8/12/2019 Basep Plate Design Metric

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5/31/2014 Basep Plate Design Metric

http://baseplatedesign.com/

Base Plate Online Calculation per EN 1992-1-1, EN 1993-1-1 and EN 1993-1-8

Base Plate Dimensions

H = 300 mm

B = 200 mm

Critical section location

s = 190 mm

Column base forces

Axial force & bending moment

N = 400 kN

M = 140 kN*m

Force eccentricity

e = M / N = 350.0 mm

Bolt characteristics and location Steel base plate characteristics Concrete class C25/30

f = 241.3 mm Steel grade S 235 EN 1992-1-1:2004 Section 3 Table 3.1

Hold down bolts (no. and diameter) Steel yield strength fck= 25 MPa

nB= 2 f= 16 mm fy= 235 N/mm2 EN 1992-1 -1:2004 Section 3.1.3 Table 3.1

Ab= nB*p*f2/4 tension bolts area for thickness under 40mm sandstone aggregates

Ab= 402.1 mm2 fy= 215 N/mm2 Ecm= 31 Gpa * 0.7 = 21.7 GPa

Bolt class 6.8 for thickness over 40mm Ecm= 21700 N/mm2

Yield strength (EN 1993-1-8 Section 3 Table 3.1) Partial factor for steel elements Partial factor for concrete for ULS

fyb= 480

N/mm2

factor for bending per EN 1993-1 -8 EN 1992-1-1:2004 Section 2 Table 2.1N Partial factor for bolts Section 6.1 (1) and Note 2B gc= 1.5

(EN 1993-1-8 Section 2 Table 2.1) gM0= 1.00 Design compressive concrete strength

gM2= 1.25 Steel modulus of elasticity EN 1993-1 -8 Section 3.1.6 & Formula 3.15

Bolt design strength (fyd= fy/ gM2) EN 1993-1-8 - Section 3.2.6 (1) acc= 1

fyd-b= 384.0 N/mm2 Es= 210000 N/mm2 fcd= acc* fck/ gc= 16.67 MPa

For baseplates with large eccentricity (tension in bolts) e = M / N > H/6 350.0 mm > 50.0 mm

Three unknowns: From similar triangles

Fb- Axial force in steel hold down bolts a/b = (N/Ab)/(sc*n) = N/(Ab*sc*n)=>

Check - Stress in one bolt

Y - active area under base plate a/b = (H/2-Y+f)/Y sbolt= F1.bolt/(p*f2/4)

sc- maximum pressure under base plate => N/(Ab*sc*n) = (H/2-Y+f)/Y sbolt= 727.4 N/mm2 > fyd-b

And three equations: => sc= Fb*Y/(Ab*n*(H/2-Y+f)) (3) not OK, bolt effective s tress

1. Forces equilibrium From (1), (2) and (3): is larger than bolt design s tress

Y*sc/2-Fb-N=0 -Fb*(H/2-Y/3-e)+Fb=

(Fb*Y2*B) from (3) => sc= 46.3 MPa

Fb+N=Y*sc*B/2 (1) (H/2-Y/3+b) 2*Ab*n*(H/2-Y+f) Check - pressure under baseplate

2. Bending moment equilibrium Solve for Y: Y3+K1*Y

2+K2*Y+K3=0 sc= 46.34 MPa > fcd

Fb*f+(Fb+N)*(H/2-Y/3)-N*e=0 where base plate dimensions are OK,

Fb=-N*(H/2-Y/3-e)/(H/2-Y/3+f) (2a) K1=3*(e-H/2)= 600 stress under base plate is

N=-Fb*(H/2-Y/3-e)/(H/2-Y/3+f) (2) K2=(f+e)*(6*n*Ab)/B= 69032 smaller than the concrete capacity

3. Elastic behaviour of the concrete K3=-K2*(H/2+f)= -27012102 Stress at the critical section location

support and steel hold-down bolts: Y = 149.3 mm ssc = sc*(Y - s) / Y = 0.00 MPa

a/b = eb/ec= (sb/Es)/(sc/Ec) Tension in the 2 hold down bolts:

Es=sb/es Ec= sc/ec from (2a)=> Fb= 292.5 kN

sb= Fb/Ab F1.bolt=Fb/nB= 146.2 kN (in one bolt)

n = Es/Ec= 9.7

modular ratio of elasticity, s teel to concrete

References:

Design critical moment - at critical section 1. Design of Welded Structures - O. W. Blodgett

MEd.plate= (sc*Y/2)*(s-Y/3)*B 2. EN 1992-1-1 :2004 - Eurocode 2: Design of

MEd.plate= 97.01 kN*m concrete structures - Part 1-1: General rules

and rules for buildings

Bending plastic design resistance 3. EN 1993-1-1:2005 - Eurocode 3: Design of

per EN 1993-1-1 Section 6.2.5 (2) Formula 6.13 (4) and (5) => [fy* (B*tpl2)/4]/ gM0 MEd.plate steel structures - Part 1-1: General rul es and

MC,Rd= Mpl,rd= (Wpl* fy)/ gM0 (4) => tpl> sqrt[4 * MEd.plate* gM0 / (B * fy)] rules for buildings

Plastic section modulus of rectangular sections tpl- base plate thickness 4. EN 1993-1-8:2005 - Eurocode 3: Design of

Wpl= B*tpl2/4 (5) tpl> 95.0 mm with fy= 215 N/mm2 steel structures - Part 1-8: Design of joints