## Function

- Define the tendon properties such as tendon area and instantaneous prestress losses.

## Call

From the main menu, select **[Load] tab > [Type : Prestress] > [Prestress Loads] group > [Tendon Property]**

## Input

Add/Modify Tendon Property dialog box

### Tendon Name

Tendon name being defined

### Tendon Type

Define the tendon type among Pre-Tension, Post-Tension and External.

**Internal(Pre-Tension)** : Prestressing tendons prior to casting concrete, which transmits prestress through bonding between concrete and tendons.

**Internal(Post-Tension)** : Post-tensioning tendons through hardened concrete members - tendons are gradually stressed and anchored to the members.

**External** : Tendons are placed external to concrete members and stressed.

Depending on the Tendon Type (Pre-Tension, Post-Tension and External), the entry fields for variables related to tension losses in tendons and duct diameter are either activated or inactivated.

If the tendon placement location is External, the tendon is displayed as a straight line in Display.

### Material

Select the material properties of the tendon. Click to the right to add new or modify/delete previously defined tendon properties.

For pre-tension type tendon, consider the elastic deformation loss due to axial force and moment acting on the tendon.

Weight density of tendon is not taken into account in the calculation of self weight because tendon is considered as equivalent loads rather than elements. In practice, the self weight of reinforcement including tendons is taken into account by increasing weight density of concrete.

### Total Tendon Area

Specify the total area of the tendon. You may either directly specify the cross-sectional area or click to enter the standard cross-sectional area and the number of strands for auto-calculation of the total area.

Classification | Tendon Type | |||||
---|---|---|---|---|---|---|

12. 4 | 12. 7B | 15. 2B | G15. 2 | 28. 6 | ||

Number of Strands |
EA | 12 | 12 | 12 | 19 | 1 |

Tendon Area |
㎠ | 11.148 | 11.8452 | 16.644 | 26.353 | 5.324 |

Duct Diameter |
cm | 6.8 | 6.8 | 7.8 | 11.5 | 5 |

Wobble Friction Factor λ |
/m | 0.004 | 0.004 | 0.004 | 0 | 0.004 |

Curvature Friction Factor μ |
/rad | 0.3 | 0.3 | 0.3 | 0.3 | 0.3 |

Anchorage Slip |
mm | 11 | 12 | 11 | 5 | 5 |

Relaxation |
% | 5 | 5 | 5 | 1.5 | 2.5 |

Young's Modulus |
N/㎟ | 200000 | 200000 | 200000 | 200000 | 200000 |

Yield Strength σpy |
N/㎟ | 1450 | 1600 | 1600 | 1600 | 1500 |

Tensile Strength σpu |
N/㎟ | 1700 | 1850 | 1850 | 1860 | 1800 |

### Duct Diameter

When the Tendon Type is Post-Tension, input for the diameter of duct is required. Based on the tendon area, the duct diameter is automatically calculated, which is then referred to for duct diameter input.

### Strand Diameter

When the Tendon Type is Pre-Tension, the diameter of strand should be entered. The program automatically calculates the diameter of strand corresponding to the specified Total Tendon Area. The diameter of the strand is used to compute Transfer Length.

### Relaxation Coefficient

The relaxation application method can be chosen between Magura method and CEB-FIP code. If you want to ignore the effect of relaxation, you can check off the checkbox on the right side of the input field.

**When Magura is selected**

**When Magura is selected**

Select 10 or 45 for Relaxation Coefficient (C), which relates to the product. Relaxation coefficients of 10 and 45 may be used for general steel and low-relaxation steel respectively. Losses due to steel relaxation are determined from the following equation:

**When European is selected**

**When European is selected**

The following expressions are applied for Class 1 (Ordinary), Class 2 (Low) and Class 3 (Hot rolled) to calculate relaxation loss with time.

∆σpr: Absolute value of the relaxation losses

σpi: Absolute value of the initial prestress for post-tensioning and maximum tensile stress applied to the tendon minus the immediate losses occurred

t: Time after tensioning (in hours)

µ = σpi /fpk, where fpk is the characteristic value of the tensile strength of the prestressed steel.

ρ1000: Relaxation loss (in %), at 1000 hours after tensioning and at a mean temperature of 20°C

**When CEB-FIP(2010) is selected**

**When CEB-FIP(2010) is selected**

Enter the loss ratio after 1000 hours steel relaxation by the percentage of initial prestress. Prestress loss due to steel relaxation is determined from the following equation:

where,

: initial stress

: loss ratio after 1000 hours due to steel relaxation

: progress of steel relaxation at the last time step

The progress of steel relaxation with time is as follows:

Time in hour |
1 |
5 |
20 |
100 |
200 |
500 |
1000 |

Slow Development | 20 | 35 | 45 | 65 | 75 | 85 | 100 |

Mean Development | 30 | 45 | 55 | 70 | 80 | 90 | 100 |

Rapid Development | 40 | 55 | 65 | 75 | 85 | 95 | 100 |

Following formula is applied:

where ρt: the relaxation after t hours, ρ1000 : the relaxation after 1000 hours, k =log(ρ1000/ρ100)

**When CEB-FIP(1990) is selected**

**When CEB-FIP(1990) is selected**

Enter the loss ratio after 1000 hours steel relaxation by the percentage of initial prestress. Prestress loss due to steel relaxation is determined from the following equation:

where,

: initial stress

: loss ratio after 1000 hours due to steel relaxation

: progress of steel relaxation at the last time step

The progress of steel relaxation with time is as follows:

Time in hour |
1 |
5 |
20 |
100 |
200 |
500 |
1000 |

Relaxation losses at percentage of losses in 1000 hours |
25 | 45 | 55 | 70 | 80 | 90 | 100 |

For an estimation of relaxation up to 30 years, the following formula is applied

where ρt: the relaxation after t hours, ρ1000: the relaxation after 1000 hours, k to be 0.1549

The relaxation loss after 50 years is taken as three times the 1000 hour loss. The relaxation loss between 30 years and 50 years is linearly interpolated.

**When CEB-FIP(1978) is selected**

**When CEB-FIP(1978) is selected**

Enter the final loss ratio due to steel relaxation. Prestress loss due to steel relaxation is determined from the following equation:

where,

: initial stress

: loss ratio after 1000 hours due to steel relaxation

: progress of steel relaxation at the last time step

The progress of steel relaxation with time is as follows:

Progression of relaxation(k) | Lapse |
---|---|

where : the timing of prestressing

: the time when tendon loss due to relaxation is evaluated

**When AS 5100.5-2017 is selected**

**When AS 5100.5-2017 is selected**

The design relaxation of a tendon (R) is determined from the following equation:

*k**6*: a coefficient, dependent on the duration of the prestressing force

*j*: time after prestressing, in days

*k**7*: a coefficient, dependent on the stress in the tendon as a proportion of fpb, determined from the figure below.

k*8* a coefficient, dependent on the average annual temperature (T) in degrees Celsius, taken as T/20 but not less than 1.0

*R**b*: basic relaxation of a tendon after one thousand hours at 20°C

The design relaxation of a tendon (R) is determined from the following equation:

**When INDIA (IRC:18-2000) is selected**

**When INDIA (IRC:18-2000) is selected**

Relaxation loss at 1000 days is as follows (at 20 °C ± 2 °C ):

Initial Stress | Relaxation loss for Normal relaxation steel (%) | Relaxation loss for Low relaxation steel (%) |
---|---|---|

0.5 fp | 0 | 0 |

0.6 fp | 2.5 | 1.25 |

0.7 fp | 5.0 | 2.5 |

0.8 fp | 9.0 | 4.5 |

Relaxation loss, in relation to time, is as follows:

Time (hour) | 1 | 5 | 20 | 100 | 200 | 500 | 1000 |
---|---|---|---|---|---|---|---|

Relaxation loss (%) | 15 | 25 | 35 | 55 | 65 | 85 | 100 |

**When INDIA (IRC:112-2011) is selected**

**When INDIA (IRC:112-2011) is selected**

Relaxation loss at 1000 days is as follows (at 20 °C ± 2 °C ):

Initial Stress | Relaxation loss for Normal relaxation steel (%) | Relaxation loss for Low relaxation steel (%) |
---|---|---|

0.5fp |
0 |
0 |

0.6fp |
2.5 |
1.25 |

0.7fp |
5.0 |
2.5 |

0.8fp |
9.0 |
4.5 |

Relaxation loss, in relation to time, is as follows:

Time (hour) | 1 | 5 | 20 | 100 | 200 | 500 | 1000 | |
---|---|---|---|---|---|---|---|---|

Relaxation loss (%) | Normal | 34 | 44 | 55 | 70 | 78 | 90 | 100 |

Low |
37 |
47 |
57 |
72 |
79 |
90 |
100 |

**When JTG04 is selected**

**When JTG04 is selected**

If the selects JTG04 standard in the Material Data and selects JTG04 for Relaxation Coefficient in the Tendon Property, the Characteristic Value of Strength (fpk) is automatically entered as per the JTG04 code. If the user does not select JTG04 standard in the Material Data, the user can directly enter the Characteristic Value of Strength (fpk).

In case Steelbar540, Steelbar785 or Steelbar930 is selected in the Material Data, the Application of Overstress Reduction Factor is ignored.

**When TB05 is selected**

**When TB05 is selected**

If the user selects TB05 standard in the Material Data and selects TB05 for Relaxation Coefficient in the Tendon Property, the Characteristic Value of Strength (fpk) and the Tendon Relaxation Coefficient (ξ) are automatically entered as per the TB05 code. If the user does not select TB05 standard in the Material Data, the user can directly enter the Characteristic Value of Strength (fpk) directly

**Calculation of Tendon Relaxation Coefficient (ξ) and loss due to Relaxation**

**Calculation of Relaxation Coefficient ()**

If material = Wire1470, Wire1570, Wire1670, Wire1770, Wire1860

If material = Strand1470, Strand1570, Strand1670, Strand1720, Strand1770, Strand1820, Strand1860

When

When

If material = PSB830

If material = PSB830 and Application of Overstress Reduction Factor is checked on

**Calculation of Prestress Loss**

If is greater than or equal to

If is less than

where,

: The loss of Prestressed Stress due to Tendon Relaxation

: Tendon Relaxation Coefficient

: Anchor Tendon Stress

: Tendon Tension Strength Standard Value

**When User Defined is selected**

**When User Defined is selected**

Select the user defined relaxation function in hour/day and loss ratio due to steel relaxation relation.

Click [...] button to add/modify User Defined Relaxation Function.

### Curvature Friction Factor

To account for friction loss due to the curvature of tendons

### Wobble Friction Factor

To account for straightness/ length effect (imperfection in alignment along the length of tendon, regardless of straight or draped alignment), if a prestressing force Po is applied at the jacking end, the tendon force Px can be expressed as follows:

Px = Po e-µθ

Where θ is the accumulation of changes in angle along the length being considered.

Θ is composed of two parts-

First is the intentional curvature i.e. due to the intentional curvilinear placement of tendons along the ”Design path”. It is denoted as α.

Second is the unintentional curvature. Since the tendons are secured at selected points only along a design path, in practice the actual path of a flexible tendon will have small deviations from the design path. Also, other construction factors cause added departure of tendon path from its intended profile. The deviations from the design path are referred to as ”wobble” of the tendon. The accumulation of angular change along the tendon length due to its wobble off the intended course is estimated and denoted as γ. Hence the accumulation of angular change becomes (α + γ).

Thus the corrected friction loss relationship becomes:

Px = Po e-µ(α + γ)

Px = Po e-µ{α + (γ/L)L}

(γ/L) is the **unintentional angular displacement** for internal tendons (per unit length)- specified as k in the Eurocode. Its units are radians/length. Eurocode gives the limit of unintentional angular displacement for internal tendons (per unit length).

The **Wobble coefficient** is defined as K = µ*γ/L.This is defined in terms of per unit length. For midas Civil we specify the value of wobble coefficient as Wobble Friction Factor. So to incorporate the values of k mentioned in Eurocode, we have to multiply the value with µ and then input in the program.

### Ultimate Strength

Ultimate strength

### Yield Strength

Yield strength

### External Cable Moment Magnifier

Enter the increase of effective prestress of external cable to be used for calculating failure-resisting moment. Entered stress increase will be used for PC design.

### Anchorage Slip (Draw in)

Tendon slippage at the anchor

**Begin** : Slippage at the beginning of tendon if tensioned here

**End** : Slippage at the end of tendon if tensioned here

### Bond Type

**Bonded** : After grouting, the sectional properties are calculated based on the equivalent section considering tendon. The analysis results are stored in the *.out file, which includes the sectional properties for each construction stage. You can observe the changes in sectional properties after grouting.

**Unbonded** : After prestressing, the sectional properties are calculated based on the concrete net section, excluding the duct section.

**To modify the previously entered tendon data**

Select the tendon from the list in the Tendon Property dialog box and click **Modify** to change any relevant data.

**To delete the previously entered tendon data**

Select the tendon from the list in the Tendon Property dialog box and click **Delete** to eliminate any relevant data.