Axial strength or Combined Flexural and Axial Strength

Notation

A_g = gross area of concrete section, in²
A_s = area of nonprestressed longitudinal tension reinforcement, in²
A_st = total area of nonprestressed longitudinal reinforcement, in²
α = depth of equivalent rectangular stress block, in.
b_w = width of compression face of member, in.
c = distance from extreme compression fiber to neutral axis, in.
C_c = concrete compressive force, lb
C_s = reinforcement tension force, lb
f_c^' = specified compressive strength of concrete, psi
f_y = specified yield strength for nonprestressed 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 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

Maximum axial compressive strength

Nominal axial compressive strength P_n is limited to a value of P_n,max in ACI Table 22.4.2.1.

For nonprestressed concrete members, P_o shall be calculated by:

According to ACI Table 22.4.2.1 Maximum axial compressive strength for a nonprestressed concrete member with closed tie;

The maximum design compressive strength for a nonprestressed concrete member with closed tie;

Strength reduction factors ϕ is determined according to using ACI Table 21.2.2. Since the section is compression controlled, a ϕ factor for compression control is used.

Maximum axial tensile strength

Nominal axial tensile strength P_nt is limited to a value of P_nt,max in ACI 22.4.3.1.

The maximum tensile axial load for a nonprestressed concrete member;

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 based on the following 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. When the section is compression controlled, a ϕ factor for compression control is used. When the section is within the transition region, ϕ is linearly interpolated between the two limit values.

Design assumptions

The flexural and axial strength of a member calculated by the strength design method, two basic conditions should be satisfied:

1. equilibrium

2. compatibility of strains

Equilibrium means balancing of forces acting on the element cross section at nominal strength. Stress-strain relationship for the concrete and the reinforcement at nominal strength is established within the design assumptions described follow:

• Equilibrium is satisfied at each section.

• It is assumed that strain in concrete and reinforcement is proportional to the distance from neutral axis.

Design strength is calculated by using these assumptions together with design assumptions for concrete described follow:

• Maximum strain at the extreme concrete compression fiber is assumed equal to 0.003.

• Tensile strength of concrete is neglected.

• The relationship between concrete compressive stress and strain is represented by equivalent rectangular concrete stress distribution method.

• Concrete stress of 0.85f_c^' is assumed 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:

• 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.