Stiffness and Concrete Pier Bent Moments

Curvbridger,
For vertical load analysis reinforced concrete cap stiffness can be reduced by half, but columns shall have gross properties since flexutral demans are low under static loads. For seismic analysis columns stiffness shall be reduced by half as well. Basically, the stiffness reduction of reinforced concrete members can be justified if bending moment exceeds Mcr=1.7sqrt(f'c)I/Yt.

Yakpol,

Thanks for your interest.

I follow your thinking, although I don't know on what basis 50% is selected. Code reference??

You mentioned dynamic loads and static vertical loads, but not static horizontal loads. The largest loads affecting my pier are cap shrinkage and friction forces from temperature change. I assume that any significant lateral loads applied at the cap would cause stiffness reduction in the columns. Agreed?

curvbridger,
AASHTO does not regulate the member stiffness for frame analysis. Some seismic criterias like CALTRANS SDC 1.2 (seismic design criteria) recommend a chart of Icr/Ig depending on the reinforcing ratio (varies from 0.4 to 0.6). Also you can calculate Icr as transformed section based on compression block height and steel reinforcing. The other way is to run moment-curvature analysis (Response 2000 ) of the section, then stiffness EI = Moment/Curvature. To justify stiffness reduction due to cracking compare the moment derived from uncracked model with Mcr = 7.5sqrt(f'c)I/Yt.
For the loads you describe (shrinkage and temperature) the modulus elasticity of concrete in the model shall be reduced about 50% taking into account long-term character of your loads. I cannot remember the reference but it's a common practice for thermal analysis of concrete structures.

Yakpol