Page 277 - Civil Engineering Formulas

BUILDING AND STRUCTURES FORMULAS 211

When, however, the compression flange is solid and nearly rectangular in
cross section, and its area is not less than that of the tension flange, the allow-
able stress may be taken as
12,000C b
F b (9.12)
ld /A f
When Eq. (9.12) applies (except for channels), F should be taken as the larger
b
of the values computed from Eqs. (9.12) and (9.10) or (9.11), but not more than
0.60F .
y
The moment-gradient factor C in Eqs. (9.8) to (9.12) may be computed from
b

M 1 M 1 2
C b 1.75 1.05 0.3 2.3 (9.13)
M 2 M 2
where M smaller beam end moment and M larger beam end moment.
2
1
The algebraic sign of M /M is positive for double-curvature bending and
2
1
negative for single-curvature bending. When the bending moment at any point
within an unbraced length is larger than that at both ends, the value of C b
should be taken as unity. For braced frames, C should be taken as unity for
b
computation of F and F .
by
bx
Equations (9.11) and (9.12) can be simplified by introducing a new term:
2
(l/r T ) Fy
Q (9.14)
510,000C b
Now, for 0.2 Q 1,
(2 Q)Fy (9.15)
F b
3
For Q 1:
Fy
F b (9.16)
3Q
As for the preceding equations, when Eq. (9.8) applies (except for chan-
nels), F should be taken as the largest of the values given by Eqs. (9.8) and
b
(9.15) or (9.16), but not more than 0.60F .
y
LOAD-AND-RESISTANCE FACTOR DESIGN
FOR BUILDING BEAMS

For a compact section bent about the major axis, the unbraced length L of the
b
compression flange, where plastic hinges may form at failure, may not exceed
L , given by Eqs. (9.17) and (9.18) that follow. For beams bent about the
pd
minor axis and square and circular beams, L is not restricted for plastic analysis.
b