Test: Loss of Prestress - Civil Engineering (CE) MCQ

Concrete shortens, when a prestressing force is applied. As the tendons that are bonded to the adjacent concrete simultaneously shorten, they lose part of prestressing force that they carry. This is called elastic shortening of concrete.
In case of post-tensioned members, there will be no loss of pre-stress due to elastic deformation if all the wires are simultaneously tensioned.
However, if the bars are successively tensioned, there will be loss of prestress due to elastic deformation of concrete. A tendon that was tensioned last does not suffer any losses due to elastic shortening while the tendon that was tensioned first suffers the maximum amount of loss.

Additional Information:
The various losses in pre-stresses are:

Pre-tensioning:

• Elastic deformation concrete.
• Relaxation of stress in steel.
• Shrinkage of concrete.
• Creep of concrete.

Post tensioning:

• No loss due to elastic deformation if all the wires are simultaneously tensioned. If the bars are successively tensioned, there will be loss of prestress due to elastic deformation of concrete
• Relaxation of stress in steel.
• Shrinkage of concrete.
• Creep of concrete.
• Friction.
• Anchorage slip

As per IS 1343 Clauses 6.2.4:
Shrinkage

• The total shrinkage of concrete depends upon the constituents of concrete, size of the member and environmental conditions.
• For a given humidity and temperature, the total shrinkage of concrete is most influenced by the total amount of water present in the concrete at the time of mixing.
• The total shrinkage strain is composed of two components, (i) the autogenous shrinkage strain and  (ii) the drying shrinkage strain

Autogenous shrinkage strain:

• Develops during hardening of concrete
• The major part develops in the early days after casting.
• It is a linear function of concrete strength

Drying shrinkage strain:

• The drying shrinkage strain develops slowly as it a function of migration of the water through the hardened concrete.

Loss due to friction in post-tensioned members
The loss due to friction in post-tensioned members happened due to the movement of reinforcement inside the duct surface. This loss has two effects: Length and curvature effects. The loss due to friction is the summation of losses due to these two effects.  These two effects are given below:

• Length effect: 
  The stress at any distance ‘x’   is given as:
  
  Where
  K is Wobble correction
  Loss at distance x due to length effect = P_o - P_x
• Curvature effect:
  The stress at any distance ‘x’   due to curvature is given as:
  
  Where
  μ is the coefficient of friction
  α is the change in gradient between any two points of consideration    which may be written as:
  α = x/R
  R is the radius of Curvature
  Loss at distance x due to Curvature = P_o - P_x

Losses in Prestress members:

• In prestressed concrete, the most important parameter is the prestressing force.
• If the prestressing force reduces with time, prestresses also get reduced. 
• Various reductions of the prestressing force are termed as the losses in prestressing.
• Total loss of prestress consists of those losses which are instantaneous at the transfer stage as well as those which are time-dependent. 
• Loss due to friction and anchorage slip occurs only in the post-tensioned beam.

Important Points
Losses of prestress are as follows:

The various losses in pre-stressed are:
Pre-tensioning:

• Elastic deformation concrete.
• Relaxation of stress in steel.
• Shrinkage of concrete.
• Creep of concrete.

Post-tensioning:

• No loss due to elastic deformation if all the wires are simultaneously tensioned. If the bars are successively tensioned, there will be loss of prestress due to elastic deformation of concrete
• Relaxation of stress in steel.
• Shrinkage of concrete.
• Creep of concrete.
• Friction.
• Anchorage slip

From the above factors, we can say that Loss of pre-stress is not directly related to the grade of concrete.

In post-tensioning, when cables are tensioned sequentially, the loss in each cable will be different. 
Let the cable be numbered as 1,2,3,4 and they were tensioned in a sequence of 1,2,3,4.   
Since cable is 4 tensioned, at last, there will be no loss in cable 4.
The loss in prestressing force in wire 1 is maximum and it happens when cables 2,3,4 are tensioned and that will be a total loss in pre-stressing force because after that no wire is tensioned.
The final pre-stressing force to be considered after accounting for the losses will be the one that has a minimum value.
The final pre-stressing force which has a minimum value given as:
Final pre-stressing force = Initial pre-stressing force – maximum loss due to elastic shortening
Therefore, the total percentage loss in prestressing force is the percentage of loss in the cable which was maximum loss i.e. first tensioned i.e. 6 %.  

• Loss due to Friction: The friction generated at the interface of concrete and steel during the stretching of a curved tendon in a post-tensioned member. The loss due to friction does not occur in pre-tensioned members because there is no concrete during the stretching of the tendons.

Important Points

• Loss due to Elastic Shortening: When the tendons are cut and the prestressing force is transferred to the member, the concrete undergoes immediate shortening due to the prestress.
• Loss due to Relaxation: Relaxation is assumed to mean the loss of stress in steel under nearly constant strain at a constant temperature. It is similar to the creep of concrete. This loss is generally of the order of 2 to 8% of the initial stress.
• Loss due to Anchorage Slip: In a post-tensioned member, the is loss of prestress due to the consequent reduction in the length of the tendon. The loss due to anchorage does not occur in pre-tensioned members.

In the case of post tensioned members the tendons are housed in ducts preformed in concrete. The ducts are either straight or follow a curved profile depending upon the design requirements.
Consequently 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.
Loss of stress due to the curvature effect, which depends upon the tendon form or alignment which generally follows a curved profile along the length of the beam.
Loss of stress due to the wobble effect, which depends upon the local deviations in the alignment of cable. The wobble or wave effect is the result of accidental or unavoidable misalignment.

Frictional losses can be reduced by several methods:
Over tensioning the tendons by an amount equal to the maximum frictional loss
Jacking the tendons from both ends of the beam, generally adopted when the tendons are long or when the angles of bending are large.

Losses of prestressing:

Since the loss of priestess depends on several factors such as properties of concrete and steel, method of curing, degree of prestressing, and method of prestressing, it is difficult to analyze the exact loss in prestressing forces. However, typical values of losses encountered under normal conditions of work are recommended by Lin as outlined below:

∴ The loss in pre-tensioning is primarily due to shrinkage and creep with 7 and 8 percent respectively.

Loss of stress due to relaxation of steel

• Relaxation is assumed to mean the loss of stress in steel under nearly constant strain at constant temperature.
• It is similar to creep of concrete. Loss due to relaxation varies widely for different steels and the steel manufacturers based on test data may supply its magnitude.
• This loss is generally of the order of 2 to 8% of the initial stress. This is generally - 1000 hours of referred to at loading at 27˚ C.

Elastic deformation of concrete:

• When the pre-stress is applied to the concrete, an elastic shortening of concrete takes place. This results in an equal and simultaneous shortening of the pre-stressing steel.

Friction loss in post tensioned members:

• This loss occurs only in the post tensioned members. There are small frictional losses in the jacking equipment. The friction between tendons and surrounding materials is not small and may be considered partly a length effect (wobble effect) and partly a curvature effect.

Loss due to anchorage slip:

• In most tensioning systems, when the cable is tensioned and the jack is released to transfer pre-stress to concrete, the friction wedges employed to grip the wires, slip over a small distance before the wires are finally housed between the wedges. The magnitude of slip depends upon the type of wedge.