This page provides information on how the program calculates prestress losses based on the loss parameters supplied by the user. Friction and anchorage loss parameters are specified by the user and the program calculates losses that are applied to both tendons modeled as loads and tendons modeled as elements. The other losses (due to elastic shortening, creep, shrinkage, and relaxation) are computed by the analysis for tendons modeled by elements or they are directly specified by the user for tendons modeled as loads. When tendons are modeled as elements, these other losses specified by the user (if any) are applied in addition to the losses computed by the analysis.

On this page:

Overview

The prestress losses accounted for in SAP2000 can be classified as follows:

• short term losses (immediate losses that occur before and during transfer):
  • anchorage set (anchorage slip losses)
  • elastic shortening
  • friction losses, due to length (or wobble) effect and curvature effect
• long term losses
  • due to concrete creep
  • due to steel relaxation
  • due to shrinkage

Short Term Losses

Anchorage Set Losses

The anchorage set slip is specified by the user. Losses due to anchorage set slip are NOT uniformly distributed along the entire length of the tendon. Rather, the length of the tendon affected by anchorage set is calculated as a function of the friction losses:

where,

• Unknown macro: {math}

  Delta_

  Unknown macro: {set}
  = Anchorage set

• Unknown macro: {math}

  A_

  Unknown macro: {PS}
  = Cross sectional area of the tendon

• Unknown macro: {math}

  E_P

  = Young’s modulus of the tendon

• Unknown macro: {math}

  P

  = frictional loss expressed as a change in force per unit length calculated from a tendon force variation diagram

Elastic Shortening Losses

Elastic shortening losses are computed by the analysis for tendons modeled as elements.

Friction Losses

Due to friction between the tendon and the duct during jacking, the tendon force at the jacking end is greater than the tendon force as some distance away from the jacking end. The friction loss has two parts: the length or wobble effect and the curvature effect. The tendon force

at the distance

from the jacking end can be expressed as:

where:

• Unknown macro: {math}

  P_0

  = tendon forces at the jacking end
• Unknown macro: {math}

  mu

  = curvature friction coefficient
• Unknown macro: {math}

  alpha

  = cumulative angle (in radians) by which tangent to the tendon profile has changed between the jacking end and location x
• Unknown macro: {math}

  K

  = wobble friction coefficient
• Unknown macro: {math}

  x

  = distance along tendon from jacking end to point under consideration

Long Term Losses

All long term losses require to run staged construction with dependent material properties and the losses are automatically calculated by the analysis based on the material model selected for the time-dependent behavior for concrete creep, concrete shrinkage and steel relaxation.

Concrete Creep Losses

The following material models can be considered for concrete creep:

• Ceb-Fip Model Code 1990

Concrete Shrinkage Losses

The following material models can be considered for concrete shrinkage:

• Ceb-Fip Model Code 1990

Steel Relaxation Losses

The following material models can be considered for prestressing steel relaxation:

• Ceb-Fip Model Code 1990

References

• Deepak Choudry: Analysis of Curved Nonprismatic Reinforced and Prestressed Concrete Box Girder Bridges, Report No. UCB/SEMM-86/13, December 1986 (contains equations for tendon losses)
• Ceb-Fip Model Code 1990