Evo Design - structural design Calculation No. 001-BASEPLATE CALCULATION SHEET Project No. onlinestructuraldesign.com SAMPLE CALCULATION Project Title: Base plate calculation interactive online spreadsheet Calc. By Date Rev. MN 16.04.2014 0 Subject/Feature: Column Base Plate Design - Online Calculation Report Checked By Date CN 16.04.2014 per EN 1992-1-1, EN 1993-1-1 and EN 1993-1-8 Input Output Base plate size in plan Base plate thickness Column base forces Max. pressure under baseplate Materials (steel, concrete, bolts) Max. tension in bolts / bolt verification Profile dimensions h = mm profile height b = mm profile width Base Plate Dimensions H = mm B = mm Base plate thickness is determined in the calculation s = mm critical section location (usually in the middle of the flange) Bolt locations on plate f = mm nB = 2 number of hold down bolts (bolts in tension) f = 20 mm bolt diameter (parameters that can not be modified in the demo version) Materials Steel bolt characteristics per EN 1993-1-8 Bolt class 4.6 4.8 5.6 5.8 6.8 8.8 10.9 Section 3 Table 3.1 bolt classes recommended by the Eurocode; Bold yield strength The National Annex may exclude certain bolt classes. fyb = N/mm2 Partial factor for steel bolts per EN 1993-1-8 gM2 = Section 2 Table 2.1 partial safety factors recommended by the Eurocode; Bolt design strength fyd = fy / gM2 Numerical values for safety factors may be defined fyd-b = N/mm2 in the National Annex Steel base plate characteristics Steel grade S 235 S 275 S 355 S 450 Steel yield strength fy = N/mm2 for thickness under 40mm fy = N/mm2 for thickness between 40mm and 80mm Partial factor for steel elements (in bending) per EN 1993-1-1 gM0 = Section 6.1 (1) and Note 2B value recommended by the Eurocode; value to be used can be found in the Eurocode National Annex References: Design of Welded Structures - O. W. Blodgett (James F. Lincoln Arc Welding Foundation) EN 1992-1-1:2004 - Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings EN 1993-1-1:2005 - Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings EN 1993-1-8:2005 - Eurocode 3: Design of steel structures - Part 1-8: Design of joints Calculation No. CALCULATION SHEET Project No. onlinestructuraldesign.com Project Title: Calc. By Date Rev. Subject Ckd. By Date Steel modulus of elasticity per EN 1993-1-1 Es = 210000 N/mm2 Section 3.2.6 (1) Concrete characteristics Concrete class C12/15 C16/20 C20/25 C25/30 C30/37 C35/45 C40/50 C45/55 C50/60 C55/67 C60/75 C70/85 C80/95 C90/105 per EN 1992-1-1:2004 fck = MPa concrete characteristic cylinder strength Section 3 Table 3.1 Partial factor for concrete for ultimate limit states per EN 1992-1-1:2004 Section 2 Table 2.1N gc = values for Persistent & Transient design situations recommended by the Eurocode; values to be used may be found in the Eurocode National Annexes Design compressive concrete strength per EN 1992-1-1:2004 Section 3.1.6 & Formula 3.15 acc = Coefficient taking account of long term effects fcd = acc * fck / gc = MPa on the compressive strength and of unfavourable effects resulting from the way the load is applied value may be found in the EC National Annex Concrete modulus of elasticity Ecm = GPa for concrete class per EN 1992-1-1:2004 Section 3.1.3 Table 3.1 Aggregates = basalt limestone quartzite sandstone Section 3.1.3 (2) Values in Table 3.1 are given for quartzite aggregates Ecm = Values for limestone and sandstone are reduced Ecm = N/mm2 by 10% and 30% respectively. For basalt aggregates the value should be increased by 20% Column base forces N = kN axial force pair of column base forces. Mx and My are not M = kN*m bending moment considered simultaneous. e = M/F = mm H/6 = mm eccentricity e References: Design of Welded Structures - O. W. Blodgett (James F. Lincoln Arc Welding Foundation) EN 1992-1-1:2004 - Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings EN 1993-1-1:2005 - Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings EN 1993-1-8:2005 - Eurocode 3: Design of steel structures - Part 1-8: Design of joints Calculation No. CALCULATION SHEET Project No. onlinestructuraldesign.com Project Title: Calc. By Date Rev. Subject Ckd. By Date sc = N/HB+6*M/B*H2 sc = MPa sc fcd fcd = MPa Design of the Base Plate Thickness Critical section location s = mm smin = MPa ssc = smin+(sc-smin)*(H - s) / H = MPa Design critical moment - at critical section MEd.plate = [(σsc*s/2)*(s/3)+(σc*s/2)*(s*2/3)]*B = kN*m Calculation No. CALCULATION SHEET Project No. onlinestructuraldesign.com Project Title: Calc. By Date Rev. Subject Ckd. By Date Three equations, three unknowns: Fb, Y, sc (Axial force in steel hold down bolts, active area under base plate, aximum pressure under base plate) 1. Forces equilibrium Y*sc/2 - Fb -N = 0 Fb + N = Y*sc*B/2 (1) 2. Bending moment equilibrium Fb * f + (Fb + N) * (H/2 - Y/3) - N * e = 0 Fb = -N * (H/2 - Y/3 -e)/(H/2 - Y/3 + f) (2a) N = -Fb * (H/2 - Y/3 -e)/(H/2 - Y/3 + f) (2) 3. Representing the elastic behaviour of the concrete support and the steel hold-down bolt: a/b = eb/ec = (sb / Es) / (sc / Ec) since Es = sb / es modulus of elasticity of steel bolt Ec = sc / ec modulus of elasticity of concrete nb = number of steel hold down bolts Ab = p*f2/4 = mm2 area of steel hold down bolts sb = Fb / Ab n = Es / Ec = modular ratio of elasticity, steel to concrete a/b = (N/Ab)/(sc*n) = N/(Ab*sc*n) From similar triangles => a/b = (H/2-Y+f)/Y => N/(Ab*sc*n) = (H/2-Y+f)/Y => => sc = Fb * Y / (Ab * n *(H/2 - Y + f)) (3) From (1), (2) and (3) -Fb * (H/2 - Y/3 -e)/(H/2 - Y/3 + b) + Fb = (Fb * Y2 * B) / [2 * Ab * n *(H/2 - Y + f)] Solve for Y: Y3 + 3 * (e - H/2) * Y2 + [(6 * n * Ab)/B] * (f + e) * Y -  [(6 * n * Ab)/B] * (H/2 + f) * (f + e) = 0 or Y3 + K1 * Y2 + K2 * Y + K3 = 0 where K1 = 3 * (e - H/2) = K2 = [(6 * n * Ab)/B] * (f + e) = K3 = - K2 * (H/2 + f) = Y = mm References: Design of Welded Structures - O. W. Blodgett (James F. Lincoln Arc Welding Foundation) EN 1992-1-1:2004 - Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings EN 1993-1-1:2005 - Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings EN 1993-1-8:2005 - Eurocode 3: Design of steel structures - Part 1-8: Design of joints Calculation No. CALCULATION SHEET Project No. onlinestructuraldesign.com Project Title: Calc. By Date Rev. Subject Ckd. By Date Fb = kN (in per (2a) hold down bolts max. tension (in all bolts) F1.bolt = Fb / kN hold down bolt max. tension - in 1 bolt F1.bolt /(p*f2/4) = N/mm2 fyd-b N/mm2 sc = MPa per (3) sc fcd fcd = MPa effective max. pressure under baseplate is compared with the concrete design compressive strength Design of the Base Plate Thickness Critical section location s = mm Stress at the critical section location ssc = sc*(Y - s) / Y = MPa Design critical moment - at critical section MEd.plate = [(ssc*s/2)*(s/3)+(sc*s/2)*(s*2/3)]*B = kN*m MEd.plate = (sc*Y/2)*(s-Y/3)*B = kN*m MC,Rd = Mpl,rd = (Wpl * fy)/ gM0 Bending plastic design resistance (4) per EN 1993-1-1 Section 6.2.5 (2) Formula 6.13 Design resistance for bending about one principal axis for class 1 or 2 cross sections Plastic section modulus of rectangular sections Wpl = B*tpl2/4 (5) (tpl = base plate thickness) from (4) and (5) => [fy * (B*tpl2)/4]/ gM0 > MEd.plate MEd.plate = kN*m => tpl > sqrt[4 * MEd.plate * gM0 / (B * fy)] => tpl > mm (with fy = N/mm2) References: Design of Welded Structures - O. W. Blodgett (James F. Lincoln Arc Welding Foundation) EN 1992-1-1:2004 - Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings EN 1993-1-1:2005 - Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings EN 1993-1-8:2005 - Eurocode 3: Design of steel structures - Part 1-8: Design of joints