Types of Losses in Prestress of Prestressed Concrete

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Losses in Prestress of Prestressed Concrete

The force which is used to stretch the wire to the required length must be available all the time as prestressing force if the steel is to be prevented from contracting. Contraction of steel wire occurs due to several causes, affecting reduction in the prestress. This reduction in the prestressing force is called loss in prestress. In a prestressed concrete beam, the loss is due to the following:

1. Elastic shortening
2. Shrinkage of concrete
3. Creep of concrete
4. Frictional loss
5. Relaxation of steel
6. Anchorage take-up

Table: Types of Losses of Prestress

S.No.	Types of Losses	Pre-Tensioning	Post-Tensioning
1	Elastic deformation of concrete	Yes	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.
2	Relaxation of stress in steel	Yes	Yes
3	Shrinkage of concrete	Yes	Yes
4	Creep of concrete	Yes	Yes
5	Friction	No	Yes
6	Anchorage grip	No	Yes

1. Loss due to Elastic Shortening

When the prestress is transmitted to the concrete member, there is contraction due to prestress. This contraction causes a loss of stretch in the wire. When some of the stretch is lost, prestress gets reduced. Let be the compressive stress at the level of steel. Unit contraction in concrete, Unit contraction in steel is also equal to Compressive stress in steel = = Therefore, loss in prestress, = compressive stress in steel is computed as follows for different cases: a) If a straight tendon is provided with an eccentricity ‘e’ throughout its length (fig. below) b) If a parabolic cable is provided with eccentricity e1 at the ends and e2 at the centre, Shear stress at the end section = Stress at the centre = Average stress= In the post tensioned beams several cables are provided. The cables are stretched in succession. When a cable is stretched, this cable suffers no loss, but the cable stretched before suffers a loss due to prestress in the cable being stretched. Thus the cable which is stretched first will suffer maximum loss due to stretching of (n – 1) cables where n is the total number of cables. The cable stretched last will not suffer any loss. To calculate the loss due to elastic shortening, loss in the first cable is calculated and half of this value is taken as the average loss of all the cables.

2. Loss due to Shrinkage of Concrete

There is contraction due to drying of concrete and shrinkage strain occurs in concrete. Shrinkage strain causes the steel to lose its stretch, resulting in the loss of prestress. Loss of stretch = shrinkage strain . Therefore, loss in prestress = = 0.0003 for pre-tensioned elements, and for post-tensioned beams Where ‘t’ is the age of concrete.

3. Loss due to Creep of Concrete

Creep is the time dependent deformation due to permanent force. In prestressed concrete, prestress is the permanent force in the member, causing compressive stress at the level of steel. Hence there is creep strain in the member. Creep strain = Ce x Elastic strain Elastic strain = (fc/Ec) fe is the stress in concrete at the level of steel. Loss in prestress = creep strain x Es

4. Loss due to Creep in steel (Relaxation of steel)

When the stresses in steel is more than half of its yield stress there is creep in steel also. Force of prestress falls as a result of creep in steel. Then there is a loss of prestress. Percentage creep varies from 1 to 5%. Creep in steel is also termed as relaxation of steel. Relaxation loss may be estimated using table below:

Initial Stress	Relaxation loss (N/mm2)
0.5fp
0.6fp	35
0.7fp	70
0.8fp	90

fp is the characteristic strength of steel. There are several means of reducing or balancing the loss of prestress due to creep. Choice of proper steel helps to reduce this loss. Prestressed wires have lesser creep. Galvanised wires also have no creep. Hence choice of proper steel will help to reduce the los of prestress due to creep. Further, creep in steel takes place mostly during few days. Under constant strain, creep stops entirely after about 15 days. Therefore, creep of steel could be reduced considerably by overstressing steel about 10% above its initial stress and then releasing it to the initial stress.

5. Loss due to Friction

Frictional loss occurs only in post tensioned beams. When the cable is stressed, friction between the sides of the duct and the cable does not permit full tension to be transmitted. Therefore at a point away from the jacking end prestress is less. Frictional loss is due to:

1. Length effect, and
2. Curvature effects.

Friction between the tendon and its surrounding material is the length effect and is sometimes described as wobbling effect. Friction due to length effect depends on the length, stress in the tendon (cable) and the coefficient of friction between the contact materials. Curvature effect is caused by the friction due to designed curvature of the cable. Loss due to these effects is estimated as follows: Consider a small length of the cable. Let ds be its length and R be the radius of curvature. (Figure below). Let be the angle subtended at the centre by the length ds. Let F be prestress at one end and F – dF the prestress at the other end. If N is the normal component of F, we have If is the coefficient of friction, frictional loss = dF= Frictional loss due to wobble effect is calculated as dF = –KFds where K is coefficient of wave effect. Therefore, total frictional loss = dF = or if F is the prestress at a distance S subtending an angle , integrating the above equation between limits F and Fx, we have Value of and K may be taken as follows:

Material in Contact
For steel and concrete	0.55
For steel and steel	0.30
For steel and lead	0.25

Loss of force = F – Fx Frictional loss can be reduced by adapting the following measures:

1. Cables should pass through metal tubes
2. The bends should be through as small an angle as possible.
3. Radius of curvature for bends should be large
4. Prestressing the wire from both ends
5. Over-tensioning the wires.

Total Loss of Prestress in Prestressed Concrete

If prestress is measured at the time of pulling the wire, the stress is termed as the jacking stress. Deducting the loss due to anchorage take-up and friction, initial prestress is obtained. Effective stress is usually the initial stress minus other four losses namely: Loss due to

1. elastic shortening
2. shrinkage of concrete
3. creep of concrete
4. relaxation of steel

if jacketing stress is treated as the initial stress, effective stress is jacketing stress minus all losses. Since in most cases frictional loss and the anchorage take-up can be compensated by overstressing, total loss is due to elastic shortening, shrinkage of concrete, creep of concrete and relaxation of steel. Total losses for pre-tensioned and post-tensioned beams are as follows:

Loss due to	Pre-tensioning	Post-tensioning
1. Elastic shortening	3	1
2. Creep of concrete	6	5
3. Shrinkage of concrete	7	6
4. Creep of steel	2	3
Total	18%	15%

Loss can be expressed as percentage or in terms of stress or in terms of total deformation or in terms of strain.