Simplified method Example

 

We consider a column with a 0.3 x 0.4 m rectangular section and a 3.10 m height. The concrete class is C25/30. The loads and combinations on the column are the following:

 

 

Loads definition dialog

 

Loads definition dialog

 

Loads definition dialog

 

 

Combination Description

 

Combination Report - Combination Description

 

 

 

Formula

 

 

 

Reinforcement along XOZ plane

Load combination 104 : +1.35x[1 G]+1.5x[2 Q]

 

NEd = 825 kN

NRd = kh × ks × α × [b × h × fcd × As × fyd]

kh = (0.75 + 0.5 × h) × (1 - 6 × ρ × δ)

 

 

formula

 

 

 

Calculation of d':

 

Main longitudinal Main transversal reinforcement

 

 

 

 

concrete covers

 

 

 

 

forumula

 

The value for λx is automatically calculated and it is displayed in the Buckling Length dialog and the Geometry chapter of reports.

 

buckling length

 

 

 

 

λx = 25.06

fyk = 500 and λ < 40 => ks = 1.00

formula

 

Replacing kh and ρ in the NRd equation, the following expression is obtained:

formula

 

We get a second-degree equation, with As as the unknown:

 

formula

 

We can determine As directly, by solving this second-degree equation.

We get:

formula

 

 

Calculation when the determinant of the second-degree equation is negative

It is considered that kh,initial = 0.93.

From the equation below, an initial value for As can be calculated:

NEd = kh × ks × α × [b × h × fcd × As × fyd]

formula

 

Using this value for As, ρ can be determined:

formula

 

The next step is to calculate kh by replacing ρ in the equation below:

kh = (0.75 + 0.5 × h) × (1 - 6 × ρ × δ)

Using the new value for kh, the final reinforcement area As is calculated:

formula

 

After the real reinforcement is calculated (As, real ≥ As), the real ρ, and then NRd is calculated.

formula

 

The program verifies if NRd ≥ NEd.

Calculation when h ≥ 0.5 m

It is considered that kh,initial = 1.

From the equation below, an initial value for As can be calculated:

 

NEd = kh × ks × α × [b × h × fcd × As × fyd]

 

Using this value for As, ρ can be determined:

formula

The next step is to calculate kh by replacing ρ in the equation below:

formula

 

After the real reinforcement is calculated (As, real ≥ As), the real ρ, and then NRd is calculated.

NRd calculation

 

The program verifies if NRd ≥ NEd.