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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:- Elastic shortening
- Shrinkage of concrete
- Creep of concrete
- Frictional loss
- Relaxation of steel
- 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 â€˜eâ€™ throughout its length (fig. below) b) If a parabolic cable is provided with eccentricity e1 at the ends and e2Â 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 â€“ 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 â€˜tâ€™ is the age of concrete.3.Â Loss due toÂ 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 = CeÂ x Elastic strain Elastic strain = (fc/Ec) fe is the stress in concrete at the level of steel. Loss in prestress = creep strain x Es4. 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 |
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:- Length effect, and
- Curvature effects.
Material in Contact | |
For steel and concrete | 0.55 |
For steel and steel | 0.30 |
For steel and lead | 0.25 |
- Cables should pass through metal tubes
- The bends should be through as small an angle as possible.
- Radius of curvature for bends should be large
- Prestressing the wire from both ends
- 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- elastic shortening
- shrinkage of concrete
- creep of concrete
- relaxation of steel
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% |