Evo Design  structural
engineering

Calculation
No.



001RC COLUMN


INTERACTIVE ONLINE
CALCULATION SHEET

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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 Capacity  Axial Force Bending Moment


Checked By

Date




Interaction (ACI318)


CN

16.04.2014





InputÂ

Output



Column dimensions

Moment
capacity


Reinforcement

Column
interaction diagram


Materials (steel,
concrete, bolts)








RC Column Capacity
 Axial Force  Bending Moment Interaction (ACI 318)



Axial force  bending moment interaction Â ultimate limit state




Column dimensions








h =

15

in











b =

15

in

(parameters that can not be modified in the demo
version)





A_{g} = h * b =


in^{2}

RC Element Area
















Reinforcement








cover


in

cover to the center of the bars






d =


in

depth of bottom reinforcement (h cover)






d_{c} =


in

depth of top reinforcement (h cover)



















Tension side
reinforcement











#



bar size








n =



no of bars










A_{s} =


in^{2}

area of
tension reinforcement


r_{tens.reinf} =


%

percentage
of tension reinforcement




Compression side reinforcement


#



bar size


n =



no of bars




A_{s.b} =


in^{2}

area of
compression reinforcement


r_{comp.reinf} =


%

percentage
of compression reinforcement















A_{s.t} = A_{s} + A_{s.b} =


in^{2}

total area of
reinforcement








r =


%

element total percentage of reinforcement

per ACI 318










Section
10.9.1










Reinf
percentage should be between 0.01Ag and 0.08Ag


Confinement reinforcement (tied or spiral)




























Materials


Concrete






f_{c}' =


ksi

concrete characteristicÂ




cylinder
strength


Reinforcement type





see reinforcement types here


Grade













f_{y} =


ksi

reinforcement
yield strength















References:


ACI31805  Building code requirements for structural
concrete






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Reinforcement
modulus of elasticity

per ACI 318


E_{s} =


ksi






Section 8.5.2










Modulus of
elasticity of reinforcement


Yield reinforcement
strain:











f_{y} / E_{s} =















The relationship
between concrete compressive stress and concrete strain is satisfied

per ACI
31805


by an equivalent
rectangular concrete stress distribution defined by a 0.85*f_{c}' uniform

Sections
10.2.6 and 10.2.7


stress over an
equivalent compression zone bounded by edges of the cross section and



a straight line
located parallel to the neutral axis at a distanceÂ a = b_{1}*cÂ from the fiber ofÂ



maximum compressive
strain.








Section strength reduction factor


f =Â

0.90

For tension controlled sections



per ACI
31805



0.70

Compression controlled section with spiral
reinforcement


Section 9.3



0.65

Compression controlled section other reinforced
members


Â Values of f strength reduction factor
















Maximum usable strain at extreme concrete compression fiber


is

0.003







per ACI
31805










Section
10.2.3










Maximum
usable strain at extreme concrete










compression
fiber shall be assumed equal to 0.003;










The relation
between concrete compressive stress andÂ










concrete
strain is assumed rectangular










Section
10.2.7.1










0.85f_{c}' value uniformly
distributed over an equivalent










compression
zone bounded by edges of the cross section










and
a straigth line located parale to the neutral axis at a










distance
a = b_{1}*c from the fiber of max. compression strain









































b_{1} =



factor relating depth of equivalent


per ACI
31805





rectangular compressive stress block


Section
10.2.7.3





to neutral axis depth


between 2500
and 4000 psi b1 = 0.85, above 4000 b_{1} will










be reduced
lineary at a rate of 0.05 per 1000 psi but not










lower than 0.65




a =

b_{1} * c


depth of equivalent rectangular


Section
10.2.7.1





stress block















Section
10.2.3



stress in
reinforcement below f_{y} shall be taken as E_{s} times



steel
strain. For strains greater than that correspondingÂ










to fy,
stress in reinforcement shall be considered










independent
of strain and equal to f_{y}.


















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Point 1  Pure
compression



f =Â


compression controlled section



Section
strength reduction factor















fP_{n,max} =Â


f[0.85f_{c}'(A_{g}A_{st})+f_{y}A_{st}]




per ACI 318









eq. 101 and
102


fP_{n,max} =Â


kips






Maximum
allowable value of the nominal axial strength










of cross
section multipliedÂ by the strength
reduction factor


Point 2  f_{s} = 0


Concrete strain:






Concrete has
reached ultimate concrete design


The neutral axis is
located in the center of the bottom reinforcement


compressive
shortening strain andÂ f_{s} = 0


c =

dÂ =


in





Neutral axis
location  in this case in the center of










the bottom
reinforcement


Top reinforcement
strain (compression):


*(cd_{c})/c=









Yield reinforcement
strain:




=>
















f =Â


compression controlled section



Section
strength reduction factor















a =

b_{1} * c =


in

depth of equivalent rectangular










stress block






fP_{n} =Â

f
*Â [ 0.85* f_{c}' * a * b +


A_{s.b}]





















fP_{n} =Â


kips
























fM_{n} =Â

f
*Â [(0.85* f_{c}' * a * b) * (h/2  a/2) +


A_{s.b} ) * (h/2  d_{c} )]


















fM_{n} =Â


ft kips
























Point 3  f_{s} = 0.5 * f_{y}


Concrete strain:






Concrete has
reached ultimate concrete design




Â compressive shortening strain andÂ f_{s} = 0.5 * f_{y}


Bottom
reinforcement strain (tension):

e_{t} = ( 0.5 * f_{y} ) / E_{s} =









c =


in






From the
relation [c / (d  c)] = 0.003 / e_{t}















Top reinforcement
strain (compression):


*(cd_{c})/c =









Yield reinforcement
strain:




=>
















f =Â


compression controlled section




Section
strength reduction factor















a =

b_{1} * c =


in

depth of equivalent rectangular










stress block






fP_{n} =Â

f
*Â [ 0.85* f_{c}' * a * b +


A_{s.b} Â e_{t} * E_{s} * A_{s} ]



















fP_{n} =Â


kips
























fM_{n} =Â

f
*Â [(0.85* f_{c}' * a * b) * (h/2  a/2) +


A_{s.b} ) * (h/2  d_{c} ) + e_{t} * E_{s} * A_{s} * (d  h/2)]
















fM_{n} =Â


ft kips
































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Point 4  f_{s} =Â f_{y} (Balanced point)

per ACI
31805


Concrete strain:






Section
10.3.2




Concrete has
reached ultimate concrete design


Bottom
reinforcement strain (tension):

e_{t} = f_{y} / E_{s} =




Â compressive shortening strain andÂ tension reinforcement










reaches the
strain corresponding to f_{y}Â (f_{s} = f_{y})















c =


in






From the
relation [c / (d  c)] = 0.003 / e_{t}















Top reinforcement
strain (compression):


*(cd_{c})/c =









Yield reinforcement
strain:




=>
















f =Â


compression controlled section



Section
strength reduction factor















a =

b_{1} * c =


in

depth of equivalent rectangular










stress block






fP_{n} =Â

f
*Â [ 0.85* f_{c}' * a * b +


A_{s.b} Â f_{y} * A_{s} ]



















fP_{n} =Â


kips
























fM_{n} =Â

f
*Â [(0.85* f_{c}' * a * b) * (h/2  a/2) +


A_{s.b} ) * (h/2  d_{c} ) + f_{y} * A_{s} * (d  h/2)]
















fM_{n} =Â


ft kips





































Point 4b  f_{s} =Â f_{y} Transition from Compression controlled section to Tension
Controlled

per ACI
31805


Concrete strain:






Section
9.3.2.2




For sections
in which the net tensile strain at nominal


Bottom
reinforcement strain (tension):

e_{t} = f_{y} / E_{s} =




strength e_{t} is between the limits for compression










controlled
ans tension controlled sections f will be










linearly
increased from that for compression controlled to 0.9












c =


in






From the
relation [c / (d  c)] = 0.003 / e_{t}















Top reinforcement
strain (compression):


*(cd_{c})/c =









Yield reinforcement
strain:




=>
















f =Â


transition from compression controlledÂ to tension controlled section

Section
strength reduction factor















a =

b_{1} * c =


in

depth of equivalent rectangular










stress block






fP_{n} =Â

f
*Â [ 0.85* f_{c}' * a * b +


A_{s.b} Â f_{y} * A_{s} ]



















fP_{n} =Â


kips
























fM_{n} =Â

f
*Â [(0.85* f_{c}' * a * b) * (h/2  a/2) +


A_{s.b} ) * (h/2  d_{c} ) + f_{y} * A_{s} * (d  h/2)]
















fM_{n} =Â


ft kips
































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Point 4c  f_{s} =Â f_{y} Transition from Compression controlled section to Tension
Controlled

per ACI
31805


Concrete strain:






Section
9.3.2.2




Concrete has
reached ultimate concrete design


Bottom
reinforcement strain (tension):

e_{t} = f_{y} / E_{s} =




compressive
shortening strain andÂ tension
reinforcement










is in
transition from tension controlled to tensin controlled















c =


in






From the
relation [c / (d  c)] = 0.003 / e_{t}















Top reinforcement
strain (compression):


*(cd_{c})/c =









Yield reinforcement
strain:




=>
















f =Â


transition from compression controlledÂ to tension controlled section

Section
strength reduction factor















a =

b_{1} * c =


in

depth of equivalent rectangular










stress block






fP_{n} =Â

f
*Â [ 0.85* f_{c}' * a * b +


A_{s.b} Â f_{y} * A_{s} ]



















fP_{n} =Â


kips
























fM_{n} =Â

f
*Â [(0.85* f_{c}' * a * b) * (h/2  a/2) +


A_{s.b} ) * (h/2  d_{c} ) + f_{y} * A_{s} * (d  h/2)]
















fM_{n} =Â


ft kips





































Point 5  e_{t} =Â 0.005  tension
controlled section


Concrete strain:






Concrete has
reached ultimate concrete design




compressive
shortening strain andÂ et has reached
0.005


Bottom
reinforcement strain (tension):

e_{t} =

0.0050



corresponding
to f = 0.9 (tension
controlled section)















c =


in






From the
relation [c / (d  c)] = 0.003 / e_{t}















Top reinforcement
strain (compression):


*(cd_{c})/c =









Yield reinforcement
strain:




=>
















f =Â


tension controlled section




Section
strength reduction factor















a =

b_{1} * c =


in

depth of equivalent rectangular










stress block






fP_{n} =Â

f
*Â [ 0.85* f_{c}' * a * b +


A_{s.b} Â f_{y} * A_{s} ]



















fP_{n} =Â


kips
























fM_{n} =Â

f
*Â [(0.85* f_{c}' * a * b) * (h/2  a/2) +


A_{s.b} ) * (h/2  d_{c} ) + f_{y} * A_{s} * (d  h/2)]
















fM_{n} =Â


ft kips


























































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Point 6  Pure Bending


Concrete strain:






Concrete has
reached ultimate concrete design




compressive
shortening strain andÂ et has reached
0.005


Bottom
reinforcement strain (tension):

e_{t} =




corresponding
to f = 0.9 (tension
controlled section)


c =


in






From the
relation [c / (d  c)] = 0.003 / e_{t}















Top reinforcement
strain (compression):


*(cd_{c})/c =









Yield reinforcement
strain:




=>
















f =Â


tension controlled section




Section
strength reduction factor















a =

b_{1} * c =


in

depth of equivalent rectangular










stress block






fP_{n} =Â

f
*Â [ 0.85* f_{c}' * a * b +


A_{s.b} Â f_{y} * A_{s} ]



















fP_{n} =Â


kips
























fM_{n} =Â

f
*Â [(0.85* f_{c}' * a * b) * (h/2  a/2) +


A_{s.b} ) * (h/2  d_{c} ) + f_{y} * A_{s} * (d  h/2)]
















fM_{n} =Â


ft kips
























Point 7  Maximum tension


f =Â


tension controlled section




Section
strength reduction factor















fP_{n} =Â

Â =  f * f_{y} * [A_{s.b} + A_{s} ]























fP_{n} =Â


kips
























fM_{n} =Â

0.00

ft kips
























Data
for the MN interaction graph:












N_{cap}

M_{cap}











Point 1


0.00











Point 2













Point 3













Point 4













Point 4b













Point 4c













Point 5













Point 6













Point 7


0.00

























N_{eff}

M_{eff}











CO1













CO2













CO3










































