Concrete Beam Design
A Concrete Beam at the Balanced Condition
Flexural Design: Find Moment Capacity Given Concrete Beam Cross Section
1. Find the depth of the equivalent rectangular stress block (a):
where:
f_{y} = The yield strength of the steel (e.g. 40 ksi, 60 ksi)
f'_{c} = The compression strength of the concrete (e.g. 4 ksi, 6 ksi)
b = the width of the concrete beam
2. Check to see whether or not the section is tension controlled:
If \left({a\over d}\right) \le \left({a_b\over d}\right) then the section will be assumed to be tension controlled.
where:
d = depth of to the rebar
{a_b\over d} = {β_1}{\left(87,000\over 87,000 + f_y\right)}
Note: For f'_{c} ≤ 4 ksi, β_{1} = 0.85
3. Compute the nominal moment capacity (M_{n}):
Most common concrete beam equation: M_n = A_sf_y\left(d{a\over2}\right)

where:
d = the depth of the concrete beam (note: that this is not the same as the height of the beam)
4. Compute the factored moment capacity (øM_{n}):
Above in Section #2 it was determined whether or not the section is tension controlled. The results from Section #2 will determine what ø (reduction factor) you should use. This will then be compared to the factored moment you find acting on the beam.
For a beam to work:
where:
References
 American Concrete Institute, "ACI 318", 2005