Mat Foundation - Design Output

The Design Output for the Mat Foundation Design Module of Foundation Advanced presents a cryptic formula for calculating the steel percentage required.  The minimum area of steel required is given as 0.0018 for Grade 60 bar per ACI 318-11, Section 7.12.2.1.b.  The maximum area of steel is given by limiting the steel to 0.75 times the balanced reinforcement ratio.  What is confusing is the formula given for the steel percentage required.  Please provide the basis of the formula, including ACI 318-11 equation/code references.

  • The formula that is used for calculating the percentage of steel follows from first principle. In case you are interested in verifying it through hand calculations, start with the equilibrium of forces in the cross section ( namely C=T ) and then compute the depth of the rectangular stress block ( a ) as a function of m, Ast and b ( where m=fy/0.85fc ).

    Now the equation of moment Mu/phi = Ast x fy x ( d – a/2). Substitute the value of "a" obtained above in this equation and divide both sides by bd^2 and you would arrive at a quadratic equation for row (=Ast/bd). The real root of that quadratic equation is the equation you see in the calculation sheet.

    The ACI 318-11 clause 10.3.5 arrives at minimum reinforcement by limiting the strain in steel to 0.004. Earlier versions of the ACI code specified this as a percentage ( 0.75 ) of the balanced reinforcement ratio. However these are actually same as is explained in R 10.3.5