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Non-prestressed Concrete Columns Formulas and Calculator

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Nominal Axial Compressive Strength Non-prestressed Concrete Columns per. ACI 318-14 American Concrete Institute (ACI) Formulas and Calculator

The following formulas are taken from the ACI code please note the the associated formulas and calculator may not account for all code variations or requirements.

column with pure axial compression
Figure 1
Pinned on bottom Roller all directions top

Load case
Eq. 1
Lc = 1.2 DL + 1.6 LL

For a column with pure axial compression, pinned at the bottom and roller pinned horizontal at top with Load and Resistance Factor Design (LRFD) criteria a

Per. ACI 318-14, paragraph 10.5.1.1, applicable factored load combination,
Eq. 2
(a) Φ Pn ≥ Po
(b) Φ Mn ≥ Po
(c) Φ Vn ≥ Vo
(d) Φ Tn ≥ To

10.5.2.1 Pn and Mn shall be calculated in accordance with 22.4.

ACI 318-14, specifies that the nominal axial compressive strength Pn shall not exceed Pn,max in accordance with Table 1, where Po is calculated by Eq. (x) for nonprestressed members and composite steel and concrete members, and by Eq. (x) for prestressed members.

Table 1, Maximum axial strength (ACI 318-14, Chap. 22, Table 22.4.2.1)

Member Loading Transverse reinforcement
Pn,max =
Nonrestressed Ties conforming to
0.80 Po
Spirals conforming to
0.85 Po
Prestressed Ties
0.80 Po
Spirals
0.85 Po
Composite steel and concrete columns in accordance to ACI requirements all
0.85 Po

Eq. 3
Pn,max = Table 1

Nominal Axial Compressive Strength for nonprestressed members and composite steel and concrete members, Po

Eq. 4 (ACI 318-14, 22.4.2.2)
Po = [ 0.85 f'c ( Ag - Ast ) + fy Ast ]

Eq. 5
Pn, max = (table 1 ) Po
Pn = Φ Pn, max [ 0.85 f'c ( Ag - Ast ) + fy Ast ]

Table 2, Φ Strength Reduction Factors (ACI 318-14, Table 21.2.1)
Action or structural element
Φ
Exceptions
(a)
Moment, axial force, or
combined moment and
axial force
0.65 to
0.90 in
accordance
with 21.2.2
Near ends of pretensioned members where strands are not fully developed, ϕ shall be in accordance with 21.2.3.
(b)
Shear
0.75
Additional requirements
are given in 21.2.4 for
structures designed to
resist earthquake effects.
(c)
Torsion
0.75
-
(d)
Bearing
0.65
-
(e)
Post-tensioned anchorage zones
0.85
-
(f)
Brackets and corbels
(f)
Brackets and corbels
0.75
(h)
Components of connections of precast members controlled by yielding of steel elements in tension
0.90
(i)
Plain concrete elements
0.60
(j)
Anchors in concrete
elements
0.45 to
0.75 in
accordance with Chapter 17, ACI 318-14

Where

Po = nominal axial strength at zero eccentricity, lb
Pnt = nominal axial compressive strength of member, lb
Pnt, max = maximum nominal axial tensile strength of member, lb
f'c = specified compressive strength of concrete, psi
fy = specified yield strength for nonprestressed reinforcement (steel rebar), psi
fse = effective stress in prestressing reinforcement, after allowance for all prestress losses, psi
Ag = gross area of concrete section, in.2 For a hollow section, Ag is the area of the concrete only and does not include the area of the void(s)
Ast = total area of nonprestressed longitudinal reinforcement including bars or steel shapes, and excluding prestressing reinforcement, in.2
Apd = total area occupied by duct, sheathing, and prestressing reinforcement, in.2
Apt = total area of prestressing reinforcement, in.2
Ep = modulus of elasticity of prestressing reinforcement, psi
DL = Dead load lbsf
LL = live load lbsf
Lc = load case lbsf

Related

Source:

Building Code Requirements for Structural Concrete (ACI 318-08)

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