CIVIL ENGINEERING FORMULAS

250 CHAPTER TEN

ALLOWABLE-STRESS DESIGN FOR BRIDGE COLUMNS

In the AASHTO bridge-design specifications, allowable stresses in concentri-
cally loaded columns are determined from the following equations:
WhenKl/ris less than Cc,

(10.3)

WhenKl/ris equal to or greater than Cc,

(10.4)

See Table 10.1.

LOAD-AND-RESISTANCE FACTOR
DESIGN FOR BRIDGE COLUMNS

Compression members designed by LFD should have a maximum strength, kip
(kN),

(10.5)

whereAsgross effective area of column cross section, in^2 (mm^2 ).

For

(10.6)

For

Fcr (10.7)

2 E

(KLc/r)^2



286,220

(KLc/r)^2

KLc/r   22

2 E/Fy ,

FcrFy 1 

Fy

4

2 E

KLc

r 

2



KLc/r 22

2 E/Fy ,

Pu0.85AsFcr

Fa

2 E

2.12(Kl/r)^2



135,000

(Kl/r)^2

Fa

Fy

2.12

1 

(Kl/r)^2

2 C^2 c 

TABLE 10.1 Column Formulas for Bridge Design

Yield

strength, Allowable stress, ksi (MPa)

ksi (MPa) Cc Kl/rCc Kl/r Cc

36 (248) 126.1 16.98–0.00053(Kl/r)^2

50 (345) 107.0 23.58–0.00103(Kl/r)^2

90 (620) 79.8 42.45–0.00333(Kl/r)^2

100 (689) 75.7 47.17–0.00412(Kl/r)^2

135,000

(Kl/r)^2