# Calculation of Immediate Deflections

Immediate Deflection is calculated automatically

**Notation**

* E_{c }= *modulus of elasticity of concrete, psi

*modulus of rupture of concrete, psi*

**f**_{r }=*specified compressive strength of concrete, psi*

**f**_{c}^{'}_{ }=

**I**_{cr}**moment of inertia of cracked section transformed to concrete, in**

_{ }=^{4}

*effective moment of inertia for calculation of deflection, in*

**I**_{e }=^{4}

*moment of inertia of gross concrete section about controidal axis, neglecting reinforcement, in*

**I**_{g }=^{4}

*maximum moment in member due to service loads at stage deflection is calculated, in.-lb*

**M**_{a }=*cracking moment, in.-lb*

**M**_{cr }=*distance from centroidal axis of gross section, neglecting reinforcement, to tension surface, in.*

**y**_{t }=*density, unit weight, of normalweight concrete, lb/ft*

**w**_{c}=_{ }^{3}

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.

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