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:
fy = 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, β1 = 0.85
3. Compute the nominal moment capacity (Mn):
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Most common concrete beam equation:
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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 (øMn):
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