Evo Design  structural design

Calculation No.












001BASEPLATE


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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 199211, EN 199311 and EN 199318















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











n_{B}
=

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 199318


Bolt class








Section 3 Table 3.1










bolt classes recommended by the Eurocode;


Bold yield strength







The National Annex may exclude certain bolt classes.


f_{yb}
=


N/mm^{2}


















Partial factor for steel bolts






per EN 199318


g_{M2} =








Section 2 Table 2.1










partial safety factors recommended by the Eurocode;


Bolt design strength

f_{yd} = f_{y} / g_{M2}





Numerical values for safety factors may be defined


f_{ydb}
=


N/mm^{2}






in the National Annex















Steel base plate characteristics











Steel grade


























Steel yield strength












f_{y}
=


N/mm^{2}

for thickness under 40mm







f_{y}
=


N/mm^{2}

for thickness between 40mm and 80mm




















Partial factor for steel elements (in bending)





per EN 199311


g_{M0} =








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 199211:2004  Eurocode 2: Design of concrete structures  Part 11: General rules and rules for buildings


EN 199311:2005  Eurocode 3: Design of steel structures  Part 11: General rules and rules for buildings


EN 199318:2005  Eurocode 3: Design of steel structures  Part 18: Design of joints






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Steel modulus of elasticity




per EN 199311


E_{s}
=

210000

N/mm^{2}






Section 3.2.6 (1)















Concrete characteristics









Concrete class







per EN 199211:2004


f_{ck}
=


MPa

concrete characteristic cylinder strength


Section 3 Table 3.1















Partial factor for concrete for ultimate limit states




per EN 199211:2004










Section 2 Table 2.1N


g_{c} =








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 199211:2004










Section 3.1.6 & Formula 3.15


a_{cc} =








Coefficient taking account of long term effects


f_{cd}
=

a_{cc} * f_{ck} / g_{c}

=


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









E_{cm}
=


GPa for

concrete class




per EN 199211:2004










Section 3.1.3 Table 3.1


Aggregates =







Section 3.1.3 (2)










Values in Table 3.1 are given for quartzite aggregates


E_{cm}
=




Values for limestone and sandstone are reduced


E_{cm}
=


N/mm^{2}






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. M_{x} and M_{y} 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 199211:2004  Eurocode 2: Design of concrete structures  Part 11: General rules and rules for buildings


EN 199311:2005  Eurocode 3: Design of steel structures  Part 11: General rules and rules for buildings


EN 199318:2005  Eurocode 3: Design of steel structures  Part 18: Design of joints






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s_{c} =

N/HB+6*M/B*H^{2}











s_{c} =


MPa











s_{c}


f_{cd}


f_{cd}
=


MPa


































Design of the Base Plate Thickness











Critical section location











s =


mm
























s_{min} =


MPa











s_{sc} =

s_{min}+(s_{c}s_{min})*(H  s) / H =


MPa





















Design critical moment  at critical section










M_{Ed.plate} =

[(σ_{sc}*s/2)*(s/3)+(σ_{c}*s/2)*(s*2/3)]*B =


kN*m





































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Three equations, three unknowns:

F_{b},
Y, s_{c}










(Axial force in steel hold down bolts, active area










under base plate, aximum pressure under base plate)

















































1. Forces equilibrium











Y*s_{c}/2  F_{b} N = 0












F_{b} + N = Y*s_{c}*B/2

(1)























2. Bending moment equilibrium











F_{b} * f + (F_{b} + N) * (H/2  Y/3)  N * e = 0









F_{b} = N * (H/2  Y/3 e)/(H/2  Y/3 + f)



(2a)






N = F_{b} * (H/2  Y/3 e)/(H/2  Y/3 + f)



(2)


















3. Representing the elastic behaviour of the concrete








support and the steel holddown bolt:









a/b =

e_{b}/e_{c} =

(s_{b} / E_{s}) / (s_{c} / E_{c})










since

E_{s} =

s_{b} / e_{s}




modulus of elasticity of steel bolt




E_{c} =

s_{c} / e_{c}




modulus of elasticity of concrete




n_{b} =






number of steel hold down bolts




A_{b} =


p*f^{2}/4 =


mm^{2}


area of steel hold down bolts




s_{b} =

F_{b} /
A_{b}












n =

E_{s} /
E_{c} =





modular ratio of elasticity, steel to concrete
















a/b =

(N/A_{b})/(s_{c}*n) =

N/(A_{b}*s_{c}*n)






















From similar triangles



=>








a/b =

(H/2Y+f)/Y
























=>

N/(A_{b}*s_{c}*n) =

(H/2Y+f)/Y

=>





















=>

s_{c} =

F_{b} * Y / (A_{b} * n *(H/2  Y + f))



(3)


















From (1), (2) and (3)













F_{b} * (H/2  Y/3 e)/(H/2  Y/3 + b) + F_{b} =

(F_{b} * Y^{2} * B) / [2 * A_{b} * n *(H/2  Y + f)]

















Solve for Y:














Y^{3} + 3 * (e  H/2) * Y^{2} + [(6 * n * A_{b})/B] * (f + e) * Y
 [(6 * n * A_{b})/B] * (H/2 + f) * (f + e) = 0



or













Y^{3} + K_{1} * Y^{2} + K_{2} * Y + K_{3} = 0



where













K_{1} =

3 * (e  H/2) =










K_{2} =

[(6 * n * A_{b})/B] * (f + e) =










K_{3} =

 K_{2} * (H/2 + f) =










Y =


mm























References:













Design of Welded Structures  O. W. Blodgett (James F. Lincoln Arc Welding Foundation)


EN 199211:2004  Eurocode 2: Design of concrete structures  Part 11: General rules and rules for buildings


EN 199311:2005  Eurocode 3: Design of steel structures  Part 11: General rules and rules for buildings


EN 199318:2005  Eurocode 3: Design of steel structures  Part 18: Design of joints






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F_{b}
=


kN (in





per (2a) hold down bolts max. tension (in all bolts)


F_{1.bolt} = F_{b} /



kN





hold down bolt max. tension  in 1 bolt


F_{1.bolt} /(p*f^{2}/4) =


N/mm^{2}


f_{ydb}











N/mm^{2}







s_{c} =


MPa






per (3)





s_{c}


f_{cd}


f_{cd}
=


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











s_{sc} =

s_{c}*(Y  s) / Y =


MPa



















Design critical moment  at critical section










M_{Ed.plate} =

[(s_{sc}*s/2)*(s/3)+(s_{c}*s/2)*(s*2/3)]*B =


kN*m




M_{Ed.plate} =

(s_{c}*Y/2)*(sY/3)*B =


kN*m






















M_{C,Rd} = M_{pl,rd} =

(W_{pl} * f_{y})/ g_{M0}

Bending plastic design resistance


(4)













per EN 199311










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










W_{pl}
=

B*t_{pl}^{2}/4







(5)





(t_{pl} = base plate thickness)






















from (4) and (5)

=> [f_{y} * (B*t_{pl}^{2})/4]/ g_{M0} > M_{Ed.plate}






















M_{Ed.plate} =


kN*m












=> t_{pl} > sqrt[4 * M_{Ed.plate} * g_{M0 }/ (B * f_{y})]










=> t_{pl} >


mm

(with f_{y} =


N/mm^{2})



















References:













Design of Welded Structures  O. W. Blodgett (James F. Lincoln Arc Welding Foundation)


EN 199211:2004  Eurocode 2: Design of concrete structures  Part 11: General rules and rules for buildings


EN 199311:2005  Eurocode 3: Design of steel structures  Part 11: General rules and rules for buildings


EN 199318:2005  Eurocode 3: Design of steel structures  Part 18: Design of joints














