Check for the Max Allowable Steel Area (Concrete)
ACI 318 B.10.3.3[1] ensures ductile failure by limiting the maximum allowable tension steel in a concrete section. For a singly reinforced beam the following procedure can be used to find the Maximum Steel Area:
- Solve for As-max
A_{s-max} = {0.75A_{sb}}
- Solve for Asb
A_{sb} = {0.85f'_cA_{cb}\over f_y}
where:
Acb= The area of the balanced concrete in compression
- Solve for Acb
A_{cb} = {a_b*b} = {β_1}{\left(87,000\over 87,000 + f_y\right)d}*b
where:
b = the base of the beam
ab = the depth of the compression block = {β_1}{\left(87,000\over 87,000 + f_y\right)d}
ab = the depth of the compression block = {β_1}{\left(87,000\over 87,000 + f_y\right)d}
β1 = ratio of depth of the equivalent stress block to the depth of the actual neutral axis
fy = the yield strength of the steel
d = depth of the concrete beam to the rebar?
fy = the yield strength of the steel
d = depth of the concrete beam to the rebar?
- Shortcut for Asb
A_{sb} = {{\left(0.85β_1f'_c\over f_y\right)}{\left(87,000\over 87,000 + f_y\right)bd}}
This shortcut combines the previous two steps into one equation.
References:
- American Concrete Institute, "ACI 318", 2005