Concrete Long Term Creep Deflections per. ACI 318 Equations

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Concrete Long Term Creep Deflections per. ACI 318 Equations

Civil Engineering and Design
Strength of Materials Basics and Equations | Mechanics of Materials

Long-term deflection is caused by creep and shrinkage of the concrete. The long-term deformation develops rapidly at first and then slows down, being largely complete after approximately five years. As specified by ACI 318 Sec. 9.5.2.5, the long-term deformation, Δ_a, is obtained by multiplying the immediate deflection produced by the portion of the load that is sustained by an amplification factor, %. In computing the sustained part of the immediate deflection, judgment is required to decide what fraction of the prescribed service live load can be assumed to be acting continuously. The longterm deflection is taken as

The longterm deflection is taken as

Eq. 1
Δ_a = λ · Δ_i

Eq. 2
λ = i / ( 1 + 50 ρ' )

Eq. 3, compression steel ratio at midspan
ρ' = A'_s / ( b · d )

ρ' is the compression steel ratio at midspan for simply supported and continuous beams, and at supports for cantilevers. i is an empirical factor that accounts for the rate of the additional deflection. i is 1.0 at three months, 1.2 at six months, 1.4 at one year, and 2 at five years or more.

The total deflection is the sum of the instantaneous plus the long-term deflections.

Reference

ACI 318 Building Code Requirements for Structural Steel, paragraph 10.5 Minimum reinforcement of flexural members
Civil Engineering Reference Manual, Fifteenth Edition, Chapter 48, p. 50.7, Paragraph 16 (Long-Term Deflections), Michael R. Lindeburg, PE