Evo Design - structural engineering Calculation No.    
001-RC Column  
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 - M-N interaction diagram (EC2)   Checked By Date    
      CN 16.04.2014    
   
Input  Output            
Column dimensions Moment capacity            
Reinforcement            
Materials (steel, concrete, bolts)            
   
RC Column - Axial Force - Bending Moment Interaction per EN 1992-1-1:2004*  
Axial force - bending moment interaction -  ultimate limit state Section 3  
              column size and reinf.jpg          
Column dimensions              
bx = 300 mm (parameters that can not be            
bz = 300 mm modified in the demo version)            
Ap = mm2 (Element area = bx * by)              
                         
Reinforcement              
c = mm cover                  
d = mm (bx - c)                  
                         
Tension side reinforcement                    
f =  mm bars diameter              
n =   no of bars              
As.a = mm2 area of tension reinforcement  
preinf.a = % percentage of tension reinforcement  
   
Compression side reinforcement  
f =  mm bars diameter  
n =   no of bars  
As.b = mm2 area of compression reinforcement  
preinf.b = % percentage of compression reinforcement  
preinf.a+b = % element percentage of reinforcement  
   
Materials  
Concrete class
  per EN 1992-1-1:2004  
fck = MPa concrete characteristic  Section 3 Table 3.1  
  cylinder strength  
Reinforcement type  
    see reinforcement types here  
fyk = MPa reinforcement yield strength  
   
Partial factors for materials for ultimate limit states per EN 1992-1-1:2004  
  Section 2 Table 2.1N  
gc =   values for Persistent & Transient design situations  
gs =   recommended by the Eurocode; values to be used  
  may be found in the Eurocode National Annexes  
Design compressive concrete strength per EN 1992-1-1:2004  
  Section 3.1.6 & Formula 3.15  
acc =             Coefficient taking account of long term effects  
fcd = acc * fck / gc = 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 1993-1-1:2004 - Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings  
 
Calculation No.    
 
CALCULATION SHEET Project No.      
            onlinestructuraldesign.com  
Project Title:   Calc. By Date Rev.  
                   
Subject   Ckd. By Date    
                   
   
Ultimate concrete compressive shortening strain  
ecu3 = Fig. 3.4 - EC2.JPG per EN 1992-1-1:2004  
1000 Section 3.1.3 Table 3.1  
   
                per EN 1992-1-1:2004  
                Section 3.1.7 (2) Figure 3.4  
                Bi-linear stress-strain relation  
                         
                         
                         
                         
                         
                         
                         
                         
                         
Design reinforcement strength  
fyd = fyk / gs   = MPa per EN 1992-1-1:2004  
  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  
euk =   per EN 1992-1-1:2004  
100 Annex C - Table C1      
  function of reinf. ductility class  
Design reinf. strain at maximum force  
eud = * euk = % per EN 1992-1-1:2004  
  Section 3.2.7 Note 1  
The value of eud for use in a Country may be  
found in its National Annex.  
 The recommended value is 0.9*euk  
Reinforcement modulus of elasticity per EN 1992-1-1:2004  
Es = 200 GPa Section 3.2.7 (4)  
  The design value of the modulus of elasticity  
Es may be assumed to be 200 GPa  
Stress strain relations for the design of cross-section  
Fig 3.5 - EC2.JPG               per EN 1992-1-1:2004  
                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 =  
 
 
 
Calculation No.    
 
CALCULATION SHEET Project No.      
            onlinestructuraldesign.com  
Project Title:   Calc. By Date Rev.  
                   
Subject   Ckd. By Date    
                   
   
Points defining the axial force - bending moment interaction diagram  
Case 0 The entire section is in tension  
Fs.a = - As.a * fyd = kN     Reinforcement has yielded.  
Fs.b = - As.b * fyd = kN     Concrete tensile capacity is ignored.  
Ncap = Fs.a + Fs.b = kN  
Mcap = Fs.b * (bx/2 - c) - Fs.a * (bx/2 - c)  
Mcap = kN*m                    
                         
Case 1          
Concrete strain: ecu3     Concrete has reached ultimate concrete design  
Tension reinforcement strain: es.a = eud compressive shortening strain and  reinforcement  
x1 =  ecu3 * d / (-es.a + ecu3) = mm     has reached design reinforcement strain  
a1 =  l * x1 = mm  
Fb = h * a1 * bz * fcd = kN  
Fs.a = -As.a * fyd = kN  
es.b = ecu3 * (x1 - c) / x1 = /1000   Compression side reinforcement strain  
fyd/Es = /1000 Reinforcement yield strain  
                         
 
Fs.b =  - fyd * As.b compression side reinforcement is in tension and it has yielded  
Fs.b =  - Es * es.b * As.b compression side reinforcement is in tension and has not reached yield point  
Fs.b =  + fyd * As.b compression side reinforcement is in compression and it has yielded  
Fs.b =  + Es * es.b * As.b compression side reinforcement is in compression and has not reached yield point  
   
Fs.b = kN  
   
Ncap = Fb + Fs.a + Fs.b = kN  
Mcap = Fb * (bx - a1)/2 + Fs.b * (bx/2 - c) - Fs.a * (bx/2 - c)  
Mcap = kN*m  
                         
Case 2 Concrete has reached ultimate concrete design  
Concrete strain: ecu3    compressive shortening strain and  reinforcement  
Tension reinforcement strain: es.a = -fyd / Es has reached yield reinforcement strain  
  fyd/Es = /1000  
   
x2 =  ecu3 * d / (-es.a + ecu3) = mm  
a2 =  l * x2 = mm  
Fb = h * a2 * bz * fcd = kN  
Fs.a = -As.a * fyd = kN  
es.b = ecu3 * (x2 - c) / x2 = /1000 Compression reinforcement strain  
fyd/Es = /1000 Reinforcement yield strain  
   
 
Fs.b =  - fyd * As.b compression side reinforcement is in tension and it has yielded  
   - Es * es.b * As.b compression side reinforcement is in tension and has not reached yield point  
 + fyd * As.b compression side reinforcement is in compression and it has yielded  
 + Es * es.b * As.b compression side reinforcement is in compression and has not reached yield point  
   
Fs.b = kN  
   
Ncap = Fb + Fs.a + Fs.b = kN  
Mcap = Fb * (bx - a2)/2 + Fs.b * (bx/2 - c) - Fs.a * (bx/2 - c)  
Mcap = kN*m  
                         
 
 
 
Calculation No.    
 
CALCULATION SHEET Project No.      
            onlinestructuraldesign.com  
Project Title:   Calc. By Date Rev.  
                   
Subject   Ckd. By Date Rev.  
                   
   
Case 3 Concrete has reached ultimate concrete design  
Concrete strain: ecu3  compressive shortening strain and  the height  
The entire section is in compression x3 =  bx = mm of the compressed zone is equal with the section height  
   
a3 =  l * x3 = mm  
Fb = h * a3 * bz * fcd = kN  
es.b = ecu3 * (x3 - c) / x3 = /1000     Compression side reinforcement strain  
es.a = ecu3 * (x3 - d) / x3 = /1000     Tension side reinforcement strain  
fyd/Es = /1000           Reinforcement yield strain  
   
Compression side reinf. is in compression  
Fs.b =  + fyd * As.b compression side reinforcement is in compression and it has yielded  
Fs.b =  + Es * es.b * As.b compression side reinforcement is in compression and has not reached yield point  
Fs.b = kN  
   
Tension side reinf. is in compression  
Fs.a =  + fyd * As.a compression side reinforcement is in compression and it has yielded  
Fs.a =  + Es * es.a * As.a compression side reinforcement is in compression and has not reached yield point  
Fs.a = kN  
Ncap = Fb + Fs.a + Fs.b = kN  
Mcap = Fb * (bx - a3)/2 + Fs.b * (bx/2 - c) - Fs.a * (bx/2 - c)  
Mcap = kN*m  
                         
Case 4 The entire section is in compression,  
Concrete strain: ecu3 concrete has reached ultimate concrete design  
The entire section is in compression es.b = es.a = ecu3     compressive shortening strain and  reinforcement  
  is in compresiion  
fyd/Es = /1000 Reinforcement yield strain  
Fb = h * bx * bz * fcd = kN  
   
Compression side reinf. is in compression  
Fs.b =  + fyd * As.b compression side reinforcement is in compression and it has yielded  
Fs.b =  + Es * es.b * As.b compression side reinforcement is in compression and has not reached yield point  
   
Fs.b = kN  
   
Tension side reinf. is in compression  
Fs.a =  + fyd * As.a compression side reinforcement is in compression and it has yielded  
Fs.a =  + Es * es.a * As.a compression side reinforcement is in compression and has not reached yield point  
   
Fs.a = kN  
Ncap = Fb + Fs.a + Fs.b = kN  
Mcap = Fs.b * (bx/2 - c) - Fs.a * (bx/2 - c)  
Mcap =
kN*m
 
     
 
Data for the M-N interaction graph:  
   
  Ncap Mcap    
  kN kN*m  
Case 0  
Case 1  
Case 2  
Case 3  
Case 4  
       
       
  Neff Meff  
kN kN*m  
CO1  
CO2  
CO3