CIVIL ENGINEERING FORMULAS

BRIDGE AND SUSPENSION-CABLE FORMULAS 251

whereFcrbuckling stress, ksi (MPa)
Fyyield strength of the steel, ksi (MPa)
Keffective-length factor in plane of buckling
Lclength of member between supports, in (mm)
rradius of gyration in plane of buckling, in (mm)
Emodulus of elasticity of the steel, ksi (MPa)

The preceding equations can be simplified by introducing a Qfactor:

(10.8)

Then, the preceding equations can be rewritten as shown next:
ForQ1.0,

(10.9)

ForQ 1.0,

(10.10)

ADDITIONAL BRIDGE COLUMN FORMULAS*

The nomenclature for the bridge column formulas is shown at the end of their
explanation of their applications. For bridges using structural carbon steel with
sy33,000 psi for the tensile yield strength, or for structural shapes having
their ends riveted, the following formulas apply, using the nomenclature given
below for formulas from Eqs. (10.11) through (10.33) are known as the ‘secant
formula’ when the ‘sec’ expression appears in their denominator:

Qallowable load, 1b

Pultimate load, 1b

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

Fcr

Fy

2 Q

Fcr 1 

Q

2 

Fy

Q

KLc

r 

2



Fy

2

2 E

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