Page 240 - Civil Engineering Formulas

174 CHAPTER SIX

For either uniaxial or biaxial bending, f should not exceed
c
K cE E
F cE1 (6.56)
(L e1 /d 1 ) 2
where E is the modulus of elasticity multiplied by adjustment factors. Also, for
biaxial bending, f should not exceed
c
K cE E
F cE2 (6.57)
(L e2 /d 2 ) 2
and f should not be more than
b1
K bE E
F bE (6.58)
2
R B
where d is the width of the wide face and d is the width of the narrow face.
1
2
Slenderness ratio R for beams is given earlier in this section. K bE is defined
B
earlier in this section. The effective column lengths L for buckling in the d direc-
e1
1
tion and L for buckling in the d direction, E , F , and F cE2 should be determined
e2
cE1
2
as shown earlier.
As for the case of combined bending and axial tension, F c , F b1 , and F b2
should be adjusted for duration of load by applying C .
D
Nomenclature for Formulas given in Eqs. (6.59) through (6.57):
Q allowable load, lb
P ultimate load, lb
A section area of column, sq in
L length of column, in
r least radius of gyration of column section, in
S ultimate strength, psi
u
S yield point or yield strength of material, psi
y
E modulus of elasticity of material, psi
m factor of safety
(L/r) critical slenderness ratio
SOLID RECTANGULAR OR SQUARE
COLUMNS WITH FLAT ENDS*
For select structural-grade lumber in general structural use under continuously dry
conditions, the following formulas can be used for the allowable unit load, Q/A:
4
Q 1 L E
L
S 1 up to K 0.64 (6.59)
A 3 Kd d BS
*Roark—“Formulas for Stress and Strain,” McGraw-Hill.