Efficient Calculation of Inertia for Cracked Concrete Sections

Overview

Sometimes we need tiresome calculations, even though they are not critical nor difficult, but they are essential, and they take time if we do not have proper tools. One of these is the moment of inertia calculation for cracked, circular concrete sections. We need this calculation when we perform service stress checks for flexure and deflection checks.

f’c = 3.5 ksi, 2 in. cover, #5 spiral (d = 0.625 in.), 1% reinforcement with #11 (d = 1.410 in.) rebars

In the symmetrical reinforcement sections, each rebar location needs is not considered, and we can assume the rebars as a ring.

D1 = 72” – 2(2” + 0.625” + 1.410”/2) = 65.34”

Step1) Assume neutral axis location

Assume the neutral axis for the cracked section is located 28.226” from the circle center.

r cosα = (36”) cosα = 28.226”

α = 38.3663° = 0.6696 rad

Actually, it is more common and convenient to assume the angle α first then calculate the neutral axis location (r cosα).

Step2) Calculate compress zone concrete area

Step3) Calculate compression rebar area

r1 cosα1 = r cosα= 

α1 = 0.5277 rad = 30.234°

n = (29000 ksi)/(1820√3.5ksi) = 8.517

You can check more of these details in the download file.

Step4) Calculate tension rebar area

Step5) Check assumed neural axis location

Step6) Calculate the moment of inertia for the neutral axis

Step7) Check

Excel Sheet (Cracked Circular Section)

About the Editor

Seungwoo Lee PhD, P.E., S.E.

Senior Supervising Engineer at WSP USAs (Tampa, FL)

He is a Senior Supervising Engineer with a high level of expertise in the design and analysis of suspension bridges. He has a solid fundamental understanding of structures and can apply his knowledge exceptionally well to the design and analysis of highly complex structures. He is also a strong communicator, able to identify and distill the key information that is relevant to the task at hand and present it in a clear and quickly understandable manner.