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Notation
Ag = gross area of the concrete section, in2
As = area of non-prestressed longitudinal tension reinforcement, in2
Ast = total area of non-prestressed longitudinal reinforcement, in2
α = depth of equivalent rectangular stress block, in.
bw = width of compression face of the member, in.
c = distance from extreme compression fiber to the neutral axis, in.
Cc = concretecompressive force, lb
Cs = reinforcement tension force, lb
fc'= specified compressive strength of concrete, psi
fy = specified yield strength for non-prestressed reinforcement, psi
Mn = nominal flexural strength at section, in.-lb
Pn = nominal axial compressive strength of member, lb
Pn,max = maximum nominal axial compressive strength of a member, lb
Pnt = nominal axial tensile strength of member, lb
Pnt,max = maximum nominal axial tensile strength of member, lb
Po = nominal axial strength at zero eccentricity, lb
ϕ = strength reduction factor
εt = net tensile strain in the extreme layer of longitudinal tension reinforcement at nominal strength, excluding strains due to effective prestress, creep, shrinkage, and temperature
β1 = factor relating depth of equivalent rectangular compressive stress block to depth of neutral axis
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Maximum axial compressive strength
Nominal axial compressive strength Pn is limited to a value of Pn,max =0.8Po for non-prestressed members.
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Strength reduction factors ϕ is determined according to using ACI Table 21.2.2. Since the section is tension controlled, a ϕ factor for tension control is used.
Strain, εt | Section Classification | ϕ |
|---|---|---|
εt ≤ εty | Compression Controlled Moment | 0.65 |
εty < εt < (εty + 0.003) | Transition region | 0.65 + 0.25[(εt - εty)/0.003] |
εt ≥ (εty + 0.003) | Compression Controlled Moment | 0.90 |
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Design assumptions
The flexural and axial strength of a member calculated by the strength design method, two basic conditions should be satisfied:
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The distance between the fiber of maximum compressive stress and the neutral axis, c, is perpendicular to the neutral axis.
The value of β1 is determined using ACI Table 22.2.2.4.3.
fc' , psi | β1 |
|---|---|
2500 ≤ fc' ≤ 4000 | 0.85 |
4000 < fc' < 8000 | 0.85 - 0.05(fc' -4000)/1000 |
fc' ≥ 8000 | 0.65 |
Combined Flexural and Axial Strength
Nominal flexural strength Mn and axial strength are calculated using Design Assumptions. While finding the flexural design strength, combined with axial force ϕMn, it should be found in which control zone the cross-section is. When the section is tension controlled, a ϕ factor for tension control is used. A ϕ factor for compression control is used when the section is compression controlled. When the section is within the transition region, ϕ is linearly interpolated between the two limit values.
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Download ideCAD for ACI 318-19 |