Deflection in a one-way spanning concrete and steel manhole cover

[cve60069]

Hello

I am wanting to calculate the deflection in a manhole-cover I am drawing (attached).

The concrete is effectively a reinforced-slab with the reinforcement welded to the steel-frame. The frame is 5mm thick (or more depending on my calculations).

How should I calculate the deflection, please. My feeling is to calculate the neutral-axis of the whole-slab using a transformed section based on the 'E' values, obtain a transformed 'I' and hence the deflection based on a formula. This method, I assume, considers the slab to be composite and I am sure I shall be reminded that, due to strain-compatibility issues, this will not be the case and what of the neutral-axis after cracking of the concrete? I could use the transformed-section method for the concrete and reinforcement, but not for the reinforced-concrete and steel-tray. I thought of using superposition by adding the deflection of the slab + deflection of the tray, distributing the load in proportion to the relative 'EI' but I will have two neutral-axis - one for the concrete and one for the steel. I am still not convinced.

Any tips would be greatly appreciated.

Regards

 

[Splitrings]

Chapter 9 of ACI 318 specifies a method of calculating deflections. It uses an I somewhere between the Icracked and Igross.

 

[briancpotter]

Your last method, I think, is the closest approximation to what the slab will actually experience. It's hard to see it acting as a composite section without some sort of mechanism for shear transfer between the steel pan and the concrete - studs, etc.

Because EI of the steel pan will be so low, I think it's reasonable to ignore it and simply calculate the deflection of the concrete. Your span is short enough that deflection shouldn't be a major issue.

Brian C Potter, PE

http://simplesupports.wordpress.com

 

[Splitrings]

I thought your question was awful basic. I just realized there is a steel section on the bottom side of the concrete.

If you did have a means of transfering the shear between the pan and the concrete you could calculate the deflection based on a transformed section the gross area of concrete. With the transformed section you would know what the tensile stress is at the interface of the pan and concrete. If it was below the tensile strength of concrete your assumption might be reasonable. If not, you'd assume the concrete cracked and you'd need to recalculate I based on the cracked section.