Page Comparison

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Notation

A_{g =} gross area of the concrete section, in²
A_{s =} area of non-prestressed longitudinal tension reinforcement, in²
A_st = total area of non-prestressed longitudinal reinforcement, in²
α = depth of equivalent rectangular stress block, in.
b_w = width of compression face of the member, in.
c = distance from extreme compression fiber to the neutral axis, in.
C_{c =} concretecompressive force, lb
C_{s =} reinforcement tension force, lb
f_c^'₌ specified compressive strength of concrete, psi
f_y = specified yield strength for non-prestressed reinforcement, psi
M_n = nominal flexural strength at section, in.-lb
P_{n =} nominal axial compressive strength of member, lb
P_n,max = maximum nominal axial compressive strength of a member, lb
P_{nt =} nominal axial tensile strength of member, lb
P_nt,max = maximum nominal axial tensile strength of member, lb
P_{o =} nominal axial strength at zero eccentricity, lb
ϕ = strength reduction factor
ε_t = 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 P_n is limited to a value of P_n,max =0.8P_o 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.

Flexural Strength

Nominal flexural strength M_n and axial strength are calculated using Design Assumptions. While finding the flexural design strength, combined with axial force ϕM_n, 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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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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• Maximum strain at the extreme concrete compression fiber is assumed to equal to 0.003.

• The tensile strength of concrete is neglected.

• The equivalent rectangular concrete stress distribution method represents the relationship between concrete compressive stress and strain.

• Concrete stress of 0.85f_c^' is assumed to be uniformly distributed over. Equivalent rectangular concrete stress zone bounded by edges of the cross-section and a line parallel to the neutral axis located a distance α from the fiber of maximum compressive strain, as calculated by:

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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.

Combined Flexural and Axial Strength

Nominal flexural strength M_n and axial strength are calculated using Design Assumptions. While finding the flexural design strength, combined with axial force ϕM_n, 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.

Nominal flexural strength M_n with zero compression is calculated as described in the title of Flexural Strength per ACI 318-19 with ideCAD. Similarly, with the same design assumptions combined nominal flexural and axial strength M_n and P_n are calculated as shown below.

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From the equation of equilibrium:

Nominal flexural strength M_n:

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