CIVIL ENGINEERING FORMULAS

174 CHAPTER SIX

For either uniaxial or biaxial bending, fcshould not exceed

(6.56)

whereEis the modulus of elasticity multiplied by adjustment factors. Also, for
biaxial bending, fcshould not exceed

(6.57)

andfb 1 should not be more than

(6.58)

whered 1 is the width of the wide face and d 2 is the width of the narrow face.
Slenderness ratio RBfor beams is given earlier in this section. KbEis defined
earlier in this section. The effective column lengths Le 1 for buckling in the d 1 direc-
tion and Le 2 for buckling in the d 2 direction,E,FcE1, and FcE2should be determined
as shown earlier.
As for the case of combined bending and axial tension, , , and
should be adjusted for duration of load by applying CD.
Nomenclature for Formulas given in Eqs. (6.59) through (6.57):

Qallowable load, lb

Pultimate load, lb

Asection area of column, sq in

Llength of column, in

rleast radius of gyration of column section, in

Suultimate strength, psi

Syyield point or yield strength of material, psi

Emodulus of elasticity of material, psi

mfactor 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:

(6.59)

Q

A

S 1 

1

3 

L

Kd

4

up to

L

d

K0.64

B

E

S

Fc Fb 1 Fb 2

FbE

KbEE

R^2 B

FcE2

KcEE

(Le 2 /d 2 )^2

FcE1

KcEE

(Le 1 /d 1 )^2

*Roark—“Formulas for Stress and Strain,” McGraw-Hill.