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*

*Combination
Report - Combination Description*

**Reinforcement
along XOZ plane**

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

N_{Ed} =
825 kN

N_{Rd} =
k_{h} × k_{s} ×
α × [b × h × f_{cd} × A_{s} ×
f_{yd}]

k_{h} =
(0.75 + 0.5 × h) × (1 - 6 × ρ × δ)

The value for λ_{x} is
automatically calculated and it is displayed in the Buckling
Length dialog and the Geometry chapter of reports.

λ_{x} =
25.06

f_{yk} =
500 and λ < 40 =>** k _{s} =
1.00**

Replacing k_{h} and
ρ in the N_{Rd} equation, the
following expression is obtained:

We get a second-degree equation, with A_{s }as
the unknown:

We can determine A_{s} directly, by solving this second-degree
equation.

We get:

the determinant Δ ≥ 0: in this case, the solutions are real and the reinforcement areas are determined as above

the determinant Δ < 0: in this case, the solutions are complex and the following algorithm is used to determine the reinforcement areas.

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

It is considered
that k_{h,initial} = 0.93.

From
the equation below, an initial value for A** _{s }**can
be calculated:

N_{Ed} = k_{h} ×
k_{s} × α × [b × h × f_{cd} ×
A_{s} × f_{yd}]

Using
this value for A** _{s}**, ρ can
be determined:

The
next step is to calculate k_{h} by
replacing ρ in the equation below:

k_{h} =
(0.75 + 0.5 × h) × (1 - 6 × ρ × δ)

Using the
new value for k_{h}, the final reinforcement
area A_{s} is calculated:

After the
real reinforcement is calculated (A_{s, real} ≥ A_{s}), the real ρ, and then N_{Rd} is calculated.

The program
verifies if N_{Rd} ≥ N_{Ed}.

**Calculation when**** h
≥ 0.5 m**

It is considered
that** **k_{h,initial} =
1.

From
the equation below, an initial value for A_{s }can
be calculated:

N_{Ed} =
k_{h} × k_{s} ×
α × [b × h × f_{cd} × A_{s} ×
f_{yd}]

Using
this value for A** _{s}**, ρ can
be determined:

The next
step is to calculate k_{h} by
replacing ρ in the equation below:

After the
real reinforcement is calculated (A_{s, real} ≥ A_{s}), the real ρ, and then N_{Rd} is calculated.

The
program verifies if N_{Rd} ≥ N_{Ed}.