Evo Design - structural engineering Calculation No.        
001-WOOD COLUMN  
CALCULATION SHEET Project No.      
            onlinestructuraldesign.com SAMPLE CALCULATION  
Project Title: Wood element - interactive design spreadsheet   Calc. By Date Rev.  
                  MN 16.04.2014 0  
Subject Wood Column Subjected to Combined Compression and Bending Checked By Date    
                  CN 16.04.2014    
                         
Input Output                
Element section and dimensions Element verification                
Material Element stability                
Loads                  
                             
Wood Column Subjected to Combined Compression and Bending   per EN 1992-1-1:2004* & EN 338  
                         
Maximum working loads (Ultimate Limit State)                  
FEd= kN*m axial force (compression)                  
My,Ed= kN*m bending moment y-y                  
Mz,Ed= kN*m bending moment z-z                  
                             
Element dimensions - Rectangular cross section                
Ly.b = 300 cm element buckling length about y-y                
Lz.b = 300 cm element buckling length about z-z                
h = 20 cm height                      
d = 10 cm width (parameters that can not be modified in the demo version)          
                             
Section Properties                  
A = d*h = cm2 section area            
IY = d*h3/12 = cm4 moment of inertia about y-y axis            
Iz = d3*h/12 = cm4 moment of inertia about z-z axis            
iy = (Iy/A)0.5 = cm radius of gyration about y-y            
iz = (Iz/A)0.5 = cm radius of gyration about z-z            
                             
ly = Ly.b / iy =   slenderness ratio corresponding to bending about the y-axis      
lz = Lz.b / iz =   slenderness ratio corresponding to bending about the z-axis      
                             
Material characteristics     per EN 338-97 - Table 1      
Wood strength class:
                   
fm,k = N/mm2           Characteristic bending strength  
fc,0,k = kN/mm2           Characteristic compressive strength      
E0,05 = kN/mm2           Fifth percentile value of modulus of elasticity  
gm =             per EN 1995-1-1 - Table 2.3  
                1.3 for solid timber, 1.25 for glued laminated timber  
kh = min( (150/h)0.2 ; 1.3) =       per EN 1995-1-1 - Section 3.2 (3), formula (3.1)  
            for timber with density less than 700 kg/m3 and  
                h < 150mm the characteristic valus of fm,k and  
                ft,0,k may be increased by the factor kh  
kmod =             per EN 1995-1-1 - Table 3.1  
                Load duration classes per EN 1995-1-1  
                Section 2.3.1.2 - Table 2.1 and 2.2  
                Service classes per EN 1995-1-1 - Section 2.3.1.3      
                             
fc.0.d = kmod * fc,0,k / gm =   N/mm2   design compressive strength and      
fm.y.d = fm.y.d = kmod *kh * fm,k / gm = N/mm2   design bending strength about y and z axis      
                per EN 1995-1-1 - Section 2.4.1, formula (2.14)      
                             
References:      
EN 1995-1-1:2004 - Eurocode 5: Design of timber structures - Part 1-1: Common rules and rules for buildings          
EN 338 : 2003 - Structural Timber; Strength Classes                    
     
Calculation No.        
     
CALCULATION SHEET Project No.          
            onlinestructuraldesign.com      
Project Title:   Calc. By Date Rev.      
                       
Subject   Ckd. By Date        
                       
                             
sc,0,d = F,Ed / A = N/mm2       Design compressive stress      
sm.y.d = My,Ed * (h/2) / Iy = N/mm2       Design bending stress about the principal y axis      
sm.z.d = Mz,Ed * (d/2) / Iz = N/mm2       Design bending stress about the principal z axis      
                             
km = 0.7 for rectangular sections       per EN 1995-1-1 - Section 6.1.6 (2)      
                             
Stresses verification - Combined bending and axial compression   per EN 1995-1-1 - Section 6.2.4      
Check on for y-y axis                          
(sc,0,d / fc,0,d )2 + ( sm.y.d / fm.y.d ) + km * ( sm.z.d / fm.z.d ) = per EN 1995-1-1 - Section 6.2.4, formula (6.19)      
                       
Check on for z-z axis                          
(sc,0,d / fc,0,d )2 + km * ( sm.y.d / fm.y.d ) + ( sm.z.d / fm.z.d ) = per EN 1995-1-1 - Section 6.2.4, formula (6.20)  
                   
                             
Strability verification - Combined bending and axial compression   per EN 1995-1-1 - Section 6.3.2      
Relative slenderness ratio corresponding to about y axis (deflection in the z direction)            
lrel,y = (ly /p) * (fc,0,k / E0,05)0.5=       per EN 1995-1-1 - Section 6.3.2, formula (6.21)      
Relative slenderness ratio corresponding to about z axis (deflection in the y direction)            
lrel,z = (lz /p) * (fc,0,k / E0,05)0.5=       per EN 1995-1-1 - Section 6.3.2, formula (6.22)      
                             
bc = (0.2 for solid timber and 0.1 for glued laminated timber) factor per EN 1995-1-1 - formula (6.29)      
ky = 0.5 * (1 + bc * (lrel,y - 0.3) + l2rel,y ) =     factor per EN 1995-1-1 - formula (6.27)      
kz = 0.5 * (1 + bc * (lrel,z - 0.3) + l2rel,z ) =     factor per EN 1995-1-1 - formula (6.28)      
                             
kc,y = 1 / [ky + (k2y - l2rel,y)0.5] =       factor per EN 1995-1-1 - formula (6.25)      
kc,z = 1 / [kz + (k2z - l2rel,z)0.5] =       factor per EN 1995-1-1 - formula (6.26)      
                             
Check on for y-y axis                          
sc,0,d / ( kc,y * fc,0,d ) + ( sm.y.d / fm.y.d ) + km * ( sm.z.d / fm.z.d ) = per EN 1995-1-1 - Section 6.3.2, formula (6.23)      
                       
Check on for z-z axis                          
sc,0,d / ( kc,z * fc,0,d ) + km * ( sm.y.d / fm.y.d ) + ( sm.z.d / fm.z.d ) = per EN 1995-1-1 - Section 6.3.2, formula (6.24)      
                       
                         
References:  
EN 1995-1-1:2004 - Eurocode 5: Design of timber structures - Part 1-1: Common rules and rules for buildings      
EN 338 : 2003 - Structural Timber; Strength Classes