FINITE ELEMENT ANALYSIS OF INNOVATIVE SOLUTIONS OF PRECAST CONCRETE BEAM-COLUMN DUCTILE CONNECTIONS

“FINITE ELEMENT ANALYSIS OF INNOVATIVE

SOLUTIONS OF PRECAST CONCRETE BEAM-COLUMN

DUCTILE CONNECTIONS”

Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering

Pierluigi Olmati

[email protected]

Franco Bontempi

[email protected]

Angela Saviotti

[email protected]

1/21


“Finite element analysis of innovative solutions of precast concrete beam-column

ductile connections”

2/21

Treated models


2D MODEL:

‐Model “A” with mortar stratum for beam‐column connection;

‐Model “B” without mortar stratum for beam‐column connection.

•3D MODEL:

‐Model “A” with mortar stratum for beam‐column connection;

‐Model “B” without mortar stratum for beam‐column connection.

3D “A” 3D “B”



2D “A” 2D “B”

3/21



•FEM analytical program: DIANA V. 9.3

•Geometry and Mesh of the structure, to assign boundary

conditions and loads: Midas FX+ for DIANA

•Non-linear mechanisms :

-Cracking of the concrete

-Yielding of the steel.


CONCRETE – Total Strain Crack Model

Tensile Behavior Compressive Behavior

STEEL – Von Mises

4/21

Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections

Beam

L=3770 mm

Column

H=4700 mm

STRUCTURE


5/21

BOUNDARY CONDITIONS AND LOADS

LOAD CONDITION

SEISMIC SITUATION


2D


6/21



MODEL “A” MODEL “B”

7/21

MODEL 2DMESH

Four‐node quadrilateral plane

stress elements (Q8MEM)

Three‐node triangle plane stress

elements (T6MEM)

Concrete, Mortar, Rubber and Steel Plates



Beam and Column:

Concrete C40/50

Rubber padConnection

Stratum:

Mortar

Steel Plates

MODEL “A”

MODEL “B”

Zoom of Beam-Column jointReinforcing Steel

Two‐node straight truss

elements (L2 TRU)

8/21

Linear Elasticity Ideal Plasticity Linear Elasticity Ideal Linear Elasticity

Tension Softening

curve based on

fracture energy

A1 X X X

B1 X X X

A2.1 X X X

B2.1 X X X

A3.1 X X X

B3.1 X X X

A4.4 X X X

B4.4 X X X

STEEL CONCRETE

Compressive Behavior Tensile Behavior

NON LINEAR ANALYSIS


LOAD CONDITION : Applied Horizontal Force at the top of the column 2D


9/21

Linear Elasticity Ideal Plasticity Linear Elasticity Ideal Linear Elasticity

Tension Softening

curve based on

fracture energy

A1 X X X

B1 X X X

A2.1 X X X

B2.1 X X X

A3.1 X X X

B3.1 X X X

A4.4 X X X

B4.4 X X X

STEEL CONCRETE

Compressive Behavior Tensile Behavior

LOAD CONDITION : Applied Horizontal Force at the top of the column

NON LINEAR ANALYSIS


2D


10/21



11/21

MODEL 3DMESH

Four‐node, three‐side iso‐

parametric solid pyramid

elements (TE12L)

Concrete, Mortar, Rubber and Steel Plates


158634 solid elements

9106 bar elements

31639 nodes

Total of around 142941 degree of

freedom

Two‐node straight truss

elements (L2 TRU)

Two‐node, two‐

dimensional class‐II

beam element (L7BEN)


Longitudinal reinforcement steel

Stirrups

12/21

MODEL “A”

Displacements

MODEL “B”

mm mm

LINEAR ANALYSIS


LOAD CONDITION: Applied Horizontal Force of 600 kN at the top of the column

3D


13/21

MODEL “A”

Stress on reinforcing steel

MODEL “B”

LINEAR ANALYSIS



LOAD CONDITION: Applied Horizontal Force of 600 kN at the top of the column

14/21

NON LINEAR ANALYSIS


LOAD CONDITION : Applied Horizontal Force at the top of the column 3D


15/21


NON LINEAR ANALYSIS

MODEL “A”MODEL “B”

Deformed configuration developed by the structure at

STEP 20 – Fmax= 390.2 kN, δmax=88.6 mm.


STEP 15 - Fmax= 269.83 kN, δmax=87.27 mm

mmmm


3D


16/21

NON LINEAR ANALYSIS: Stress on Reinforcing Steel



STEP 10 Fmax= 207 kN,

δmax=12.75 mm –

σmax= 206.66 N/mmq


δmax=5.17 mm

σmax=108.21 N/mmq


δmax=88.56 mm

σmax=450.0 N/mmq

STEP 15 Fmax=270 kN,

δmax=87.27 mm

σmax=450.0 N/mmq


δmax=16.9 mm

σmax=365.0 N/mmq


STEP 5 Fmax= 128.7 kN,

δmax=6.97 mm

σmax=233.0 N/mmq


3D

17/21





δmax=12.75 mm –

σmax= 206.66 N/mmq


δmax=5.17 mm

σmax=108.21 N/mmq


δmax=88.56 mm

σmax=450.0 N/mmq


δmax=87.27 mm

σmax=450.0 N/mmq


δmax=16.9 mm

σmax=365.0 N/mmq



δmax=6.97 mm

σmax=233.0 N/mmq

3D


18/21

LOAD CONDITION: Applied Horizontal Force at the top of the column

NON LINEAR ANALYSIS: Cracking Status




δmax=5.17 mm


δmax=12.75 mm


δmax=88.56 mm


δmax=6.97 mm


δmax=16.9 mm


δmax=87.27 mm

3D


19/21

20/21

• Structural continuity is an important problem, especially with regard to the strength of

the connection system between precast elements.

•DIANA software, modeling the nonlinear behavior of concrete and mortar using total

strain crack model. The reinforcing steel is modeled by a bilinear plasticity model.

• The full load capacity of the bars is developed without the failure of the concrete and

the mortar.

• The progress of the cracking of the concrete is well reproduced.

• The similarity between the results obtained with two different finite

element programs, the previously mentioned DIANA and ASTER.

• The role of the mortar stratum is weighted , it contributes both to an increase of initial

stiffness and of the final strength.

• The introduction of the connectors inside the mass of concrete.

• Structural continuity is an important problem, especially with regard to the strength of

the connection system between precast elements.

•DIANA software, modeling the nonlinear behavior of concrete and mortar using total

strain crack model. The reinforcing steel is modeled by a bilinear plasticity model.

• The full load capacity of the bars is developed without the failure of the concrete and

the mortar.

• The progress of the cracking of the concrete is well reproduced.

• The similarity between the results obtained with two different finite

element programs, the previously mentioned DIANA and ASTER.

• The role of the mortar stratum is weighted , it contributes both to an increase of initial

stiffness and of the final strength.

• The introduction of the connectors inside the mass of concrete.



21/21Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering

3D


Angela Saviotti, Pierluigi Olmati, Franco Bontempi

“FINITE ELEMENT ANALYSIS OF INNOVATIVE

SOLUTIONS OF PRECAST CONCRETE BEAM-COLUMN

DUCTILE CONNECTIONS”


Pierluigi Olmati

[email protected]

Franco Bontempi

[email protected]

Angela Saviotti

[email protected]

22/21




23/24

NON LINEAR ANALYSIS – CYCLIC ANALYSIS

MODEL “A”


SECOND LOAD CONDITION : Imposed vertical displacement at the top of the column

Deformed

configuration developed

by the structure at STEP

n. 25 imposed maximum

displacement δ=80 mm.

2D


24/24

MODEL “A”


Step 25, imposed

displacement δ=80

mm

Step 50, imposed

displacement δ=0

mm

Step 80, imposed

displacement δ= - 80 mm

Step 110, imposed

displacement δ=0 mm

Step 25

Step 50Step 80

Step 110

Step 25 σmax=450 .0 N/mmq Step 50 σmin = - 450 .0 N/mmq

Step 80 σmin= - 450 .0 N/mmq Step 110 σmin= - 203.25 N/mmq

STRESS on reinforcing steelCRACKING STATUS

Step 25

Step 50 Step 80

2D



NON LINEAR ANALYSIS – CYCLIC ANALYSIS

Step 1

25/24

26/24Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering

2D

3D




Stand‐by

MODEL “A”

Displacements

MODEL “B”

mm mm

LINEAR ANALYSIS


FIRST LOAD CONDITION: Applied Horizontal Force of 600 kN at the top of the column

2D


Stand‐by

MODEL “A”

Stresses

MODEL “B”

LINEAR ANALYSIS


FIRST LOAD CONDITION: Applied Horizontal Force of 600 kN at the top of the

column 2D


Stand‐by

FIRST LOAD CONDITION : Applied Horizontal Force at the top of the column

NON LINEAR ANALYSIS

MODEL “A”MODEL “B”


STEP 40 – Fmax= 280.9 kN, δmax=102.4 mm.


STEP 18 - Fmax= 173.06 kN, δmax=112.7 mm

mmmm


2D


Stand‐by




STEP 1 Fmax= 18 kN,

δmax=0.70 mm –

σmax=3.88 N/mmq


δmax=5.32 mm

σmax=106.9 N/mmq


δmax=102.4 mm

σmax=450.0 N/mmq

STEP 18 Fmax= 173.06

kN, δmax=112.7 mm

σmax=450.0 N/mmq


δmax=8.75 mm

σmax=436.8 N/mmq


δmax=1.12 mm

σmax=58.47 N/mmq

FIRST LOAD CONDITION : Applied Horizontal Force at the top of the column 2D


Stand‐by

FIRST LOAD CONDITION: Applied Horizontal Force at the top of the

column NON LINEAR ANALYSIS: Cracking Status




δmax=102.4 mm


δmax=5.32 mm

STEP 1 Fmax= 18 kN,

δmax=0.70 mm


δmax=1.12 mm


δmax=8.75 mm

STEP 18 Fmax= 174.0

kN, δmax=112.7 mm

2D


Stand‐by

NON LINEAR ANALYSISMODEL “A” MODEL “B”


mm mm

Deformed


by the structure at LAST

STEP imposed


Deformed

configuration developed by

the structure at LAST STEP

imposed displacement

δmax=205 mm

Force-Displacement graph: Model “A” Vs. Model “B”Stress–Strain graph of beam-column ductile connection Model “A” Vs

Model “B”

SECOND LOAD CONDITION : Imposed vertical displacement at the top of the column 2D


Stand‐by





STEP 1 Fmax= 52 kN,

δmax=4 mm

σmax=345.16 N/mmq

STEP 5 Fmax= 83 kN,

δmax=20 mm

σmax=450.0 N/mmq

STEP 1 Fmax= 153.85

kN, δmax=4 mm

σmax=51.09 N/mmq


δmax=20 mm

σmax=450.0 N/mmq

STEP 13 Fmax= 371.6kN,

δmax=52mm

σmax=450.0 N/mmq

STEP 13 Fmax= 89.74

kN, δmax=52 mm

σmax=450.0 N/mmq

2D


Stand‐by

NON LINEAR ANALYSIS: Cracking Status



STEP 1 Fmax= 153.85

kN, δmax=4 mm


δmax=20 mm


δmax=52mm


STEP 1 Fmax= 52 kN,

δmax=4 mm

STEP 5 Fmax= 83 kN,

δmax=20 mm

STEP 13 Fmax= 89.74

kN, δmax=52 mm

2D

Stand‐by

FIRST LOAD CONDITION: Applied Horizontal Force at the top of the

column

MODEL “A”

MODEL “B”

NON LINEAR ANALYSIS


2D


Stand‐by



Stand‐by

38/25

NON LINEAR ANALYSISMODEL “A” MODEL “B”


Deformed


by the structure at LAST

STEP imposed


Deformed

configuration developed by

the structure at LAST STEP

imposed displacement

δmax=150 mm

Force-Displacement graph: Model “A” Vs. Model “B”Stress–Strain graph of beam-column ductile connection Model “A” Vs

Model “B”

SECOND LOAD CONDITION : Imposed vertical displacement at the top of the column 3D


39/25






δmax=10 mm

σmax=268.1 N/mmq


δmax=10 mm

σmax=196.41 N/mmq


δmax=50 mm

σmax=450.0 N/mmq


kN, δmax= 120 mm

σmax=450.0 N/mmq


δmax=50 mm

σmax=348.3N/mmq


kN, δmax=120 mm

σmin=-450.0 N/mmq

3D


40/25

NON LINEAR ANALYSIS: Crack Strain





δmax=10 mm

εknn=0.00242 %


δmax=50 mm

εknn=0.0359 %


kN, δmax= 120 mm

εknn=0.224%


δmax=10 mm

εknn=0.00703 %


δmax=50 mm

εknn=0.0548 %


kN, δmax=120 mm

εknn=0.132 %

3D


MATERIALS

The behavior of the concrete was modeled with the total strain based

constitutive model which describe the tensile and compressive behavior of

a material with one stress‐strain relationship.

The constitutive model based on total strain is developed along the lines of

the Modified Compression Field Theory, originally proposed by Vecchio &

Collins. The three‐dimensional extension to this theory is proposed by Selby

& Vecchio. Total strain model describes the stress as a function of the

strain. This concept is known as hypo‐elasticity when the loading and

unloading behavior is along the same stress‐strain path. The non‐linear

behavior of concrete was considered in both tension and compression

including the influence of lateral cracking on the compressive strength. The

input for the Total Strain crack models comprises two parts: (1) the basic

properties like the Young's modulus, Poisson's ratio, etcetera, and (2) the

definition of the behavior in tension, shear, and compression. For a Total

Strain crack model you can choose a predefined tension softening and

compression functions by specification of the curve name and appropriate

parameters. In this study it was chosen a “LINEAR” curve for tension

softening functions based on fracture energy and a “CONSTA” curve for

compression functions

CONCRETE

Tensile Behavior

Compressive Behavior



In cracked concrete, large tensile strains

perpendicular to the principal compressive

direction reduce the concrete compressive

strength. The relationship for reduction due to

lateral cracking is the model according to

Vecchio & Collins

The fracture energy in the

present analysis was estimated

from the CEB‐FIP Model Code

1990 (CEB‐FIP 1991) formula:

where,

= Coefficient, which

depends on the maximum

aggregate size and

= Mean cylinder strength

in MPa.

Compressive Behavior

E 35220 N/mm2 E 35220 N/mm

2

ν 0.2 ν 0.2

fc 40 N/mm2

fc 40 N/mm2

GC 120 J/m2

REDCRV VC1993

Tensile Behavior

Tension Softening Curve - based on FRACTURE ENERGY

E 35220 N/mm2 E 35220 N/mm

2

ν 0.2 ν 0.2

ft 2.457 N/mm2

ft 2.457 N/mm2

GF1 89.95 J/m2

GF1 89.95 J/m2

Linear Expone

CONCRETE 40/50

TO

TA

L S

TR

AIN

CR

AC

K

Lateral Influence

Ideal and Brittle - Consta Parabolic

Stand‐by

MATERIALS

For the reinforcement, an elastic‐plastic model was used both in tension and compression, with Von Mises yield criterion.

The criterion is based on the determination of the distortion energy in a given material that is of the energy associated with

changes in the shape in that material.

STEEL

For Steel a predefined class according to the NEN 6770 code was used, and the

materials model implemented are shown in the next pictures

fYk 450 N/mm2

ftk 540 N/mm2

Ey 206000 N/mm2

ν 0.3

STEEL B450C



Stand‐by



Stand‐by

Element Steel NameCROSS-SECTIONAL AREA

[ mm2 ]

Long. Reinf. 1924.23

Cross Reinf. 100.53

Long. Reinf. 760.27

Cross Reinf. 100.53

φ35 1924.23

φ65 6636.61

φ70 7696.90

φ105 17318.03

DUCTILE

CONNECTION

BEAM

COLUMN

2D

3D

Element Steel NameCROSS-SECTIONAL AREA

[ mm2 ]

φ

[ mm ]

Long. Reinf. 962.11

Cross Reinf. 8

Long. Reinf. 380.13

Cross Reinf. 8

φ35 962.11

φ65 3318.31

φ70 3848.45

φ105 8659.01

DUCTILE

CONNECTION

BEAM

COLUMN



Stand‐by



Stand‐by



Stand‐by



Stand‐by

Design

FINITE ELEMENT ANALYSIS OF INNOVATIVE SOLUTIONS OF PRECAST CONCRETE BEAM-COLUMN DUCTILE CONNECTIONS