Reinforcement ratio of concrete beams (T sections) 2

[ElyasCivil]

Hello everyone, while reviewing my concrete notes a question rose in my mind.

In a rectangular section, why is the reinforcement ratio As/(bd), why use the effective depth (distance from top to the longitudinal reinforcement). Why not use bh where h would be the height of the member which will be a bit longer than d.

In addition i noticed that for T sections it still uses As/bwd where bw is the width of the web of the t section, why do we completely ignore the area of the concrete provided by the flanges why do we not include this in the reinforcement ratio calculation.

Thank you very much and wish you all the best.

 

[r13]

Because the example you are reading is a simply supported T beam. The design is for the positive moment, so the tension bars are placed in the bottom of the stem (web) with a code prescribed concrete cover, measured from the centroid of the bars to the bottom most fabric. For calculating positive moment reinforcement, the lever arm is measured from the top most fabric to the centroid of the rebars, that are subjected to tension, not the concrete cover, so you can't use the full height "h" in design of reinforcement.

 

[ElyasCivil]

Thanks for your reply, i just wanted to know for calculating the reinforcement ration of T sections why does it take the area of the concrete as bwd with bw being the width of the stem. It complete ignores the concrete in the flanges of the T section?

 

[r13]

Yes, in design of the positive reinforcement, the compression block is assumed to be in the slab with an effective of b[sub]e[/sub]. The lever arm between the compression block and the reinforcement is, for most cases that the compression block falls within the slab, a = Asfy/0.85fc'b[sub]e[/sub], and M[sub]n[/sub] = Asfy(d-a/2). Please see the code, or your textbook, for b[sub]e[/sub], and the the case that the compression block consists of the slab and partial beam web (NA falls below slab).

 

[jayrod12]

I feel that it's strictly to make the calculations easier and the answers more conservative. The one thing I can think of that over estimating your reinforcing ration would be unconservative is long-term deflection. Otherwise to me I don't see an issue.

 

[ElyasCivil]

Thank you very much for taking the time.