BEAM DESIGN CALCULATION Project Name : Sample Client Name : Sample Engineer Name : Sample Design File : D:\Bentley\Common data\Bentley Communities\Euro\Crack-Width\Beam Design.rcdx Analysis File : D:\Bentley\000 RCDC 2010\10.0.0\Standard model for Demo\Staad\RCDC-Staad-Demo -with RCC wall.std Analysis Last Modified : 6/16/2020 4:07:28 PM Level Designed : 7.858 m

 Sr.No. Symbol Definitions 1 α = Angle between shear reinforcement & the longitudinal axis of beam 2 αe = Ratio of Modulus of elasticity of Reinforcement to concrete 3 ϒc = Partial factor for concrete (Persistent and Transient) 4 ϒcd = Partial factor for concrete (Accidental) 5 ϒs = Partial factor for Reinforcement (Persistent and Transient) 6 ϒsd = Partial factor for Reinforcement (Accidental) 7 ϒm = Partial factor for Material properties 8 ∈c = Strain in Concrete 9 ∈cm = Mean Strain in Concrete 10 ∈sm = Mean Strain in Reinforcement 11 θ = Inclination of Concrete Strut 12 θf = Concrete Strut inclination angle in flange 13 ρ = Required tension reinforcement at mid span to resist the moment due to the design loads (or at support for cantilevers) 14 ρ' = Required compression reinforcement at mid-span to resist the moment due to the design loads (or at support for cantilevers) 15 ρp,eff = Effective reinforcement ratio 16 σs = Tensile Reinforcement stress 16 σs,perm = Maximum permissible tensile Reinforcement stress 17 ρmax = Maximum reinforcement ratio 18 ρmin = Minimum reinforcement ratio 19 δ = % redistribution of moment 20 ∅sv = Shear reinforcement bar diameter 21 A = Total Area of cross section 22 Ac = Cross Sectional Area of Concrete 23 Ac,eff = Effective area of concrete in tension surrounding the reinforcement 24 Ag = Gross area of Section 25 Ak = Area enclosed by the center lines of connecting walls 26 As = Area of Tension Reinforcement 27 As,min = Minimum area of reinforcement 28 As,max = Maximum area of reinforcement (tension + compression) 29 As,prov. = Area of Reinforcement provided 30 As,reqd. = Area of Reinforcement required 31 As2 = Area of Compression Reinforcement 32 As1 = Reinforcement for torsion to be added in longitudinal Reinforcement 33 As1,dist = Area of torsion reinforcement distributed in longitudinal Reinforcement 34 As1,sfr = Area of torsion reinforcement distributed in side face reinforcement 35 Asw = Area of Shear Reinforcement 36 Asw,prov. = Area of Shear Reinforcement provided 37 AstCrack = Area Of Tension reinforcement For Crack Width required In sqmm 38 beff = Effective Flange width 39 bw = Width of section, or width of web on flanged beams 40 BM = SLS bending moment from Analysis 41 cnom = Nominal Cover for Concrete 42 d = Effective Depth 43 d2 = Effective depth to compression reinforcement 44 Es = Design value of modulus of elasticity of reinforcing Reinforcement 45 fcd = Design value of concrete compressive strength 46 fck = Characteristic cylinder strength of Concrete 47 fctd = Tensile Strength of Concrete 48 fctk = Characteristic axial tensile strength of Concrete 49 fctm = Mean value of axial tensile strength of Concrete 50 fsc = Compressive Stress in Reinforcement 51 fyd = Design value of Yield stress of Reinforcement 52 fyk = Characteristic Yield stress of Reinforcement 53 h = Depth of Section 54 hceff = Effective height of concrete in tension 55 hf = Flange Thickness 56 K' = 0.5 57 k1 = Crack width co-efficient for high bond bars (value = 0.8) 58 k2 = Crack width co-efficient for bending (value =0.5) 59 k3 = Crack width constant (value =3.4) 60 k4 = Crack width constant (value =0.5) 61 MEd = ULS design moment from Analysis 62 MR,f = Moment Resistance of Flange 63 M2 = Nominal second order moment 64 Mgeo = Moment due to geometric imperfections 65 Mu = Factored moment 67 Spc1 & Spc2 = Spacing calculated for Non-ductile beam in mm 68 Spc3 & Spc4 = Spacing calculated for torsion in beam in mm 69 Spc5 to Spc8 = Spacing calculated for Ductile beam in mm 69 sprov = Provided Spacing for reinforcement 70 sr,max = Maximum spacing between the bars 71 sreqd = Required Spacing between the bars 72 TEd = Torsional Moment from Analysis 73 tEd = Stress due to Torsion 74 TRd,c = Torsional Cracking Moment 75 TRd,max = Design value of the maximum Torsional Moment which can be sustained by the member, limited by crushing of the compression struts. 76 tRd,max = Design Stress due to Torsion 77 vEd = Design Shear Stress 78 VEd = Design shear force at the ULS 79 vmin = Strength reduction factor 80 vRd,cmax = Maximum shear stress without shear reinforcement 81 VRd,cmax = Shear Resistance of member without shear reinforcement 82 VRd,max = Design value of the maximum shear force which can be sustained by the member, limited by crushing of the compression struts. 83 Vt = Torsional Shear to be added in main shear 84 wk = Crack width of Member 85 wk,perm = Maximum permissible crack width 86 x = Depth of Neutral Axis 87 z = Lever arm All Forces are in 'kN', 'kNm', Stress in 'N/sqmm' & Dimension are in 'mm'.

 Code References EN 02 - 2004 Sr.No. Item Clause / Table 1. As,min : 9.2.1.1 2. As,max : 9.2.1.1 3. Asw : 6.2.3 4. smin : 8.2 5. smax : 9.2.2 6. VRd,c : 6.2.2 7. TRd,c : 6.3.2 8. VRd,max : 6.2.3 9. TRd,max : 6.3.2 10. ρw,min : 9.2.2 11. Side Face Reinforcement : 7.3.2, 7.3.3 12. Crack width calculation : 7.3.4
 Code References EN 02 - 2004 Sr.No. Item Clause / Table 1. ρmax : 5.4.3.1.2, 5.5.2.1 2. ρmin : 5.4.3.1.2, 5.5.2.1 3. smin : 5.4.3.1.2, 5.5.3.1.3 4. As2,min : 5.4.3.1.2 5. fck,min : 5.4.1.1, 5.5.1.1 6. h,min : 5.5.1.2.1

 Group : G2 Beam No : B5 Analysis Reference (Member) 7.858 m : 5005 Beam Length : 8000 mm Breadth (bw) : 450 mm Depth (h) : 800 mm Effective Depth (d) : 750 mm Design Code : EN 02 - 2004 Beam Type : Regular Beam Grade Of Concrete (fck) (Cylindrical) : C20/25 N/sqmm Partial Factor for Concrete (ϒc) : 1.5 Partial Factor for Concrete (ϒcd) : 1.2 Grade Of Steel (fyk) : Fy420 N/sqmm Partial Factor for Reinforcement (ϒs) : 1.15 Partial Factor for Reinforcement (ϒsd) : 1 Clear Cover (cnom) : 20 mm Es : 2x10^5 N/sqmm K' : 0.21 As,max : 14400 sqmm As,min (flex) (B) : 461.82 sqmm As,nominal (Bn) : 720 sqmm As,min (user input) (B') : 468 sqmm

 Flexure Design Beam Bottom Beam Top Left Mid Right Left Mid Right Critical L/C - Analysis 20 11 - 13 - 11 Critical L/C - RCDC 10 1 - 3 - 1 Mu (kNm) 98.24 285.56 - 465.61 - 449.98 Mu/(bd2 x Fck) 0.019 0.056 0 0.092 0 0.089 z (mm) 712.5 710.6 712.5 683.17 712.5 685.65 Doubly Reinforced Section M' (Excess Moment for Doubly Reinforced section) (kNm) 0 0 0 0 0 0 x (Distance of N.A.) (mm) 0 0 0 0 0 0 fsc (Compressive Stress in Steel) (N/sqmm) 0 0 0 0 0 0 Asc (Area of Compression Reinf.) (sqmm) (C) 0 0 0 0 0 0 ρ (%) (Flexural) 0.097 0.326 0 0.481 0 0.532 As (sqmm) (A) 328.3 1100.32 0 1622.71 0 1796.96 Ted (kNm) 1.08 2.72 0 2.03 0 2.72 TRd,c (kNm) 74.54 59.63 59.63 74.54 59.63 59.63 As,min (Tor) (sqmm) 0 0 0 0 0 0 As,reqd (sqmm) 461.82 1100.32 720 1622.71 720 1796.96 As,prov (sqmm) 1005.3 1608.48 1005.3 3217 804.24 3217 Reinforcement Provided 5-T16 5-T163-T16 5-T16 4-T32 4-T16 4-T32

 Note: Calculation of Ast Ast, reqd = Max{B,B', A+D/2, A+C x (fsc / fyd)+D/2} (for Mu > 0) Ast = Bn (for Mu = 0) Where, A = As = Tension reinforcement required for bending moment B = As,min (flex) = Min area of flexural reinforcement Bn = As,nominal = Nominal area of reinforcement C = Asc = Compression reinforcement required for bending moment D = A sl,dist = Distributed longitudinal torsional reinforcement at section considered A sl,dist = Max(As,min (Tor), Asl x ((2B) / (2B + 2D)))

 Shear Design Left Mid Right Critical L/C - Analysis 11 11 11 Critical L/C - RCDC 1 1 1 PtPrv (%) 0.953 0.477 0.953 VEd (kN) 278.53 148.79 290.04 TEd (kNm) 2.72 2.72 2.72 θ (Degree) 21.8 21.8 21.8 TRd,c (kNm) 59.6347 59.6347 59.6347 tEd (N/sqmm) 0.047 0.047 0.047 tRd,max (N/sqmm) 5.0756 5.0756 5.0756 TRd,max (kNm) 146.7152 146.7152 146.7152 (TEd / TRd,max ) + (VEd / VRd,max) 0.3798 0.2115 0.3948 Vt (kN) 0 0 0 VEd + Vt (kN) 278.53 148.79 290.04 vEd (N/sqmm) 0.83 0.44 0.86 vRd,c (N/sqmm) 0.49 0.39 0.49 VRd,c (kN) 164.06 130.21 164.06 vRd,max (N/sqmm) 2.54 2.54 2.54 VRd,max (kN) 770.86 770.86 770.86 Asw (sqmm/m) 491.192 383.326 511.491 Legs 2 2 2 ∅sv (mm) 8 8 8 sreqd. (sqmm/m) 200 260 195 sprov (sqmm/m) 200 260 195 Asw,prov. (sqmm/m) 502.7 386.69 515.59
 Maximum Spacing Criteria Basic Spc1 =0.75d = 562 mm Spc2 = 300 mm For Torsion (X1 = 420, Y1 = 770) Spc3 = X1 = 420 mm Spc4=(X1+Y1)/4 = 295 mm

 SFR Design Beam Width (bw) = 450 mm Beam Depth (h) = 800 mm Check for Torsion : Critical L/C - RCDC = 1 Ted = 2.72 kNm TRd,c = 74.54 kNm Check for SFR h < 1000 And Ted < = TRd,c Hence, Side Face Reinforcement is not required
 Crack width as per EN 02 - 2004 Beam Bottom Beam Top Left Mid Right Left Mid Right Critical L/C - RCDC 10006 10002 10007 10003 10006 10002 BM (Unfactored) (kNm) 55.49 199.87 35.5 388.01 24.43 410.49 Reinf. In 1st layer 5-T16 5-T16 5-T16 4-T32 4-T16 4-T32 AstPrv (sqmm) 1005.3 1608.48 1005.3 3217 804.24 3217 x (mm) 211.97 256.73 211.97 333.58 192.92 333.58 αe 0.02 0.02 0.02 0.02 0.02 0.02 hc,eff (mm) 125 125 125 125 125 125 Ac,eff (sqmm) 56250 56250 56250 56250 56250 56250 ρp,eff 0.02 0.03 0.02 0.06 0.01 0.06 Srmax1 (mm) 220.19 163.12 220.19 163.12 258.24 163.12 Srmax2 (mm) 764 706 764 606 789 606 Check for Stress in Concrete σc (N/sqmm) 1.71 5.21 1.1 8.09 0.82 8.56 σc,Perm (N/sqmm) 9 9 9 9 9 9 Check For Stress In Reinforcement σs (N/sqmm) 81.25 187.02 51.98 188.81 44.31 199.75 σs,Perm (N/sqmm) 336 336 336 336 336 336 Crack Width Check fctm 2.21 2.21 2.21 2.21 2.21 2.21 ∈sm -∈cm 0.00024 0.00070 0.00016 0.00078 0.00013 0.00084 wk 0.05 0.11 0.03 0.13 0.03 0.14 wk,Perm 0.2 0.2 0.2 0.2 0.2 0.2

 Stress Limit Check as per EN 02 - 2004 Beam Bottom Beam Top Left Mid Right Left Mid Right Critical L/C - RCDC 10006 10002 10007 10003 10006 10002 BM (Unfactored) (kNm) 55.49 199.87 35.5 388.01 24.43 410.49 Reinf. In 1st layer 5-T16 5-T16 5-T16 4-T32 4-T16 4-T32 sp (mm) 82.5 82.5 82.5 94 115.3 94 AstPrv (sqmm) 1005.3 1608.48 1005.3 3217 804.24 3217 Check for Stress in Concrete σc (N/sqmm) 1.71 5.21 1.1 8.09 0.82 8.56 σc,Perm (N/sqmm) 9 9 9 9 9 9 Check for Stress in Reinforcement σs (N/sqmm) 81.25 187.02 51.98 188.81 44.31 199.75 σs,Perm(N/sqmm) 336 336 336 336 336 336

 Group : G2 Beam No : B6 Analysis Reference (Member) 7.858 m : 5006 Beam Length : 8000 mm Breadth (bw) : 450 mm Depth (h) : 800 mm Effective Depth (d) : 750 mm Design Code : EN 02 - 2004 Beam Type : Regular Beam Grade Of Concrete (fck) (Cylindrical) : C20/25 N/sqmm Partial Factor for Concrete (ϒc) : 1.5 Partial Factor for Concrete (ϒcd) : 1.2 Grade Of Steel (fyk) : Fy420 N/sqmm Partial Factor for Reinforcement (ϒs) : 1.15 Partial Factor for Reinforcement (ϒsd) : 1 Clear Cover (cnom) : 20 mm Es : 2x10^5 N/sqmm K' : 0.21 As,max : 14400 sqmm As,min (flex) (B) : 461.82 sqmm As,nominal (Bn) : 720 sqmm As,min (user input) (B') : 468 sqmm

 Flexure Design Beam Bottom Beam Top Left Mid Right Left Mid Right Critical L/C - Analysis - 11 - 11 - 11 Critical L/C - RCDC - 1 - 1 - 1 Mu (kNm) - 257.3 - 468.4 - 442.04 Mu/(bd2 x Fck) 0 0.051 0 0.093 0 0.087 z (mm) 712.5 712.5 712.5 682.73 712.5 686.9 Doubly Reinforced Section M' (Excess Moment for Doubly Reinforced section) (kNm) 0 0 0 0 0 0 x (Distance of N.A.) (mm) 0 0 0 0 0 0 fsc (Compressive Stress in Steel) (N/sqmm) 0 0 0 0 0 0 Asc (Area of Compression Reinf.) (sqmm) (C) 0 0 0 0 0 0 ρ (%) (Flexural) 0 0.293 0 0.557 0 0.522 As (sqmm) (A) 0 988.78 0 1878.52 0 1762.07 Ted (kNm) 0 0.68 0 0.68 0 0.68 TRd,c (kNm) 59.63 59.63 59.63 59.63 59.63 59.63 As,min (Tor) (sqmm) 0 0 0 0 0 0 As,reqd (sqmm) 720 988.78 720 1878.52 720 1762.07 As,prov (sqmm) 1005.3 1457.7 1005.3 3217 804.24 3217 Reinforcement Provided 5-T16 5-T164-T12 5-T16 4-T32 4-T16 4-T32

 Note: Calculation of Ast Ast, reqd = Max{B,B', A+D/2, A+C x (fsc / fyd)+D/2} (for Mu > 0) Ast = Bn (for Mu = 0) Where, A = As = Tension reinforcement required for bending moment B = As,min (flex) = Min area of flexural reinforcement Bn = As,nominal = Nominal area of reinforcement C = Asc = Compression reinforcement required for bending moment D = A sl,dist = Distributed longitudinal torsional reinforcement at section considered A sl,dist = Max(As,min (Tor), Asl x ((2B) / (2B + 2D)))

 Shear Design Left Mid Right Critical L/C - Analysis 11 11 11 Critical L/C - RCDC 1 1 1 PtPrv (%) 0.953 0.432 0.953 VEd (kN) 287.58 157.84 280.99 TEd (kNm) 0.68 0.68 0.68 θ (Degree) 21.8 21.8 21.8 TRd,c (kNm) 59.6347 59.6347 59.6347 tEd (N/sqmm) 0.0117 0.0117 0.0117 tRd,max (N/sqmm) 5.0756 5.0756 5.0756 TRd,max (kNm) 146.7152 146.7152 146.7152 (TEd / TRd,max ) + (VEd / VRd,max) 0.3777 0.2094 0.3691 Vt (kN) 0 0 0 VEd + Vt (kN) 287.58 157.84 280.99 vEd (N/sqmm) 0.85 0.47 0.83 vRd,c (N/sqmm) 0.49 0.37 0.49 VRd,c (kN) 164.06 126.01 164.06 vRd,max (N/sqmm) 2.54 2.54 2.54 VRd,max (kN) 770.86 770.86 770.86 Asw (sqmm/m) 507.152 383.326 495.531 Legs 2 2 2 ∅sv (mm) 8 8 8 sreqd. (sqmm/m) 195 260 200 sprov (sqmm/m) 195 260 200 Asw,prov. (sqmm/m) 515.59 386.69 502.7
 Maximum Spacing Criteria Basic Spc1 =0.75d = 562 mm Spc2 = 300 mm For Torsion (X1 = 420, Y1 = 770) Spc3 = X1 = 420 mm Spc4=(X1+Y1)/4 = 295 mm

 SFR Design Beam Width (bw) = 450 mm Beam Depth (h) = 800 mm Check for Torsion : Critical L/C - RCDC = 1 Ted = 0.68 kNm TRd,c = 74.54 kNm Check for SFR h < 1000 And Ted < = TRd,c Hence, Side Face Reinforcement is not required
 Crack width as per EN 02 - 2004 Beam Bottom Beam Top Left Mid Right Left Mid Right Critical L/C - RCDC 10006 10003 10007 10003 10007 10002 BM (Unfactored) (kNm) 23.05 174.46 31.21 417.53 34.56 400.29 Reinf. In 1st layer 5-T16 5-T16 5-T16 4-T32 4-T16 4-T32 AstPrv (sqmm) 1005.3 1457.7 1005.3 3217 804.24 3217 x (mm) 211.97 246.84 211.97 333.58 192.92 333.58 αe 0.02 0.02 0.02 0.02 0.02 0.02 hc,eff (mm) 125 125 125 125 125 125 Ac,eff (sqmm) 56250 56250 56250 56250 56250 56250 ρp,eff 0.02 0.03 0.02 0.06 0.01 0.06 Srmax1 (mm) 220.19 172.96 220.19 163.12 258.24 163.12 Srmax2 (mm) 764 719 764 606 789 606 Check for Stress in Concrete σc (N/sqmm) 0.71 4.7 0.96 8.71 1.16 8.35 σc,Perm (N/sqmm) 9 9 9 9 9 9 Check For Stress In Reinforcement σs (N/sqmm) 33.75 179.24 45.7 203.18 62.66 194.78 σs,Perm (N/sqmm) 336 336 336 336 336 336 Crack Width Check fctm 2.21 2.21 2.21 2.21 2.21 2.21 ∈sm -∈cm 0.00010 0.00064 0.00014 0.00086 0.00019 0.00081 wk 0.02 0.11 0.03 0.14 0.05 0.13 wk,Perm 0.2 0.2 0.2 0.2 0.2 0.2

 Stress Limit Check as per EN 02 - 2004 Beam Bottom Beam Top Left Mid Right Left Mid Right Critical L/C - RCDC 10006 10003 10007 10003 10007 10002 BM (Unfactored) (kNm) 23.05 174.46 31.21 417.53 34.56 400.29 Reinf. In 1st layer 5-T16 5-T16 5-T16 4-T32 4-T16 4-T32 sp (mm) 82.5 82.5 82.5 94 115.3 94 AstPrv (sqmm) 1005.3 1457.7 1005.3 3217 804.24 3217 Check for Stress in Concrete σc (N/sqmm) 0.71 4.7 0.96 8.71 1.16 8.35 σc,Perm (N/sqmm) 9 9 9 9 9 9 Check for Stress in Reinforcement σs (N/sqmm) 33.75 179.24 45.7 203.18 62.66 194.78 σs,Perm(N/sqmm) 336 336 336 336 336 336

 Group : G2 Beam No : B7 Analysis Reference (Member) 7.858 m : 5007 Beam Length : 8000 mm Breadth (bw) : 450 mm Depth (h) : 800 mm Effective Depth (d) : 750 mm Design Code : EN 02 - 2004 Beam Type : Regular Beam Grade Of Concrete (fck) (Cylindrical) : C20/25 N/sqmm Partial Factor for Concrete (ϒc) : 1.5 Partial Factor for Concrete (ϒcd) : 1.2 Grade Of Steel (fyk) : Fy420 N/sqmm Partial Factor for Reinforcement (ϒs) : 1.15 Partial Factor for Reinforcement (ϒsd) : 1 Clear Cover (cnom) : 20 mm Es : 2x10^5 N/sqmm K' : 0.21 As,max : 14400 sqmm As,min (flex) (B) : 461.82 sqmm As,nominal (Bn) : 720 sqmm As,min (user input) (B') : 468 sqmm

 Flexure Design Beam Bottom Beam Top Left Mid Right Left Mid Right Critical L/C - Analysis - 11 - 11 - 11 Critical L/C - RCDC - 1 - 1 - 1 Mu (kNm) - 260.05 - 457.38 - 447.56 Mu/(bd2 x Fck) 0 0.051 0 0.09 0 0.088 z (mm) 712.5 712.5 712.5 684.48 712.5 686.03 Doubly Reinforced Section M' (Excess Moment for Doubly Reinforced section) (kNm) 0 0 0 0 0 0 x (Distance of N.A.) (mm) 0 0 0 0 0 0 fsc (Compressive Stress in Steel) (N/sqmm) 0 0 0 0 0 0 Asc (Area of Compression Reinf.) (sqmm) (C) 0 0 0 0 0 0 ρ (%) (Flexural) 0 0.296 0 0.542 0 0.529 As (sqmm) (A) 0 999.35 0 1829.65 0 1786.29 Ted (kNm) 0 0.47 0 0.47 0 0.47 TRd,c (kNm) 59.63 59.63 59.63 59.63 59.63 59.63 As,min (Tor) (sqmm) 0 0 0 0 0 0 As,reqd (sqmm) 720 999.35 720 1829.65 720 1786.29 As,prov (sqmm) 1005.3 1457.7 1005.3 3217 804.24 3217 Reinforcement Provided 5-T16 5-T164-T12 5-T16 4-T32 4-T16 4-T32

 Note: Calculation of Ast Ast, reqd = Max{B,B', A+D/2, A+C x (fsc / fyd)+D/2} (for Mu > 0) Ast = Bn (for Mu = 0) Where, A = As = Tension reinforcement required for bending moment B = As,min (flex) = Min area of flexural reinforcement Bn = As,nominal = Nominal area of reinforcement C = Asc = Compression reinforcement required for bending moment D = A sl,dist = Distributed longitudinal torsional reinforcement at section considered A sl,dist = Max(As,min (Tor), Asl x ((2B) / (2B + 2D)))

 Shear Design Left Mid Right Critical L/C - Analysis 11 11 11 Critical L/C - RCDC 1 1 1 PtPrv (%) 0.953 0.432 0.953 VEd (kN) 285.51 155.78 283.05 TEd (kNm) 0.47 0.47 0.47 θ (Degree) 21.8 21.8 21.8 TRd,c (kNm) 59.6347 59.6347 59.6347 tEd (N/sqmm) 0.0081 0.0081 0.0081 tRd,max (N/sqmm) 5.0756 5.0756 5.0756 TRd,max (kNm) 146.7152 146.7152 146.7152 (TEd / TRd,max ) + (VEd / VRd,max) 0.3736 0.2053 0.3704 Vt (kN) 0 0 0 VEd + Vt (kN) 285.51 155.78 283.05 vEd (N/sqmm) 0.85 0.46 0.84 vRd,c (N/sqmm) 0.49 0.37 0.49 VRd,c (kN) 164.06 126.01 164.06 vRd,max (N/sqmm) 2.54 2.54 2.54 VRd,max (kN) 770.86 770.86 770.86 Asw (sqmm/m) 503.508 383.326 499.175 Legs 2 2 2 ∅sv (mm) 8 8 8 sreqd. (sqmm/m) 195 260 200 sprov (sqmm/m) 195 260 200 Asw,prov. (sqmm/m) 515.59 386.69 502.7
 Maximum Spacing Criteria Basic Spc1 =0.75d = 562 mm Spc2 = 300 mm For Torsion (X1 = 420, Y1 = 770) Spc3 = X1 = 420 mm Spc4=(X1+Y1)/4 = 295 mm

 SFR Design Beam Width (bw) = 450 mm Beam Depth (h) = 800 mm Check for Torsion : Critical L/C - RCDC = 1 Ted = 0.47 kNm TRd,c = 74.54 kNm Check for SFR h < 1000 And Ted < = TRd,c Hence, Side Face Reinforcement is not required
 Crack width as per EN 02 - 2004 Beam Bottom Beam Top Left Mid Right Left Mid Right Critical L/C - RCDC 10006 10003 10007 10003 10007 10002 BM (Unfactored) (kNm) 26.65 175.03 29.96 410.58 32.23 403.64 Reinf. In 1st layer 5-T16 5-T16 5-T16 4-T32 4-T16 4-T32 AstPrv (sqmm) 1005.3 1457.7 1005.3 3217 804.24 3217 x (mm) 211.97 246.84 211.97 333.58 192.92 333.58 αe 0.02 0.02 0.02 0.02 0.02 0.02 hc,eff (mm) 125 125 125 125 125 125 Ac,eff (sqmm) 56250 56250 56250 56250 56250 56250 ρp,eff 0.02 0.03 0.02 0.06 0.01 0.06 Srmax1 (mm) 220.19 172.96 220.19 163.12 258.24 163.12 Srmax2 (mm) 764 719 764 606 789 606 Check for Stress in Concrete σc (N/sqmm) 0.82 4.72 0.92 8.56 1.08 8.42 σc,Perm (N/sqmm) 9 9 9 9 9 9 Check For Stress In Reinforcement σs (N/sqmm) 39.02 179.82 43.87 199.79 58.44 196.41 σs,Perm (N/sqmm) 336 336 336 336 336 336 Crack Width Check fctm 2.21 2.21 2.21 2.21 2.21 2.21 ∈sm -∈cm 0.00012 0.00065 0.00013 0.00084 0.00018 0.00082 wk 0.03 0.11 0.03 0.14 0.05 0.13 wk,Perm 0.2 0.2 0.2 0.2 0.2 0.2

 Stress Limit Check as per EN 02 - 2004 Beam Bottom Beam Top Left Mid Right Left Mid Right Critical L/C - RCDC 10006 10003 10007 10003 10007 10002 BM (Unfactored) (kNm) 26.65 175.03 29.96 410.58 32.23 403.64 Reinf. In 1st layer 5-T16 5-T16 5-T16 4-T32 4-T16 4-T32 sp (mm) 82.5 82.5 82.5 94 115.3 94 AstPrv (sqmm) 1005.3 1457.7 1005.3 3217 804.24 3217 Check for Stress in Concrete σc (N/sqmm) 0.82 4.72 0.92 8.56 1.08 8.42 σc,Perm (N/sqmm) 9 9 9 9 9 9 Check for Stress in Reinforcement σs (N/sqmm) 39.02 179.82 43.87 199.79 58.44 196.41 σs,Perm(N/sqmm) 336 336 336 336 336 336

 Group : G2 Beam No : B8 Analysis Reference (Member) 7.858 m : 5008 Beam Length : 7960 mm Breadth (bw) : 450 mm Depth (h) : 800 mm Effective Depth (d) : 750 mm Design Code : EN 02 - 2004 Beam Type : Regular Beam Grade Of Concrete (fck) (Cylindrical) : C20/25 N/sqmm Partial Factor for Concrete (ϒc) : 1.5 Partial Factor for Concrete (ϒcd) : 1.2 Grade Of Steel (fyk) : Fy420 N/sqmm Partial Factor for Reinforcement (ϒs) : 1.15 Partial Factor for Reinforcement (ϒsd) : 1 Clear Cover (cnom) : 20 mm Es : 2x10^5 N/sqmm K' : 0.21 As,max : 14400 sqmm As,min (flex) (B) : 461.82 sqmm As,nominal (Bn) : 720 sqmm As,min (user input) (B') : 468 sqmm

 Flexure Design Beam Bottom Beam Top Left Mid Right Left Mid Right Critical L/C - Analysis - 11 21 11 - 12 Critical L/C - RCDC - 1 11 1 - 2 Mu (kNm) - 277.05 98.78 453.59 - 462.46 Mu/(bd2 x Fck) 0 0.055 0.02 0.09 0 0.091 z (mm) 712.5 711.84 712.5 685.08 712.5 683.67 Doubly Reinforced Section M' (Excess Moment for Doubly Reinforced section) (kNm) 0 0 0 0 0 0 x (Distance of N.A.) (mm) 0 0 0 0 0 0 fsc (Compressive Stress in Steel) (N/sqmm) 0 0 0 0 0 0 Asc (Area of Compression Reinf.) (sqmm) (C) 0 0 0 0 0 0 ρ (%) (Flexural) 0 0.316 0.098 0.537 0 0.477 As (sqmm) (A) 0 1065.68 330.08 1812.91 0 1610.55 Ted (kNm) 0 2.96 1.05 2.96 0 2.38 TRd,c (kNm) 59.63 59.63 74.54 59.63 59.63 74.54 As,min (Tor) (sqmm) 0 0 0 0 0 0 As,reqd (sqmm) 720 1065.68 461.82 1812.91 720 1610.55 As,prov (sqmm) 1005.3 1570.8 1005.3 3217 804.24 3217 Reinforcement Provided 5-T16 5-T165-T12 5-T16 4-T32 4-T16 4-T32

 Note: Calculation of Ast Ast, reqd = Max{B,B', A+D/2, A+C x (fsc / fyd)+D/2} (for Mu > 0) Ast = Bn (for Mu = 0) Where, A = As = Tension reinforcement required for bending moment B = As,min (flex) = Min area of flexural reinforcement Bn = As,nominal = Nominal area of reinforcement C = Asc = Compression reinforcement required for bending moment D = A sl,dist = Distributed longitudinal torsional reinforcement at section considered A sl,dist = Max(As,min (Tor), Asl x ((2B) / (2B + 2D)))

 Shear Design Left Mid Right Critical L/C - Analysis 11 11 11 Critical L/C - RCDC 1 1 1 PtPrv (%) 0.953 0.465 0.953 VEd (kN) 288.84 159.76 275.07 TEd (kNm) 2.96 2.96 2.96 θ (Degree) 21.8 21.8 21.8 TRd,c (kNm) 59.6347 59.6347 59.6347 tEd (N/sqmm) 0.0512 0.0512 0.0512 tRd,max (N/sqmm) 5.0756 5.0756 5.0756 TRd,max (kNm) 146.7152 146.7152 146.7152 (TEd / TRd,max ) + (VEd / VRd,max) 0.3949 0.2274 0.377 Vt (kN) 0 0 0 VEd + Vt (kN) 288.84 159.76 275.07 vEd (N/sqmm) 0.86 0.47 0.82 vRd,c (N/sqmm) 0.49 0.38 0.49 VRd,c (kN) 164.06 129.19 164.06 vRd,max (N/sqmm) 2.54 2.54 2.54 VRd,max (kN) 770.86 770.86 770.86 Asw (sqmm/m) 509.386 383.326 485.099 Legs 2 2 2 ∅sv (mm) 8 8 8 sreqd. (sqmm/m) 195 260 205 sprov (sqmm/m) 195 260 205 Asw,prov. (sqmm/m) 515.59 386.69 490.44
 Maximum Spacing Criteria Basic Spc1 =0.75d = 562 mm Spc2 = 300 mm For Torsion (X1 = 420, Y1 = 770) Spc3 = X1 = 420 mm Spc4=(X1+Y1)/4 = 295 mm

 SFR Design Beam Width (bw) = 450 mm Beam Depth (h) = 800 mm Check for Torsion : Critical L/C - RCDC = 1 Ted = 2.96 kNm TRd,c = 74.54 kNm Check for SFR h < 1000 And Ted < = TRd,c Hence, Side Face Reinforcement is not required
 Crack width as per EN 02 - 2004 Beam Bottom Beam Top Left Mid Right Left Mid Right Critical L/C - RCDC 10006 10003 10007 10003 10007 10002 BM (Unfactored) (kNm) 32.64 195.13 55.69 413.43 28.26 385.38 Reinf. In 1st layer 5-T16 5-T16 5-T16 4-T32 4-T16 4-T32 AstPrv (sqmm) 1005.3 1570.8 1005.3 3217 804.24 3217 x (mm) 211.97 254.32 211.97 333.58 192.92 333.58 αe 0.02 0.02 0.02 0.02 0.02 0.02 hc,eff (mm) 125 125 125 125 125 125 Ac,eff (sqmm) 56250 56250 56250 56250 56250 56250 ρp,eff 0.02 0.03 0.02 0.06 0.01 0.06 Srmax1 (mm) 220.19 165.4 220.19 163.12 258.24 163.12 Srmax2 (mm) 764 709 764 606 789 606 Check for Stress in Concrete σc (N/sqmm) 1.01 5.13 1.72 8.62 0.95 8.04 σc,Perm (N/sqmm) 9 9 9 9 9 9 Check For Stress In Reinforcement σs (N/sqmm) 47.8 186.74 81.54 201.18 51.25 187.53 σs,Perm (N/sqmm) 336 336 336 336 336 336 Crack Width Check fctm 2.21 2.21 2.21 2.21 2.21 2.21 ∈sm -∈cm 0.00014 0.00069 0.00024 0.00085 0.00015 0.00078 wk 0.03 0.11 0.05 0.14 0.04 0.13 wk,Perm 0.2 0.2 0.2 0.2 0.2 0.2

 Stress Limit Check as per EN 02 - 2004 Beam Bottom Beam Top Left Mid Right Left Mid Right Critical L/C - RCDC 10006 10003 10007 10003 10007 10002 BM (Unfactored) (kNm) 32.64 195.13 55.69 413.43 28.26 385.38 Reinf. In 1st layer 5-T16 5-T16 5-T16 4-T32 4-T16 4-T32 sp (mm) 82.5 82.5 82.5 94 115.3 94 AstPrv (sqmm) 1005.3 1570.8 1005.3 3217 804.24 3217 Check for Stress in Concrete σc (N/sqmm) 1.01 5.13 1.72 8.62 0.95 8.04 σc,Perm (N/sqmm) 9 9 9 9 9 9 Check for Stress in Reinforcement σs (N/sqmm) 47.8 186.74 81.54 201.18 51.25 187.53 σs,Perm(N/sqmm) 336 336 336 336 336 336

 Group : G2 Beam No : B9 Analysis Reference (Member) 7.858 m : 5051 Beam Length : 1880 mm Breadth (bw) : 450 mm Depth (h) : 800 mm Effective Depth (d) : 750 mm Design Code : EN 02 - 2004 Beam Type : Cantilever Beam Grade Of Concrete (fck) (Cylindrical) : C20/25 N/sqmm Partial Factor for Concrete (ϒc) : 1.5 Partial Factor for Concrete (ϒcd) : 1.2 Grade Of Steel (fyk) : Fy420 N/sqmm Partial Factor for Reinforcement (ϒs) : 1.15 Partial Factor for Reinforcement (ϒsd) : 1 Clear Cover (cnom) : 20 mm Es : 2x10^5 N/sqmm K' : 0.21 As,max : 14400 sqmm As,min (flex) (B) : 461.82 sqmm As,nominal (Bn) : 720 sqmm As,min (user input) (B') : 468 sqmm

 Flexure Design Beam Bottom Beam Top Left Mid Right Left Mid Right Critical L/C - Analysis - - - 19 19 23 Critical L/C - RCDC - - - 9 9 13 Mu (kNm) - - - 23.86 13.42 - Mu/(bd2 x Fck) 0 0 0 0.005 0.003 0 z (mm) 712.5 712.5 712.5 712.5 712.5 712.5 Doubly Reinforced Section M' (Excess Moment for Doubly Reinforced section) (kNm) 0 0 0 0 0 0 x (Distance of N.A.) (mm) 0 0 0 0 0 0 fsc (Compressive Stress in Steel) (N/sqmm) 0 0 0 0 0 0 Asc (Area of Compression Reinf.) (sqmm) (C) 0 0 0 0 0 0 ρ (%) (Flexural) 0 0 0 0.024 0.013 0 As (sqmm) (A) 0 0 0 79.73 44.85 0 Ted (kNm) 0 0 0 0 0 0 As,reqd (sqmm) 720 720 720 461.82 461.82 720 As,prov (sqmm) 804.24 804.24 804.24 3217 2513.28 2513.28 Reinforcement Provided 4-T16 4-T16 4-T16 4-T32 4-T204-T20 4-T204-T20

 Note: Calculation of Ast Ast, reqd = Max{B,B', A+D/2, A+C x (fsc / fyd)+D/2} (for Mu > 0) Ast = Bn (for Mu = 0) Where, A = As = Tension reinforcement required for bending moment B = As,min (flex) = Min area of flexural reinforcement Bn = As,nominal = Nominal area of reinforcement C = Asc = Compression reinforcement required for bending moment D = A sl,dist = Distributed longitudinal torsional reinforcement at section considered A sl,dist = Max(As,min (Tor), Asl x ((2B) / (2B + 2D)))

 Shear Design Left Mid Right Critical L/C - Analysis 11 11 11 Critical L/C - RCDC 1 1 1 PtPrv (%) 0.953 0.745 0.745 VEd (kN) 25.39 16.93 8.46 TEd (kNm) 0 0 0 θ (Degree) 21.8 21.8 21.8 VEd + Vt (kN) 25.39 16.93 8.46 vEd (N/sqmm) 0.08 0.05 0.03 vRd,c (N/sqmm) 0.49 0.45 0.45 VRd,c (kN) 164.06 151.1 151.1 vRd,max (N/sqmm) 2.54 2.54 2.54 VRd,max (kN) 770.86 770.86 770.86 Asw (sqmm/m) 383.326 383.326 383.326 Legs 2 2 2 ∅sv (mm) 8 8 8 sreqd. (sqmm/m) 260 260 260 sprov (sqmm/m) 260 260 260 Asw,prov. (sqmm/m) 386.69 386.69 386.69
 Maximum Spacing Criteria Basic Spc1 =0.75d = 562 mm Spc2 = 300 mm

 SFR Design Beam Width (bw) = 450 mm Beam Depth (h) = 800 mm Check for Torsion : Critical L/C - RCDC = 1 Ted = 0 kNm TRd,c = 74.54 kNm Check for SFR h < 1000 And Ted < = TRd,c Hence, Side Face Reinforcement is not required
 Crack width as per EN 02 - 2004 Beam Bottom Beam Top Left Mid Right Left Mid Right Critical L/C - RCDC - - - 10001 10001 10001 BM (Unfactored) (kNm) 0 0 0 15.91 7.07 0.44 Reinf. In 1st layer 4-T32 4-T20 4-T20 AstPrv (sqmm) 3217 2513.28 2513.28 x (mm) 333.58 304.85 304.85 αe 0.02 0.02 0.02 hc,eff (mm) 125 125 125 Ac,eff (sqmm) 56250 56250 56250 ρp,eff 0.06 0.04 0.04 Srmax1 (mm) 163.12 144.1 144.1 Srmax2 (mm) 606 643 643 Check for Stress in Concrete σc (N/sqmm) 0.33 0.16 0.01 σc,Perm (N/sqmm) 9 9 9 Check For Stress In Reinforcement σs (N/sqmm) 7.74 4.34 0.27 σs,Perm (N/sqmm) 336 336 336 Crack Width Check fctm 2.21 2.21 2.21 ∈sm -∈cm 0.00002 0.00001 0.00000 wk 0 0 0 0 0 0 wk,Perm 0.2 0.2 0.2

 Stress Limit Check as per EN 02 - 2004 Beam Bottom Beam Top Left Mid Right Left Mid Right Critical L/C - RCDC - - - 10001 10001 10001 BM (Unfactored) (kNm) 0 0 0 15.91 7.07 0.44 Reinf. In 1st layer 4-T32 4-T20 4-T20 sp (mm) 94 110 110 AstPrv (sqmm) 3217 2513.28 2513.28 Check for Stress in Concrete σc (N/sqmm) 0.33 0.16 0.01 σc,Perm (N/sqmm) 9 9 9 Check for Stress in Reinforcement σs (N/sqmm) 7.74 4.34 0.27 σs,Perm(N/sqmm) 336 336 336