Axial strength or Combined Flexural and Axial Strength.

İnternational Design Codes

ACI 318-19 : Axial strength or Combined Flexural and Axial Strength per ACI 318-19 with ideCAD

TSC 2018 : TSC Axial strength or Combined Flexural and Axial Strength

Notation in ACI

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

Flexural Strength

Nominal flexural strength M_n and axial strength are calculated based on the following Design Assumptions.

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:

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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 Codes.