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What is the equation of formula to calculate flexural rigidity of RC Slab

Dear eveyone,

I need to know the formula or expression to calculate the flexural rigidity (D) of RC Slab reiforced with steel bars. I know that for plain concrete, D can be taken as Et3/12(1-v2). However, I have no idea what is D when steel bars are added to slab. I really appreciate for any kind help. Thanks

Comments

Dear elmi,

I think the formula you need is the following:

D=[(h^3-d^3)/12-b^2*d]*Ec/(1-ν^2)+(b^2*d+d^3/12)*Es/(1-ν^2)

where:

h is the total thickness of the plate (including reinforcement)

b is the distance from the center of gravity of the reinforcement alone to the center of gravity of the plate, if it is supposed to contain no reinforcement at all

d is the thickness of the reinforcement and

Es and Ec are the modulus of elasticity of the reinforcement and the concrete respectively

Besides, because I cannot find a way to attach a file here, in orde to show you the various geometric details of the plate, I recommend that you send me an email at gpapazafeiropoulos@yahoo.gr to discuss further the topic and to clarify the details and the assumptions of the model form which I derived the above equation. Note please that the above equation is valid if and only if the Poisson ratio of the concrete is equal to the Poisson ratio of the steel reinforcement.

Best regards,

George Papazafeiropoulos

Second Lieutenant, Hellenic Air Force

Civil Engineer, PhD Candidate

Wenbin Yu's picture

It is technically a composte beam. Although some engineering constants can be approximately by using some assumptions like the famous Euler-Bernoulli assumptions. However, it is unnecessary if you use the variational asymptotic method to carry out a rigorous dimensional reduction from 3D elasticity to a beam model. This approach is implemented in a general-purpose cross-sectional analysis tool, VABS , which can adequately deal with your problem.

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