Evo Design - structural design Calculation No.    
                  001-BASEPLATE  
CALCULATION SHEET Project No.      
            onlinestructuraldesign.com 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 1992-1-1, EN 1993-1-1 and EN 1993-1-8  
              notatii baseplate.jpg          
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                    
nB = 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 1993-1-8  
Bolt class
            Section 3 Table 3.1  
                bolt classes recommended by the Eurocode;  
Bold yield strength             The National Annex may exclude certain bolt classes.  
fyb = N/mm2              
                   
Partial factor for steel bolts           per EN 1993-1-8  
gM2 =             Section 2 Table 2.1  
                partial safety factors recommended by the Eurocode;  
Bolt design strength fyd = fy / gM2         Numerical values for safety factors may be defined  
fyd-b = N/mm2           in the National Annex  
                         
Steel base plate characteristics                    
Steel grade
                     
                         
Steel yield strength                      
fy = N/mm2 for thickness under 40mm            
fy = N/mm2 for thickness between 40mm and 80mm            
                         
Partial factor for steel elements (in bending)         per EN 1993-1-1  
gM0 =             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 1992-1-1:2004 - Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings  
EN 1993-1-1:2005 - Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings  
EN 1993-1-8:2005 - Eurocode 3: Design of steel structures - Part 1-8: Design of joints  
 
Calculation No.    
 
CALCULATION SHEET Project No.      
            onlinestructuraldesign.com  
Project Title:   Calc. By Date Rev.  
                   
Subject   Ckd. By Date    
                   
                         
Steel modulus of elasticity       per EN 1993-1-1  
Es = 210000 N/mm2           Section 3.2.6 (1)  
                         
Concrete characteristics                
Concrete class
          per EN 1992-1-1:2004  
fck = MPa concrete characteristic cylinder strength   Section 3 Table 3.1  
                         
Partial factor for concrete for ultimate limit states       per EN 1992-1-1:2004  
                Section 2 Table 2.1N  
gc =             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 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  
                effects resulting from the way the load is applied  
                value may be found in the EC National Annex  
                         
Concrete modulus of elasticity                
Ecm = GPa for concrete class     per EN 1992-1-1:2004  
                Section 3.1.3 Table 3.1  
Aggregates =
          Section 3.1.3 (2)  
                Values in Table 3.1 are given for quartzite aggregates  
Ecm =   Values for limestone and sandstone are reduced  
Ecm = N/mm2           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. Mx and My 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 1992-1-1:2004 - Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings  
EN 1993-1-1:2005 - Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings  
EN 1993-1-8:2005 - Eurocode 3: Design of steel structures - Part 1-8: Design of joints  
 
Calculation No.    
 
CALCULATION SHEET Project No.      
            onlinestructuraldesign.com  
Project Title:   Calc. By Date Rev.  
                   
Subject   Ckd. By Date    
                   
                         
sc = N/HB+6*M/B*H2                    
sc = MPa         Baseplate small e.JPG          
sc fcd   fcd = MPa            
           
           
                         
Design of the Base Plate Thickness                    
Critical section location                    
s = mm                    
                         
smin = MPa                    
ssc = smin+(sc-smin)*(H - s) / H = MPa              
                         
Design critical moment - at critical section                  
MEd.plate = [(σsc*s/2)*(s/3)+(σc*s/2)*(s*2/3)]*B = kN*m            
                         
                         
 
Calculation No.    
 
CALCULATION SHEET Project No.      
            onlinestructuraldesign.com  
Project Title:   Calc. By Date Rev.  
                   
Subject   Ckd. By Date    
                   
        Base plate behaviour.JPG,notatii baseplate_2.jpg                
Three equations, three unknowns: Fb, Y, sc                  
(Axial force in steel hold down bolts, active area                  
under base plate, aximum pressure under base plate)                  
                         
                         
                         
1. Forces equilibrium                  
  Y*sc/2 - Fb -N = 0                    
  Fb + N = Y*sc*B/2 (1)                  
                         
2. Bending moment equilibrium                  
  Fb * f + (Fb + N) * (H/2 - Y/3) - N * e = 0              
  Fb = -N * (H/2 - Y/3 -e)/(H/2 - Y/3 + f)     (2a)        
  N = -Fb * (H/2 - Y/3 -e)/(H/2 - Y/3 + f)     (2)        
                         
3. Representing the elastic behaviour of the concrete              
support and the steel hold-down bolt:              
  a/b = eb/ec = (sb / Es) / (sc / Ec)                
  since Es = sb / es       modulus of elasticity of steel bolt  
    Ec = sc / ec       modulus of elasticity of concrete  
    nb =         number of steel hold down bolts  
    Ab = p*f2/4 = mm2   area of steel hold down bolts  
    sb = Fb / Ab                  
    n = Es / Ec =       modular ratio of elasticity, steel to concrete  
                         
  a/b = (N/Ab)/(sc*n) = N/(Ab*sc*n)              
                         
  From similar triangles     =>            
  a/b = (H/2-Y+f)/Y                  
                         
  => N/(Ab*sc*n) = (H/2-Y+f)/Y =>            
                         
  => sc = Fb * Y / (Ab * n *(H/2 - Y + f))     (3)        
                         
From (1), (2) and (3)                      
  -Fb * (H/2 - Y/3 -e)/(H/2 - Y/3 + b) + Fb = (Fb * Y2 * B) / [2 * Ab * n *(H/2 - Y + f)]      
                         
Solve for Y:                        
  Y3 + 3 * (e - H/2) * Y2 + [(6 * n * Ab)/B] * (f + e) * Y -  [(6 * n * Ab)/B] * (H/2 + f) * (f + e) = 0  
  or                      
  Y3 + K1 * Y2 + K2 * Y + K3 = 0  
  where                      
  K1 = 3 * (e - H/2) =              
  K2 = [(6 * n * Ab)/B] * (f + e) =              
  K3 = - K2 * (H/2 + f) =              
  Y = mm                  
                         
References:                        
Design of Welded Structures - O. W. Blodgett (James F. Lincoln Arc Welding Foundation)  
EN 1992-1-1:2004 - Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings  
EN 1993-1-1:2005 - Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings  
EN 1993-1-8:2005 - Eurocode 3: Design of steel structures - Part 1-8: Design of joints  
 
Calculation No.    
 
CALCULATION SHEET Project No.      
            onlinestructuraldesign.com  
Project Title:   Calc. By Date Rev.  
                   
Subject   Ckd. By Date    
                   
                         
Fb = kN (in       per (2a) hold down bolts max. tension (in all bolts)  
F1.bolt = Fb / kN         hold down bolt max. tension - in 1 bolt  
F1.bolt /(p*f2/4) = N/mm2 fyd-b      
          N/mm2            
sc = MPa           per (3)        
sc fcd   fcd = MPa   effective max. pressure under baseplate is compared   
  with the concrete design compressive strength  
   
              notatii baseplate_4.jpg          
Design of the Base Plate Thickness                    
Critical section location                    
s = mm              
                         
Stress at the critical section location                    
ssc = sc*(Y - s) / Y = MPa          
                         
Design critical moment - at critical section                  
MEd.plate = [(ssc*s/2)*(s/3)+(sc*s/2)*(s*2/3)]*B = kN*m      
MEd.plate = (sc*Y/2)*(s-Y/3)*B = kN*m                
                         
MC,Rd = Mpl,rd = (Wpl * fy)/ gM0 Bending plastic design resistance   (4)        
                per EN 1993-1-1  
                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                  
Wpl = B*tpl2/4             (5)        
(tpl = base plate thickness)                
                         
from (4) and (5) => [fy * (B*tpl2)/4]/ gM0 > MEd.plate                
                         
MEd.plate = kN*m                    
  => tpl > sqrt[4 * MEd.plate * gM0 / (B * fy)]                
  => tpl > mm (with fy = N/mm2)          
                         
References:                        
Design of Welded Structures - O. W. Blodgett (James F. Lincoln Arc Welding Foundation)  
EN 1992-1-1:2004 - Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings  
EN 1993-1-1:2005 - Eurocode 3: Design of steel structures - Part 1-1: General rules and rules for buildings  
EN 1993-1-8:2005 - Eurocode 3: Design of steel structures - Part 1-8: Design of joints