Anchorage set losses

Anchorage set losses are caused by by the movement of the tendon prior to seating of the wedges or the anchorage gripping device. A common value of these losses is about 10mm (AASHTO LRFD 2007).

If <tex>\Delta_a</tex> is the anchorage slip and <tex>L_a</tex> is the length along the tendon affected by the anchorage slip, then:

<tex>\Delta_a = \int_0^{L_a} \Delta_{\epsilon} dx</tex>

where <tex>\Delta_{\epsilon}</tex> is the decrease in the tendon due to anchorage slip.

Uniform distribution of anchorage losses

Assuming that the anchorage slip losses are uniformly distributed over the entire length of the tendon (in other words <tex>\Delta_{\epsilon}</tex> is constant), then the following equations can be written:

<tex>\Delta_a = \Delta_{\epsilon} L</tex>

<tex>\Delta_{\epsilon} = \frac{\Delta_a}{L}</tex>

Noting that

<tex>\Delta_{\sigma} = E_p \Delta_{\epsilon}</tex> and <tex>\Delta F = A_p \Delta \sigma</tex>

we can write the final equation for the loss of prestress force:

<tex>\Delta F = A_p E_p \frac{\Delta_a}{L}</tex>

where:

• <tex>A_p</tex> ... area of the prestressing tendon
• <tex>E_p</tex> ... Young's modulus of the prestressing tendon
• <tex>\Delta F</tex> ... loss of prestressing force
• <tex>L</tex> ... length of the tendon

References

• AASHTO LRFD Bridge Design Specifications, SI Units, 4th Edition, 2007; Article 5.9.5.2.1, p. 5-109
• Deepak Choudry: Analysis of Curved Nonprismatic Reinforced and Prestressed Concrete Box Girder Bridges, Report No. UCB/SEMM-86/13, December 1986; p. 45 (Section 3.4.2: Anchorage Slip Losses)