Comparison of Theoretical and Software Results of Prestressed Tendon Loss

October 23, 2020
BLOG BRIDGE INSIGHT

With the advent of the IT era in the 21st century, information that was previously unavailable in the engineering market has become possible. Engineering simulation using a computer program is one of them, and it is currently used in most engineering industries.


In order to perform a correct structural analysis simulation using such a computer analysis program, it is necessary to compare and verify the contents of engineering theory and the results calculated by the program. It is an essential process in industries such as construction and transportation, which are directly related to human safety.

 

Comparison of Theoretical and Software Results of Prestressed Tendon Loss

 

In this post, we will compare the theoretical contents to the analysis results in a structural analysis program about the prestressed concrete equilibrium equation and the prestressed tendon loss.

 

PSC bridge is a bridge type that secures the stability of the structure by introducing artificial deformation and stress using tendon to the concrete member. The stress introduction by tendon depends on the tendon shape and tension. The shape of the tendon is defined as the distance from the neutral axis of the member. If the neutral axis changes for each construction stage, such as the composite section in the construction stage, this should be appropriately reflected.

 

Tension can be divided into immediate losses, such as friction or anchorage losses, and time-dependent losses that occur as the construction stage progresses, such as elasticity change or relaxation. Such tendon losses must be properly reflected in the analysis.

 


 

1. Verification of Equivalent Tendon Force

 

Assuming that there is no Tendon Losses, the equivalent tendon force is calculated as follows.

Verification of Equivalent Tendon Force
Case. Simple beam model with the tendon placed in a curve.

 

 

Material and section properties are following:

 

Modulus of Elasticity (Conc),

Ec

10,000

Modulus of Elasticity (Steel)

Es

150,000

Area of Steel

Ast

0.01

Yield Stress

Fy

100,000

Diameter of Duct

dduct

0.04 m

Tensile Stress

fso

80,000

Eccentricity

ei

0.3 m

Span length

L

10 m

 

→ Theoretical approach method and calculation results

 

i. Calculate the tension force at each at each L/4 position for one beam, and calculation the equivalent tendon force acting on the beam. Ignoring the tendon losses, the tension at each L/4 position of the beam is as follows.

 

ii. Here, the arrangement of the tendons in each section is assumed to be linear.

 

Theoretical approach method and calculation results 1Theoretical approach method and calculation results 2Theoretical approach method and calculation results 3

 

iii. The neutral axis moves because the area of the tension member and the duct is calculated as a transformed cross section. Where, each position is described as e0=i, e1=1/4, e2=2/4.

 

Theoretical approach method and calculation results 4

 

After the change of the neutral axis by the effective section,

Theoretical approach method and calculation results 5

 

iv. Where Pi=Pj and ei=ej,

Theoretical approach method and calculation results 6

 

Therefore, the equivalent tendon force acting on each section is shown in the below figure.

 

Theoretical approach method and calculation results 7Theoretical approach method and calculation results 8

v. Member force diagram

Member force diagram

 

 

→ Modelling and structural analysis result by midas Civil

 

i. Input Model

Input Model

ii. Input Load

Input load

iii. Analysis Results

Analysis Results

→ Comparison of theoretical results and analysis results using midas Civil

Comparison of theoretical results and analysis results using midas Civil


 

 

2. Tendon Losses due to Friction, Anchorage Slip, and Relaxation

 

Case. Simple beam model with the tendon placed in a curve
Case. Simple beam model with the tendon placed in a curve

 

Material and section properties are following:

 

Modulus of Elasticity (Conc)

  Ec

10,000

 

Anchorage slip

Lslip

0.05 m

Modulus of Elasticity (Steel)

  Es

150,000

 

Relaxation coefficient

Crelax

45

Area of Steel

  Ast

0.01

 

Curvature friction factor

μ

0.3

Yield Stress

  Fy

100,000

 

Wobble friction factor

k

0.0066/m

Diameter of Duct

  dduct

0.04 m

 

 

t1

100 day

Tensile Stress

  fso

80,000

 

 

Eccentricity

  ei

0.3 m

 

 

 

  ej

0.3 m

 

 

Span length

 L

10 m

 

 

 

 

 

Theoretical approach method and calculation results

 

i) Loss due to friction


The tension at each L/4 point is as follows.

 

i) Loss due to friction

 

 

 

ii) Loss due to anchorage slip


Let the length of the tendon subject to reverse friction be set, calculate the tendon loss due to settlement activity based on where this length is in any of the four sections.

Loss due to anchorage slipTendon loss graph by anchorage slip

 

 

 

(a) Section I 

Section I(b) Section ii 

Section ii 

The rest remains, PL/2, P3L/4, PL unchanged.

 

 

iii) Loss due to relaxation

 

Loss due to relaxation is calculated as follows.

Loss due to relaxationHere, fsi is the stress before loss due to relaxation occurs, and t is the elapsed time (hr). Crelax is relaxation coefficient (45 in this example), and fy (100,000 N/m2) is yield stress.

Therefore, the tension force considering the loss due to relaxation at each point is as follows.
the tension force considering the loss due to relaxation at each point

→ Modelling and structural analysis result by midas Civil

 

i) Input Model

Modelling and structural analysis result by midas Civil 1

ii) Input Load

Modelling and structural analysis result by midas Civil 2

 

 

 

iii) Analysis Results

 

(a) Loss due to friction

Loss due to frictionLoss due to friction

 

(b) Loss due to anchorage slip

2930

 

(c) Loss due to relaxation

Loss due to anchorage slip 232-1

 

→ Comparison of theoretical results and analysis results using midas Civil

 

→ Comparison of theoretical results and analysis results using midas Civil

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TaeGook Kim | Technical Engineer | MIDASIT

- Civil engineer within MIDASIT Technical Planning Team

- Over 3 years of experience in technical and marketing for MIDAS Programs

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