## Robot Structural Analysis

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# EC8-4.3.1 (7) Reduced moment of Inertia

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Hi All

I'm trying to use the reduced moment of inertia of the cross sections of concrete elements to fulfill the rules of EC8-4.3.1 (7) and DM14/01/2008. Both codes require that:* "Unless a more accurate analysis of the cracked elements is performed, the elastic flexural and shear stiffness properties of concrete and masonry elements may be taken to be equal to one-half of the corresponding stiffness of the uncracked elements**"*.

The mechanism offered by the moment of inertia reduction is dedicated to this?

How should be interpreted what reported in the manual *"The Reduction of mom. of inertia option lets you specify coefficients reducing the section's moments of inertia (Ix, Iy, or Iz) in a section definition (RC beam or RC column). The reduction is associated with properties of a given section and it is not a global anlaysis parameter. Reduced moments of inertia are displayed (in tables or in dialogs) as current section properties. Reduced properties are considered in static calculations and are transferred to the design modules**" *

How the reduced moment of inertia affect the calcuation of the reinforcement as, according to the manual, the reduced value is passed to design modules?

In my opinion ULS and SLS verification should not be be affected by the reduced value !?

Any suggestion ?

Thanks

Solved! Go to Solution.

# Re: EC8-4.3.1 (7) Reduced moment of Inertia

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The coefficients entered in this dialog influence values of moments of inertia only in static analysis of the model. The RC Design modules calculate reduction of stiffness (when appropriate) based on cross sections of elements themselves. The only influence of these coefficients in the RC design modules are when you want to calculate buckling lengths of columns based on the stiffness of adjoining elements and when you scale 'elastic' deflections calculated during static analysis of the entire model to get 'cracked' deflection of a designed beam. For the latter the reduction of stiffness calculated by the design module is compared not to the uncracked (elastic) stiffness of the beam (static analysis) but to its reduced value (coefficient * Iy).

*If you find your post answered press the Accept as Solution button please. This will help other users to find solutions much faster. Thank you.*

**Artur Kosakowski**

# Re: EC8-4.3.1 (7) Reduced moment of Inertia

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Hi Atrtur,

Thank you for your attention. Remain for me something to understand in your answer:

*“when you scale 'elastic' deflections calculated during static analysis of the entire model to get 'cracked' deflection of a designed beam. For the latter the reduction of stiffness calculated by the design module is compared not to the unchecked (elastic) stiffness of the beam (static analysis) but to its reduced value (coefficient * Iy).”*

What do you mean with* ‘scaled’ 'elastic' deflection and 'cracked' deflection ?*. The displacement calculated with a reduced inertia should already be "scaled" in the sense that the reduction should simulate the situation just before the formation of plastic hinges. It should simulate the sections "cracked" !

I noticed also that in RC module the inflection of a beam varies using the reduced moment of inertia (see picture ..probably the explanation of symbols is not correct). In the latter case the beam have reduced inertia.

Thanks

# Re: EC8-4.3.1 (7) Reduced moment of Inertia

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Gabriele,

“when you scale 'elastic' deflections calculated during static analysis of the entire model to get 'cracked' deflection of a designed beam. For the latter the reduction of stiffness calculated by the design module is compared not to the unchecked (elastic) stiffness of the beam (static analysis) but to its reduced value (coefficient * Iy).”

What do you mean with‘scaled’ 'elastic' deflection and 'cracked' deflection ?. The displacement calculated with a reduced inertia should already be "scaled" in the sense that the reduction should simulate the situation just before the formation of plastic hinges. It should simulate the sections "cracked" !

Discussing a RC Beam there are two locations where you can see the values of its deflection. First you can see it after calculating the model (this is what I mean by the elastic deflection) where as you correctly expect the reduced value of moment of inertia is used but the next step is to calculate it in the RC Beam design module. As you well know when you export a beam from the model to the design module the design is based on values of internal forces 'taken' from the static calculations of the model rather than based on 'loads' applied to the beam as when you use the design module in the stand alone mode. If so the deflection calculated in the design module (this is what I refer to as cracked deflection) is based on the 'elastic' deflection calculated for the beam in the model and the reduced value of beam stiffness (calculated for real value of reinforcement and corresponding cracks) estimated in the RC Beam design module as we can see on the screen capture you attached below.

I noticed also that in RC module the inflection of a beam varies using the reduced moment of inertia (see picture ..probably the explanation of symbols is not correct). In the latter case the beam have reduced inertia.

Not going into the details it can be assumed that the 'cracked' value of deflection calculated in the design module will be just the scaled value of the 'elastic' deflection of the same beam calculated in the model and the scaling factor is the ratio between the elastic stiffness of the beam and the 'cracked' stiffness of the beam. As you already reduced the elastic stiffness in the model the scaling factor has to be modified as well (in such case we have to take into account that the value of the 'elastic' deflection of the beam in the model is already increased due to the manually reduced moment of inertia).

*If you find your post answered press the Accept as Solution button please. This will help other users to find solutions much faster. Thank you.*

**Artur Kosakowski**

# Re: EC8-4.3.1 (7) Reduced moment of Inertia

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Hi Artur;

I think I have (or I hope) understood nearly all. If I use the reduction of moment of inertia I will have, for the whole structure, the behavior similar to a ‘cracked’ one. The period of the structure became longer, the stresses became smaller and, finally, the displacement became larger with respect to the forces due the reduced moment of inertia.

In this case, if I well understand, you are saying that in order to calculate the “plastic displacement”, as required by regulations (i.e. scaling them by q for T>Tc), I shold take in account that part of the displacement are already there due to the reduction of moment of inertia

I don’t agree because the reduction of the moment of inertia simulates the secant stiffness of the material in an ideal bilinear diagram elastic perfectly plastic just a moment before the plastic hinge creation. So, in my opinion, the displacement calculated should be amplified as required by rules as this operation represent a quite rough way to find the final plastic displacement due to the equal displacement or energy principle. This is a behavior at the whole structure scale.

I think that when you are dealing with the design of a single RC element (i.e. a concrete beam) the moment of inertia of the RC element came from the exact calculation of the neutral axis position and the amount of reinforcement and so on. In this case, in my opinion, you have the ‘true’ cracked moment of inertia but “false” internal forces lower than the “real forces” due to the longest period of the structure. So in this case the calculated displacement should be true !!.

I don’t know if I have cheated myself with my hand with all this reasoning…. But it seems that it works fine.

Thanks Artur

# Reduced shear stiffness

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Hi I don't want to open a new thread for a similar question

1)Is there also a way in robot to use reduced values of Ay and Az of RC section members?

2) Why the values of Ay and Az of a simply rectangular RC section defined by the user appear with zero value in the properties table while default rc sections appear with their right values? (see picture). Is there a way to set the real values of Ay and Az for all sections (retangular at least)?

thanks in advance

# Re: Reduced shear stiffness

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1) Not directly but you can try to reduce the cross section size and increase Ix, Iy and Iz.

2) Planned to be corrected in v.2014

**Please note: **Our quality assurance teams may need to reschedule some fixes. Please rely on the above timeline information as a guideline only and **not** a guarantee. We appreciate your understanding in this matter.

**Artur Kosakowski**

# Re: EC8-4.3.1 (7) Reduced moment of Inertia

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Something really much useful would be the ability to change any kind of value of moments of inertia (or Ay, Az e.t.c) directly through the Inspector dialog box.

# Re: EC8-4.3.1 (7) Reduced moment of Inertia

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Thank you Artur for your answer,

even if I don't consider the reduction of shear stiffness as much important as the reduction of the EI, and yes as you mentioned I could use an "equivalent" section, however it would be nice to have the opportunity to reduce its value directly through the software, just to make our life simpler .

# Re: EC8-4.3.1 (7) Reduced moment of Inertia

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Tuctas wrote:

Something really much useful would be the ability to change any kind of value of moments of inertia (or Ay, Az e.t.c) directly through the Inspector dialog box.

and then double click on the section label (which might have been assigned to many bars but the change done to one of them) and see different values (the ones that were originally defined)

**Artur Kosakowski**