Column Stability Factor of a Wood Column
06-07-2015, 07:21 PM
Post: #1
 Eddie W. Shore Senior Member Posts: 1,491 Joined: Dec 2013
Column Stability Factor of a Wood Column
The program CPWOOD calculates the slenderness and the column stability factor of a Douglas-Fir wood column.

Equations:

Slenderness (unit-less):

s = L / d
where:
L = effective length of the wood column, in inches (effective length assumed)
d = effective depth of the wood column, in inches (effective depth assumed)

Column Stability Factor (unit-less):

cp = (1 + r)/(2 * c) - √( (1 + r)^2/(2 * c)^2 – r/c )
where:
r = Fce / Fc
Fce = buckling stress of the wood
Fce = (kce * E)/(s^2)
kce = 0.3 (assumed)
E = elasticity modulus in psi (pounds per square inch)
Fc = allowable design value for compression parallel to the wood’s grain (in pounds per square inch)
c = factor. (0.8 for sawn lumber, 0.85 for round poles, 0.9 for glued laminated timber)

You can select from several types of woods or enter your own Fc* and E.

cap = cp * Fc * w * d (in pounds)

Code:
EXPORT CPWOOD() BEGIN // EWS 2015-06-07 LOCAL n1a,n1b,s1,c1,w; LOCAL l,d,r,fce,cap,sl,mlc; LOCAL na,nb,n2,s2,c2,c; // WWPA Timber - 2008  // 1st is placeholder // Fc (psi) n1a:={0,1150,1000,700,1050, 975,925,875,925,800}; // E (psi) n1b:={0,1.6ᴇ6,1.6ᴇ6,1.3ᴇ6,1.2ᴇ6, 1.3ᴇ6,1.1ᴇ6,1.3ᴇ6,1ᴇ6,1.1ᴇ6}; s1:={"Enter Your Own", "Douglas Fir Larch (Std)", "Douglas Fir Larch (#1)", "Douglas Fir Larch (#2)", "Douglas Fir South (Std)", "Hem Fir (Std)", "Moutain Hemlock (Std)", "Sitka Spruce (Std)", "Western Cedar (Std)", "Western Woods (Std)" }; // column type n2:={0.8,0.85,0.9}; s2:={"sawn lumber", "round poles", "glued laminated timber"}; // Input INPUT({l,d,w,{c1,s1}}, "Wood Column - Sawn Lumber", {"Length (in):","Depth (in):", "Width (in)","Wood:"}, {"effective (in)", "effective (in)", "Douglas Fir"}); // Selection IF c1>1 THEN na:=n1a[c1]; nb:=n1b[c1]; ELSE INPUT({na,nb}, "Lumber Characteristics", {"Fc* (psi):","E (million psi):"}, {"compression parallel to grain", "elasticity modulus (in millions)"}); nb:=nb*ALOG(6); END; INPUT({{c2,s2}}, "Select Column Type"); c:=n2[c2]; // Calculations // slenderness sl:=l/d; // Fce fce:=(0.3*nb)/(l/d)^2; // ratio r:=fce/na; // column load capacity cap:=(1+r)/(2*c)-√((1+r)^2/ (2*c)^2-r/c); // Maximum Load Capacity mlc:=na*cap*w*d; // Output PRINT(); PRINT("Results:"); PRINT("---------"); PRINT("Slenderness = "); PRINT(sl); PRINT("Column Load Capacity ="); PRINT(cap); PRINT("Column Load Capacity ="); PRINT(mlc+" lb"); RETURN {sl,cap,mlc}; END;

Sources:

Ambrose, James “Simplified Engineering for Architects and Builders” John Wiley & Sons. 9th Edition. New York, 2000

Western Wood Products Association “Western Lumber Product Use Manual” 2008. http://www.wwpa.org. Table 5: Posts & Timbers Design Values, page 11. URL used: http://www.engr.sjsu.edu/dmerrick/164/WWPA_PUM.pdf, retrieved June 7, 2015

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