CIVIL ENGINEERING FORMULAS

126 CHAPTER FIVE

tdiameter of column or overall depth of column, in (mm)

ddistance from extreme compression fiber to centroid of tension rein-

forcement, in (mm)

fvyield point of reinforcement, lb/in^2 (MPa)

Design of columns controlled by compression is based on the following
equation, except that the allowable load Nmay not exceed the allowable load P,
given earlier, permitted when the column supports axial load only:

(5.21)

where faaxial load divided by gross concrete area, lb/in^2 (MPa)

fbx,fbybending moment about xandyaxes, divided bysection modulus

of corresponding transformeduncracked section, lb/in^2 (MPa)

Fballowable bending stress permitted for bending alone, lb/in^2

(MPa)

Fa0.34(1pgm)fc

The allowable bending load on columns controlled by tension varies linearly
with the axial load from M 0 when the section is in pure bending to Mbwhen the
axial load is Nb.

For spiral columns,

(5.22)

For tied columns,

(5.23)

whereAsttotal area of longitudinal reinforcement, in^2 (mm^2 )

fvyield strength of reinforcement, lb/in^2 (MPa)

Dsdiameter of circle through centers of longitudinal reinforcement, in

(mm)

Asarea of tension reinforcement, in^2 (mm^2 )

ddistance from extreme compression fiber to centroid of tension rein-

forcement, in (mm)

NbandMbare the axial load and moment at the balanced condition (i.e., when
the eccentricity eequalsebas determined). At this condition, NbandMbshould
be determined from

(5.24)

When bending is about two axes,

(5.25)

Mx

M 0 x



My

M 0 y

 1

MbNbeb

M 0 0.40Asfy(dd)

M 0 0.12AstfyDs

fa

Fa



fbx

Fb



fby

Fb

1.0