Page 1
“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
Page 2
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
“Finite element analysis of innovative solutions of precast concrete beam-column
ductile connections”
2/21
Page 3
Treated models
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
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”
“Finite element analysis of innovative solutions of precast concrete beam-column
ductile connections”
2D “A” 2D “B”
3/21
Page 4
“Finite element analysis of innovative solutions of precast concrete beam-column
ductile connections”
•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.
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
CONCRETE – Total Strain Crack Model
Tensile Behavior Compressive Behavior
STEEL – Von Mises
4/21
Page 5
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Beam
L=3770 mm
Column
H=4700 mm
STRUCTURE
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
5/21
Page 6
BOUNDARY CONDITIONS AND LOADS
LOAD CONDITION
SEISMIC SITUATION
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
2D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
6/21
Page 7
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
MODEL “A” MODEL “B”
7/21
Page 8
MODEL 2DMESH
Four‐node quadrilateral plane
stress elements (Q8MEM)
Three‐node triangle plane stress
elements (T6MEM)
Concrete, Mortar, Rubber and Steel Plates
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
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
Page 9
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
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
LOAD CONDITION : Applied Horizontal Force at the top of the column 2D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
9/21
Page 10
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
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
2D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
10/21
Page 11
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
11/21
Page 12
MODEL 3DMESH
Four‐node, three‐side iso‐
parametric solid pyramid
elements (TE12L)
Concrete, Mortar, Rubber and Steel Plates
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
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)
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Longitudinal reinforcement steel
Stirrups
12/21
Page 13
MODEL “A”
Displacements
MODEL “B”
mm mm
LINEAR ANALYSIS
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
LOAD CONDITION: Applied Horizontal Force of 600 kN at the top of the column
3D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
13/21
Page 14
MODEL “A”
Stress on reinforcing steel
MODEL “B”
LINEAR ANALYSIS
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
LOAD CONDITION: Applied Horizontal Force of 600 kN at the top of the column
14/21
Page 15
NON LINEAR ANALYSIS
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
LOAD CONDITION : Applied Horizontal Force at the top of the column 3D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
15/21
Page 16
LOAD CONDITION : Applied Horizontal Force at the top of the column
NON LINEAR ANALYSIS
MODEL “A”MODEL “B”
Deformed configuration developed by the structure at
STEP 20 – Fmax= 390.2 kN, δmax=88.6 mm.
Deformed configuration developed by the structure at
STEP 15 - Fmax= 269.83 kN, δmax=87.27 mm
mmmm
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
3D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
16/21
Page 17
NON LINEAR ANALYSIS: Stress on Reinforcing Steel
MODEL “A” MODEL “B”
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
STEP 10 Fmax= 207 kN,
δmax=12.75 mm –
σmax= 206.66 N/mmq
STEP 5 Fmax= 128 kN,
δmax=5.17 mm
σmax=108.21 N/mmq
STEP 20 Fmax= 390 kN,
δmax=88.56 mm
σmax=450.0 N/mmq
STEP 15 Fmax=270 kN,
δmax=87.27 mm
σmax=450.0 N/mmq
STEP 10 Fmax= 205 kN,
δmax=16.9 mm
σmax=365.0 N/mmq
LOAD CONDITION : Applied Horizontal Force at the top of the column
STEP 5 Fmax= 128.7 kN,
δmax=6.97 mm
σmax=233.0 N/mmq
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
3D
17/21
Page 18
NON LINEAR ANALYSIS: Stress on Reinforcing Steel
MODEL “A” MODEL “B”
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
STEP 10 Fmax= 207 kN,
δmax=12.75 mm –
σmax= 206.66 N/mmq
STEP 5 Fmax= 128 kN,
δmax=5.17 mm
σmax=108.21 N/mmq
STEP 20 Fmax= 390 kN,
δmax=88.56 mm
σmax=450.0 N/mmq
STEP 15 Fmax=270 kN,
δmax=87.27 mm
σmax=450.0 N/mmq
STEP 10 Fmax= 205 kN,
δmax=16.9 mm
σmax=365.0 N/mmq
LOAD CONDITION : Applied Horizontal Force at the top of the column
STEP 5 Fmax= 128.7 kN,
δmax=6.97 mm
σmax=233.0 N/mmq
3D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
18/21
Page 19
LOAD CONDITION: Applied Horizontal Force at the top of the column
NON LINEAR ANALYSIS: Cracking Status
MODEL “A” MODEL “B”
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
STEP 5 Fmax= 128 kN,
δmax=5.17 mm
STEP 10 Fmax= 207 kN,
δmax=12.75 mm
STEP 20 Fmax= 390 kN,
δmax=88.56 mm
STEP 5 Fmax= 128.7 kN,
δmax=6.97 mm
STEP 10 Fmax= 205 kN,
δmax=16.9 mm
STEP 15 Fmax=270 kN,
δmax=87.27 mm
3D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
19/21
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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.
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Page 21
21/21Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
3D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Angela Saviotti, Pierluigi Olmati, Franco Bontempi
Page 22
“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]
22/21
Page 23
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
MODEL “A” MODEL “B”
23/24
Page 24
NON LINEAR ANALYSIS – CYCLIC ANALYSIS
MODEL “A”
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
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
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
24/24
Page 25
MODEL “A”
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
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
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
SECOND LOAD CONDITION : Imposed vertical displacement at the top of the column
NON LINEAR ANALYSIS – CYCLIC ANALYSIS
Step 1
25/24
Page 26
26/24Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
2D
3D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Page 27
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Stand‐by
Page 28
MODEL “A”
Displacements
MODEL “B”
mm mm
LINEAR ANALYSIS
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
FIRST LOAD CONDITION: Applied Horizontal Force of 600 kN at the top of the column
2D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Stand‐by
Page 29
MODEL “A”
Stresses
MODEL “B”
LINEAR ANALYSIS
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
FIRST LOAD CONDITION: Applied Horizontal Force of 600 kN at the top of the
column 2D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Stand‐by
Page 30
FIRST LOAD CONDITION : Applied Horizontal Force at the top of the column
NON LINEAR ANALYSIS
MODEL “A”MODEL “B”
Deformed configuration developed by the structure at
STEP 40 – Fmax= 280.9 kN, δmax=102.4 mm.
Deformed configuration developed by the structure at
STEP 18 - Fmax= 173.06 kN, δmax=112.7 mm
mmmm
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
2D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Stand‐by
Page 31
NON LINEAR ANALYSIS: Stress on Reinforcing Steel
MODEL “A” MODEL “B”
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
STEP 1 Fmax= 18 kN,
δmax=0.70 mm –
σmax=3.88 N/mmq
STEP 7 Fmax= 105 kN,
δmax=5.32 mm
σmax=106.9 N/mmq
STEP 40 Fmax= 280.9 kN,
δmax=102.4 mm
σmax=450.0 N/mmq
STEP 18 Fmax= 173.06
kN, δmax=112.7 mm
σmax=450.0 N/mmq
STEP 7 Fmax= 107.6 kN,
δmax=8.75 mm
σmax=436.8 N/mmq
STEP 1 Fmax= 17.7 kN,
δmax=1.12 mm
σmax=58.47 N/mmq
FIRST LOAD CONDITION : Applied Horizontal Force at the top of the column 2D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Stand‐by
Page 32
FIRST LOAD CONDITION: Applied Horizontal Force at the top of the
column NON LINEAR ANALYSIS: Cracking Status
MODEL “A” MODEL “B”
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
STEP 40 Fmax= 280.9 kN,
δmax=102.4 mm
STEP 7 Fmax= 105 kN,
δmax=5.32 mm
STEP 1 Fmax= 18 kN,
δmax=0.70 mm
STEP 7 Fmax= 17.7 kN,
δmax=1.12 mm
STEP 7 Fmax= 107.6 kN,
δmax=8.75 mm
STEP 18 Fmax= 174.0
kN, δmax=112.7 mm
2D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Stand‐by
Page 33
NON LINEAR ANALYSISMODEL “A” MODEL “B”
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
mm mm
Deformed
configuration developed
by the structure at LAST
STEP imposed
displacement δ=201 mm.
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
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Stand‐by
Page 34
NON LINEAR ANALYSIS: Stress on Reinforcing Steel
MODEL “A” MODEL “B”
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
SECOND LOAD CONDITION : Imposed vertical displacement at the top of the column
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
STEP 5 Fmax= 320 kN,
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
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Stand‐by
Page 35
NON LINEAR ANALYSIS: Cracking Status
MODEL “A” MODEL “B”
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
STEP 1 Fmax= 153.85
kN, δmax=4 mm
STEP 5 Fmax= 320 kN,
δmax=20 mm
STEP 13 Fmax= 371.6kN,
δmax=52mm
SECOND LOAD CONDITION : Imposed vertical displacement at the top of the column
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
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Page 36
FIRST LOAD CONDITION: Applied Horizontal Force at the top of the
column
MODEL “A”
MODEL “B”
NON LINEAR ANALYSIS
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
2D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Stand‐by
Page 37
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Stand‐by
Page 38
38/25
NON LINEAR ANALYSISMODEL “A” MODEL “B”
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
Deformed
configuration developed
by the structure at LAST
STEP imposed
displacement δ=120 mm.
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
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Page 39
39/25
NON LINEAR ANALYSIS: Stress on Reinforcing Steel
MODEL “A” MODEL “B”
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
SECOND LOAD CONDITION : Imposed vertical displacement at the top of the column
STEP 1 Fmax= 123.6 kN,
δmax=10 mm
σmax=268.1 N/mmq
STEP 1 Fmax= 143.9 kN,
δmax=10 mm
σmax=196.41 N/mmq
STEP 5 Fmax= 232.5kN,
δmax=50 mm
σmax=450.0 N/mmq
STEP 12 Fmax= 223.13
kN, δmax= 120 mm
σmax=450.0 N/mmq
STEP 5 Fmax= 139.4 kN,
δmax=50 mm
σmax=348.3N/mmq
STEP 12 Fmax= 139.95
kN, δmax=120 mm
σmin=-450.0 N/mmq
3D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Page 40
40/25
NON LINEAR ANALYSIS: Crack Strain
MODEL “A” MODEL “B”
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
SECOND LOAD CONDITION : Imposed vertical displacement at the top of the column
STEP 1 Fmax= 143.9 kN,
δmax=10 mm
εknn=0.00242 %
STEP 5 Fmax= 232.5kN,
δmax=50 mm
εknn=0.0359 %
STEP 12 Fmax= 223.13
kN, δmax= 120 mm
εknn=0.224%
STEP 1 Fmax= 123.6 kN,
δmax=10 mm
εknn=0.00703 %
STEP 5 Fmax= 139.4 kN,
δmax=50 mm
εknn=0.0548 %
STEP 12 Fmax= 139.95
kN, δmax=120 mm
εknn=0.132 %
3D
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Page 41
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
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
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
Page 42
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
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Stand‐by
Page 43
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
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
Page 44
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Stand‐by
Page 45
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Stand‐by
Page 46
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Stand‐by
Page 47
Faculty of Civil and Industrial EngineeringDepartment of Structural and Geotechnical Engineering
Angela Saviotti ‐ Finite element analysis of innovative solutions of precast concrete beam‐column ductile connections
Stand‐by