CIVIL ENGINEERING FORMULAS

BUILDING AND STRUCTURES FORMULAS 209

LOAD-AND-RESISTANCE FACTOR
DESIGN FOR BUILDING COLUMNS

Plastic analysis of prismatic compression members in buildings is permitted if
does not exceed 800 and Fu65 ksi (448 MPa). For axially loaded

members with b/tr, the maximum load Pu, ksi (MPa6.894ksi), may be
computed from

(9.7)

whereAggross cross-sectional area of the member
Fcr0.658Fyfor2.25
0.877Fy/for 2.25
(Kl/r)^2 (Fy/ 286,220)

The AISC specification for LRFD presents formulas for designing members
with slender elements.

ALLOWABLE-STRESS DESIGN FOR BUILDING BEAMS

The maximum fiber stress in bending for laterally supported beams and girders
isFb0.66Fyif they are compact, except for hybrid girders and members with
yield points exceeding 65 ksi (448.1 MPa). Fb0.60Fyfor noncompact

Pu0.85AgFcr

Fy (l/r)

2.0

2.0

2.0

2.10

1.0

1.0

1.0

1.2

0.7

0.80

0.5

(a) (b) (c) (d) (e) (f )

0.65

Recommended design value when

ideal conditions are approximated

End condition

Rotation fixed and translation fixed

Rotation fixed and translation free

Rotation free and translation free

Rotation free and translation fixed

TheoreticalK value

Buckled shape of column

is shown by dashed line

FIGURE 9.1 Values of effective-length factor Kfor columns.