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.

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} = \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