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How does ideCAD calculate immediate deflections according to ACI 318-19?

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E_c = modulus of elasticity of concrete, psi
f_r = modulus of rupture of concrete, psi
f_c^'₌ specified compressive strength of concrete, psi
I_{cr =} moment of inertia of cracked section transformed to concrete, in⁴
I_e = effective moment of inertia for calculation of deflection, in⁴
I_g = moment of inertia of gross concrete section about controidal axis, neglecting reinforcement, in⁴
M_a = maximum moment in member due to service loads at stage deflection is calculated, in.-lb
M_cr = cracking moment, in.-lb
y_t = distance from centroidal axis of gross section, neglecting reinforcement, to tension surface, in.
w_c =density, unit weight, of normalweight concrete, lb/ft³

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According to ACI 24.2.3.1, Immediate deflections deflection is calculated using eleastic elastic deflection formulas, considering the effects of cracking and reinforcement on member stiffness.

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According to ACI 24.2.3.4 Modulüs of elasticity, E_c is calculated in accordance with the following equation.

According to ACI 24.2.3.5, the effective moment of inertia I_{eis calculated in accordance with the following equation and ACI Table 24.2.3.5.}

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According to ACI 24.2.3.6for , continuous one-way salbs slabs and beams, I_e, can be taken as the average of values obtained from ACI Table 24.2.3.5. for For the critical positive and negative moment sections.

According to ACI 24.2.3.7 for prismatic one-way salbs slabs and beams, Ie, I_e can be taken as the average of values obtained from ACI Table 24.2.3.5. at At midspan for simple and continuous spans , and at support for cantilevers.

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