Post on 16-Oct-2021
Computational Modeling of Concrete Structures
Gianluca Cusatis
The Lattice Discrete Particle Model for the Simulation ofReinforced Concrete Elements
Tokyo Institute of Technology
July 27, 2018
1 / 11 July-2018 :: Gianluca Cusatis
Presentation Outline
1 Simulation of Reinforced Concrete
2 / 11 Simulation of Reinforced Concrete July-2018 :: Gianluca Cusatis
Rebar model and its interaction with concrete
Rebar model
σs ={Esεs εs ≤ εyfy εs > εy
with εy = fy/Es
Rebar Concrete Interaction
f(t) = φ(u)v(t)
v(x, t) = vc(x, t)− vr(x, t)
φ(u) = Penalty Stiffness
3 / 11 Simulation of Reinforced Concrete July-2018 :: Gianluca Cusatis
Under-Reinforced Concrete Beam Behavior
0 5 10 15 20 250
5
10
15
20
25
30
35
Mid−span displacement [mm]
Mid−s
pan
mom
ent [
KN
.m]
Exp.fy=600 MPa
fy=540 MPa
−36−30−24−18−12 −6 0 60
4
8
12
16
20
24
28
Stress [MPa]
Dep
th [c
m]
UncrackedCrackedUltimate
-19.7
2.24
0 5 10 15 20 250
5
10
15
20
25
30
35
Mid Span Displacement [mm]
Mid
span
Mom
ent [
KN
.m]
ExperimentalSimulated
c) d)
a)
120 cm
280 cm
10 cm 10 cm
b)
-35.7
1.11
-3.41
3.36
Uncracked Cracked Yielding
Uncracked
Cracked Yielding
Reinforcement and Stirrup detail
Yielding
0.0
0.0 0.0
fy
fy
Figure: a) Geometry; b) moment-displacement curve; c) stress distribution atmid-span; and d) average stress distribution at mid-span.
4 / 11 Simulation of Reinforced Concrete July-2018 :: Gianluca Cusatis
Ductile Flexural Failure
BeamReinforcement Mn Pmin Pmax Psim
Top Bottom Stirrups [KNm] [KN] [KN] [KN]B1 (2) No. 3 (2) No. 3 No. 3 @ 150 mm 33.81 41.81 46.71 42.5B2 (3) No. 6 (2) No. 3 No. 3 @ 150 mm 158.43 194.83 218.85 208.17B5 (5) No. 8 (2) No. 3 No. 4 @ 150 mm 386.41 475.96 533.79 528B6 (5) No. 8 (3) No. 8 No. 4 @ 150 mm 419.57 515.99 579.60 536.16
5 / 11 Simulation of Reinforced Concrete July-2018 :: Gianluca Cusatis
Ductile Flexural Failure, Cont.
6 / 11 Simulation of Reinforced Concrete July-2018 :: Gianluca Cusatis
Ductile Flexural Failure, Cont.
Mid Span Displacement [mm]10 14 18 22 26 30 34
Mid
Spa
n Lo
ad [K
N]
500
525
550
575
600
625
1
2 3
4 5
6 7 8 9 10
1
2
3
4
5
6
7
8
9
10
Axial Strain [x10-3]
2.464 2.468 2.469 2.470
7 / 11 Simulation of Reinforced Concrete July-2018 :: Gianluca Cusatis
Over-Reinforced Concrete Beams
Beam L× b× h [mm] a [mm] As [mm2]Group IL11×15 4600×110×150 1960 400L11×30 4600×110×300 1960 800L11×60 4600×110×600 1900 1600Group IIS5×7 1150×55×75 480 100
M11×15 2300×110×150 960 400L22×30 4600×220×300 1900 1600Group IIIS11×15 1150×110×150 460 400M11×30 2300×110×300 930 800L11×60 4600×110×600 1900 1600
8 / 11 Simulation of Reinforced Concrete July-2018 :: Gianluca Cusatis
Over-Reinforced Concrete Beams, Cont.
c)
a)
b)
c) -1.0 -0.75 -0.50 -0.25 0.0 Principal Stress [MPa] Axial Force [N]
-24 80 160 240 320 395
Figure: a) Before failure but after the elastic stage; b) at the onset of failure(maximum load) showing concrete crushing; c) rebars axial force andcompressive principal stress distribution before failure showing the arch actionmechanism.
9 / 11 Simulation of Reinforced Concrete July-2018 :: Gianluca Cusatis
Over-Reinforced Concrete Beams, Cont.
with d = h, µ = 3Pua/(bd2), µ = µ0(1 + d/D0)
−1/2
10 / 11 Simulation of Reinforced Concrete July-2018 :: Gianluca Cusatis
Over-Reinforced Concrete Beams, Cont.
Group BeamPu [KN] (δPu [%]) Pred. Error [%] µu [MPa]
Exp. LDPM ACI318 LDPM ACI318 Exp. LDPM ACI318
IL11×15 12.4 (19.4) 10.9 (1.8) 10.9 -11.4 -11.9 44.4 39.3 39.1L11×30 50.8 (6.2) 39 (2.9) 43.6 -23.1 -14.2 45.6 35 39.1L11×60 159.1 (11.1) 142.4 (1.5) 179.8 -10.5 9.6 34.6 31 39.1
IIS5×7 5.6 (20.8) 6.1 (3.3) 5.6 9.8 -0.2 39.2 43 39.1
M11×15 22.8 (7.9) 22.6 (1.5) 22.2 -1 -2.4 40.1 39.7 39.1L22×30 84.2 (2.2) 85.8 (1.3) 89.9 1.9 6.7 36.7 37.4 39.1
IIIS11×15 52.8 (44.3) 65.5 (3.7) 46.4 24 -12.2 44.5 55.2 39.1M11×30 101.9 (9.1) 92.4 (1) 91.8 -9.3 -9.9 43.4 39.3 39.1L11×60 159.1 (11.1) 142.4 (1.5) 179.8 -10.5 9.6 34.6 31 39.1
Groupµ0 [MPa] D0 [mm]
Exp. Num. Exp. Num.I 55.6 43.4 324 501II 44.1 44.6 540 553III 80.8 87.7 97 68
µ = µ0(1 + d/D0)−1/2
11 / 11 Simulation of Reinforced Concrete July-2018 :: Gianluca Cusatis