SSNP108 - Concrete element prestressed in compression

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SSNP108 - Concrete element prestressed in compression

Date:

18/12/03

Author (S):

C. CHAVANT, X. DESROCHES, L. VIVAN

Key

V6.03.108-B

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Manual of Validation

V6.03 booklet: Nonlinear statics of the plane systems

HT-66/03/008/A

Organization (S):

EDF-R & D/AMA, CS

Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.108

SSNP108 - Prestressed concrete element
in compression

Summary:

One considers an elementary structure made up of a square concrete plate crossed by a cable of
prestressed whose neutral fiber is confused with the horizontal axis of symmetry of the plate. The vertical edge
left of the plate is fixed. The cable is put in traction at its two ends in order to prestress
toggle plate. The losses of voltage along the cable are neglected.

The goal of this case-test is to validate, on a simple configuration, the method of calculation of the state of balance
of a prestressed structure of concrete. The results are validated by comparison with an analytical solution.

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SSNP108 - Concrete element prestressed in compression

Date:

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C. CHAVANT, X. DESROCHES, L. VIVAN

Key

V6.03.108-B

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Problem of reference

1.1 Geometry

The concrete plate is square; the sides have even length L = H = 2 Mr.
The thickness of the plate is worth E = 0,6 Mr.
The cable crosses the plate horizontally, with middle height, without eccentricity in the thickness. The surface of
the cross-section of the cable is worth S

has

= 1,5.10

2 m

With

H = 2 m

L = 2 m

1 m

1.2

Properties of materials

Material concrete constituting the plate:

Young modulus E

= 3.10

Material steel constituting the cable:

Young modulus E

has

= 2,1.10

The Poisson's ratio is taken equal to 0 for two materials; the direction thus is privileged
of normal load application (direction

The losses of voltage being neglected, the various parameters being used for their estimate are fixed at 0.

1.3

Boundary conditions and loadings

The lower node of the left edge of the plate, i.e. the node origin (0;0), are embedded: all
DDLs of translation and rotation are locked.
The higher node of this same left edge, i.e. the node (0;2), is supported bi-
laterally: DDLs of translation locked are

and

One applies at the two ends of the cable (which are fixed on the concrete in A and B) a normal effort of
traction: ( F

;0) with node A (0;1) and (F

;0) with the node B (2;1), with F

= 2.10

NR.

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SSNP108 - Concrete element prestressed in compression

Date:

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C. CHAVANT, X. DESROCHES, L. VIVAN

Key

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Reference solution

2.1 Solution

formal

Displacements in the cable and the concrete are continuous and homogeneous. Thus displacement

horizontal on the interval [0;L] is worth

U X

L X

()

The normal stresses in the concrete plate and the steel wire rope are written respectively
(assumption of elasticity):

has

where

= FS

has

is initial prestressing in the cable

and

is horizontal displacement with the X-coordinate

The balance of the unit plates and cables is written:

B B

has has

E eH E S

The normal effort in the cable is worth:

has

has has

E S uL F F

E eH

E S

The total effort on the vertical section of the concrete plate is worth:

has has

E eH uL

E eH

E S

= -

One deduces from it the linear density of normal effort on the concrete plate

has has

E E

E eH

E S

= -

2.2

Numerical values of reference

The numerical values of reference are:

= 1,11013974.10

has

= 1,99825153.10

= 9,99125765.10

NR/m

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SSNP108 - Concrete element prestressed in compression

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3 Modeling

With

3.1

Characteristics of modeling

The figure below gives a simplified representation of the mesh.

NB002001

NC001001

NB001001

NB002002

NC001005

NB001002

The concrete plate is represented by an element

DKT

, supported by a mesh quadrangle to 4

nodes.

A thickness E = 0,6 m is affected for him, as well as a material concrete for which are defined them
behaviors

ELAS

(Young modulus E

= 3.10

AP) and

BPEL_BETON

: parameters

characteristics of this relation are fixed at 0 bus one neglects the losses of voltage along the cable of
prestressed.

The node

NB001001

is embedded:

DRX

DRY

and

DRZ

are locked. The node

NB002001

supported bilaterally:

and

are locked.

The cable is represented by 4 elements

MECA_BARRE

, supported by 4 meshs segments with 2 nodes.

A surface of cross-section S

has

= 1,5.10

their is affected, as well as a material steel for which are

defined behaviors

ELAS

(Young modulus E

has

= 2,1.10

AP) and

BPEL_ACIER

: parameters

characteristics of this relation are fixed at 0 (neglected losses of voltage), except for
stress ultimate elastic for which a zero value is illicit (F

prg

= 1,77.10

AP).

The voltage F

= 2.10

NR is applied to the nodes

NC001001

and

NC001005

. This value of voltage is

coherent with the values of section and yield stress, for a cable of prestressed of type
wiring.

The calculation of the state of balance of the unit plates and cable is carried out in only one pitch, it
behavior being elastic.

3.2

Stages of calculation and functionalities tested

The main stages of calculation correspond to the functionalities which one wishes to validate:

operator

DEFI_MATERIAU

: definition of the relations of behavior

BPEL_BETON

and

BPEL_ACIER

, in the particular case where losses of voltage along the cable of

prestressed are neglected (default values of the parameters);

operator

DEFI_CABLE_BP

: determination of a constant profile of voltage along the cable of

prestressed, losses being neglected; calculation of the coefficients of the relations kinematics
between the DDL of the nodes of the cable and the DDL of the nodes “close” to the concrete plate;

operator

AFFE_CHAR_MECA

: definition of a loading of the type

RELA_CINE_BP

;

operator

STAT_NON_LINE

, option

COMP_INCR

: calculation of the state of balance by holding account

loading of the type

RELA_CINE_BP

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SSNP108 - Concrete element prestressed in compression

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Results of modeling A

4.1 Values

tested

4.1.1 Linear density of normal effort on the vertical section of the concrete plate

One compares the values extracted the field

SIEF_ELNO_ELGA

resulting from

STAT_NON_LINE

with the values

theoretical of reference. The extraction is done on the mesh

QD001001

representing the concrete plate.

The component to which the tests relate is

NXX

The tolerance of relative variation compared to the reference is worth 10

Node

Value of reference

Computed value

Relative variation

NB001001

 9,99125765.10

NR/m

 9,9912576495569.10

NR/m

 4,43.10

NB001002

 9,99125765.10

NR/m

 9,9912576495569.10

NR/m

 4,43.10

NB002001

 9,99125765.10

NR/m

 9,9912576495569.10

NR/m

 4,43.10

NB002002

 9,99125765.10

NR/m

 9,9912576495569.10

NR/m

 4,43.10

4.1.2 Horizontal displacement of the nodes of the concrete plate

One compares the values extracted the field

DEPL

resulting from

STAT_NON_LINE

with the theoretical values of

reference.
The component to which the tests relate is

The tolerance of relative variation compared to the reference is worth 10

Node

Value of reference

Computed value

Relative variation

NB001002

 1,11013974.10

 1,1101397388397.10

 1,05.10

NB002002

1,11013974.10

1,1101397388397.10

 1,05.10

4.1.3 Normal effort in the cable

One compares the values extracted the field

SIEF_ELNO_ELGA

resulting from

STAT_NON_LINE

with the values

theoretical of reference. The extraction is done on the meshs

SG001001

for the node

NC001001

SG001002

for the node

NC001002

SG001003

for the node

NC001003

, and

SG001004

for

nodes

NC001004

and

NC001005

The component to which the tests relate is

The tolerance of relative variation compared to the reference is worth 10

Node

Value of reference

Computed value

Relative variation

NC001001

1,99825153.10

1,9982515299113.10

 4,44.10

NC001002

1,99825153.10

1,9982515299113.10

 4,44.10

NC001003

1,99825153.10

1,9982515299113.10

 4,44.10

NC001004

1,99825153.10

1,9982515299113.10

 4,44.10

NC001005

1,99825153.10

1,9982515299113.10

 4,44.10

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SSNP108 - Concrete element prestressed in compression

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4.1.4 Horizontal displacement of the nodes of the cable

One compares the values extracted the field

DEPL

resulting from

STAT_NON_LINE

with the theoretical values of

reference.
The component to which the tests relate is

The tolerance of relative variation compared to the reference is worth 10

Node

Value of reference

Computed value

Relative variation

NC001002

 2,77534935.10

 2,7753493470988.10

 1,05.10

NC001003

 5,55069869.10

 5,5506986941982.10

7,56.10

NC001004

 8,32604804.10

 8,3260480412974.10

1,56.10

NC001005

 1,11013974.10

 1,1101397388389.10

 1,05.10

4.2 Remarks

The computed values correspond indeed to those theoretically awaited. One obtains well
a compactness for the concrete plate.

One observes an infinitesimal difference between horizontal displacement with the node

NC001005

belonging to the cable and horizontal displacement to the nodes

NB001002

and

NB002002

plate

of concrete. The recorded values should be identical, but the round-off errors appearing
in the coefficients of the relations kinematics explain this infinitesimal difference.

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SSNP108 - Concrete element prestressed in compression

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V6.03 booklet: Nonlinear statics of the plane systems

HT-66/03/008/A

5 Modeling

5.1

Characteristics of modeling

For this modeling, the nodes “cables” and “concrete” are confused.
The figure below gives a simplified representation of the mesh.

The concrete plate is represented by 10 elements

DKT

, supported by 10 meshs

QUAD4

A thickness E = 0,6 m is affected for him, as well as a material concrete for which are defined them
behaviors

ELAS

(Young modulus E

= 3.10

AP) and

BPEL_BETON

: parameters

characteristics of this relation are fixed at 0 bus one neglects the losses of voltage along the cable of
prestressed.

Nodes

N1, N5 and N3

are embedded:

DRX

DRY

and

DRZ

are locked.

The cable is represented by 5 elements

MECA_BARRE

, supported by 5 meshs

SEG2

A surface of cross-section S

has

= 1,5.10

their is affected, as well as a material steel for which are

defined behaviors

ELAS

(Young modulus E

has

= 2,1.10

AP) and

BPEL_ACIER

: parameters

characteristics of this relation are fixed at 0 (neglected losses of voltage), except for
stress ultimate elastic for which a zero value is illicit (F

prg

= 1,77.10

AP).

The voltage F

= 2.10

NR is applied to the nodes

and

. This value of voltage is coherent with

values of section and yield stress, for a cable of prestressed of wiring type.

The calculation of the state of balance of the unit plates and cable is carried out in only one pitch, it
behavior being elastic.

5.2

Stages of calculation and functionalities tested

The main stages of calculation correspond to the functionalities which one wishes to validate:

operator

DEFI_MATERIAU

: definition of the relations of behavior

BPEL_BETON

and

BPEL_ACIER

, in the particular case where losses of voltage along the cable of

prestressed are neglected (default values of the parameters);

operator

DEFI_CABLE_BP

: determination of a constant profile of voltage along the cable of

operator

AFFE_CHAR_MECA

: definition of a loading of the type

RELA_CINE_BP

;

operator

STAT_NON_LINE

, option

COMP_INCR

: calculation of the state of balance by holding account

loading of the type

RELA_CINE_BP

operator

POST_RELEVE_T

NOM_CMP= `

on all the field

SIEF_ELNO_ELGA

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SSNP108 - Concrete element prestressed in compression

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Results of modeling B

6.1 Values

tested

6.1.1 Linear density of normal effort on the vertical section of the concrete plate

Node

Value of reference

Computed value

Relative variation

 9,99125765.10

NR/m

 9,8387753336725.10

NR/m

1.526%

 9,99125765.10

NR/m

 9,8387753336725.10

NR/m

1.526%

6.1.2 Normal effort in the cable

Node

Value of reference

Computed value

Relative variation

1,99825153.10

1,9982248921222.10

 0.001%

1,99825153.10

1,9943932520206.10

 0.193%

6.1.3 Normal effort in the cable via control POST_RELEVE_T

Node

Value of reference

Computed value

1,998224892.10

1,9982248921222.10

1,994393252.10

1,9943932520206.10

6.2 Remarks

The computed values correspond indeed to those theoretically awaited. One obtains well
a compactness for the concrete plate.

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SSNP108 - Concrete element prestressed in compression

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Summary of the results

The results obtained are validated by comparison with an analytical solution of reference with one
very good precision.

The particular functionalities tested are as follows:

operator

DEFI_MATERIAU

: definition of the parameters characteristic of the materials steel

and concrete allowing the calculation of the voltage along the cable of prestressing, following the rules
BPEL;

operator

DEFI_CABLE_BP

: calculation of the voltage along the cable and the coefficients of

relations kinematics between the DDL of the nodes of the cable and the DDL of the “close” nodes
concrete plate;

operator

AFFE_CHAR_MECA

: definition of a loading of the type

RELA_CINE_BP

;

operator

STAT_NON_LINE

, option

COMP_INCR

: calculation of the state of balance by holding account

loading of the type

RELA_CINE_BP