Calculation number : Revision : 0 Page 1 of 8 GENERAL File: document1.xcol Applied standards: Consequence class Structural Class : NEN-EN 1992-1-1 + C2:2011/NB:2011 (nl) : NEN-EN 1992-1-2 + C1:2011/NB:2011 (nl) : CC2 : S4 COLUMN: column A2 INPUT DATA Column dimensions : h c = 400 mm b c = 400 mm L=3500 mm Concrete grade C45/55 Creep coefficient 3,20 Granule diameter 31,5 mm Environmental class XC1 Prefab yes Reworked no Cover c 25 mm Steel grade B500B Basic reinforcement 4x20 Add. reinforcement 8x20 4-side symmetrical Stirrup diameter 10 mm Buckling Y 5.7 a l 0;y = 3500 mm Buckling Z 5.7 a l 0;z = 3500 mm Connection Thickness bedding 30 mm Concrete grade mortar C20/25 Mortal type b; aangieten of injecteren Concrete grade support C20/25 Steel grade B500B Reinforcement connection 2x16 edge distance 75 mm Load cases No. Description Type Nx My;t My;c My;b Mz;t Mz;c Mz;b [kn] [knm] [knm] [knm] [knm] [knm] [knm] 1permanent Permanent 100,0 50,0 0,0 0,0 0,0 0,0 0,0 2veranderlijk B:office 50,0 120,0 0,0 0,0 0,0 0,0 0,0 Load Combinations No. Description Type Load cases (ψ x γ) 1:permanent 2:veranderlijk 1(6.10a) ULS 1,00 x 1,35 0,50 x 1,50 2(6.10b) ULS 1,00 x 1,20 1,00 x 1,50 3(6.11a) ULS fire 1,00 x 1,00 1,00 x 1,00 4 Quasi permanent 1,00 x 1,00 0,60 x 1,00
Calculation number : Revision : 0 Page 2 of 8 CALCULATION according to Eurocode 2 : EN 1992-1-1 en EN 1992-1-2 hoh = 103 mm < hoh max = 150 mm s = 83 mm > s min = 37 mm s cl,tmax = Min[ 20Ø; Min[h,b];400 ] = Min[ 20 x 20; Min[400;400]; 400 ] = 400 mm...9.5.3(3) Minimum stirrup reinforcement is: Ø6-400 1: ULS bending about Y-axis Decisive combination 2: (6.10b) N Edx = 195 kn; M Edy;top = 240 knm; M Edy;centre = 0 knm; M Edy;bottom = 0 knm; 5.8.3.2 Slenderness and effective length of isolated members i = I A = 2133333333 160000 l 0 = l = 3500 mm = 115,5 mm...(fig.5.7 a)) l = l 0 / i = 3500 / 115,5 = 30,31...(5.14) 5.2 Geometric imperfections a h = min [ max [ 2 / l ; 2/3 ]; 1.00] = min [ max [ 2 / 3,5 ; 2/3 ]; 1.00] = 1 a m = 0,5 (1+1/m) = 0,5 (1+1/1) = 1 q i = q i a h a m = 1/300 x 1 x 1 = 0,00333...(5.1) e i = q i l 0 / 2 = 0,0033 x 3500 / 2 = 5,8 mm...(5.2) 5.8.4 Creep j ef = j (infinite,t0) M 0Eqp / M 0Ed = 3,2 x 122,76/241,14 = 1,63...(5.19) 5.8.3.1 Slenderness criterion for isolated members A = 1 / (1 + 0,2 j ef ) = 1 / (1 + 0,2 x 1,63) = 0,754 w = A s f yd / (A c f cd ) = 3770 x 434,8 / (160000 x 30) = 0,341 B = 1 + 2 w = 1 + 2 x 0,341 = 1,297 r m = M 01 / M 02 = 0 / 240 = 0 C = 1,7 - r m = 1,7-0 = 1,7 n = N Ed / (A c f cd ) = 195000 / (160000 x 30) = 0,0406 l lim = 20.A.B.C / n = 20 x 0,754 x 1,297 x 1,7 / 0,0406 = 165,06...(5.13N) l < l lim 2nd order calculation is not required 5.8.8.2 Bending moments M 0e = max [0,6 M 02 + 0,4 M 01 ; 0,4 M 02 ] =...(5.32) = max [ 0,6 x 240 + 0,4 x 0; 0,4 x 240 ] = 144 knm M 0Ed = M 0e + N Ed e i = 144 + 195 x 5,8 = 145,138 knm
Calculation number : Revision : 0 Page 3 of 8 M 2 = N Ed e 2 = 195 x 0 = 0 knm...(5.33) M Ed = max [ M 0Ed + M 2 ; M 02 + N Ed e i ; M 01 + 0,5 M 2 + N Ed e i ] =...(5.31) = max [ 145,138 + 0 ; 240 + 195 x 5,8; 0 + 0,5 x 0 + 195 x 5,8] = = 241,138 knm e t = M Ed / N Ed = 241,138 / 195 = 1236,6 mm e min = max [ h/30, 20 ] = max [ 400/30, 20 ]= 20,0 mm...6.1(4) 0,10 N Ed A s,min = max [ f yd 0,10 x 195000 ; 0,002 A c ] = max[ 434,8 A s,max = 0,04 A c = 0,04 x 160000 = 6400 mm 2 ; 0,002 x 160000] = 320 mm 2...(9.12N) N Edx = 195 kn; M Ed = 241,138 knm; A ben = 2988 mm 2 M Ed M Rd 241,138 = 291,207 = 0,83 < 1,0 A s,min = 320 mm 2 < A s = 3770 mm 2 < A s,max = 6400 mm 2 Sectional calculation Angle bending axis and neutral line a = 0,000 0 ; xu = 92,3 mm; d = 278,2 mm Centroid section y' = 0,0 z' = -200,0 (y = 0,0 z = 0,0)
Calculation number : Revision : 0 Page 4 of 8 y' z' Wap. As Δε σc Δσs [mm] [mm] [mm 2 ] [o/oo] [N/mm 2 ] [N/mm 2 ] 0,0 0,0-3,500-30,0 155,0-45,0 1Ø20 314-1,794-358,7-155,0-45,0 1Ø20 314-1,794-358,7-51,7-45,0 1Ø20 314-1,794-358,7 51,7-45,0 1Ø20 314-1,794-358,7 155,0-148,3 1Ø20 314 2,125 424,9-155,0-148,3 1Ø20 314 2,125 424,9 155,0-251,7 1Ø20 314 6,043 434,8-155,0-251,7 1Ø20 314 6,043 434,8 51,7-355,0 1Ø20 314 9,961 434,8-155,0-355,0 1Ø20 314 9,961 434,8-51,7-355,0 1Ø20 314 9,961 434,8 155,0-355,0 1Ø20 314 9,961 434,8 y' z' Fc Fs dy' dz' F F.dy' F.dz' [mm] [mm] [kn] [kn] [mm] [mm] [kn] [knm] [knm] 0,0-35,9-830,7 0,0 164,1-830,7 0,0-136,3 155,0-45,0-112,7 155,0 155,0-112,7-17,5-17,5-155,0-45,0-112,7-155,0 155,0-112,7 17,5-17,5-51,7-45,0-112,7-51,7 155,0-112,7 5,8-17,5 51,7-45,0-112,7 51,7 155,0-112,7-5,8-17,5 155,0-148,3 133,5 155,0 51,7 133,5 20,7 6,9-155,0-148,3 133,5-155,0 51,7 133,5-20,7 6,9 155,0-251,7 136,6 155,0-51,7 136,6 21,2-7,1-155,0-251,7 136,6-155,0-51,7 136,6-21,2-7,1 51,7-355,0 136,6 51,7-155,0 136,6 7,1-21,2-155,0-355,0 136,6-155,0-155,0 136,6-21,2-21,2-51,7-355,0 136,6-51,7-155,0 136,6-7,1-21,2 155,0-355,0 136,6 155,0-155,0 136,6 21,2-21,2 totaal: -195,0 0,0-291,2 2: ULS bending about Z-axis Decisive combination 2: (6.10b) N Edx = 195 kn; M Edz;top = 0 knm; M Edz;centre = 0 knm; M Edz;bottom = 0 knm; 5.8.3.2 Slenderness and effective length of isolated members i = I A = 2133333333 160000 l 0 = l = 3500 mm = 115,5 mm...(fig.5.7 a)) l = l 0 / i = 3500 / 115,5 = 30,31...(5.14) 5.2 Geometric imperfections a h = min [ max [ 2 / l ; 2/3 ]; 1.00] = min [ max [ 2 / 3,5 ; 2/3 ]; 1.00] = 1 a m = 0,5 (1+1/m) = 0,5 (1+1/1) = 1 q i = q i a h a m = 1/300 x 1 x 1 = 0,00333...(5.1) e i = q i l 0 / 2 = 0,0033 x 3500 / 2 = 5,8 mm...(5.2)
Calculation number : Revision : 0 Page 5 of 8 5.8.4 Creep j ef = j (infinite,t0) M 0Eqp / M 0Ed = 3,2 x 0,76/1,14 = 3,2...(5.19) 5.8.3.1 Slenderness criterion for isolated members A = 1 / (1 + 0,2 j ef ) = 1 / (1 + 0,2 x 3,2) = 0,61 w = A s f yd / (A c f cd ) = 3770 x 434,8 / (160000 x 30) = 0,341 B = 1 + 2 w = 1 + 2 x 0,341 = 1,297 r m = 1 C = 1,7 - r m = 1,7-1 = 0,7 n = N Ed / (A c f cd ) = 195000 / (160000 x 30) = 0,0406 l lim = 20.A.B.C / n = 20 x 0,61 x 1,297 x 0,7 / 0,0406 = 54,94...(5.13N) l < l lim 2nd order calculation is not required 5.8.8.2 Bending moments M 0e = max [0,6 M 02 + 0,4 M 01 ; 0,4 M 02 ] =...(5.32) = max [ 0,6 x 0 + 0,4 x 0; 0,4 x 0 ] = 0 knm M 0Ed = M 0e + N Ed e i = 0 + 195 x 5,8 = 1,138 knm M 2 = N Ed e 2 = 195 x 0 = 0 knm...(5.33) M Ed = max [ M 0Ed + M 2 ; M 02 + N Ed e i ; M 01 + 0,5 M 2 + N Ed e i ] =...(5.31) = max [ 1,138 + 0 ; 0 + 195 x 5,8; 0 + 0,5 x 0 + 195 x 5,8] = = 1,138 knm e t = M Ed / N Ed = 1,138 / 195 = 5,8 mm e min = max [ h/30, 20 ] = max [ 400/30, 20 ]= 20,0 mm...6.1(4) M Ed = N Ed e min = 195 x 20 = 3,9 knm 0,10 N Ed A s,min = max [ f yd 0,10 x 195000 ; 0,002 A c ] = max[ 434,8 A s,max = 0,04 A c = 0,04 x 160000 = 6400 mm 2 ; 0,002 x 160000] = 320 mm 2...(9.12N) N Edx = 195 kn; M Ed = 3,9 knm; A ben = 0 mm 2 M Ed M Rd = 3,900 291,207 = 0,01 < 1,0 A s,min = 320 mm 2 < A s = 3770 mm 2 < A s,max = 6400 mm 2
Calculation number : Revision : 0 Page 6 of 8 Sectional calculation Angle bending axis and neutral line a = 0,000 0 ; xu = 92,3 mm; d = 278,2 mm Centroid section y' = 200,0 z' = 0,0 (y = 200,0 z = 200,0) y' z' Wap. As Δε σc Δσs [mm] [mm] [mm 2 ] [o/oo] [N/mm 2 ] [N/mm 2 ] 200,0 200,0-3,500-30,0 45,0 155,0 1Ø20 314-1,794-358,7 148,3 155,0 1Ø20 314-1,794-358,7 251,7 155,0 1Ø20 314-1,794-358,7 355,0 155,0 1Ø20 314-1,794-358,7 45,0 51,7 1Ø20 314 2,125 424,9 355,0 51,7 1Ø20 314 2,125 424,9 45,0-51,7 1Ø20 314 6,043 434,8 355,0-51,7 1Ø20 314 6,043 434,8 45,0-155,0 1Ø20 314 9,961 434,8 148,3-155,0 1Ø20 314 9,961 434,8 251,7-155,0 1Ø20 314 9,961 434,8 355,0-155,0 1Ø20 314 9,961 434,8 y' z' Fc Fs dy' dz' F F.dy' F.dz' [mm] [mm] [kn] [kn] [mm] [mm] [kn] [knm] [knm] 200,0 164,1-830,7 0,0 164,1-830,7 0,0-136,3 45,0 155,0-112,7-155,0 155,0-112,7 17,5-17,5 148,3 155,0-112,7-51,7 155,0-112,7 5,8-17,5 251,7 155,0-112,7 51,7 155,0-112,7-5,8-17,5 355,0 155,0-112,7 155,0 155,0-112,7-17,5-17,5 45,0 51,7 133,5-155,0 51,7 133,5-20,7 6,9 355,0 51,7 133,5 155,0 51,7 133,5 20,7 6,9 45,0-51,7 136,6-155,0-51,7 136,6-21,2-7,1 355,0-51,7 136,6 155,0-51,7 136,6 21,2-7,1 45,0-155,0 136,6-155,0-155,0 136,6-21,2-21,2 148,3-155,0 136,6-51,7-155,0 136,6-7,1-21,2 251,7-155,0 136,6 51,7-155,0 136,6 7,1-21,2 355,0-155,0 136,6 155,0-155,0 136,6 21,2-21,2 totaal: -195,0 0,0-291,2
Calculation number : Revision : 0 Page 7 of 8 3: Controle voeg Decisive combination 2: (6.10b) N Edx = 195 kn; M Edy;bottom = 0 knm; 10.9.4.3 Verbindingen die drukkrachten overdragen...nen-en 1992-1-1+C2:2011/NB:2011 Mortelvoeg: aangieten of injecteren k 1 = 0,9 b x u 400 113,4 k 4 = min [ v ; v ] = min [ 30 ; 30 ] = 3,779 f md 15 k 3 = min [ k 5 f cd ; 1,00 ] = min [ 0,5 x ; 1,00 ] = 0,563 13,33 k 2 = k 3 5(1 - k 3 ) + k 3 k 2 = 0,563 x 4 5 x (1-0,563) + 0,563 x 3,779 2 = 0,906 5(1 - k 3 ) + k 2 4 5 x (1-0,563) + 3,779 2 f vd = k 1 k 2 f cd = 0,9 x 0,906 x 13,333 = 10,877 N/mm 2 M Ed M Rd = 3,900 57,660 = 0,07 < 1,0 Sectional calculation Angle bending axis and neutral line a = 0,000 0 ; xu = 113,3 mm; d = 200,0 mm Centroid section y' = 0,0 z' = -200,0 (y = 0,0 z = 0,0) y' z' Wap. As Δε σc Δσs [mm] [mm] [mm 2 ] [o/oo] [N/mm 2 ] [N/mm 2 ] 0,0 0,0-3,500-10,9-125,0-200,0 1Ø16 201 2,676 434,8 125,0-200,0 1Ø16 201 2,676 434,8
Calculation number : Revision : 0 Page 8 of 8 y' z' Fc Fs dy' dz' F F.dy' F.dz' [mm] [mm] [kn] [kn] [mm] [mm] [kn] [knm] [knm] 0,0-44,1-369,8 0,0 155,9-369,8 0,0-57,7-125,0-200,0 87,4-125,0 0,0 87,4-10,9 0,0 125,0-200,0 87,4 125,0 0,0 87,4 10,9 0,0 totaal: -195,0 0,0-57,7 Conclusion: Column complies.