CIVIL ENGINEERING FORMULAS

COLUMN FORMULAS 97

Restraining bulk-

head partially

fixed

P

P

P

P

P P

P P

c = 1.00

c = 1.25 to 1.50

c = 2.00 c = 4.00

FIGURE 3.9 Values of c, column-end fixity, for determining the critical L/ratio of dif-

ferent loading conditions.

ULTIMATE STRENGTH DESIGN CONCRETE COLUMNS

At ultimate strength Pu, kip (N), columns should be capable of sustaining loads as
given by the American Concrete Institute required strengthequations in Chap. 5,
“Concrete Formulas” at actual eccentricities. Pu, may not exceed Pn, where is
the capacity reduction factor and Pn, kip (N), is the column ultimate strength. If
P 0 , kip (N), is the column ultimate strength with zero eccentricity of load, then

(3.32)

where fyyield strength of reinforcing steel, ksi (MPa)

fc28-day compressive strength of concrete, ksi (MPa)

Aggross area of column, in^2 (mm^2 )

Astarea of steel reinforcement, in^2 (mm^2 )

For members with spiral reinforcement then, for axial loads only,

(3.33)

For members with tie reinforcement, for axial loads only,

(3.34)

Eccentricities are measured from the plastic centroid. This is the centroid of
the resistance to load computed for the assumptions that the concrete is stressed
uniformly to 0.85 fcand the steel is stressed uniformly to fy.

Pu0.80P 0

Pu0.85P 0

P 0 0.85fc(AgAst)fyAst