Losses of Prestress - 2

We seen in last blog different types of prestress losses as per IS 1343:2012, clause, 19.5.2, lets see remaining losses, 

1. Loss due to Creep of Concrete

2.Loss due to Shrinkage of Concrete

3.Loss due to Relaxation of Steel

4.Loss due to Elastic Shortening of Concrete

5.Loss due to Slip of Anchorage 

6.Loss due to Friction 

Loss due to Elastic Shortening of Concrete: (19.5.2.4)

This type of loss occurs when the prestressing tendons upon release from tensioning devices cause the concrete to be compressed. This loss is proportional to the modular ratio and initial stress in the concrete and shall be calculated as below, 

For Pretensioning, the loss of prestress in the tendons at transfer shall be calculated on a modular ratio basis using the stress in the adjacent concrete. ( cl 19.5.2.4)

 Loss = m. Fc

For post-tensioned, tendons which are not stressed simultaneously, there is a progressive loss of prestress during transfer due to the gradual application of the prestressing forces. This loss of prestress should be calculated on the basis of half the product of the stress in the concrete adjacent to the tendons averaged along their lengths and the modular ratio. Alternatively, the loss of prestress may be exactly computed based on the sequence of tensioning. ( cl 19.5.2.4)

Case - I, when all wires are tensioned simultaneously (i.e. all wires are tensioned at the same time) then total loss is 0, because the applied prestressing is recorded after the elastic shortening of concrete or wires are anchored only after elastic shortening of the concrete.  

Case - II, when all the wires are tensioned successively or sequentially (i.e. one wire at a time tensioned) then stressing in one bar will cause loss in other bar or there will be loss previously stressed wires. 

  

Where,

n = Number of wires or tendons  

m = Modular ratio

Fc = Stress in concrete

Loss due to Slip of Anchorage: (19.5.2.5)

In post tension member, when the prestress is transfer to the concrete the wedges slips through a certain distance before they get properly seated in the conical space, therefore anchorage block moves before it settles on the concrete. Therefore there is loss of prestress due to the reduction in the length of tendon.  

Any loss of prestress which may occur due to slip of wires during anchoring or due to the strain of anchorage shall be allowed for in the design. ( cl 19.5.2.5)

Loss due to Friction : (19.5.2.6)

The friction generated at the interface of concrete and steel during stretching of curved tendons, leads to drop in the prestress along the member from the stretching.  

The design shall take into consideration all losses in prestress that may occur during tensioning due to friction between the prestressing tendons and the surrounding concrete or any fixture attached to the steel or concrete. (cl19.5.2.6)

For straight or moderately curved structures, with curved or straight cables, the value of prestressing force Px at a distance x metres from tensioning end and acting in the direction of the tangent to the curve of the cable, shall be calculated as below:

Where, 

P0 = Prestressing force in the prestressed steel at the tensioning end acting in the direction of tangent             to the force of the cable,

α  = Cumulative angle in radians through which the tangent to the cable profile has turned between any         two points under consideration, 

μ = Coefficient of friction in curve,

k = Coefficient for wave effect.

Values of  μ and k is given in cl 19.5.2.6 table

To Calculate α,

Jacking from one end : 

Jacking from both end :

Losses of Prestress - 1

As per IS 1343:2012 clause 19.5.2 page no. 24 there are six type of losses,

1. Loss due to Creep of Concrete
2. Loss due to Shrinkage of Concrete 
3. Loss due to Relaxation of Steel 
4. Loss due to Elastic Shortening of Concrete
5. Loss due to Slip of Anchorage 
6. Loss due to Friction 

Classification of losses,

Pre-tension	Post-tension
Elastic deformation of concrete	No Loss due to elastic deformation if all the wires are simultaneously tensioned. If the wires are successively tensioned, there will be loss of Prestress due to elastic deformation of concrete.
Relaxation of stress in steel	Relaxation of stress in steel
Shrinkage of concrete	Shrinkage of concrete
Creep of concrete	Creep of concrete
	Anchorage slip
	Friction

Loss due to Creep of Concrete: (19.5.2.1)

Creep is defined as the increase in deformation with time under constant loading. The sustained prestress in the concrete of a prestressed member results in creep of concrete which effectively reduced the stress in high tension steel. The loss of stress in steel due to cress of concrete can be estimates if the magnitude of ultimate creep strain or creep coefficient is known. 

It is a time dependent loss or long term loss, and this is second highest loss in prestress.   

Loss in prestress = Creep strain x Es

                                     = ɸ x elastic strain x Es

             = ɸ.Fc.m

where, 

Es = Modulus of elasticity of steel

ɸ   = creep coefficient 

Fc  = stress in concrete 

m = modular ratio 

Loss due to Shrinkage of Concrete: (19.5.2.2)

Shrinkage of concrete is define as contraction of concrete due to loss of moisture, Due to shrinkage of concrete the prestress in the tendon is reduced with time. It is a time dependent loss or gradual loss or long term loss. This loss due to shrinkage is the highest loss in prestress.

IS 1343:2012 the shrinkage strain is,

1. For Pre-tensioned Member : 

2. For Post-tensioned Member : 

where, 

t = age of concrete at transfer in days 

Loss in prestress = Shrinkage strain x Es

where,

Es = Modulus of elasticity of steel

Loss due to Relaxation of Steel: (19.5.2.3)

Relaxation of steel  is define as decrease in stress with time under constant strain i.e. when we stress the steel at a certain stress, wire do not remain at some stress. The stress decreases with time.

Loss in prestress = 2 - 8 % of initial prestress.   

As per IS 1343:2012, relaxation losses for prestress steel at 1000 hrs at 27 oC.

Initial Stress	Relaxation Loss
0.5 fp	0 mpa
0.6 fp	35 mpa
0.7 fp	70 mpa
0.8 fp	90 mpa