Calculation of Immediate Deflections

Notation

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

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

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

According to ACI 24.2.3.5 effective moment of inertia I_e is calculated in accordance with following equation and ACI Table 24.2.3.5.

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

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