The various types of losses in prestress.
may be taken to reduce these losses
· LOSS DUE TO ELASTIC DEFORMATION OF CONCRETE:
The 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 steel.
Es= modulus of elasticity of steel. Ec= modulus of elasticity of concrete. ?e= EcEs/=modular ratio.
Strain in concrete at the level of steel = (fc/ Ec)
Stress in steel corresponding to this strain = (fc/ Ec) Es
Loss of stressfc in steel = ?e
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 aggregates
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
tensioning and [200x106/log10(t+2)]
Where, 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.
ULTIMATE CREEP STRAIN METHOD:
If ?cc = ultimate creep strain for a sustained unit stress
fc = Compressive stress in concrete at the level of steel. Es = modulus of elasticity of steel.
Loss of stress in steel due to creep of concrete = ?cc fc Es
CREEP COEFFICIENT METHOD:
If = creep coefficient
?c = creep strain
?e = elastic strain
?e = modular ratio
fc = stress in concrete
Es = modulus of elasticity of steel.
Ec = modulus of elasticity of concrete.
Creep coefficient( ) = c/(??e)
Loss 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 types:
(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.
Px = Poe-(µ?+ kx)
· LOSS DUE TO ANCHORAGE SLIP:
In 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.
? = (PL/AEs)
Where ? = slip of anchorage, mm
L = length of the cable,mm
A = cross sectional area of the cable, mm2
Es = modulus of elasticity of steel.
P = Prestressed force in the cable.