Your starting assumptions are not correct. Complete lack of friction may occur only of the duct is perfectly straight line with enough free space so the tendon doesn't touch it. In practice most ducts have curves or imperfections and could be tight around the tendon. On the other hand there is friction - the ducts are not that smooth and the tendon is made by twisted wires. The friction is not that huge as for bounded tendons but it is present and could not be ignored.

Best regards,

thank you very much sir.

As much as i understand from your answer you are talking about steel to steel friction which is given as 0.30 in Indian standard code. But as you said the tendons are not straight, they could be curved, will it not be a better idea to use the horizontal curvature of the bend to  estimate friction loss rather taking the coefficient of friction as the parameter. Because curvature can vary however we will take same coefficient of friction value for all curvature

Yes, of course you need to estimate friction losses for each particular case with respect to actual curvature. There are procedures and values how to do that in codes. But you need to include friction losses always.

sir the procedure is for calculation of curvature in vertical profile. I am talking about horizontal curvature. i don't think any code provide any information on consideration of horizontal curvature of tendons for friction loss calculation

Hi Prashant,

The loss of prestress in tendons of (i) pretension or (ii) post-tensioned concrete members can be classified in two main categories as follows:

(1) The immediate loss

(2) The time dependent loss

Your question regarding post-tension concrete members is about the first case “(1) The immediate stress loss” before they are subjected to grouting.

The reasons for the “(1) The immediate loss” are classified in two main categories as follows:

(1-1)          Loss of prestress due to initial sudden elastic deformation of concrete (general loss in tendon stress)

(1-2)          The loss of stress along the tendon due to friction (gradient variation in tension along the length of tendon)

Your question is about case “(1-2) The loss of stress along the tendon”. There are two main cases contribute to the loss of stress along the tendon as follows:

(1-2-1) Friction in the jack and anchorage

The loss of prestress due to friction in the jack and anchorage is very minor in general and may be considered for the type of jack and anchorage system to be used.

(1-2-2) Friction along the tendon

Friction loss should be determined from an analysis of the forces exerted by the tendon on the duct.

(i) The curvature of duct along the tandem (the main direction)

(ii) The friction coefficient between duct and tendon (the main direction)

(ii) The deviation of tendon on the perpendicular direction (the installed tendon supports are not normally aligned on a perfectly straight line, and therefore there is a deviation from straight line in tendon) [you need to imagine the 3D picture of tendon)  

Friction losses occur along the tendon during the stressing operation. Friction between the tendon and the duct causes a gradual reduction in prestress with the distance along the tendon from the jacking end (Lpa).

The coefficient of friction between the tendon and the duct depends basically on the condition of the surfaces in contact, their structure and their preparation. Frictional forces depend on the way in which the prestressing tendon is formed and housed, i.e. the cable profile. Therefore, the magnitude of the friction loss depends on the total angular change of the tendon over the length Lpa, as well as the size and type of the duct containing the tendon. 

The loss of stress can be calculated by formulation provided in Clause 3.4.2.4 AS 3600-2009 (The Australian standard for the design of reinforced concrete). Please see the attached image.

For further information please see:

AS 3600-2009 Supp 1 (2014) AS 3600-2009 Supp 1:2014 Concrete structures-Commentary (Supplement to AS 3600-2009). Sydney, Australia

AS 3600 (2009) Concrete Structures. Australian Standard, Sydney, Australia

Design of prestressed concrete to AS3600-2009, Second edition 2016  by  Raymond Ian Gilbert , Neil Colin Mickleborough , Gianluca Ranzi

In your code, they have chosen the middle ground coefficient of .30. I really dont see a difference if the curve is horizontal or vertical, the coefficient of friction has been determined to be 0.30. This is a set number, not based on how many drapes.

ACI uses friction and wobble coefficients, with wobble using a curve and wobble coefficient depending on the strand, bonding and duct.

If there is a concern, or if the tendon length is very long, you may consider stressing for both ends, or temporarily overstressing the tendon, then relaxing the tension, then stressing to design value. During post-tensioning, it is usually permitted to stress the tendon temporarily to a maximum of about 80% of the specified tensile strength of the tendon. After anchoring, the stress in the tendon at anchorage is usually limited to 70%.

Wherever the prestressing steel rubs against the duct, there will be friction. This takes place where there is a intended curvature or an unintended curvature (due to positioning tolerances, draped shape between supports etc). This is also independent of vertical or horizontal curvature or positioning, respectively. The absolute loss depends on the duct material or, more precisely, on the materials involved (steel and duct material). The corresponding coefficient can be found in codes, lliterature or prestressing providers' technical documentation.

The duct is grouted and the frictionis between duct and deviators.

Thank you very much for the over-whelming response. i have very well understood why friction occurs in unbonded tendons and how un-intended curvature is taken into consideration. Ii will continue to work on this field and try to develop some robust approach to estimate friction loss in unbonded tendons due to un-intended curvatures.

Interesting....

Please share me the best answer might you trust...

Regards…