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