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## Ductility check |

The above cross section of a column is within the critical region at the base C30/37 of a structure designed in DCM ductility class.

C30/37 is the concrete class and B450C is the steel grade.

We want to perform a verification of resistance and a verification of ductility with reference both uniaxial than biaxial forces. The uniaxial acting forces in y direction are (first combination):

N = 400 kN; Mx= 100 kNm; My = 0; Vy = 150 kN; Vx = 0

The biaxial forces (second combination) Mx,My, Vy,Vx have the same vectorial intensity but an inclination of 45° with respect x axis:

N = 400 kN; Mx = 70.71; My = 70.71; Vy = 106 kN; Vx = 106 kN.

The curvature ductility factor (§ 5.2.3.4(3) EC8) is μΦ = 6.8 for all seismic directions.

INPUT DATA

The concrete design strength is: fcd = αcc⋅ fck / γc = 1.00 ⋅ 50 / 1.5 = 20.0 Mpa

The steel design yield strength is: fyd = fyk/ γs = 450/1.15 = 391.3 Mpa

In this example we first control, in particular, the parameters γc, γs , αcc , cot θ in Code and reinforcement option window.

In the below General Data windows we should selected the typology "Rectangular section of column". We select DCM as Ductility class and set the above curvature ductility factor (6.8).

In the below Section Data window we select and assign:

- The option "Check" to perform resistance check and "6" as diameter of stirrups in order to perform the check of stirrups for shear resistance check and ductility check.

- Materials classes for concrete and steel bars (for longitudinal and stirrups reinforcement)

- Dimension and cover of the rectangular concrete section and the bar reinforcement provision.

- Stirrups diameter and pitch: Note that in this first input it is not possible to assign specific cross-tie: it will be possible only after a first run in the Stirrups-Ductility window.

The report for moment forces capacity check is:

The safety factor for biaxial second combination is lesser than the first uniaxial combination as you also see by the interaction diagram:

The capacity and ductility shear check report is:

Shear resistance of concrete struts and of stirrups are they are considerably greaterthen both the first(uniaxial) and the second (biaxial) combination. The ductility checks performed with the (5.15)EC8 equation are positive for both combinations.

The direct moment-curvature diagram for the uniaxial combination (design value of materials and confining of stirrups) leads to a slightly negative check for the ductility factor μΦ = 6.17 < 6.8.

The direct moment-curvature diagram for the biaxial combination leads to a considerably negative check for the ductility factor μΦ = 4.56 < 6.8 so showing the limit of the (5.15) check in biaxial assessment: