BEAM DESIGN CALCULATION Project Name : 1 Client Name : 1 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-#165-#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-#164-#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