Sunday, June 7, 2015

HP Prime: Column Stability Factor of a Wood Column

HP Prime:  Column Stability Factor of a Wood Column

Happy June!

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.    

Wood
Fc (psi)
E (in millions of psi)
Douglas Fir Larch (Standard)
1150
1.6
Douglas Fir Larch (Grade 1)
1000
1.6
Douglas Fir Larch (Grade 2)
700
1.3
Douglas Fir South (Standard)
1050
1.2
Hem Fir (Standard)
975
1.3
Mountain Hemlock (Standard)
925
1.1
Sitka Spruce (Standard)
875
1.3
Western Cedar (Standard)
925
1.6
Western Woods (Standard)
800
1.1

  
Column Load Capacity:
cap = cp * Fc * w * d   (in pounds)

Program CPWOOD:

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;

Example:

Data: 
Length:  72 in, Depth: 10.5 in, Width: 10.5 in, Wood:  Douglas Fir Larch (Standard), sawn lumber

Output:
Slenderness = 6.85714285714
Column Stability Factor = 0.97589228026
Column Load Capacity = 123,730.942484 lb

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.  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


Eddie


This blog is property of Edward Shore.  2015

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