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  1-ACI350-06 &ACI224R-01,2- Design of Reinforced Concrete by Jack C. McCormac_9th Ed-2013-1118129849_ACI 318-11.pdf pages 43 (Example 2.3), 6.10 Control of Flexural Cracksand excel sheets for chapter 6 http://www.mediafire.com/download/k42shb458odynac/Sheets_used_in_Design_of_Reinfsqdewfwffdesghfgorced_Concrete_by_Jack_C._McCormac_9th_Ed-2013-1118129849_ACI_318-11.rar3- RCM ACI Builder v 5.3.0.0 by Eng. Hussein Ridahttp://www.structural-experts.com/showthread.php?tid=7424- Moment of Inertia of Cracked Section Transformed to Concrete http://www.concrete.org/technical/ckc/314/314_design_aid_J_1-14_001.pdf5-Quadratic eqhttp://www.sosmath.com/algebra/quadraticeq/quadraformula/quadraformula.html6- Equivalent Stiffness , Is =Ic/nhttp://www.bgstructuralengineering.com/BGSMA/BGSMA_Itr/BGSMA_ITR02.htmfor axial force, εc = εc fc/Ec = fs/Es ==> F/(Ac Ec) = F/(As Es) ==> thus As Es = Ac Ec ==> As = Ac * Ec/Es = Ac /n and for moment, εc = εc fc/Ec = fs/Es ==> M*y/(Is Es) = M*y/(Ic Ec) == > Is = Ic Ec/Es = Ic/n
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