Evo Design  structural engineering

Calculation
No.





001WOOD 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
199211:2004* & EN 338
















Maximum working
loads (Ultimate Limit State)










F_{Ed}=


kN*m

axial force (compression)










M_{y,Ed}=


kN*m

bending moment yy










M_{z,Ed}=


kN*m

bending moment zz

























Element dimensions
 Rectangular cross section










L_{y.b} =

300

cm

element buckling length about yy









L_{z.b} =

300

cm

element buckling length about zz









h =

20

cm

height












d =

10

cm

width

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





















Section Properties










A =

d*h =


cm^{2}

section area







I_{Y} =

d*h^{3}/12 =


cm^{4}

moment of inertia about yy axis







I_{z} =

d^{3}*h/12 =


cm^{4}

moment of inertia about zz axis







i_{y} =

(I_{y}/A)^{0.5} =


cm

radius of gyration about yy







i_{z} =

(I_{z}/A)^{0.5} =


cm

radius of gyration about zz






















l_{y} =

L_{y.b} / i_{y} =



slenderness
ratio corresponding to bending about the yaxis




l_{z} =

L_{z.b} / i_{z} =



slenderness
ratio corresponding to bending about the zaxis



















Material
characteristics



per EN 33897  Table 1




Wood strength
class:












f_{m,k} =


N/mm^{2}






Characteristic
bending strength


f_{c,0,k} =


kN/mm^{2}






Characteristic
compressive strength




E_{0,05} =


kN/mm^{2}






Fifth
percentile value of modulus of elasticity


g_{m} =








per EN 199511  Table 2.3










1.3 for
solid timber, 1.25 for glued laminated timber


k_{h} =

min( (150/h)^{0.2} ; 1.3) =





per EN
199511  Section 3.2 (3), formula (3.1)









for timber
with density less than 700 kg/m^{3} and










h < 150mm
the characteristic valus of f_{m,k} and










f_{t,0,k} may be increased
by the factor k_{h}


k_{mod} =








per EN 199511  Table 3.1










Load
duration classes per EN 199511










Section 2.3.1.2  Table 2.1 and 2.2










Service classes per EN 199511  Section 2.3.1.3



















f_{c.0.d} =

k_{mod} * f_{c,0,k}

/ g_{m} =



N/mm^{2}


design
compressive strength and




f_{m.y.d} =

f_{m.y.d} =

k_{mod} *k_{h} * f_{m,k}

/ g_{m} =


N/mm^{2}


design
bending strength about y and z axis












per EN
199511  Section 2.4.1, formula (2.14)



















References:




EN
199511:2004  Eurocode 5: Design of timber structures  Part 11: 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


































s_{c,0,d} =

F_{,Ed} / A =


N/mm^{2}




Design
compressive stress




s_{m.y.d} =

M_{y,Ed} * (h/2) / I_{y} =


N/mm^{2}




Design
bending stress about the principal y axis




s_{m.z.d} =

M_{z,Ed} * (d/2) / I_{z} =


N/mm^{2}




Design
bending stress about the principal z axis



















k_{m} =

0.7

for rectangular sections




per EN
199511  Section 6.1.6 (2)



















Stresses
verification  Combined bending and axial compression


per EN
199511  Section 6.2.4




Check on for yy
axis














(s_{c,0,d} / f_{c,0,d} )^{2} + ( s_{m.y.d} / f_{m.y.d} ) + k_{m} * ( s_{m.z.d} / f_{m.z.d} ) =



per EN 199511  Section 6.2.4, formula (6.19)

















Check on for zz
axis














(s_{c,0,d} / f_{c,0,d} )^{2} + k_{m} * ( s_{m.y.d} / f_{m.y.d} ) + ( s_{m.z.d} / f_{m.z.d} ) =



per EN
199511  Section 6.2.4, formula (6.20)




























Strability
verification  Combined bending and axial compression


per EN
199511  Section 6.3.2




Relative
slenderness ratio corresponding to about y axis (deflection in the z
direction)







l_{rel,y} =

(l_{y} /p) *
(f_{c,0,k} / E_{0,05})^{0.5}=





per EN
199511  Section 6.3.2, formula (6.21)




Relative
slenderness ratio corresponding to about z axis (deflection in the y
direction)







l_{rel,z} =

(l_{z} /p) *
(f_{c,0,k} / E_{0,05})^{0.5}=





per EN
199511  Section 6.3.2, formula (6.22)



















b_{c} =


(0.2 for solid timber and 0.1 for glued laminated
timber)

factor per
EN 199511  formula (6.29)




k_{y} =

0.5 * (1 + b_{c} * (l_{rel,y}  0.3) + l^{2}_{rel,y} ) =




factor per
EN 199511  formula (6.27)




k_{z} =

0.5 * (1 + b_{c} * (l_{rel,z}  0.3) + l^{2}_{rel,z} ) =




factor per
EN 199511  formula (6.28)



















k_{c,y} =

1 / [k_{y} + (k^{2}_{y}  l^{2}_{rel,y})^{0.5}] =





factor per
EN 199511  formula (6.25)




k_{c,z} =

1 / [k_{z} + (k^{2}_{z}  l^{2}_{rel,z})^{0.5}] =





factor per
EN 199511  formula (6.26)



















Check on for yy
axis














s_{c,0,d} / ( k_{c,y} * f_{c,0,d} ) + ( s_{m.y.d} / f_{m.y.d} ) + k_{m} * ( s_{m.z.d} / f_{m.z.d} ) =



per EN
199511  Section 6.3.2, formula (6.23)

















Check on for zz
axis














s_{c,0,d} / ( k_{c,z} * f_{c,0,d} ) + k_{m} * ( s_{m.y.d} / f_{m.y.d} ) + ( s_{m.z.d} / f_{m.z.d} ) =



per EN
199511  Section 6.3.2, formula (6.24)






























References:


EN
199511:2004  Eurocode 5: Design of timber structures  Part 11: Common
rules and rules for buildings




EN
338 : 2003  Structural Timber; Strength Classes






















