General 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 25/30. The loads on the column are the following:

 

Top loads

Bottom loads

Combinations

 

 

 

The workflow followed by the program to establish the reinforcement area is the following:

This calculation is done individually for X and Y directions.

The program starts from a minimum reinforcement area:

 

minimum reinforcement area

 

 

This method consists of two verifications:

 

 

1. NEd ≤ NRd

 

2. eint

 

 

 

The increment step of the iterative calculation of reinforcement bars can be defined in the Design Assumptions dialog, as Reinforcement precision.

 

 

Reinforcement precision

 

 

 

The detailed report gives the final theoretical reinforcement that verifies the relation.

The following example follows will use the reinforcement areas from the report to exemplify the calculation for total external eccentricity, eext.

As,x = 1.2 cm2

As,y = 1.2 cm2

The detailed calculation below is given for combination 105, giving the maximum Acorresponding to the last iteration.

This method consists of two verifications:

NEd ≤ NRd

and

eint ≥ eext

eext is the total external eccentricity

eext = e1 + e2

e1 is the 1st order eccentricity

e2 is the 2nd order eccentricity

e1 = e+ ei

e0 is the initial eccentricity

ei is the geometrical imperfections eccentricity

eccentricity

 

εc is the concrete strain

 

εc

 

εc1

(Compressive strain in the concrete at the peak stress fc)

 

fcm

 

φ(∞,t0 is the final creep coefficient.

This value is displayed in the report in the Creep Coefficient chapter.

φ(∞,t0) = 2.71

M0Eqp is the first-order bending moment in a quasi-permanent load combination (SLS).

M0Ed is the first-order bending moment in design load combination (ULS).

Regardless of the method used for element calculation, the geometrical imperfections should be considered only at ULS.

We consider an initial eccentricity defined by:

initial eccentricity

 

M0Ed= M0Ed,input + NEd × e= 40.5 + 837.32 × 0.02 = 57.246 kNm (in design load combination 105)

M0Eqp= M0Eqp,input 30 kNm (in quasi-permanent load combination 114)

formula

 

εs = 3.19‰ (the value for which the section is balanced)

 

ec

(the bottom concrete strain value for which the section is balanced)

 

Model

 

Since, in the design phase, the real d’ is not known, the program will use in calculation the concrete cover from the Concrete cover dialog:

 

 

concrete cover

 

 

In the initial stage, the calculation will be done using the value from the Viewport. After a certain number of iterations, a longitudinal reinforcement area and a transversal reinforcement area with specific diameters will result.

 

Diameters

 

 

In the final stage, the calculation is done again with the real d’ obtained as:

 

d

 

The report will reflect the final stage, with the real value of d’.

 

the real value of d

 

The value for l0 is automatically calculated. It is displayed in the Buckling Length dialog and the Geometry chapter of the report.

 

The value for l0