Base Plate Calculations i

Baseplate_calculation_SI

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Calculation No.

CALCULATION SHEET Project No.

onlinestructuraldesign.com

Project Title: Calc. By Date Rev.

Subject/Feature: CheckedBy Date

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 = mm bolt diameter

Materials Steel bolt characteristics per EN 1993-1-8

Bolt class 8.8 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 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.




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 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 effectsresulting 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 = 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.





Three equations, three unknowns: Fb, Y, sc (Axial force in steel hold down bolts, active area under base plate, maximum 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.





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

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

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Base Plate Calculations i

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