Effective moment of inertia for circular columns

[WARose]

I've looked all over the place and I cannot find a formula for a accurate estimate of moment of inertia for a RC column.

ACI 318-11 certainly has a few formulas on this (i.e. 10-14, 10-15, etc). But a lot of research I have seen has shown those formulas to be inaccurate.

I might be able to do a transformed area calculation.

 

[BridgeSmith]

There are numerous methods for estimating the effective (cracked) moment of inertia for reinforced concrete and all have a fairly wide margin of error overall. Some are fairly accurate within a narrow range of reinforcement ratios and bending stress levels, but the variability in concrete rupture stress makes estimating Ie with good accuracy virtually impossible.

For an uncracked section, Ie = Ig and you can calculate it using transformed section properties, although the accuracy of that is not terribly good either, since there is significant variation in modulus of elasticity for concrete, as well.

If the stress level is high enough for the concrete to crack, I usually 'envelope' the design, using the least favorable Ie values calculated from the high and low concrete rupture stress values.

 

[KootK]

Given the uncertainties that HotRod mentioned, I think that representation as an equal area square is about as good as anything else. In addition, consideration of creep complicates things even further as it will tend to shift axial stress to the rebar as well as gradually relieve long term moments.

 

[JAE]

There was this article some time ago from the ACI Structural Journal.

Title: Refined Stiffness of Slender Circular Reinforced Concrete Columns
Author(s): M. R. Ehsani and F. Alameddine
Publication: Structural Journal
Volume: 84
Issue: 5
Appears on pages(s): 419-427
Keywords: bridge piers; columns (supports); loads (forces); stiffness; moments of inertia; slenderness ratio; structural design; Structural Research
Date: 9/1/1987
Abstract:
The ACI Building Code (ACI 318-83) expressions for estimating the stiffness of a cracked section were examined and found to be too conservative for circular cross sections. A parametric study was performed, and the significant variables were determined.

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[skeletron]

There are some formulas in A23.3-14 for effective stiffness (EI) of a column. One is based on the moment of inertia of the gross section and a modifier taking into the account the effect of sustained loads. The alternate equation uses a similar sustained load factor but also incorporates the stiffness given by the reinforcing bar pattern. The commentary indicates an Ist value "for 4, 8, or infinite bars."

Both equations are lower bound values.

 

[azcats]

Hah - Dr. Ehsani was one of my professors.