# 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, in**

_{ }=^{2}

**A**_{s}**area of nonprestressed longitudinal tension reinforcement, in**

_{ }=^{2}

**A**_{st }**=**total area of nonprestressed longitudinal reinforcement, in

^{2}

*depth of equivalent rectangular stress block, in.*

**α =***width of compression face of member, in.*

**b**_{w }=*distance from extreme compression fiber to neutral axis, in.*

**c =**

**C**_{c}**concrete**

_{ }=**compressive force, lb**

**C**_{s}**reinforcement tension force, lb**

_{ }=*distance from extreme compression fiber to centroid of longitudinal tension reinforcement, in.*

**d =***dead load*

**D =***earthquake load*

**E**_{ }=*specified compressive strength of concrete, psi*

**f**_{c}^{'}_{ }=*specified yield strength for nonprestressed reinforcement, psi*

**f**_{y }=*live load*

**L**_{ }=*roof live load*

**L**_{r}_{ }=*nominal flexural strength at section, in.-lb*

**M**_{n }=

**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**

_{ }=*rain load*

**R**_{ }=*snow load*

**S**_{ }=*nominal torsional moment strength, in.-lb*

**T**_{n }_{ }=*factored torsional moment at section, in.-lb*

**T**_{u }_{ }=*nominal shear strength, lb*

**V**_{n }=*factored shear force at section, lb*

**V**_{u }=*wind load*

**W**_{ }=**ϕ**

*strength reduction factor*

**=***net tensile strain in extreme layer of longitudinal tension reinforcement at nominal strength, excluding strains due to effective prestress, creep, shrinkage, and temperature*

**ε**_{t }=**β**factor relating depth of equivalent rectangular compressive stress block to depth of neutral axis

_{1 }=**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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