I will say yes.
I use computor aided softwere for a long time now, so I might be wrong, but in first principle you use the compression strength of the concrete only unless the beam is overstressed.
As long as you account for the moment imposed by the axial force by the moment arm (distance between neutral axis and centroidal axis), it doesn't matter.
Having said that, however, I know it's more common to sum moments about the centroidal axis for columns.
You're correct. As I think about it I know you're right, but I do remember running into all kinds of problems making a column interaction diagram when I took moments about the neutral axis. I must have just had my spreadsheet set up wrong, because you're absolutely right.
I have always found that compression reinfoecement does very little for increase the flexural capacity and the cracked stiffness of the cross-section so I ignore it for the calculations. It can have some positive effects to help reduce the additional curvatures from creep and shrinkage.
For a slab poured monolithic with beam (T-beam), does this mean that any reinforcing provided in the slab (outside the stirrups) should not be considered when using the rho prime for deflection calcs?
Compression reinforcement in and of itself does little to increase capacity. What it DOES do is increase the ductility of the beam, which in turn will allow you to add more tension steel with an accompanying increase in capacity.
StrEIT.. I do that all the time.. you had me doubting myself with your second post.
Compression reinforcement probably won't make a huge difference to the ultimate moment capacity of a slab, but it will often make a big difference to the section stiffness for deflection calculations, so if you are doing an automated calculation why not include it?
If the steel requires tieing, it should be tied whether you include it in the capacity analysis or not.
As for the location of the axis for moments in compression (or tension) members, it depends on the position of the beam/strut in the structural analysis. Assuming that the columns were modelled as line members placed on the centroidal axis then the resistance moment should also be about the centroidal axis. You can do that either by taking moments about the centroidal axis or by taking moments about the neutral axis, then adding the moment due to the applied axial load applied at the centroid (making sure to get the sign right!)
I've managed to convince myself back to my original position - that the moments need to be summed about the centroidal axis, not the neutral axis.
I have a very simple example that I think will make my point. The example is for a homogeneous material, but the same principle applies. Look at a 1"x12" plate with an axial load of 100k and a moment of 200k-in (about the strong axis). This results in a stress distribution of 16.67ksi at the top and 0 at the bottom (putting the neutral axis at the bottom fiber). Because the entire section is in compression, it will be much easier to see my point. We have a single compressive force acting at 2" above the centroidal axis (12*2/3-6). If you take this compressive force about the centroidal axis you will get the correct moment of 200 k-in. If, however, you take the moment about the neutral axis (the bottom fiber that is unstressed), you will get a moment of 100k * 8" = 800 k-in, which is not correct.
For column interaction diagrams, the moments should be about the compression plastic centroid in the compression zone of the interaction diagram (for a symmetrical column with symmetrical reinforcement, this is the elastic centroid), and the tension elastic centroid in the tension zone (the centroid of the reinforcement tension force with all reinfroceemnt at yield)!
RE the original question, this has been answered above.
RE Tying of compression reinforcement, different codes have different rules on when steel must be tied. Some do not require tying os smaller bars, some do not require tying depending on the stress level in the bar. At service level stresses, tying is not normally necessary, only for ultimate strength.
You're forgetting that the sum of internal AND external forces provides equilibrium.. you've just accounted for the interior forces.. Take that 800 k-in moment from the interior forces and add the moment from the point load -100 kip*6in=-600k-in and you get 200 kip-in, which is the applied external moment.
I don't know why several people have said that you must take moments about this or that axis.. We could take moments about any axis we want.. For some reason, a lot of engineers tend to forget this very fundamental concept..
