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RC COLUMN DESIGN
In accordance with EN1992-1-1:2004 incorporating Corrigendum January 2008 and the UK national annex
Tedds calculation version 1.3.05
Design summary
Description Unit Provided Required Utilisation Result
Moment capacity (y) kNm 303.78 190.55 0.63 PASS
Moment capacity (z) kNm 235.89 148.37 0.63 PASS
Biaxial bending utilisation 0.98 PASS
z
8 no. 25 mm diameter longitudinal bars
500 mm
Max link spacing 400 mm generally, 240 mm for
y y
500 mm above and below slab/beam and at laps
z
400 mm
Column input details
Column geometry
Overall depth (perpendicular to y axis); h = 500 mm
Overall breadth (perpendicular to z axis); b = ;400; mm
Clear height between restraints about y axis; ly = ;3500; mm
Clear height between restraints about z axis; lz = ;3500; mm
Stability in the z direction; Braced
Stability in the y direction; Braced
Concrete details
Concrete strength class; C40/50
Partial safety factor for concrete (2.4.2.4(1)); C = 1.50
Coefficient cc (3.1.6(1)); cc = 0.85
Maximum aggregate size; dg = 20 mm
Reinforcement details
Nominal cover to links; cnom = 35 mm
Longitudinal bar diameter; = 25 mm
Link diameter; v = 8 mm
Total number of longitudinal bars; N=8
No. of bars per face parallel to y axis; Ny = ;3
No. of bars per face parallel to z axis; Nz = ;3
Area of longitudinal reinforcement; As = N 2 / 4 = 3927 mm2
Characteristic yield strength; fyk = 500 N/mm2
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Partial safety factor for reinft (2.4.2.4(1)); S = 1.15
Modulus of elasticity of reinft (3.2.7(4)); Es = 200 kN/mm2
Fire resistance details
Fire resistance period; R = 60 min
Exposure to fire; Exposed on more than one side
Ratio of fire design axial load to design resistance; fi = 0.70
Axial load and bending moments from frame analysis
Design axial load; NEd = 4500.0 kN
Moment about y axis at top; Mtopy = ;125.0; kNm
Moment about y axis at bottom; Mbtmy = ;125.0; kNm
Moment about z axis at top; Mtopz = ;75.0; kNm
Moment about z axis at bottom; Mbtmz = ;75.0; kNm
Joint details at end 1 of column
Beam/slab concrete strength class; C30/37
Beams/slabs providing rotational restraint about y axis
Depth on side A; hA1y = 500 mm
Width on side A; bA1y = 300 mm
Length on side A; lA1y = 7200 mm
Depth on side B; hB1y = 500 mm
Width on side B; bB1y = 300 mm
Length on side B; lB1y = 7200 mm
Beams providing rotational restraint about z axis
Depth on side A; hA1z = 400 mm
Width on side A; bA1z = 300 mm
Length on side A; lA1z = 6000 mm
Depth on side B; hB1z = 400 mm
Width on side B; bB1z = 300 mm
Length on side B; lB1z = 6000 mm
Joint details at 2 of column
Relative flexibility end 2 for buckling about y axis; k2y = 1000.000
Relative flexibility end 2 for buckling about z axis; k2z = 1000.000
Calculated column properties
Concrete properties
Area of concrete; Ac = h b = 200000 mm2
Column characteristic comp. cylinder strength; fck = 40 N/mm2
Column design comp. strength (3.1.6(1)); fcd = cc fck / C = 22.7 N/mm2
Column mean value of cyl. strength (Table 3.1); fcm = fck + 8 MPa = 48.0 N/mm2
Column secant modulus of elasticity (Table 3.1); Ecm = 22000 MPa (fcm / 10 MPa)0.3 = 35.2 kN/mm2
Beam/slab characteristic comp. cylinder strength; fck_b = 30 N/mm2
Beam/slab mean value of cyl. strength (3.1.6(1)); fcm_b = fck_b + 8 MPa = 38.0 N/mm2
Beam/slab secant mod. of elasticity (Table 3.1); Ecm_b = 22000 MPa (fcm_b / 10 MPa)0.3 = 32.8 kN/mm2
Rectangular stress block factors
Depth factor (3.1.7(3)); sb = 0.8
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Stress factor (3.1.7(3)); = 1.0
Strain limits
Compression strain limit (Table 3.1); cu3 = 0.00350
Pure compression strain limit (Table 3.1); c3 = 0.00175
Design yield strength of reinforcement
Design yield strength (3.2.7(2)); fyd = fyk / S = 434.8 N/mm2
Check nominal cover for fire and bond requirements
Min. cover reqd for bond (to links) (4.4.1.2(3)); cmin,b = max(v, - v) = 17 mm
Min axis distance for fire (EN1992-1-2 T 5.2a); afi = 40 mm
Allowance for deviations from min cover (4.4.1.3); cdev = 10 mm
Min allowable nominal cover; cnom_min = max(afi - / 2 - v, cmin,b + cdev) = 27.0 mm
PASS - the nominal cover is greater than the minimum required
Effective depths of bars for bending about y axis
Area per bar; Abar = 2 / 4 = 491 mm2
Spacing of bars in faces parallel to z axis (c/c); sz = (h - 2 (cnom + v) - ) / (Nz - 1) = 194 mm
Layer 1 (in tension face); dy1 = h - cnom - v - / 2 = 445 mm
Layer 2; dy2 = dy1 - sz = 250 mm
Layer 3; dy3 = dy2 - sz = 56 mm
2nd moment of area of reinft about y axis; Isy = 2 Abar Ny (dy1-h/2)2 = 11142 cm4
Radius of gyration of reinft about y axis; isy = (Isy / As) = 168 mm
Effective depth about y axis (5.8.8.3(2)); dy = h / 2 + isy = 418 mm
Effective depths of bars for bending about z axis
Area of per bar; Abar = 2 / 4 = 491 mm2
Spacing of bars in faces parallel to y axis (c/c); sy = (b - 2 (cnom + v) - ) / (Ny - 1) = 145 mm
Layer 1 (in tension face); dz1 = b - cnom - v - / 2 = 344 mm
Layer 2; dz2 = dz1 - sy = 200 mm
Layer 3; dz3 = dz2 - sy = 56 mm
2nd moment of area of reinft about z axis; Isz = 2 Abar Nz (dz1-b/2)2 = 6150 cm4
Radius of gyration of reinft about z axis; isz = (Isz / As) = 125 mm
Effective depth about z axis (5.8.8.3(2)); dz = b / 2 + isz = 325 mm
Relative flexibility at end 1 for buckling about y axis
Second moment of area of column; Iy = b h3 / 12 = 416667 cm4
Second moment of area of beam on side A; IA1y = bA1y hA1y3 / 12 = 312500 cm4
Second moment of area of beam on side B; IB1y = bB1y hB1y3 / 12 = 312500 cm4
Relative flexibility (PD6687 cl. 2.10); k1y = max(0.1, (Ecm Iy / ly) / [2 Ecm_b (IA1y/lA1y + IB1y/lB1y)]) = 0.735
Joint details at 2 of column
Relative flexibility end 2 for buckling about y axis; k2y = 1000.000
Relative flexibility at end 1 for buckling about z axis
Second moment of area of column; Iz = h b3 / 12 = 266667 cm4
Second moment of area of beam on side A; IA1z = bA1z hA1z3 / 12 = 160000 cm4
Second moment of area of beam on side B; IB1z = bB1z hB1z3 / 12 = 160000 cm4
Relative flexibility (PD6687 cl. 2.10); k1z = max(0.1, (Ecm Iz / lz) / [2 Ecm_b (IA1z/lA1z + IB1z/lB1z)]) = 0.766
Relative flexibility end 2 for buckling about z axis; k2z = 1000.000
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Calculated effective length (cl. 5.8.3.2)
Eff. length about y axis (braced) (5.8.3.2(3)); l0y = 0.5 ly [(1 + k1y/(0.45+k1y))(1 + k2y/(0.45+k2y))]0.5 = 3150 mm
Eff. length about z axis (braced) (5.8.3.2(3)); l0z = 0.5 lz [(1 + k1z/(0.45+k1z))(1 + k2z/(0.45+k2z))]0.5 = 3159 mm
Column slenderness about y axis
Radius of gyration; iy = h / (12) = 14.4 cm
Slenderness ratio (5.8.3.2(1)); y = l0y / iy = 21.8
Column slenderness about z axis
Radius of gyration; iz = b / (12) = 11.5 cm
Slenderness ratio (5.8.3.2(1)); z = l0z / iz = 27.4
Design bending moments
Frame analysis moments about y axis combined with moments due to imperfections (cl. 5.2 & 6.1(4))
Ecc. due to geometric imperfections (y axis); eiy = l0y /400 = 7.9 mm
Min end moment about y axis; M01y = min(abs(Mtopy), abs(Mbtmy)) + eiy NEd = 160.4 kNm
Max end moment about y axis; M02y = max(abs(Mtopy), abs(Mbtmy)) + eiy NEd = 160.4 kNm
Slenderness limit for buckling about y axis (cl. 5.8.3.1)
Factor A; A = 0.7
Mechanical reinforcement ratio; = As fyd / (Ac fcd) = 0.377
Factor B; B = (1 + 2 ) = 1.324
Moment ratio; rmy = M01y / M02y = ;1.000
Factor C; Cy = 1.7 - rmy = 0.700
Relative normal force; n = NEd / (Ac fcd) = 0.993
Slenderness limit; limy = 20 A B Cy / (n) = 13.0
y>=limy - Second order effects must be considered
Frame analysis moments about z axis combined with moments due to imperfections (cl. 5.2 & 6.1(4))
Ecc. due to geometric imperfections (z axis); eiz = l0z /400 = 7.9 mm
Min end moment about z axis; M01z = min(abs(Mtopz), abs(Mbtmz)) + eiz NEd = 110.5 kNm
Max end moment about z axis; M02z = max(abs(Mtopz), abs(Mbtmz)) + eiz NEd = 110.5 kNm
Slenderness limit for buckling about y axis (cl. 5.8.3.1)
Factor A; A = 0.7
Mechanical reinforcement ratio; = As fyd / (Ac fcd) = 0.377
Factor B; B = (1 + 2 ) = 1.324
Moment ratio; rmz = M01z / M02z = ;1.000
Factor C; Cz = 1.7 - rmz = 0.700
Relative normal force; n = NEd / (Ac fcd) = 0.993
Slenderness limit; limz = 20 A B Cz / (n) = 13.0
z>=limz - Second order effects must be considered
Local second order bending moment about y axis (cl. 5.8.8.2 & 5.8.8.3)
Relative humidity of ambient environment; RH = 50 %
Column perimeter in contact with atmosphere; u = 1800 mm
Age of concrete at loading; t0 = 28 day
Parameter nu; nu = 1 + = 1.377
Approx value of n at max moment of resistance; nbal = 0.4
Axial load correction factor; Kr = min(1.0 , (nu - n) / (nu - nbal)) = 0.393
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Reinforcement design strain; yd = fyd / Es = 0.00217
Basic curvature; curvebasic_y = yd / (0.45 dy) = 0.0000115 mm-1
Notional size of column; h0 = 2 Ac / u = 222 mm
Factor 1 (Annex B.1(1)); 1 = (35 MPa / fcm)0.7 = 0.802
Factor 2 (Annex B.1(1)); 2 = (35 MPa / fcm)0.2 = 0.939
Relative humidity factor (Annex B.1(1)); RH = [1 + ((1 - RH / 100%) / (0.1 mm-1/3 (h0)1/3)) 1] 2 = 1.560
Concrete strength factor (Annex B.1(1)); fcm = 16.8 (1 MPa)1/2 / (fcm) = 2.425
Concrete age factor (Annex B.1(1)); t0 = 1 / (0.1 + (t0 / 1 day)0.2) = 0.488
Notional creep coefficient (Annex B.1(1)); 0 = RH fcm t0 = 1.848
Final creep development factor; (at t = ¥); c = 1.0
Final creep coefficient (Annex B.1(1)); = 0 c = 1.848
Ratio of SLS to ULS moments; rMy = 0.65
Effective creep ratio; efy = rMy = 1.201
Factor ; y = 0.35 + fck / 200 MPa - y / 150 = 0.405
Creep factor; Ky = max(1.0 , 1 + y efy) = 1.486
Modified curvature; curvemod_y = Kr Ky curvebasic_y = 0.0000067 mm-1
Curvature distribution factor; c = 10
Deflection; e2y = curvemod_y l0y2 / c = 6.7 mm
Nominal 2nd order moment; M2y = NEd e2y = 30.1 kNm
Design bending moment about y axis (cl. 5.8.8.2 & 6.1(4))
Equivalent moment from frame analysis; M0ey = max(0.6 M02y + 0.4 M01y, 0.4 M02y) = ;160.4; kNm
Design moment; MEdy = max(M02y, M0ey + M2y, M01y + 0.5M2y, NEd max(h/30, 20 mm))
MEdy = 190.6 kNm
Local second order bending moment about z axis (cl. 5.8.8.2 & 5.8.8.3)
Basic curvature; curvebasic_z = yd / (0.45 dz) = 0.0000149 mm-1
Ratio of SLS to ULS moments; rMz = 0.65
Effective creep ratio (5.8.4(2)); efz = rMz = 1.201
Factor ; z = 0.35 + fck / 200 MPa - z / 150 = 0.368
Creep factor; Kz = max(1.0 , 1 + z efz) = 1.441
Modified curvature; curvemod_z = Kr Kz curvebasic_z = 0.0000084 mm-1
Curvature distribution factor; c = 10
Deflection; e2z = curvemod_z l0z2 / c = 8.4 mm
Nominal 2nd order moment; M2z = NEd e2z = 37.8 kNm
Design bending moment about z axis (cl. 5.8.8.2 & 6.1(4))
Equivalent moment from frame analysis; M0ez = max(0.6 M02z + 0.4 M01z, 0.4 M02z) = ;110.5; kNm
Design moment; MEdz = max(M02z, M0ez + M2z, M01z + 0.5M2z, NEd max(b/30, 20 mm))
MEdz = 148.4 kNm
Moment capacity about y axis with axial load NEd
Moment of resistance of concrete
By iteration:-
Position of neutral axis; y = 481.0 mm
Concrete compression force (3.1.7(3)); Fyc = fcd min(sb y , h) b = 3488.9 kN
Moment of resistance; MRdyc = Fyc [h / 2 - (min(sb y , h)) / 2] = 201.0 kNm
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Moment of resistance of reinforcement
Strain in layer 1; y1 = cu3 (1 - dy1 / y) = 0.00027
Stress in layer 1; y1 = min(fyd, Es y1) = 53.1 N/mm2
Force in layer 1; Fy1 = Ny Abar y1 = 78.2 kN
Moment of resistance of layer 1; MRdy1 = Fy1 (h / 2 - dy1) = -15.2 kNm
Strain in layer 2; y2 = cu3 (1 - dy2 / y) = 0.00168
Stress in layer 2; y2 = min(fyd, Es y2) - fcd = 313.5 N/mm2
Force in layer 2; Fy2 = 2 Abar y2 = 307.8 kN
Moment of resistance of layer 2; MRdy2 = Fy2 (h / 2 - dy2) = 0.0 kNm
Strain in layer 3; y3 = cu3 (1 - dy3 / y) = 0.00310
Stress in layer 3; y3 = min(fyd, Es y3) - fcd = 412.1 N/mm2
Force in layer 3; Fy3 = Ny Abar y3 = 606.9 kN
Moment of resistance of layer 3; MRdy3 = Fy3 (h / 2 - dy3) = 118.0 kNm
Resultant concrete/steel force; Fy = 4481.8 kN
PASS - This is within half of one percent of the applied axial load
Combined moment of resistance
Moment of resistance about y axis; MRdy = 303.8 kNm
PASS - The moment capacity about the y axis exceeds the design bending moment
Moment capacity about z axis with axial load NEd
Moment of resistance of concrete
By iteration:-
Position of neutral axis; z = 382.5 mm
Concrete compression force (3.1.7(3)); Fzc = fcd min(sb z , b) h = 3468.0 kN
Moment of resistance; MRdzc = Fzc [b / 2 - (min(sb z , b)) / 2] = 163.0 kNm
Moment of resistance of reinforcement
Strain in layer 1; z1 = cu3 (1 - dz1 / z) = 0.00035
Stress in layer 1; z1 = min(fyd, Es z1) = 69.5 N/mm2
Force in layer 1; Fz1 = Nz Abar z1 = 102.4 kN
Moment of resistance of layer 1; MRdz1 = Fz1 (b / 2 - dz1) = -14.8 kNm
Strain in layer 2; z2 = cu3 (1 - dz2 / z) = 0.00167
Stress in layer 2; z2 = min(fyd, Es z2) - fcd = 311.3 N/mm2
Force in layer 2; Fz2 = 2 Abar z2 = 305.6 kN
Moment of resistance of layer 2; MRdz2 = Fz2 (b / 2 - dz2) = 0.0 kNm
Strain in layer 3; z3 = cu3 (1 - dz3 / z) = 0.00299
Stress in layer 3; z3 = min(fyd, Es z3) - fcd = 412.1 N/mm2
Force in layer 3; Fz3 = Nz Abar z3 = 606.9 kN
Moment of resistance of layer 3; MRdz3 = Fz3 (b / 2 - dz3) = 87.7 kNm
Resultant concrete/steel force; Fz = 4482.9 kN
PASS - This is within half of one percent of the applied axial load
Combined moment of resistance
Moment of resistance about z axis; MRdz = 235.9 kNm
PASS - The moment capacity about the z axis exceeds the design bending moment
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Biaxial bending
Determine if a biaxial bending check is required (5.8.9(3))
Ratio of column slenderness ratios; ratio = max(y, z) / min(y, z) = 1.25
Eccentricity in direction of y axis; ey = MEdz / NEd = 33.0 mm
Eccentricity in direction of z axis; ez = MEdy / NEd = 42.3 mm
Equivalent depth; heq = iy (12) = 500 mm
Equivalent width; beq = iz (12) = 400 mm
Relative eccentricity in direction of y axis; erel_y = ey / beq = 0.082
Relative eccentricity in direction of z axis; erel_z = ez / heq = 0.085
Ratio of relative eccentricities; ratioe = min(erel_y, erel_z) / max(erel_y, erel_z) = 0.973
ratioe > 0.2 - Biaxial bending check is required
Biaxial bending (5.8.9(4))
Design axial resistance of section; NRd = (Ac fcd) + (As fyd) = 6240.7 kN
Ratio of applied to resistance axial loads; ratioN = NEd / NRd = 0.721
Exponent a; a = 1.54
Biaxial bending utilisation; UF = (MEdy / MRdy)a + (MEdz / MRdz)a = 0.979
PASS - The biaxial bending capacity is adequate
