BEAM DESIGN CALCULATION Project Name : Sample Client Name : Sample Engineer Name : Sample Analysis File : D:\Bentley\Common data\Bentley Communities\Euro\Validation sheets\Beam Design\STAAD file\Sample model_01.std Analysis Last Modified : 8/12/2020 10:39:06 PM Level Designed : 4.2 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 : G1 Beam No : B1 Analysis Reference (Member) 4.2 m : 4005 Beam Length : 8000 mm Breadth (bw) : 450 mm Depth (h) : 700 mm Effective Depth (d) : 650 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 : 12600 sqmm As,min (flex) (B) : 400.24 sqmm As,nominal (Bn) : 630 sqmm As,min (user input) (B') : 409.5 sqmm

 Flexure Design Beam Bottom Beam Top Left Mid Right Left Mid Right Critical L/C - RCDC 1 1 - 1 - 1 Mu (kNm) 142.15 1043.9 - 608.79 - 994.05 Mu/(bd2 x Fck) 0.037 0.275 0 0.16 0 0.261 z (mm) 617.5 490.3 617.5 539.31 617.5 490.3 Doubly Reinforced Section M' (Excess Moment for Doubly Reinforced section) (kNm) 0 245.38 0 0 0 195.53 x (Distance of N.A.) (mm) 0 399.24 0 0 0 399.24 fsc (Compressive Stress in Steel) (N/sqmm) 0 365.22 0 0 0 365.22 Asc (Area of Compression Reinf.) (sqmm) (C) 0 1119.78 0 0 0 892.29 ρ (%) (Flexural) 0.215 1.907 0 1.057 0 1.83 As (sqmm) (A) 630.32 5579.14 0 3090.85 0 5351.65 Ted (kNm) 0 0 0 0 0 0 As,reqd (sqmm) 630.32 5579.14 630 3090.85 630 5351.65 As,prov (sqmm) 3217 6434 3217 3217 1256.64 5629.75 Reinforcement Provided 4-T32 4-T324-T32 4-T32 4-T32 4-T20 4-T323-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 - RCDC 3 2 2 PtPrv (%) 1.1 2.2 1.925 VEd (kN) 640.12 361.28 736.46 TEd (kNm) 0 0 0 θ (Degree) 21.8 21.8 21.8 VEd + Vt (kN) 640.12 361.28 736.46 vEd (N/sqmm) 2.19 1.24 2.52 vRd,c (N/sqmm) 0.65 0.8 0.79 VRd,c (kN) 191.12 233.28 230.32 vRd,max (N/sqmm) 3.17 3.17 3.17 VRd,max (kN) 835.09 835.09 835.09 Asw (sqmm/m) 1302.55 735.147 1498.59 Legs 4 4 4 ∅sv (mm) 8 8 8 sreqd. (sqmm/m) 150 225 130 sprov (sqmm/m) 150 225 130 Asw,prov. (sqmm/m) 1340.53 893.69 1546.77
 Maximum Spacing Criteria Basic Spc1 =0.75d = 488 mm Spc2 = 300 mm

 SFR Design Beam Width (bw) = 450 mm Beam Depth (h) = 700 mm Check for Torsion : Critical L/C - RCDC = 1 Ted = 0 kNm TRd,c = 62.25 kNm Check for SFR h < 1000 And Ted < = TRd,c Hence, Side Face Reinforcement is not required