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.
%2c%201%25%20reinforcement%20with%20%2311%20(d%20=%201.410%20in.)%20rebars.png?width=199&height=133&name=f%E2%80%99c%20=%203.5%20ksi%2c%202%20in.%20cover%2c%20%235%20spiral%20(d%20=%200.625%20in.)%2c%201%25%20reinforcement%20with%20%2311%20(d%20=%201.410%20in.)%20rebars.png)
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”
%20=%2065.34%E2%80%9D.png?width=201&height=129&name=D1%20=%2072%E2%80%9D%20%E2%80%93%202(2%E2%80%9D%20%2B%200.625%E2%80%9D%20%2B%201.410%E2%80%9D%202)%20=%2065.34%E2%80%9D.png)
Step1) Assume neutral axis location
%20Assume%20neutral%20axis%20location.png?width=219&height=163&name=Step1)%20Assume%20neutral%20axis%20location.png)
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
%20Calculate%20compress%20zone%20concrete%20area.png?width=624&height=331&name=Step2)%20Calculate%20compress%20zone%20concrete%20area.png)
%20Calculate%20compress%20zone%20concrete%20area_2.png?width=417&height=60&name=Step2)%20Calculate%20compress%20zone%20concrete%20area_2.png)
Step3) Calculate compression rebar area
%20Calculate%20compression%20rebar%20area.png?width=203&height=165&name=Step3)%20Calculate%20compression%20rebar%20area.png)
r1 cosα1 = r cosα= 
α1 = 0.5277 rad = 30.234°
n = (29000 ksi)/(1820√3.5ksi) = 8.517
%20(1820%E2%88%9A3.5ksi)%20=%208.517.png?width=510&height=71&name=n%20=%20(29000%20ksi)%20(1820%E2%88%9A3.5ksi)%20=%208.517.png)
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)
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.
