Page 316 - Civil Engineering Formulas

250 CHAPTER TEN

TABLE 10.1 Column Formulas for Bridge Design
Yield
strength, Allowable stress, ksi (MPa)
ksi (MPa) C c Kl/r C c Kl/r C c
36 (248) 126.1 16.98–0.00053(Kl/r) 2
50 (345) 107.0 23.58–0.00103(Kl/r) 2 135,000
90 (620) 79.8 42.45–0.00333(Kl/r) 2 (Kl/r) 2
100 (689) 75.7 47.17–0.00412(Kl/r) 2

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:
When Kl/r is less than C ,
c
2
F y (Kl/r) 2
F a 1 (10.3)
2.12 2C c
When Kl/r is equal to or greater than C ,
c
2

E 135,000
F a (10.4)
2.12(Kl/r) 2 (Kl/r) 2
See Table 10.1.

LOAD-AND-RESISTANCE FACTOR
DESIGN FOR BRIDGE COLUMNS

Compression members designed by LFD should have a maximum strength, kip
(kN),
P u 0.85A s F cr (10.5)
2
2
where A gross effective area of column cross section, in (mm ).
s
2
For KL c /r 2 2
E/F y ,
F cr F y 1 F y 2 (10.6)
2
KL c
4
E r
2
For KL c /r 2 2
E/F y ,
2

E 286,220
F cr (10.7)
(KL c /r) 2 (KL c /r) 2