Evo Design - structural engineering Calculation No.    
001-RC COLUMN  
INTERACTIVE ONLINE CALCULATION SHEET Project No.      
            onlinestructuraldesign.com 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    
   
Input  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 -  ultimate limit state  
   
Column dimensions              
h = 15 in                    
b = 15 in (parameters that can not be modified in the demo version)        
Ag = h * b = in2 RC Element Area              
               
Reinforcement              
cover in cover to the center of the bars          
d = in depth of bottom reinforcement (h- cover)          
dc = in depth of top reinforcement (h- cover)          
                         
Tension side reinforcement                    
#
  bar size              
n =   no of bars              
   
As = in2 area of tension reinforcement  
rtens.reinf = % percentage of tension reinforcement  
   
Compression side reinforcement  
#
  bar size  
n =   no of bars  
   
As.b = in2 area of compression reinforcement  
rcomp.reinf = % percentage of compression reinforcement  
                         
As.t = As + As.b = in2 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          
fc' =
ksi concrete characteristic     
  cylinder strength  
Reinforcement type  
    see reinforcement types here  
Grade
                     
fy = ksi reinforcement yield strength  
                         
References:  
ACI318-05 - Building code requirements for structural concrete  
 
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Project Title:   Calc. By Date Rev.  
                   
Subject   Ckd. By Date    
               
                         
Reinforcement modulus of elasticity per ACI 318  
Es = ksi           Section 8.5.2  
                Modulus of elasticity of reinforcement  
Yield reinforcement strain:                    
fy / Es =                      
   
The relationship between concrete compressive stress and concrete strain is satisfied per ACI 318-05  
by an equivalent rectangular concrete stress distribution defined by a 0.85*fc' 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 distance  a = b1*c  from the fiber of     
maximum compressive strain.          
   
Section strength reduction factor  
f =  0.90 For tension controlled sections     per ACI 318-05  
  0.70 Compression controlled section with spiral reinforcement   Section 9.3  
  0.65 Compression controlled section other reinforced members    Values of f strength reduction factor    
                         
Maximum usable strain at extreme concrete compression fiber  
is 0.003             per ACI 318-05  
              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 and   
                concrete strain is assumed rectangular  
                Section 10.2.7.1  
                0.85fc' 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 = b1*c from the fiber of max. compression strain  
                         
                         
                         
b1 =   factor relating depth of equivalent   per ACI 318-05  
      rectangular compressive stress block   Section 10.2.7.3  
      to neutral axis depth   between 2500 and 4000 psi b1 = 0.85, above 4000 b1 will  
                be reduced lineary at a rate of 0.05 per 1000 psi but not  
                lower than 0.65      
a = b1 * c   depth of equivalent rectangular   Section 10.2.7.1  
      stress block            
                Section 10.2.3  
  stress in reinforcement below fy shall be taken as Es times  
  steel strain. For strains greater than that corresponding   
                to fy, stress in reinforcement shall be considered  
                independent of strain and equal to fy.  
   
   
   
   
 
 
 
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Project Title:   Calc. By Date Rev.  
                   
Subject   Ckd. By Date    
               
   
Point 1 - Pure compression    
f =  compression controlled section     Section strength reduction factor  
                         
fPn,max =  f[0.85fc'(Ag-Ast)+fyAst]       per ACI 318  
              eq. 10-1 and 10-2  
fPn,max =  kips           Maximum allowable value of the nominal axial strength  
                of cross section multiplied  by the strength reduction factor  
Point 2 - fs = 0  
Concrete strain:         Concrete has reached ultimate concrete design  
The neutral axis is located in the center of the bottom reinforcement   compressive shortening strain and  fs = 0  
c = d  = in         Neutral axis location - in this case in the center of  
                the bottom reinforcement  
Top reinforcement strain (compression): *(c-dc)/c=              
Yield reinforcement strain:     =>  
                         
f =  compression controlled section     Section strength reduction factor  
                         
a = b1 * c = in depth of equivalent rectangular          
        stress block          
fPn =  f *  [ 0.85* fc' * a * b + As.b]              
fPn =  kips                    
fMn =  f *  [(0.85* fc' * a * b) * (h/2 - a/2) + As.b ) * (h/2 - dc )]        
                         
fMn =  ft -kips                    
Point 3 - fs = 0.5 * fy  
Concrete strain:         Concrete has reached ultimate concrete design  
     compressive shortening strain and  fs = 0.5 * fy  
Bottom reinforcement strain (tension): et = ( 0.5 * fy ) / Es =              
c = in           From the relation [c / (d - c)] = 0.003 / et  
Top reinforcement strain (compression): *(c-dc)/c =              
Yield reinforcement strain:     =>  
f =  compression controlled section       Section strength reduction factor  
                         
a = b1 * c = in depth of equivalent rectangular          
        stress block          
fPn =  f *  [ 0.85* fc' * a * b + As.b -  et * Es * As ]          
                         
fPn =  kips                    
                         
fMn =  f *  [(0.85* fc' * a * b) * (h/2 - a/2) + As.b ) * (h/2 - dc ) + et * Es * As * (d - h/2)]    
                         
fMn =  ft -kips                    
 
 
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CALCULATION SHEET Project No.      
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Project Title:   Calc. By Date Rev.  
                   
Subject   Ckd. By Date    
               
   
Point 4 - fs =  fy (Balanced point) per ACI 318-05  
Concrete strain:         Section 10.3.2  
    Concrete has reached ultimate concrete design  
Bottom reinforcement strain (tension): et = fy / Es =      compressive shortening strain and  tension reinforcement  
                reaches the strain corresponding to fy  (fs = fy)  
                         
c = in           From the relation [c / (d - c)] = 0.003 / et  
                         
Top reinforcement strain (compression): *(c-dc)/c =              
Yield reinforcement strain:     =>  
                         
f =  compression controlled section     Section strength reduction factor  
                         
a = b1 * c = in depth of equivalent rectangular          
        stress block          
fPn =  f *  [ 0.85* fc' * a * b + As.b -  fy * As ]          
                         
fPn =  kips                    
                         
fMn =  f *  [(0.85* fc' * a * b) * (h/2 - a/2) + As.b ) * (h/2 - dc ) + fy * As * (d - h/2)]    
                         
fMn =  ft -kips                    
                         
                         
Point 4b - fs =  fy Transition from Compression controlled section to Tension Controlled per ACI 318-05  
Concrete strain:         Section 9.3.2.2  
    For sections in which the net tensile strain at nominal  
Bottom reinforcement strain (tension): et = fy / Es =     strength et 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 / et  
                         
Top reinforcement strain (compression): *(c-dc)/c =              
Yield reinforcement strain:     =>  
                         
f =  transition from compression controlled  to tension controlled section Section strength reduction factor  
                         
a = b1 * c = in depth of equivalent rectangular          
        stress block          
fPn =  f *  [ 0.85* fc' * a * b + As.b -  fy * As ]          
                         
fPn =  kips                    
                         
fMn =  f *  [(0.85* fc' * a * b) * (h/2 - a/2) + As.b ) * (h/2 - dc ) + fy * As * (d - h/2)]    
                         
fMn =  ft -kips                    
                         
 
 
 
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Project Title:   Calc. By Date Rev.  
                   
Subject   Ckd. By Date    
               
                         
Point 4c - fs =  fy Transition from Compression controlled section to Tension Controlled per ACI 318-05  
Concrete strain:         Section 9.3.2.2  
    Concrete has reached ultimate concrete design  
Bottom reinforcement strain (tension): et = fy / Es =     compressive shortening strain and  tension reinforcement  
                is in transition from tension controlled to tensin controlled  
                         
c = in           From the relation [c / (d - c)] = 0.003 / et  
                         
Top reinforcement strain (compression): *(c-dc)/c =              
Yield reinforcement strain:     =>  
                         
f =  transition from compression controlled  to tension controlled section Section strength reduction factor  
                         
a = b1 * c = in depth of equivalent rectangular          
        stress block          
fPn =  f *  [ 0.85* fc' * a * b + As.b -  fy * As ]          
                         
fPn =  kips                    
                         
fMn =  f *  [(0.85* fc' * a * b) * (h/2 - a/2) + As.b ) * (h/2 - dc ) + fy * As * (d - h/2)]    
                         
fMn =  ft -kips                    
                         
                         
Point 5 - et =  0.005 - tension controlled section  
Concrete strain:         Concrete has reached ultimate concrete design  
    compressive shortening strain and  et has reached 0.005  
Bottom reinforcement strain (tension): et = 0.0050     corresponding to f = 0.9 (tension controlled section)  
                         
c = in           From the relation [c / (d - c)] = 0.003 / et  
                         
Top reinforcement strain (compression): *(c-dc)/c =              
Yield reinforcement strain:     =>  
                         
f =  tension controlled section       Section strength reduction factor  
                         
a = b1 * c = in depth of equivalent rectangular          
        stress block          
fPn =  f *  [ 0.85* fc' * a * b + As.b -  fy * As ]          
                         
fPn =  kips                    
                         
fMn =  f *  [(0.85* fc' * a * b) * (h/2 - a/2) + As.b ) * (h/2 - dc ) + fy * As * (d - h/2)]    
                         
fMn =  ft -kips                    
                         
                         
                         
 
 
 
Calculation No.    
 
CALCULATION SHEET Project No.      
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Project Title:   Calc. By Date Rev.  
                   
Subject   Ckd. By Date    
               
                         
Point 6 - Pure Bending  
Concrete strain:         Concrete has reached ultimate concrete design  
    compressive shortening strain and  et has reached 0.005  
Bottom reinforcement strain (tension): et =     corresponding to f = 0.9 (tension controlled section)  
c = in           From the relation [c / (d - c)] = 0.003 / et  
                         
Top reinforcement strain (compression): *(c-dc)/c =              
Yield reinforcement strain:     =>  
                         
f =  tension controlled section       Section strength reduction factor  
                         
a = b1 * c = in depth of equivalent rectangular          
        stress block          
fPn =  f *  [ 0.85* fc' * a * b + As.b -  fy * As ]          
                         
fPn =  kips                    
                         
fMn =  f *  [(0.85* fc' * a * b) * (h/2 - a/2) + As.b ) * (h/2 - dc ) + fy * As * (d - h/2)]    
                         
fMn =  ft -kips                    
                         
Point 7 - Maximum tension  
f =  tension controlled section       Section strength reduction factor  
                         
fPn =   = - f * fy * [As.b + As ]                  
       
               
fPn =  kips                    
                         
fMn =  0.00 ft -kips                    
                         
Data for the M-N interaction graph:                    
  Ncap Mcap                    
Point 1 0.00                    
Point 2                    
Point 3                    
Point 4                    
Point 4b                    
Point 4c                    
Point 5                    
Point 6                    
Point 7 0.00                    
                         
  Neff Meff                    
CO1                    
CO2                    
CO3