Lightweight Concrete for High Strength - Expanded Shale & Clay

D.2.2. AASHTO-LRFD Refined Estimates of Time-Dependent Losses
According to AASHTO-LRFD (1998), the total loss of prestress, not including anchorage
seating loss, is the sum of the elastic shortening, creep, shrinkage, and steel relaxation losses,
given by Equation D.6. Equation D.6 applies to prestressed members with spans no greater than
250 ft., NWC and compressive strength above 3,500 psi.
∆ f = ∆f
+ ∆f
+ ∆f
+ ∆f
+ ∆f
(D.6)
pT
pES
pCR
pSH
pR1 pR2
where
∆f pT : total prestress losses (ksi)
∆f pES : elastic shortening loss (ksi)
∆f pCR : creep of concrete loss (ksi)
∆f pSR : shrinkage of concrete loss (ksi)
∆f pR1 : initial steel relaxation loss (ksi)
∆f pR2 : after transfer steel relaxation loss (ksi)
Elastic Shortening. According to AASHTO-LRFD, the Elastic shortening loss is given by
Equation D.7.
E
p
∆ f
pES
= ⋅ f
cgp
(D.7)
E
ci
where,
∆f pES : elastic shortening loss (ksi)
f
cgp
⎛ Pi
= ⎜
⎝ Ag
Pi
⋅ e
+
I
g
2
⎞ M
⎟ −
⎠ I
g
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)
D-5