Lightweight Concrete for High Strength - Expanded Shale & Clay

Aps
⋅ f
py
PPR = : partial prestressing ratio
A ⋅ f + A ⋅ f
ps
py
s
y
A ps : area of prestressing steel (in 2 )
f py : yield stress of prestressing steel (ksi)
A s : area of non-prestressing steel (in 2 )
f y : yield stress of non-prestressing steel (ksi)
D.2.4. ACI-209 Method
Based on creep and shrinkage equations presented in section B.3.1, ACI through its committee
209, proposed a general expression for estimating loss of prestress in prestressed concrete beams
as shown in Equation D.13. ACI-209 considered data from SLC in developing their equations;
therefore, the following equations are applicable to SLC.
[ ES + CR + SH + ( f ) ]
sr t
λ
t
=
×100
(D.13)
f
si
where
λ t : prestress losses in percent of the initial tensioning stress
ES: elastic shortening loss (ksi)
CR: creep of concrete loss (ksi)
SH: shrinkage of concrete loss (ksi)
(f sr ) t : steel relaxation loss (ksi)
f si : initial tensioning stress (ksi)
Elastic Shortening. Elastic shortening can be estimated by Equation D.14
ES = n ⋅
(D.14)
f c
where
ES: elastic shortening loss (ksi)
n: modular ratio at the time of prestressing
f
c
=
P
A
i
g
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)
D-8