21. Worked example #7: Calculating doubly reinforced moment capacity

Reinforced Concrete Design to EC2
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Questions and discussion for this lecture live here. Fire away by hitting Reply below :fire:

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Hello Sean,

I have three questions regarding the calculations of moment capacity for the doubly reinforced rectangular sections.

  1. In the singly reinforced section there was a check for the ratio of z/d and limit it to 0.95. Does it apply also to doubly reinforced sections?
  2. Is it acceptable to not subtract the area of concrete where compression steel is placed?
  3. The max area of steel of 0.04 is defined for both compression and tension steel or just tension steel?

Thank you in advance,
Ahmed.

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Hi Ahmed,

  1. This limit wouldn’t be relevant for a doubly reinforced section since we would only ever have such a section (i.e. provide compression steel) if the compression block was fully utilised - as such we would expect z to be relatively far from the limiting max value of 0.95d that applies to singly reinforced sections.
  2. Yes this is acceptable - the influence of double counting this area is negligible - especially by comparison to other potential sources of inaccuracy.
  3. This limit applied to for all longitudinal steel - so yea, tension and compression.

Seán

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So, as far as I understand, we assume/define x to be 0.45d in our calculations to stick to EC2. By the end, however, when we are forced to choose actual steel areas different from those calculated, wouldn’t that change the value of x? -That is, wouldn’t it be necessary to check that x is still less than 0.45d with the proposed reinforcement?

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Hey @hektorsabroe,

Yes, technically by providing an area of steel different to the value we calculated, it will alter the position of x. However, once the area of steel provided is approximately equal to what our calculation dictates, the variation in x will be negligible - so no need to recheck the position of x.

Remember, we’re working with a model, which is always just an approximation of true behaviour - a good approximation but an approximation nonetheless. There are actually many more sources of uncertainty baked into our model that will likely drown out the discrepancy introduced by inaccuracy in the steel area, e.g. the material factors, the characteristic strengths, the actual dimensions and positioning of steel achieved on site etc.

Seán

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6

Awesome. That makes sense! Thanks a lot.
I guess that when the EC2 limit is placed at 0.45d, it leaves a lot of room for small variations, and we’re still not worried at all about approaching the “real” limit of 0.618d.

Hektor

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Yes - exactly.

It’s funny how we tend to place so much importance on precision in analysis and design when the real world is usually a lot more uncertain!

S

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