Lightweight Concrete for High Strength - Expanded Shale & Clay

E ps : elastic modulus of prestressing steel (ksi)
E ci : elastic modulus of concrete at transfer (ksi)
f
cir
= K
cir
⎛ Pi
⋅⎜
⎝ Ag
Pi
⋅ e
+
I
g
2
⎞ M
⎟ −
⎠ I
g
g
⋅ e
: net compressive stress in the section at the center of gravity
of the prestressing force (cgs) immediately after transfer (ksi)
where
K cir : a constant, 0.9 for pretensioned members
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)
Creep of concrete. The final loss of prestress due to creep is given by Equation D.3.
⎛ E
ps ⎞
CR = K
cr
⋅
⎜ ⋅ ( f
cir
− f
cds
)
E
⎟
(D.3)
⎝ c ⎠
where
CR: creep loss (ksi)
⎧2.0 for NWC
K
cr
= ⎨
: creep constant
⎩1.6 for SLC
E c : elastic modulus of concrete at design age (ksi)
E ps : elastic modulus of prestressing steel (ksi)
M
e
sd
f
cds
= : stress in concrete at the cgs due to all superimposed dead loads (ksi)
I
g
M sd : Moment due to all superimposed permanent dead loads and sustained loads after
prestressing (kip-inches)
I g : gross moment of inertia (in 4 )
D-3