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