Lightweight Concrete for High Strength - Expanded Shale & Clay

∆f
log(24 ⋅t)
⎛ f
⎜
⎞
55⎟
⎝ ⎠
pj
pR1 = ⋅ − 0. ⋅ f
⎜
pj
(D.10)
40 f ⎟
py
where,
∆f pR1 : initial steel relaxation loss (ksi)
t: time since prestressing (days)
f pj : initial prestress (ksi)
f py : yield strength of the prestressing steel (ksi)
∆f
= − ⋅ ∆f
− 2 ⋅
( ∆f
+ ∆f
)
pR2 20 0.4
pES
0.
pSR pCR
(D.11)
where
∆f pR2 : after transfer steel relaxation loss (ksi)
∆f pES : elastic shortening loss (ksi)
∆f pCR : creep of concrete loss (ksi)
∆f pSR : shrinkage of concrete loss (ksi)
D.2.3. AASHTO-LRFD Lump Sum Estimate of Time-Dependent Losses
Lump sum method is based on data taken from a large number of prestressed structures, and it
gives an estimate of final prestress losses due to concrete creep and shrinkage and steel
relaxation. According to AASHTO-LRFD (1998), Lump sum method is applicable to members
that are made from NWC, so it is not suitable for predicting losses in SLC. Lump sum method
proposes eleven equations depending on the type of beam section and prestressing element
(strands, bars). For I-shaped girders prestressed with 235, 250, or 270 ksi wires or strands, the
time-dependent losses can be obtained from Equation D.12.
⎡ f
c
' −6.0⎤
∆f
pTD
= 33 .0 ⋅ ⎢1.0
− 0.15⋅
⎥ + 6. 0 ⋅ PPR
(D.12)
⎣
6.0 ⎦
where
∆f pTD : time-dependent losses (ksi)
f c ’: compressive strength of concrete cylinders at 28 days (ksi)
D-7