various types of losses in prestress.
may be taken to reduce these losses
· LOSS DUE TO ELASTIC DEFORMATION OF CONCRETE:
loss of prestress due to elastic deformation of concrete depends on the
modular ratio and the average stress in concrete at
the level of steel. If fc= prestress in concrete at the level of
Es= modulus of elasticity of steel. Ec=
modulus of elasticity of concrete. ?e= EcEs/=modular ratio.
in concrete at the level of steel = (fc/ Ec)
in steel corresponding to this strain = (fc/ Ec) Es
stressfc in steel
If the initial stress
in steel is known, the percentage loss of stress due to the elastic deformation
of concrete can be computed.
· LOSS DUE TO SHRINKAGE OF CONCRETE:
The shrinkage of concrete in prestressed members
results in a shortening of tensioned wires and hence contributes to the loss of
stress. The shrinkage of concrete is influenced by the type of cement and
and the methowd
of curing used of high-strength concrete with low water cement ratios result in
a reduction in shrinkage and consequent loss of prestress.
According IS1343 for the loss of prestress due to
the shrinkage of concrete
= total residual shrinkage strain having values of 300x106 for pre
t = age of concrete at transfer in days.
The loss of stress in steel due to the shrinkage of
concrete is estimated as, Loss of stress = ?cs x Es
· LOSS DUE TO CREEP OF CONCRETE:
The sustained prestress in the concrete of a
prestressed member results in creep of concrete which effectively reduces the
stress in high-tensile steel. The loss of stress in steel due to creep of
concrete can be estimated if the magnitude of ultimate creep strain or creep
coefficient is known.
CREEP STRAIN METHOD:
If ?cc = ultimate creep strain for a
sustained unit stress
= Compressive stress in concrete at the level of steel. Es = modulus of
elasticity of steel.
of stress in steel due to creep of concrete = ?cc fc Es
If = creep coefficient
= creep strain
= elastic strain
fc = stress in concrete
= modulus of elasticity of steel.
= modulus of elasticity of concrete.
coefficient( ) = c/(??e)
of stress in steel = fc ?e
· LOSS DUE TO RELAXATION OF STRESS INN STEEL:
Most of the code provides for the loss of stress due
to relaxation of steel as a percentage of the initial stress in steel. The
Indian standard code recommends a value varying from 0 to 90 N/mm2
for stress in wire varying from 0.5 fup to 0.8 fup .
· LOSS OF STRESS DUE TO FRICTION:
On tensioning the curved tendons, loss of stress
occurs in the post-tensioned members due to friction between the tendons and
the surrounding concrete ducts. The magnitude of this loss is of the following
(a) Loss of stress due to the curvature
effects, which depends upon the tendon from or alignment which generally
follows a curved profile along the length of the beam.
(b) Loss of stress effect, which depends
upon the local deviation in the alignment of the cable. The wobble or wave
effect is the result of accidental or unavoidable misalignment, since ducts or
sheaths cannot be perfectly located to follow predetermined profile throughout
the length of the beam.
= Poe-(µ?+ kx)
· LOSS DUE TO ANCHORAGE SLIP:
most post-tensioned system, when the cable is tensioned and the jack is
released to transfer prestress to concrete, the friction wedges, employed to
grip the wires, slip over a small distance before the wires are firmly housed
between the wedges. The magnitude of slip depends upon the type of wedge and
the stress in the wire.
slip of anchorage,
= length of the cable,mm
= cross sectional area of the cable, mm2
= modulus of elasticity of steel.
= Prestressed force in the cable.