Questions and discussion for this lecture live here. Fire away by hitting Reply below 
Hi, do these equations still apply to a box girder section? What would the stresses look like for this type of shape? Thank you 
Hey @graving,
In theory, you can still apply the same principles to the analysis of a box section like this. But you can’t do it blindly, you need to make sensible modifications to account for the fact that you have a tapered section and there’s a giant hole in the middle of it!
If I was looking for a first approximation, I would probably start by treating this as two T-beams, sharing the load. This will almost certainly underestimate the capacity of the section but will give you an idea of the approximate capacity of the section.
Hope that helps.
Seán
Sean, could you please explain why we use z=d-0. 4x, where x= 0.45d , for concrete MsubRd; and z= d[0.5+√(0.25+k/1.134)] for area of steel required? Shouldn’t they both be the same?
Re steel, didnt we sub the understanding that 0.4x=d-z, to get an expression for z? Is the difference that we’re not going to assume x=0.45d? And if not, why not?
Thanks in advance!
Great question.
When we derive the ultimate moment capacity of a singly reinforced beam to be M_Rd = 0.167 b d^2 f_ck, we did this by pushing the compression block as far down the section as we’re permitted to, so the lever arm is z = d-0.4x with x=0.45d (as you correctly say).
Now, when we derive the lever arm equation, it’s completely equivalent and consistent with what I’ve said above, i.e. if you set M_Ed = M_Rd (just plug in any numbers), and work out z using z = d[0.5+√(0.25-k/1.134)], you’ll get the exact same lever arm as z = d-0.4x with x=0.45d.
One important note:
The equation that I show in the summary at 19:13 shows a ‘+’ when it should be a ‘-’. You copied the incorrect ‘-’ sign in your question, I guess that’s where your confusion stemmed from. I provided the correct version originally at 16:30…a typo got me at the very end!
Sorry if that confused you…hopefully this clears it up. Shout if you still have questions.
Thanks for posting and apologies for sending you wrong at the very end!
Seán