CIVIL ENGINEERING FORMULAS

222 CHAPTER NINE

Whenfa/Fa0.15, the following equation may be used instead of the preced-
ing two:

(9.54)

In the preceding equations, subscripts xandyindicate the axis of bending about
which the stress occurs, and

Faaxial stress that would be permitted if axial force alone existed, ksi (MPa)

Fbcompressive bending stress that would be permitted if bending

moment alone existed, ksi (MPa)

 ,ksi (MPa); as for Fa,Fb, and 0.6Fy, may be

increased one-third for wind and seismic loads

lbactual unbraced length in plane of bending, in (mm)

rbradius of gyration about bending axis, in (mm)

Keffective-length factor in plane of bending

facomputed axial stress, ksi (MPa)

fbcomputed compressive bending stress at point under consideration,

ksi (MPa)

Cmadjustment coefficient

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 fa, ksi (MPa), at the toe of
the web fillet exceeds Fa0.66Fyw, where Fywis the minimum specified yield
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,

(9.55)

where Rconcentrated load of reaction, kip (kN)
twweb thickness, in (mm)
Nlength of bearing, in (mm), (for end reaction, not less than k)
kdistance, in (mm), from outer face of flange to web toe of fillet

For a concentrated load applied close to the beam end,

fa (9.56)

R

tw(N2.5k)

fa

R

tw(N 5 k)

Fe 149,000/(Klb/rb)^2 Fe

fa

Fa



fbx

Fbx



fby

Fby

 1