COLUMN FORMULAS 99The axial-load capacity Pukip (N), of short, rectangular members subject to
axial load and bending may be determined from
(3.34)(3.35)
where eccentricity, in (mm), of axial load at end of member with respect to
centroid of tensile reinforcement, calculated by conventional methods
of frame analysis
bwidth of compression face, in (mm)
adepth of equivalent rectangular compressive-stress distribution, in
(mm)
As area of compressive reinforcement, in^2 (mm^2 )
Asarea of tension reinforcement, in^2 (mm^2 )
ddistance from extreme compression surface to centroid of tensile
reinforcement, in (mm)
ddistance from extreme compression surface to centroid of compres-
sion reinforcement, in (mm)
fstensile stress in steel, ksi (MPa)
The two preceding equations assume that adoes not exceed the column
depth, that reinforcement is in one or two faces parallel to axis of bending, and
that reinforcement in any face is located at about the same distance from the
axis of bending. Whether the compression steel actually yields at ultimate
strength, as assumed in these and the following equations, can be verified by
strain compatibility calculations. That is, when the concrete crushes, the strain
in the compression steel, 0.003 (cād)/c,must be larger than the strain when
the steel starts to yield, fy/Es. In this case, cis the distance, in (mm), from the
extreme compression surfaceto the neutral axis and Esis the modulus of elastic-
ity of the steel, ksi (MPa).
The load, Pbfor balanced conditions can be computed from the preceding Pu
equation with fsfyand
(3.36)The balanced moment, in.kip (k.Nm), can be obtained from
(3.37)Asfy (ddd)Asfyd0.85fcbabdd ab
2 MbPbeb87,000 1 d
87,000fy 1 cbaabePue0.85fcbada
2 Asfy (dd)Pu(0.85fcbaAsfyAsfs)