CIVIL ENGINEERING FORMULAS

96 CHAPTER THREE

whereGshear modulus of elasticity, psi (MPa)

Jtorsional constant

Across-sectional area, in^2 (mm^2 )

Ippolar moment of inertiaIxIy,in^4 (mm^4 )

If the section possesses a significant amount of warping rigidity, the axial buck-

ling load is increased to

(3.28)

whereCwis the warping constant, a function of cross-sectional shape and

dimensions.

ALLOWABLE DESIGN LOADS FOR ALUMINUM COLUMNS

Euler’s equation is used for long aluminum columns, and depending on the

material, either Johnson’s parabolic or straight-line equation is used for short

columns. These equations for aluminum follow

Euler’s equation

(3.29)

Johnson’s generalized equation

(3.30)

The value of n, which determines whether the short column formula is the

straight-line or parabolic type, is selectedfrom Table 3.5. The transition from the

long to the short column range is given by

(3.31)

where Feallowable column compressive stress, psi (MPa)

Fcecolumn yield stress and is given as a function of Fcy(compres-

sive yield stress), psi (MPa)

Llength of column, ft (m)

radius of gyration of column, in (mm)

Emodulus of elasticity—noted on nomograms, psi (MPa)

ccolumn-end fixity from Fig. 3.9

n,K,kconstants from Table 3.5



L



cr

B

kcE

Fce

FcFce



1 K



(L/)

B

cE

Fce



n



Fe

c 

2 E

(L/)^2

P

A

Ip

GJ

2 ECw

L^2