the limit for rho is still 0.75rho balanced. You can increase the actual tension As above that as long as you have the same amount of compression steel in the top. You also have to ensure ties comply with column requirements (since there are now compression bars).
I haven't seen a limit on the amount of compression reinforcement provided the tension only As (total As - compressive As) is below the 0.75rho balanced limit.
You also have to ensure the compression bars yield.
Compression Steel can be used to increase the strain in the tension steel by decreasing the size of the concrete compression zone and raising the netural axis. The increased strain will allow for more tension steel to be added. You can use strain compatibity to determine the steel strains. The compression steel may or may not yield depending on its location relative to the N.A. Compression steel will usually only give same increases because the moment are does not change much.
ash060-
Can you correct me if I am wrong please?
My understanding is that the compression steel MUST yield. If it doesn't then you making an incorrect assumption in the beam calcs. If the compression steel doesn't yield then the steel - steel couple can't be (d-d')As'fy because the compression steel will not have reached fy.
If you assume that the compression steel yields when you run the numbers you can verify this after calculating the N.A. depth. You can assume that the compression steel stress is an unknown. Than you would solve for the N.A. depth using a quadratic equation. After you know the compression steel stress sub fs for fy in the equation above.
Thanks. Can someone help me out a little. I was reading through a MacGregor text that goes a little more into detail than my concrete book. They use a ton of formulas to determine if the compression steel yields. Is it acceptable to use similar triangles to determine the strain in the steel (either compression or tension) rathr than using a ton of tables and equations? It seems so much more straightforward to use a linear strain relationship and use similar triangles.
From force equilibirum you can write a quadratic equation for the location of the neutral axis assuming plane sections remain plane. You will need to account for a couple of conditions in your final calculations depending on whether the compression steel yields. It does not have to yield though. If the compression steel is not yielded you will use the actual stress in the steel f's instead of the yield strength. You'll figure that out once you derive the quadratic equation mentioned above.
I get that. My question now is if you can just use a linear strain distribution (assuming plane sections remain plane) - using similar triangles - to calculate the strain in the compression steel instead of using all of the formulas and tables in a text.
Another follow-up question i would ask, in a seismic provision, is it allow to design a beam resisting earthquake for doubly reinforced? According to ACI 318-02, seismic provision that the limit of rho is 0.025, can i still use compression bars to increase my tensile strenth of beam? Or do i making my beam brittle if i put to much of rebars or increased tensile rebars?
Adding compression reinforcing without adding additional tensile reinforcing will not increase the moment capacity of the beam by much. Adding compression reinforcing will make the beam more ductile. The compression reinforcing causes the N.A. to shift towards the top of the beam causing the strain in the tension steel to increase leading to a more ductile section.
