Column Combined Flexural and Axial Design.

Three-dimensional interaction failure surface of a column is calculated automatically

İnternational Design Codes

ACI 318-19 : Column Combined Flexural and Axial Design

TSC 2018 : Axial Force and Biaxial Moment Interaction for Columns

Notation in ACI 318-19

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
d = distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.
D = dead load
E = earthquake load
f_c^'= specified compressive strength of concrete, psi
f_y= specified yield strength for nonprestressed reinforcement, psi
L = live load
L_r = roof live load
M_n= nominal flexural strength at section, in.-lb
M_u = factored moment 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
P_u = factored axial force; to be taken as positive for compression and negative for tension, lb
R = rain load
S = snow load
T_n = nominal torsional moment strength, in.-lb
T_u = factored torsional moment at section, in.-lb
V_n= nominal shear strength, lb
V_u= factored shear force at section, lb
W = wind load
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

Required strength

Required strength is calculated in accordance with the factored load combinations. Combined Axial and Flexural Required strengths of a column occur simultaneously for a column. Therefore, for each applicable factor load combination specified in Codes.

Design strength

Combined nominal flexural and axial strength are calculated as shown below.

From the equation of equilibrium:

Nominal flexural strength:

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Column Shear Design.

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