Reinforced concrete column capacity for axial force and bending about Y-axis Eurocode 2, EN 1992-1-1 (2004)

To determine the capacity of a reinforced concrete column for axial force and bending about the Y-axis according to Eurocode 2 (EN 1992-1-1), the following steps can be followed:

Calculate the design axial force (NEd): This is the combination of axial loads acting on the column, such as dead loads, live loads, and any other relevant loads.

Calculate the design bending moment (My,Ed): This is the moment acting about the Y-axis due to lateral loads or eccentricity of the applied loads.

Determine the effective height (hef) of the column: The effective height is used to account for the influence of lateral restraints on the column. It is typically taken as the distance between the points of contraflexure.

Calculate the slenderness ratio (λ): The slenderness ratio is the ratio of the effective height (hef) to the radius of gyration (r). The radius of gyration can be calculated using the column dimensions and properties.

Determine the design resistance for axial force (Nc,Rd): The design resistance for axial force is given by:

Nc,Rd = φc * fcd * Ac + φs * fyk * Asc

Where:

φc: Resistance factor for concrete
fcd: Design compressive strength of concrete
Ac: Cross-sectional area of the column
φs: Resistance factor for reinforcement
fyk: Characteristic yield strength of reinforcement
Asc: Area of tensile reinforcement
Determine the design resistance for bending about the Y-axis (My,Rd): The design resistance for bending is given by:

My,Rd = φs * fyk * W * (1 – β * λ^2)

Where:

φs: Resistance factor for reinforcement
fyk: Characteristic yield strength of reinforcement
W: Plastic section modulus of the column cross-section
β: Coefficient that depends on the type of column cross-section
λ: Slenderness ratio
Verify the capacity requirements: Compare the design axial force (NEd) with the design resistance for axial force (Nc,Rd), and compare the design bending moment (My,Ed) with the design resistance for bending (My,Rd). Ensure that the applied loads do not exceed the resistance capacity of the column.