Evo Design  structural
engineering

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SAMPLE
CALCULATION


Project
Title:

Reinforced Concrete Column  interactive design
spreadsheet


Calc. By

Date

Rev.





MN

16.04.2014

0


Subject

RC Column  MN interaction diagram (EC2)


Checked By

Date






CN

16.04.2014





InputÂ

Output







Column dimensions

Moment capacity







Reinforcement







Materials (steel,
concrete, bolts)









RC Column  Axial
Force  Bending Moment Interaction

per EN
199211:2004*


Axial force 
bending moment interaction Â ultimate
limit state

Section 3















Column dimensions








b_{x} =

300

mm

(parameters that can not be







b_{z} =

300

mm

modified in the demo version)







A_{p} =


mm^{2}

(Element area = b_{x} * b_{y})





















Reinforcement








c =


mm

cover










d =


mm

(b_{x}
 c)























Tension side
reinforcement











f =Â


mm

bars diameter








n =



no of bars








A_{s.a} =


mm^{2}

area of
tension reinforcement


p_{reinf.a} =


%

percentage
of tension reinforcement




Compression side reinforcement


f =Â


mm

bars
diameter


n =



no of bars


A_{s.b} =


mm^{2}

area of
compression reinforcement


p_{reinf.b} =


%

percentage
of compression reinforcement


p_{reinf.a+b} =


%

element
percentage of reinforcement




Materials


Concrete class



per EN
199211:2004


f_{ck} =


MPa

concrete characteristicÂ

Section 3
Table 3.1



cylinder
strength


Reinforcement type





see reinforcement types here


f_{yk} =


MPa

reinforcement
yield strength




Partial factors for
materials for ultimate limit states

per EN
199211:2004



Section 2
Table 2.1N


g_{c} =



values for
Persistent & Transient design situations


g_{s} =



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










effectsresulting
from the way the load is applied










value may be
found in the EC National Annex


References:


EN 199311:2004  Eurocode 2: Design of concrete structures
 Part 11: General rules and rules for buildings






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Ultimate concrete compressive shortening strain


e_{cu3} =



per EN
199211:2004


1000

Section 3.1.3
Table 3.1












per EN
199211:2004










Section 3.1.7
(2) Figure 3.4










Bilinear
stressstrain relation























































































































Design reinforcement strength


f_{yd} =

f_{yk}
/ g_{s}


=


MPa

per EN
199211:2004



Section 3.1.7
Figure 3.8


Reinforcement ductility class





ductility
class A, B or C



defining
reinf. strain at maximum force


Characteristic reinf. strain at maximum force


e_{uk} =



per EN
199211:2004


100

Annex C  Table C1





function of
reinf. ductility class


Design reinf. strain at maximum force


e_{ud} =


* e_{uk}

=


%

per EN
199211:2004



Section 3.2.7
Note 1


The value of e_{ud} for use in a Country may be


found in its National Annex.


Â The recommended value
is 0.9*e_{uk}


Reinforcement
modulus of elasticity

per EN
199211:2004


E_{s} =

200

GPa

Section 3.2.7
(4)



The design
value of the modulus of elasticity


E_{s}
may be assumed to be 200 GPa


Stress strain relations for the design of crosssection










per EN
199211:2004










Section 3.1.7
(3)










A
rectangular stress distribution is assumed










l, defining the effective height
of the compression










zone and h, defining the effective strength
are










derived from
formulas 3.19, 3.20, 3.21 and 3.22







































l =




h =











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Points defining the axial force  bending moment interaction
diagram


Case 0

The entire
section is in tension


F_{s.a} =

 A_{s.a} * f_{yd}

=


kN



Reinforcement
has yielded.


F_{s.b} =

 A_{s.b} * f_{yd}

=


kN



Concrete
tensile capacity is ignored.


N_{cap} =

F_{s.a} + F_{s.b}

=


kN


M_{cap} =

F_{s.b} * (b_{x}/2  c)  F_{s.a} * (b_{x}/2  c)


M_{cap} =


kN*m
























Case 1






Concrete strain:

e_{cu3}



Concrete has
reached ultimate concrete design


Tension
reinforcement strain:

e_{s.a}

= e_{ud}

compressive
shortening strain andÂ reinforcement


x_{1} =Â

e_{cu3} * d / (e_{s.a} + e_{cu3})

=


mm



has reached
design reinforcement strain


a_{1} =Â

l *
x_{1}

=


mm


F_{b} =

h * a_{1} * b_{z} * f_{cd}

=


kN


F_{s.a} =

A_{s.a} * f_{yd}

=


kN


e_{s.b} =

e_{cu3} * (x_{1}  c) / x_{1}

=


/1000


Compression
side reinforcement strain


f_{yd}/E_{s} =


/1000

Reinforcement
yield strain


















F_{s.b} =

Â  f_{yd} * A_{s.b}


compression
side reinforcement is in tension and it has yielded


F_{s.b} =

Â  E_{s} * e_{s.b} * A_{s.b}


compression
side reinforcement is in tension and has not reached yield point


F_{s.b} =

Â + f_{yd} * A_{s.b}


compression
side reinforcement is in compression and it has yielded


F_{s.b} =

Â + E_{s} * e_{s.b} * A_{s.b}


compression
side reinforcement is in compression and has not reached yield point




F_{s.b} =


kN




N_{cap} =

F_{b} + F_{s.a} + F_{s.b}

=


kN


M_{cap} =

F_{b} * (b_{x}  a_{1})/2 + F_{s.b} * (b_{x}/2  c)  F_{s.a} * (b_{x}/2  c)


M_{cap} =


kN*m















Case 2

Concrete has
reached ultimate concrete design


Concrete strain:

e_{cu3}


Â compressive shortening strain andÂ reinforcement


Tension
reinforcement strain:

e_{s.a}

= f_{yd} / E_{s}

has reached
yield reinforcement strain



f_{yd}/E_{s} =


/1000




x_{2} =Â

e_{cu3} * d / (e_{s.a} + e_{cu3})

=


mm


a_{2} =Â

l *
x_{2}

=


mm


F_{b} =

h * a_{2} * b_{z} * f_{cd}

=


kN


F_{s.a} =

A_{s.a} * f_{yd}

=


kN


e_{s.b} =

e_{cu3} * (x_{2}  c) / x_{2}

=


/1000

Compression
reinforcement strain


f_{yd}/E_{s} =


/1000

Reinforcement
yield strain







F_{s.b} =

Â  f_{yd} * A_{s.b}


compression
side reinforcement is in tension and it has yielded



Â  E_{s} * e_{s.b} * A_{s.b}


compression
side reinforcement is in tension and has not reached yield point


Â + f_{yd} * A_{s.b}


compression
side reinforcement is in compression and it has yielded


Â + E_{s} * e_{s.b} * A_{s.b}


compression
side reinforcement is in compression and has not reached yield point




F_{s.b} =


kN




N_{cap} =

F_{b} + F_{s.a} + F_{s.b}

=


kN


M_{cap} =

F_{b} * (b_{x}  a_{2})/2 + F_{s.b} * (b_{x}/2  c)  F_{s.a} * (b_{x}/2  c)


M_{cap} =


kN*m























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Case 3

Concrete has
reached ultimate concrete design


Concrete strain:

e_{cu3}

Â compressive shortening strain andÂ the height


The entire section
is in compression

x_{3}
=Â

b_{x} =


mm

of the
compressed zone is equal with the section height




a_{3} =Â

l *
x_{3}

=


mm


F_{b} =

h * a_{3} * b_{z} * f_{cd}

=


kN


e_{s.b} =

e_{cu3} * (x_{3}  c) / x_{3}

=


/1000



Compression
side reinforcement strain


e_{s.a} =

e_{cu3} * (x_{3}  d) / x_{3}

=


/1000



Tension side
reinforcement strain


f_{yd}/E_{s} =


/1000






Reinforcement
yield strain




Compression side
reinf. is in compression



F_{s.b} =

Â + f_{yd} * A_{s.b}


compression
side reinforcement is in compression and it has yielded


F_{s.b} =

Â + E_{s} * e_{s.b} * A_{s.b}


compression
side reinforcement is in compression and has not reached yield point


F_{s.b} =


kN




Tension side reinf.
is in compression



F_{s.a} =

Â + f_{yd} * A_{s.a}


compression
side reinforcement is in compression and it has yielded


F_{s.a} =

Â + E_{s} * e_{s.a} * A_{s.a}


compression
side reinforcement is in compression and has not reached yield point


F_{s.a} =


kN


N_{cap} =

F_{b} + F_{s.a} + F_{s.b}

=


kN


M_{cap} =

F_{b} * (b_{x}  a_{3})/2 + F_{s.b} * (b_{x}/2  c)  F_{s.a} * (b_{x}/2  c)


M_{cap} =


kN*m















Case 4

The entire
section is in compression,


Concrete strain:

e_{cu3}

concrete has
reached ultimate concrete design


The entire section
is in compression

e_{s.b} =

e_{s.a} =

e_{cu3}



compressive
shortening strain andÂ reinforcement



is in
compresiion


f_{yd}/E_{s} =


/1000

Reinforcement
yield strain


F_{b} =

h * b_{x} * b_{z} * f_{cd}

=


kN




Compression side
reinf. is in compression



F_{s.b} =

Â + f_{yd} * A_{s.b}


compression
side reinforcement is in compression and it has yielded


F_{s.b} =

Â + E_{s} * e_{s.b} * A_{s.b}


compression
side reinforcement is in compression and has not reached yield point




F_{s.b} =


kN




Tension side reinf.
is in compression



F_{s.a} =

Â + f_{yd} * A_{s.a}


compression
side reinforcement is in compression and it has yielded


F_{s.a} =

Â + E_{s} * e_{s.a} * A_{s.a}


compression
side reinforcement is in compression and has not reached yield point




F_{s.a} =


kN


N_{cap} =

F_{b} + F_{s.a} + F_{s.b}

=


kN


M_{cap} =

F_{s.b} * (b_{x}/2  c)  F_{s.a} * (b_{x}/2  c)


M_{cap} =








Data for the MN
interaction graph:





N_{cap}

M_{cap}




kN

kN*m


Case 0




Case 1




Case 2




Case 3




Case 4













N_{eff}

M_{eff}


kN

kN*m


CO1




CO2




CO3















