Anchorage set losses

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