Page 317 - Civil Engineering Formulas

BRIDGE AND SUSPENSION-CABLE FORMULAS 251

where F buckling stress, ksi (MPa)
cr
F yield strength of the steel, ksi (MPa)
y
K effective-length factor in plane of buckling
L length of member between supports, in (mm)
c
r radius of gyration in plane of buckling, in (mm)
E modulus of elasticity of the steel, ksi (MPa)
The preceding equations can be simplified by introducing a Q factor:
F y 2
2
KL c
Q (10.8)
r 2
E
Then, the preceding equations can be rewritten as shown next:
For Q 1.0,

Q
F cr 1 2 F y (10.9)

For Q 1.0,

F y
F cr (10.10)
2Q

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
s 33,000 psi for the tensile yield strength, or for structural shapes having
y
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:
Q allowable load, 1b
P ultimate load, 1b
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
*Roark—Formulas for Stress and Strain, McGraw-Hill.