The document describes numerical models created in OpenSees to simulate cyclic tests on two reinforced concrete columns, one with plain reinforcing bars and one with deformed bars. Four different element types were used to model the columns: nonlinear beam-column, beam with hinges, with and without zero-length elements. Models that included zero-length elements simulating bond-slip effects matched experimental force-displacement curves most accurately. A trilinear steel model was also proposed to better represent the stress-strain behavior of plain reinforcing bars.

1. J. Melo, H. Varum, and T. Rossetto
josemelo@fe.up.pt
NUMERICAL MODELLING OF RC COLUMNS
WITH PLAIN REINFORCING BARS
OpenSees Days Europe 2017
1st European Conference on OpenSees
Porto, Portugal, 19–20 June 2017

2. Contents
Cyclic tests of 2 similar columns, one built with plain reinforcing bars and
another one built with deformed bars
Numerical models using OpenSees with different element types
Comparison between the main numerical and experimental results
Proposal of a trilinear steel model for plain reinforcing bars
Final comments

3. Column CPA-3 was built with plain bars according to the Portuguese codes
in force until 1970s
Column CD was built with deformed bars without seismic detailing
Columns detailing
2.17m 1.50m
0.60m
0.30m
0.60m
0.30m
Deformed bars
Plain barsA
A'
B
B'
0.47m
0.60m
6 Ø12
0.30m
Ø10//0.16
5 Ø10
5 Ø10
0.30m
6 Ø12
0.30m
Section AA'
Ø8//0.20
Section BB'
2 Ø10
Dimensions and reinforcement detailing Cross-sections
Specimen Type of steel
Concrete
Steel
Ø 8 mm Ø 12 mm
(MPa) (GPa) (MPa) (GPa)
fcm ftcm fyk fuk Eym fym fum Eym
CP A235 - Plain 17.4 2.1 410 495 198 405 470 199
CD A400NRSD - Deformed 17.1 2.0 470 605 198 465 585 199

4. Specimens were tested in the horizontal position
Two hydraulic actuators were arranged at the top of the columns, one to
impose the lateral displacements (dc) and another for the axial force (N=305kN)
Displacement-controlled conditions were adopted
Test setup and loading conditions
Overview
General schematics
Fcdc
N
1.70m1.32m
Column
1.70m
F
N
c dc
Loading conditions
-90
-75
-60
-45
-30
-15
0
15
30
45
60
75
90
Topdisplacement,dC
(mm)
Step
-5
-4
-3
-2
-1
0
1
2
3
4
5
Drift(%)

5. For each specimen were developed 4 numerical models with different
elements:
Numerical models
- NonLinear Beam-Column
- NonLinear Beam-Column + Zero Length
- Beam With Hinges
- Beam With Hinges + Zero Length
Axis of the element
Elementaxis
LinearElement
Zero-length section element
Node n
Node i
Node j
Fiber sections

6. NonlinearBeamColumn element, with distributed plasticity along the element
span
BeamWithHinges element, where the plasticity is concentrated over a
specified hinge length at the elements ends
Zero-length section element that incorporates the fixed-end rotation caused
by strain penetration effects and the bond-slip mechanism:
Located at the end of the linear elements
Simulation of the bond-slip effects
Bond-slip model Bond_SP01 assigned to the steel fibres
The slippage mechanism is concentrated within the plastic hinges
Numerical models

7. Numerical and experimental results – CPA-3
-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90
-50
-40
-30
-20
-10
0
10
20
30
40
50
OpenSees
NonLinear Beam-Column Element
Force,FC
(kN)
Displacement, dC
(mm)
Exp
Num
-5 -4 -3 -2 -1 0 1 2 3 4 5
Drift (%)
-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90
-50
-40
-30
-20
-10
0
10
20
30
40
50
Force,FC
(kN)
Displacement, dC
(mm)
Exp
Num
-5 -4 -3 -2 -1 0 1 2 3 4 5
OpenSees
NonLinear Beam-Column Element
Zero-Length Element
Drift (%)
-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90
-50
-40
-30
-20
-10
0
10
20
30
40
50
OpenSees
BeamWithHingesElement
Force,FC
(kN)
Displacement, dC
(mm)
Exp
Num
-5 -4 -3 -2 -1 0 1 2 3 4 5
Drift (%)
-90 -75 -60 -45 -30 -15 0 15 30 45 60 75 90
-50
-40
-30
-20
-10
0
10
20
30
40
50
Force,FC
(kN)
Displacement, dC
(mm)
Exp
Num
-5 -4 -3 -2 -1 0 1 2 3 4 5
OpenSees
BeamWithHinges Element
Zero-Length Element
Drift (%)

8. Numerical and experimental results – CPA-3
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
0
10
20
30
40
50
60
DissipatedEnergy(kN.m)
Drift (%)
Experimental
OS - NonLinear Beam-Column
OS - NonLinear Beam-Column + Zero Length
OS - Beam With Hinges
OS - Beam With Hinges + Zero Length
Column built with plain bars
Experimental vs. Numerical
• Models with plastic hinge elements
dissipated less energy than the models
with distributed plasticity
• Models with zero-length section elements
showed better agreement with the
experimental results
• The best approach was obtained by the
beam with plastic hinges model and zero-
length section element (38% more
dissipated energy at 5% drift)

9. Numerical and experimental results – CD
-75 -60 -45 -30 -15 0 15 30 45 60 75
-50
-40
-30
-20
-10
0
10
20
30
40
50
OpenSees
NonLinear Beam-Column Element
Force,FC
(kN)
Displacement, dC
(mm)
Exp
Num
-4 -3 -2 -1 0 1 2 3 4
Drift (%)
-75 -60 -45 -30 -15 0 15 30 45 60 75
-50
-40
-30
-20
-10
0
10
20
30
40
50
Force,FC
(kN)
Displacement, dC
(mm)
Exp
Num
-4 -3 -2 -1 0 1 2 3 4
OpenSees
NonLinear Beam-Column Element
Zero-Length Element
Drift (%)
-75 -60 -45 -30 -15 0 15 30 45 60 75
-50
-40
-30
-20
-10
0
10
20
30
40
50
OpenSees
Beam With Hinges Element
Force,FC
(kN)
Displacement, dC
(mm)
Exp
Num
-4 -3 -2 -1 0 1 2 3 4
Drift (%)
-75 -60 -45 -30 -15 0 15 30 45 60 75
-50
-40
-30
-20
-10
0
10
20
30
40
50
Force,FC
(kN)
Displacement, dC
(mm)
Exp
Num
-4 -3 -2 -1 0 1 2 3 4
OpenSees
Beam With Hinges Element
Zero-Length Element
Drift (%)

10. Numerical and experimental results – CD
Column built with deformed bars
Experimental vs. Numerical
• The conclusions are similar to those
presented for specimen CPA-3
• The best approach was obtained by the
beam with plastic hinges model and zero-
length section element (8% more
dissipated energy)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
0
5
10
15
20
25
30
35
DissipatedEnergy(kN.m)
Drift (%)
Experimental
OS - NonLinear Beam-Column
OS - NonLinear Beam-Column + Zero Length
OS - Beam With Hinges
OS - Beam With Hinges + Zero Length

11. Trilinear model proposal – plain bars
Trilinear steel model proposal for RC columns with plain reinforcing bars
Model developed based on experimental results
Represents better the stiffness after cracking
The Hysteretic material model was used to implement the trilinear model
b
As
As1
As2
εc
εs
h d
d1
d2
f c
x
Fs
Fs1 N
Fc
Fs2
M
εs
f y
β⋅f y
f y /Es
Es,0
Es,1=α1⋅Es,0
Es,u
E's,u=α2⋅Es,u
Bi-linear model
Tri-linear proposed model
σs
85.039.1
30.02
085.01
+⋅−=
=
=
h
a
a
β

12. Trilinear model proposal – plain bars
The monotonic response using the proposed steel model represents better the
behaviour between cracking and load peak
Stiffness improvement
0 15 30 45 60 75 90
0
5
10
15
20
25
30
35
40
45
Exp. Num. Num. with slip
Force,FC
(kN)
Displacement, dC
(mm)
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Drift (%)

13. • The tested models provided a satisfactory simulation of the experimental force-drift
diagrams. However, neither of the models were able to properly capture the strength
degradation, nor the stiffness of the reloading branches, nor the pinching effect
(namely in the column with plain bars)
• For both columns, a better agreement between the numerical and experimental results
was obtained considering the plasticity concentrated in the plastic hinge regions
• For both columns, the best fit to the experimental results was obtained by
incorporating the effects of bar slippage in the OpenSees models with concentrated
plasticity. This was particularly relevant for the column with plain reinforcing bars
• The proposed steel model represents better the monotonic response of the columns
with plain reinforcing bars
Final comments

14. Thanks for your attention!
Credits
University of Aveiro, Portugal