Page 288 - Civil Engineering Formulas

222 CHAPTER NINE

When f /F 0.15, the following equation may be used instead of the preced-
a
a
ing two:
f a f bx f by
1 (9.54)
F a F bx F by
In the preceding equations, subscripts x and y indicate the axis of bending about
which the stress occurs, and
F axial stress that would be permitted if axial force alone existed, ksi (MPa)
a
F compressive bending stress that would be permitted if bending
b
moment alone existed, ksi (MPa)
F e 149,000/(Kl b /r b ) 2 , ksi (MPa); as for F , F , and 0.6F , F e may be
a
b
y
increased one-third for wind and seismic loads
l actual unbraced length in plane of bending, in (mm)
b
r radius of gyration about bending axis, in (mm)
b
K effective-length factor in plane of bending
f computed axial stress, ksi (MPa)
a
f computed compressive bending stress at point under consideration,
b
ksi (MPa)
C adjustment coefficient
m
WEBS UNDER CONCENTRATED LOADS
Criteria for Buildings

The AISC specification for ASD for buildings places a limit on compressive
stress in webs to prevent local web yielding. For a rolled beam, bearing stiffen-
ers are required at a concentrated load if the stress f , ksi (MPa), at the toe of
a
the web fillet exceeds F 0.66F , where F yw is the minimum specified yield
a
yw
stress of the web steel, ksi (MPa). In the calculation of the stressed area, the
load may be assumed distributed over the distance indicated in Fig. 9.4.
For a concentrated load applied at a distance larger than the depth of the
beam from the end of the beam,
R
f a (9.55)
t w (N 5k)
where R concentrated load of reaction, kip (kN)
t web thickness, in (mm)
w
N length of bearing, in (mm), (for end reaction, not less than k)
k distance, in (mm), from outer face of flange to web toe of fillet
For a concentrated load applied close to the beam end,
R
f a (9.56)
t w (N 2.5k)