/sqmm'
36 Hf = Thickness of Flange in 'mm'
37 hx = Maximum C/C horizontal spacing of hoops legs on all faces in 'mm'
38 Icr = Moment Of Inertia Of concrete crack section
39 l = Effective Length Of Beam (Clear Span) in 'mm'
40 Legs = Number Of legs Of the shear reinforcement
41 Mcr = Cracking Moment
42 Mpr1 = Hogging moments Of resistance Of member at the joint faces in 'kNm'
43 Mpr2 = Sagging moments Of resistance Of member at the joint faces in 'kNm'
44 Mu = Factored Bending Moment at a section in 'kNm'
45 Mubal = Nominal flexural strength Of Singly Reinforced Section At Balance Neutral Axis in 'kNm'
46 Ptmin = Minimum percentage steel As per clause 10.5
47 PtPrv = Provided percentage steel
48 Stirrup = Bar mark representing shear stirrup
49 S = spacing Of confining links in 'mm'
50 SCalc = Stirrup spacing calculated As per Asv in 'mm'
51 Sprv = Stirrup spacing provided in 'mm'
52 Tcr = Cracking torque under pure Torsion in 'kNm'
53 Tu = Factored Torsional Moment at a section in 'kNm'
54 Ve = Earthquake induced shear in 'kNm'
55 φVc = Reduced Shear strength provided by concrete in 'kN'
56 Vu = Factored Shear Force at a section in 'kN'
57 Vu-A1(sway Left) = VD+Lleft - (Mpr1left + Mpr2right / L ) in 'kN'
58 Vu-A2(sway Left) = VD+Lleft + (Mpr2left + Mpr1right / L ) in 'kN'
59 Vu-B1(sway Right) = VDLRight - (Mpr1left + Mpr2right / L ) in 'kN'
60 Vu-B2(sway Right) = VDLRight + (Mpr2left + Mpr1right / L ) in 'kN'
61 Vud = Design Shear Force in 'kN'
62 Vs = Nominal shear strength provided by shear reinforcement in 'kN'
63 Vu sway = Max (Vu-A1,Vu-A2) & (Vu-B1,Vu-B2) in 'kN'
64 y = Neutral axis depth.
65 Φ = Strength reduction factor
 
All Forces are in 'kN', 'kNm', Stress in 'N/sqmm' & Dimension are in 'mm'.
 
Code References
ACI 318M - 2011
Sr.No. Item Clause / Table
1. Ptmax : 10.3.5
2. As,min (flex) (B) : 10.5.1
3. As,min : 10.5.3
4. Vc : 11.2
5. Asv : 11.4.7.2
6. Min Shear Reinf : 11.4.6
7. Max Stirrup Spacing : 11.4.5.1
8. Shear Reinf - Torsion : 11.5.3.5
9. Side Face Reinforcement : 10.6.7
10. Tcr : 11.5.1
11. fs,perm : 10.6.4
12. fc,perm : 10.2.7.1
13. Wcr : Eq 4.2(a)
                                
ACI 318M - 2011 Chapter 21
Sr.No. Item Clause / Table
1. Ptmin : 21.5.2.1
2. Asmin : 21.5.2.1
3. Sclc : 21.5.3.1 & 21.5.3.2

Group : G9
Beam No : B24
Analysis Reference (Member) 15.88m : 5057,5058,5059
Beam Length : 7650 mm
Breadth (B) : 400 mm
Depth (D) : 1000 mm
Effective Depth (d) : 920 mm
Design Code : ACI 318M - 2011
Beam Type : Ductile Beam (Intermediate Frame)
Grade Of Concrete (f'c) : C40 N/sqmm
Grade Of Steel : Fy500 N/sqmm
Clear Cover (Cmin) : 50 mm
Es : 2x10^5 N/sqmm
Mubal : 3152.95 kNm
As,min (flex) (B) : 1163.72 sqmm
As,nominal (Bn) : 478.4 sqmm
As,min(user input)(B') : 478.4 sqmm
 
For Longitudinal Reinf
Beam Bottom Beam Top
Left Mid Right Left Mid Right
Critical L/C - Analysis 323 305 - 322 335 309
Critical L/C - RCDC 74 56 - 73 86 60
Mu (kNm) 266.72 537.61 - 441.3 19.99 738.76
As (flex) (sqmm) (C) 652.76 1334.15 - 1089.66 48.33 1853.06
Asc (flex) (sqmm) (A) - - - - - -
Tu (kNm) 17.8 22.6 - 22.13 11 18.16
Tcr/4 (kNm) 22.5 22.5 - 22.5 22.5 22.5
Al, min(sqmm)(Tor.) - 1718.38 - - - -
Al (sqmm) (Tor.) (E) - 406.67 - - - -
Al (Dist) (sqmm) (D) - 245.48 - - - -
Ast (sqmm) 868.17 1579.63 661.87 1163.72 478.4 1853.06
AstPrv (sqmm) 992.8 1626.2 992.8 2026.84 506.72 2026.84
Reinforcement 5-#16 5-#16
5-#13
5-#16 4-#25 4-#13 4-#25
 
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
Ast (Dist) (sqmm) = Max(Al,min (Tor), Al (Tor)) x ((2B) / (2B + 2D))
 
For Transverse Reinf
Left Mid Right
Critical L/C - RCDC 71 71 71
PtPrv (%) 0.551 0.442 0.551
Vu (kN) 289.99 258.26 383.01
Mu-Sect (kNm) 241.38 457.45 598.81
VD+L (kN) 289.5 0 281.98
Mh (kNm) 894.59 0 894.59
Ms (kNm) 447.63 0 447.63
Sway-Right (kN) 189.82 0 471.02
Sway-Left (kN) 478.54 0 188.97
Vu-Sway (kN) 478.54 0 471.02
Vu (2*Eq Comb) (kN) 362.78 - 458.62
Vud (kN) 478.54 0 471.02
Φ Vc (kN) 305.13 290.06 294.5
Vs (kN) - - 118.02
Av (sqmm/m) 373.45 373.45 373.45
Tu (kNm) 38.36 38.36 36.3
Aoh (sqmm) 282100 282100 282100
At (sqmm/m) 507.82 507.82 480.54
Legs 2 2 2
Stirrup Rebar 10 10 10
At Torsion (sqmm/m) 507.82 507.82 480.54
Av Total Reqd (sqmm/m) 507.82 507.82 785.97
Asv Reqd (sqmm/m) 598.37 507.82 785.97
SCalc (mm) 125 275 125
SPrv (mm) 125 275 125
Av Total Prv (sqmm/m) 1134.08 515.49 1134.08
          
 
Maximum Spacing Criteria
    
       Basic                               
                Spc1 = 460 mm
                Spc2 = 300 mm
       For Torsion                                 
                (X1 = 309.5, Y1 = 909.5)
                Spc3 = 300 mm
                Spc4=(X1+Y1)/4 = 305 mm
   
 
     For Ductility (Intermediate Frames)        
       Left Section,  Right Section
              Spc5 = 8 x Small Longitudinal Dia = 127 mm
              Spc6 = 24 x sv = 228 mm
              Spc7 = d / 4 = 230 mm
              Spc8 = 300 mm
             Provided Spacing = 125 mm
       
       Mid Section
              Provided Spacing = 300 mm
       
 
Skin reinforcement
  
Beam Width = 400 mm
Beam Depth = 1000 mm
Tu = 22.6 kNm
Tcr/4 = 22.5 kNm
Beam Depth > 900 and Tu > Tcr/4,
Hence Skin Reinforcement is Provided
Al Tor. (max) = 1718.38 sqmm
Asr = Max(Al(min)(Tor.), Al(Tor.)) x (2D / (2B+2D))
= 1227.42 sqmm
SR provided = 4-#16EF
Asr provided = 1588.48 sqmm
  
Spacing Criteria
           
Maximum Permissible Spacing = 194 mm
Provided Spacing = 165 mm Hence OK
        
  
 
 

Group : G9
Beam No : B25
Analysis Reference (Member) 15.88m : 5060,5061,5062
Beam Length : 7965 mm
Breadth (B) : 400 mm
Depth (D) : 1000 mm
Effective Depth (d) : 920 mm
Design Code : ACI 318M - 2011
Beam Type : Ductile Beam (Intermediate Frame)
Grade Of Concrete (f'c) : C40 N/sqmm
Grade Of Steel : Fy500 N/sqmm
Clear Cover (Cmin) : 50 mm
Es : 2x10^5 N/sqmm
Mubal : 3152.95 kNm
As,min (flex) (B) : 1163.72 sqmm
As,nominal (Bn) : 478.4 sqmm
As,min(user input)(B') : 478.4 sqmm
 
For Longitudinal Reinf
Beam Bottom Beam Top
Left Mid Right Left Mid Right
Critical L/C - Analysis - 322 334 308 - 323
Critical L/C - RCDC - 73 85 59 - 74
Mu (kNm) - 595.68 181.23 752.63 - 457.13
As (flex) (sqmm) (C) - 1482.78 441.66 1889.27 - 1129.67
Asc (flex) (sqmm) (A) - - - - - -
Tu (kNm) - 0.76 13.75 18.6 - 22.48
Tcr/4 (kNm) - 22.5 22.5 22.5 - 22.5
Al, min(sqmm)(Tor.) - - - - - -
Al (sqmm) (Tor.) (E) - - - - - -
Al (Dist) (sqmm) (D) - - - - - -
Ast (sqmm) 661.87 1482.78 587.41 1889.27 478.4 1163.72
AstPrv (sqmm) 992.8 1787.04 992.8 2026.84 506.72 2026.84
Reinforcement 5-#16 5-#16
4-#16
5-#16 4-#25 4-#13 4-#25
 
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
Ast (Dist) (sqmm) = Max(Al,min (Tor), Al (Tor)) x ((2B) / (2B + 2D))
 
For Transverse Reinf
Left Mid Right
Critical L/C - RCDC 71 71 71
PtPrv (%) 0.551 0.486 0.551
Vu (kN) 393.08 360.03 305
Mu-Sect (kNm) 612.77 386.71 260.2
VD+L (kN) 292.79 0 299.68
Mh (kNm) 894.59 0 894.59
Ms (kNm) 447.63 0 447.63
Sway-Right (kN) 180.99 0 480.7
Sway-Left (kN) 473.81 0 181.74
Vu-Sway (kN) 473.81 0 480.7
Vu (2*Eq Comb) (kN) 464.86 - 374.31
Vud (kN) 473.81 0 480.7
Φ Vc (kN) 294.54 298.81 305.13
Vs (kN) 131.38 81.63 -
Av (sqmm/m) 373.45 373.45 373.45
Tu (kNm) 36.17 36.17 38.6
Aoh (sqmm) 282100 282100 282100
At (sqmm/m) 478.89 478.89 511
Legs 2 2 2
Stirrup Rebar 10 10 10
At Torsion (sqmm/m) 478.89 478.89 511
Av Total Reqd (sqmm/m) 818.89 690.15 511
Asv Reqd (sqmm/m) 818.89 690.15 605.81
SCalc (mm) 125 205 125
SPrv (mm) 125 205 125
Av Total Prv (sqmm/m) 1134.08 691.51 1134.08
          
 
Maximum Spacing Criteria
    
       Basic                               
                Spc1 = 460 mm
                Spc2 = 300 mm
       For Torsion                                 
                (X1 = 309.5, Y1 = 909.5)
                Spc3 = 300 mm
                Spc4=(X1+Y1)/4 = 305 mm
   
 
     For Ductility (Intermediate Frames)        
       Left Section,  Right Section
              Spc5 = 8 x Small Longitudinal Dia = 127 mm
              Spc6 = 24 x sv = 228 mm
              Spc7 = d / 4 = 230 mm
              Spc8 = 300 mm
             Provided Spacing = 125 mm
       
       Mid Section
              Provided Spacing = 300 mm
       
 
Skin reinforcement
  
Beam Width = 400 mm
Beam Depth = 1000 mm
Beam Depth > 900 ,
Hence Skin Reinforcement is Provided
Asr = 1227.42 sqmm
SR provided = 4-#16EF
Asr provided = 1588.48 sqmm
  
Spacing Criteria
           
Maximum Permissible Spacing = 194 mm
Provided Spacing = 165 mm Hence OK