Page 275 - Civil Engineering Formulas

BUILDING AND STRUCTURES FORMULAS 209

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

Buckled shape of column
is shown by dashed line

Theoretical K value 0.5 0.7 1.0 1.0 2.0 2.0
Recommended design value when 0.65 0.80 1.2 1.0 2.10 2.0
ideal conditions are approximated
Rotation fixed and translation fixed
Rotation free and translation fixed
End condition
Rotation fixed and translation free
Rotation free and translation free

FIGURE 9.1 Values of effective-length factor K for columns.

LOAD-AND-RESISTANCE FACTOR
DESIGN FOR BUILDING COLUMNS

Plastic analysis of prismatic compression members in buildings is permitted if
Fy (l/r) does not exceed 800 and F 65 ksi (448 MPa). For axially loaded
u
members with b/t , the maximum load P , ksi (MPa 6.894 ksi), may be
r
u
computed from
P u 0.85A g F cr (9.7)
where A gross cross-sectional area of the member
g

F 0.658 F for 2.25
y
cr
0.877 F / for 2.25
y
2
(Kl/r) (F /286,220)
y
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
is F 0.66F if they are compact, except for hybrid girders and members with
b y
yield points exceeding 65 ksi (448.1 MPa). F 0.60F for noncompact
b y