Lightweight Concrete for High Strength - Expanded Shale & Clay

E p : elastic modulus of prestressing steel (ksi)
E ci : elastic modulus of concrete at transfer (ksi)
Creep of concrete. The final loss of prestress due to creep is given by Equation D.8.
∆f
= 12 ⋅ f − 7 ⋅ ∆f
(D.8)
pCR
cgp
cds
where,
∆f pCR : creep of concrete loss (ksi)
f
cgp
⎛ Pi
= ⎜
⎝ Ag
Pi
⋅ e
+
I
g
2
⎞ M
g
⎟ −
⎠ I
g
⋅ e
(f cgp ) : sum of the stresses in the concrete at the cgs due to
prestress force at transfer and the maximum dead load moment (ksi)
P i : initial prestressing force after anchorage seating loss (kip)
e: eccentricity of the cgs. with respect to the center of gravity of the section at the cross section
considered. Eccentricity is negative if below concrete section neutral axis (in)
A g : gross area of the section (in 2 )
I g : gross moment of inertia (in 4 )
M g : the dead load gravity moment applied to the section at time of prestressing (kip-in)
M
∆ f
cds
=
I
sd
g
e
: change in concrete stress at the center of gravity of prestressing strands due to
permanent loads, with the exception of the loads at the time the prestressing force is applied.
(ksi)
Shrinkage of concrete. The prestress loss due to drying shrinkage is given in Equation D.9.
∆ = 17 .0 − 0. 15⋅
H
(D.9)
f pSR
where,
∆f pSR : shrinkage of concrete loss (ksi)
H: relative humidity, %
Steel relaxation. Steel relaxation loss is considered to be comprised of two components:
relaxation at transfer and relaxation over the rest of the life of the girder. For low relaxation
strands, the two components are given by Equations D.10 and D.11.
D-6