Effective Stiffness - Uncracked

[lg1990]

Hello,

I am wondering if anyone has been able to use gross stiffness properties in a concrete structure if it is proven that the tensile stress in a concrete member is not present under service level loading.

This is a question from someone who works in SoCal. ACI 318-14 Section 6.6.3.1.1 notes that the tabled values shall be used unless a more rigorous calculation is used.

My thoughts are if the tensile stress is less than fr, then for an example a 1.0EI can be used for beams and columns, and 0.7EI can be used for walls.

This could be applicable to moment frame buildings in which drifts are controlling.

Side question: Why are walls the only element that has an effective stiffness based on cracking, whereas the other elements only have one value? And also, do most people just take the 0.35 penalty for walls, or do they actually check the stresses for cracking to get the 0.7 value? Compressive stresses are often checked anyways to check if SBE is required.

Thanks in advance!

 

[EZBuilding]

Table 6.6.3.1.1 provides the calculations for Alternative moments of inertia for elastic analysis at factored loads - it does not allow for an Ig greater than 0.875.

For the purposes of a crack analysis for shear walls, I check the wall stresses against the modulus of rupture at each design level I am considering - i.e. serviceability/strength. Those walls which have stresses greater than the modulus of rupture gets the reduced crack factor. I do not iterate the analysis and do it once. Additionally - at times I will not crack an entire wall which only has a small section of it "cracked". There is some levels of engineering judgement that goes towards the process. Increased big P-Delta moments due to decreased stiffness and capturing force distributions due to relative rigidity of different lateral elements are my primary thoughts during these processes.

6.6.3.1.2 allows for the stiffness of all members to be taken as 0.5Ig in lieu of performing a cracking analysis - so the 0.35 factor for all walls would be overtly conservative.

I have not designed a reinforced concrete moment frame previously - but I share your thoughts regarding the assumed stiffness of those elements during a lateral event. I would likely run though the procedure of table 6.6.3.1.1 for those columns or choose to go to the 0.5Ig for all members.

You mentioned drift controlling - don't forget that 6.6.3.2.2 allows for the moment of inertia of all elements to be increased by a factor of 1.4 for immediate lateral deflections.

 

[centondollar]

EZBuilding:
". Those walls which have stresses greater than the modulus of rupture gets the reduced crack factor. I do not iterate the analysis and do it once. Additionally - at times I will not crack an entire wall which only has a small section of it "cracked". There is some levels of engineering judgement that goes towards the process. "

If you do not iterate the solution, you will not capture the actual behavior of the structure, and strictly speaking iteration by "manually defining" cracked members is not based on structural mechanics. A non-linear analysis requires a non-linear element formulation, load-stepping (or displacement-stepping), an iterative solution algorithm (e.g., Newton-Raphson) and ensuring that the calculation converges after increments are stopped at a given load level.

Engineering judgement -i.e., recognizing one's ignorance and attempting to find the worst-case scenario for design - would be to assume that most members crack and that no members crack, and then checking these two extremes regarding internal forces, deflections and seismicity-induced forces and deflections and picking the worst-case scenario. Even then, the analysis might not be on the safe side.

 

[centondollar]

Ig1990:

"I am wondering if anyone has been able to use gross stiffness properties in a concrete structure if it is proven that the tensile stress in a concrete member is not present under service level loading."
You will very seldom have beams with bending moments less than the cracking moment, and the same goes for columns, even if the axial load is large and dominant in comparison to the column moment.

"And also, do most people just take the 0.35 penalty for walls, or do they actually check the stresses for cracking to get the 0.7 value?"
Checking stresses is not of much use - if accuracy is important - if the analysis is not based on structural mechanics; i.e., performing linear elastic analysis and then manually selecting members, "cracking them" by modifying stiffness and re-running the linear elastic analysis for an arbitrary number of times. It is usually easier to grossly underestimate the stiffness of most members by referring to tables in standards, since the alternative (if structural mechanics is to be applied correctly) is full non-linear analysis.

 

[EZBuilding]

If you do not iterate the solution, you will not capture the actual behavior of the structure, and strictly speaking iteration by "manually defining" cracked members is not based on structural mechanics. A non-linear analysis requires a non-linear element formulation, load-stepping (or displacement-stepping), an iterative solution algorithm (e.g., Newton-Raphson) and ensuring that the calculation converges after increments are stopped at a given load level.

Engineering judgement -i.e., recognizing one's ignorance and attempting to find the worst-case scenario for design - would be to assume that most members crack and that no members crack, and then checking these two extremes regarding internal forces, deflections and seismicity-induced forces and deflections and picking the worst-case scenario. Even then, the analysis might not be on the safe side.

My comments are reflected based on following ACI's Elastic Second Order Analysis procedures. You may be referencing ACI's Inelastic second-order analysis - for which I have not heard of any practicing engineers use for the design of a building during my practice. I practice in a none to low seismic area, although with very high wind loads, but your analysis comments may be more consistent in a seismic building that requires substantial levels of ductility.