Especially for sections of seismic structures may be useful a direct calculation of the curvature ductility factor [eq. (5.4),(5.5)Ec8] by means the calculation of moment-curvature diagram.
Program is able to generate moment-curvature in biaxial bending too and for any section shape. For section with only one concrete region is also possible to obtain diagrams taking in account the confining of concrete by stirrups.
In the figure below is sown such a diagram generated for a confined rectangular column in seismic zone. Diagram can be saved as a dxf file, numeric results can be printed on the screen or on paper.
Ductility checks concern the following positions of sections of structures in seismic zones:
•within critical regions at the ends of all the beams (not secondary beams)
•within critical regions at the base of columns in DCM ductility class. (are excluded all the other critical areas of the columns on the upper floors on the first)
•within all critical region of columns in DCH ductility class.
•within critical regions of ductile walls
To respect the local ductility in the above critical regions the curvature ductility factor μΦ must comply with the rule in §5.2.3.4 EC8:
μΦ ≥ 1,5 (2q0 - 1) if T1 ≥ TC (5.4) EC8
μΦ ≥ 1,5 [1+2(q0 - 1)] TC/ T1 if T1 < TC (5.5) EC8
where:
q0 basic value of the behaviour factor
T1 fundamental period of the building
TC period at the upper limit of the constant acceleration of the spectrum
For beams EC8 allows to replace (5.4) above control with the equations (5.11), (5.12).
For columns EC8 allows to replace (5.4) above control with the relation (5.15).
Building a moment-curvature diagram of the cross-section it is possible to evaluate μΦ so as to allow a direct check of the above (5.4)-(5.5).
In the figure below is shown such a diagram generated for a rectangular section of a column in seismic zone (with confinement for core section).
The moment-curvature diagrams can be of the following types:
- The first option generate a diagram using for concrete and steel the same stress-strain relationship used for design check but with the substitution of the design values with the mean ones.
- The second option refers to a diagram that, only for one concrete region section, take in account the confining of concrete core by stirrups and the spalling of concrete cover at strain strength. (See Ductility Checks)
- The third type refers to a concrete stress-strain relation parabola-trapeze (Kent-Park Type) whose parameters are assigned in the Materials Library.
- Last type generate a diagram base on the relation shown in §3.1.5 EC2. You can take into account a certain percentage of tension stiffening.