According to AS 3600 the first one seems to have marginally higher capacity with the compression steel, and the second one has much higher capacity with compression steel, but it's late here now. I'll have a proper look tomorrow.
cd72 - we must be doing something different. I get almost identical results from AS 3600 and BS 5400, and I don't know of any reason why the American codes would be any different. The attached file shows a summary of my results (sections with top steel have 1.5% to 2% higher moment capacity).
I say top steel because it is in tension, past yield in the AS 3600 calc and close to yield in BS 5400.
I used 30 mm cover top and bottom, and 4 no. 8 mm bars on the bottom, 2 no. 8 mm bars on top. I reduced the concrete strength to 20 MPa for the AS 3600 sections, because it is based on a cylinder strength, and used the standard high yield bars (500 MPa and 460 MPa). As you say, the reinforcement is way under the minimum required for a flexural member, but I'm interested in why we get different results.
You can download the spreadsheet I used for the AS 3600 calculation from:
That spreadsheet is based on strain compatability formulii and therefore takes into account the effect that i refer to for a lightly loaded beam. It appears to have an error though as it is showing full tensile stress in both top and bottom steel (something that seems to violate strain compatability).
If you use the classic formulii for concrete bending then you get two formulii
The first is the lever arm between equal amounts of top and bottom steel i.e Asfy(d-d1)
The second is the standard concrete stress block formulii for the remainder of the moment not taken from the first.
If you use this method then you can get less calculated moment capacity when you add top steel. This happens when the centre line of the steel is below the centre line of the rectangular stress block.
It really highlights how different the results can be from different methods.
That spreadsheet is based on strain compatability formulii and therefore takes into account the effect that i refer to for a lightly loaded beam. It appears to have an error though as it is showing full tensile stress in both top and bottom steel (something that seems to violate strain compatability).
It doesn't violate strain compatability. The depth of the Neutral Axis is only 17.39 mm (for AS 3600 with top steel) and the depth of the top reinforcement centroid is 34 mm, so the strain at the top steel is:
0.003*(17.39-34)/17.39 = -2.86x10^-3
Elastic stress = -573 MPa > yield
I don't know exactly what you mean by the "classic method", but if it is an approximate method that doesn't take the difference between the top and bottom steel into account, then it isn't surprising that it gives some odd results with extreme steel ratios.
Any method using strain compatability should give almost exactly the same results for any given stress block and steel parameters, possibly with some small variation depending on how the steel in the compression zone is handled. If you deduct the full concrete stress from the steel stress in all steel above the NA (to account for the displaced concrete), then it is possible that if the compression steel is between the bottom of the concrete rectangular stress block and the NA, then there could be some reduction in calculated bending capacity, but it would be very small.
Not only that, but the levels of reinforcement that we are talking about are so ridiculously below the level of any code allowed reinforcement ratio that I question whether it even warrants discussion. 200mm2 in a 600x600 section is rho of roughly 0.0006, which is less than 1/5 of ACI's minimum of 0.0033. That section would never even behave as a reinforced concrete section. I think if you want to consider reinforcement ratios that low you need to look at an elastic behavior since a RC behavior assuming cracked concrete is not physically possible. Once you look at uncracked concrete and elastic behavior, I think it's clear that the compression reinforcement will help.
I was using the same formula that I have always used for beams with discrete top and bottom steel, it is also the formula that I was taught at university and what features in some of the texts for the eurocodes.
All formulii are approximate, particularly those for reinforced concrete. But I agree that it is important to understand the limitations of the formulii that you use. This is the point that my original post was aimed at - broad brush statements dont really cover it.
Structural EIT,
A very valid point and I do mention that these are extreme cases. Though if you look at beams with minimum reinforcement and high strength concrete I believe that you can get the same type of thing happening.
When I get the chance to sit down for more than 2 minutes I will calculate some examples based on min and max steel ratios.
