Design of Non Slender Column to Eurocode 2 (BY PRASAD ·) The design of non slender column according to Eurocode 2 is discussed in this article. This article guides the design procedures to be followed. Brace Non-Slender Column Design Edge column 300mm square column Axial Load 1500kN Moment at top -40kNm Moment at Bottom 45kNm fck 30N/mm2 fyk 500N/mm2 Nominal Cover 25mm Floor to Floor height 4250mm Depth of the beam supported by the column 450mm Mtop = -40kNm Mbottom = 45kNm NEd = 1500kN Clear height = 4250-450 = 3800mm Effective length = lo = factor * l Factor = 0.85 (concise Eurocode 2, Table 5.1. This may more conservative). lo = 0.85* 3800 = 3230mm Slenderness λ = lo/i i = radios of gyration = h/√12 λ = lo/( h/√12 ) = 3.46*lo/h = 3.46*3230/300 = 37.3 Limiting Slenderness λlim λlim = 20ABC/√n A = 0.7 if effective creep factor is unknown B = 1.1 if mechanical reinforcement ratio is unknown C = 1.7 – rm = 1.7-Mo1/Mo2 Mo1 = -40kNm Mo2 C = 45kNm where lMo2l ≥ lMo1l = 1.7 – (-40/45) = 2.9 n = NEd / (Ac*fcd) fcd = fck / 1.5 = (30/1.5)*0.85 = 17 n = 1500*1000 / (300*300*17)= 0.98 λlim = 20*0.7*1.1*2.9/√0.98 = 45.1 λlim > λ hence, column is not slender. Calculation of design moments MEd = Max{Mo2, MoEd +M2, Mo1 + 0.5M2} Mo2 = Max {Mtop, Mbottom} + ei*NEd = 45 + (3.23/400)*1500 ≥ Max(300/30, 20)*1500 = 57.1kNm > 30kNm Mo2 = Min{Mtop, Mbottom} + ei*NEd = -40 + (3.23/400)*1500 ≥ Max(300/30, 20)*1500 = 27.9kNm MoEd = 0.6*Mo2+ 0.4*Mo1 ≥ 0.4*Mo2 = 0.6*57.1 + 0.4*(-27.9) ≥ 0.4*57.1 = 23.1 ≥ 22.84 M2 MEd = 0 , Column is not slender = Max{Mo2, MoEd +M2, Mo1 + 0.5M2}= Max{57.1, 23.1 +0, -27.9 + 0.5*0} = 57.1kNm MEd / [b*(h^2)*fck] = (57.1*10^6) / [300*(300^2)*30] = 0.07 NEd / (b*h*fck) = (1500*10^6) / (300*300*30 = 0.56 Assume 25mm diameter bars as main reinforcement and 10mm bars as shear links d2 d2/h = 25+10+25/2 = 47.5mm = 47.5 / 300 = 0.16 Note: d2/h = 0.20 chart is reffed to find the reinforcement area, but it is more conservative. Interpolation can be used to find the exact value. As*fyk / b*h*fck = 0.24 As = 0.24*300*300*30 / 500 = 1296mm2 Provides four 25mm bars (As Provided 1964mm2) Check for Biaxial Bending Further check is not required if 0.5 ≤ ( λy/ λz) ≤ 2.0 For rectangular column and 0.2 ≥ (ey/heq)/(ez/beq) ≥ 5.0 Here λy and λz are slenderness ratios λy is nearly equal to λz Therefore, λy/λz is nearly equal to one. Hence, λy/λz < 2 and > 0.5 OK ey/heq = (MEdz / NEd) / heq ez/beq = (MEdy / NEd) / beq (ey/heq)/(ez/beq) = MEdz / MEdy Here h=b=heq=beq, column is square MEdz = 45kNm MEdy = 30kNm Minimum moment, see the calculation of Mo2 for the method of calculation note: Moments due to imperfections need to be included only in the direction where they have the most unfavorable effect – Concise Eurocode 2 (ey/heq)/(ez/beq) = 45/30 = 1.5 > 0.2 and < 5 Therefore Biaxial check is required. (MEdz / MRdz)^a + (MEdy / MRdy)^a ≤ 1 MEdz = 45kNm MEdy = 30kNm MRdz and MRdy are the moment resistance in the respective directions, corresponding to an axial load NEd. For symetric reinforcement section MRdz = MRdy As Provided = 1964mm2 As*fyk / b*h*fck = 1964*500/(300*300*30) = 0.36 NEd / (b*h*fck) = 0.56 From the chart d2/h =0.2 MEd / [b*(h^2)*fck] = 0.098 MEd = 0.098*300*300*300*30 = 79.38kNm a a a NEd NRd NRd = an exponent = 1.0 for NEd/NRd = 0.1 = 1.5 for NEd/NRd = 0.7 = 1500kN = Ac*fcd + As*fyd = 300*300*(0.85*30/1.5) + 1964*(500/1.15) = 2383.9kN NEd/NRd = 1500/2383.9 = 0.63 By interpolating a = 1.44 (MEdz / MRdz)^a + (MEdy / MRdy)^a = (45 / 79.39)^1.44 + (30 / 79.38)^1.44 = 0.69 <1 Hence, Check for biaxial bending is ok Therefore, Provide four 25mm diameter bars.