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 Engineering
Department of Structural and Geotechnical Engineering
Pierluigi Olmati
pierluigi.olmati@uniroma1.it
Franco Bontempi
franco.bontempi@uniroma1.it
Angela Saviotti
angela.s15@libero.it
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 2D
MESH
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 pad Connection
Stratum:
Mortar
Steel Plates
MODEL “A”
MODEL “B”
Zoom of Beam-Column joint
Reinforcing 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 3D
MESH
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
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
mm
mm
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 Engineering
3D
Angela Saviotti, Pierluigi Olmati, Franco Bontempi

“FINITE ELEMENT ANALYSIS OF INNOVATIVE
SOLUTIONS OF PRECAST CONCRETE BEAM-COLUMN
DUCTILE CONNECTIONS”
Pierluigi Olmati
pierluigi.olmati@uniroma1.it
Franco Bontempi
franco.bontempi@uniroma1.it
Angela Saviotti
angela.s15@libero.it
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 steel
CRACKING STATUS
Step 25
Step 50 Step 80
2D
NON LINEAR ANALYSIS – CYCLIC ANALYSIS
Step 1
25/24

26/24Faculty of Civil and Industrial 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
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
columnNON 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 ANALYSIS
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”
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

38/25
NON LINEAR ANALYSIS
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”
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/mm
2
E 35220 N/mm
2
ν 0.2 ν 0.2
fc 40 N/mm
2
fc 40 N/mm
2
GC 120 J/m
2
REDCRV VC1993
Tensile Behavior
Tension Softening Curve - based on FRACTURE ENERGY
E 35220 N/mm
2
E 35220 N/mm
2
ν 0.2 ν 0.2
ft 2.457 N/mm
2
ft 2.457 N/mm
2
GF1 89.95 J/m
2
GF1 89.95 J/m
2
Linear Expone
CONCRETE 40/50
TOTALSTRAINCRACK
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/mm
2
ftk 540 N/mm
2
Ey 206000 N/mm
2
ν 0.3
STEEL B450C
Stand‐by

Stand‐by
Element Steel Name
CROSS-SECTIONAL AREA
[ mm
2
]
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 Name
CROSS-SECTIONAL AREA
[ mm
2
]
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

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

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